# kb

id: solar-cycle-20260505-4
file: data/en.wikipedia.org/wiki/Solar_cycle-4.md
category: reference
title: Solar cycle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Solar_cycle
date_saved: 2026-05-05T10:54:22.923963+00:00
instance: kb-cron
parent: solar-cycle-20260505-0
summary:
==== Solar radio flux ==== Emission from the Sun at centimetric (radio) wavelength is due primarily to coronal plasma trapped in the magnetic fields overlying active regions. The F10.7 index is a measure of the solar radio flux per unit frequency at a wavelength of 10.7 cm, near the peak of the observed solar radio emission. F10.7 is often expressed in SFU or solar flux units (1 SFU = 10−22 W m−2 Hz−1). It represents a measure of diffuse, nonradiative coronal plasma heating. It is an excellent indicator of overall solar activity levels and correlates well with solar UV emissions. Sunspot activity has a major effect on long distance radio communications, particularly on the shortwave bands although medium wave and low VHF frequencies are also affected. High levels of sunspot activity lead to improved signal propagation on higher frequency bands, although they also increase the levels of solar noise and ionospheric disturbances. These effects are caused by impact of the increased level of solar radiation on the ionosphere. 10.7 cm solar flux could interfere with point-to-point terrestrial communications. ==== Clouds ==== Speculations about the effects of cosmic-ray changes over the cycle potentially include: Changes in ionization affect the aerosol abundance


id: solar-cycle-20260505-5
file: data/en.wikipedia.org/wiki/Solar_cycle-5.md
category: reference
title: Solar cycle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Solar_cycle
date_saved: 2026-05-05T10:54:22.923963+00:00
instance: kb-cron
parent: solar-cycle-20260505-0
summary:
The 11-year solar cycle is thought to be one-half of a 22-year Babcock–Leighton solar dynamo cycle, which corresponds to an oscillatory exchange of energy between toroidal and poloidal solar magnetic fields which is mediated by solar plasma flows which also provides energy to the dynamo system at every step. At solar-cycle maximum, the external poloidal dipolar magnetic field is near its dynamo-cycle minimum strength, but an internal toroidal quadrupolar field, generated through differential rotation within the tachocline, is near its maximum strength. At this point in the dynamo cycle, buoyant upwelling within the Convection zone forces emergence of the toroidal magnetic field through the photosphere, giving rise to pairs of sunspots, roughly aligned east–west with opposite magnetic polarities. The magnetic polarity of sunspot pairs alternates every solar cycle, a phenomenon described by Hale's law. During the solar cycle's declining phase, energy shifts from the internal toroidal magnetic field to the external poloidal field, and sunspots diminish in number. At solar minimum, the toroidal field is, correspondingly, at minimum strength, sunspots are relatively rare and the poloidal field is at maximum strength. During the next cycle, differential rotation converts magnetic energy back from the poloidal to the toroidal field, with a


id: sunspottery-20260505-0
file: data/en.wikipedia.org/wiki/Sunspottery-0.md
category: reference
title: Sunspottery
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sunspottery
date_saved: 2026-05-05T10:54:24.159453+00:00
instance: kb-cron
parent: sunspottery-20260505-0
summary:
Sunspottery was a pejorative term assigned to a late 19th century trend to ascribe sunspots and their cycles as causes for various cyclic phenomena, including disease outbreaks and economic crises. William Stanley Jevons read a paper On the influence of the sun-spot period upon the price of corn at a meeting of the British Association for the Advancement of Science in 1875. This was followed by a great deal of media interest and a period when it became fanciful to blame the sun for all kinds of events, with the term being used pejoratively in the newspapers. Jevons later wrote to the Times in April 1879 stating that despite the abuse of his idea "the activity of commerce in England ultimately depends upon the solar activity". A pamphlet dealing with the facts of solar cycles, use, and misuse published in 1883 was reviewed by The Globe, which noted that "Sun-spottery is not what it is represented to be, but is, for the most part, humbug." Sunspot cycles affecting weather and various other phenomena have however continued to be of interest and are still a serious subject of study. == See also == Brückner-Egeson-Lockyer cycle Sunspots (economics) == References ==


id: swarm-behaviour-20260505-0
file: data/en.wikipedia.org/wiki/Swarm_behaviour-0.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
Swarm behaviour, or swarming, is a collective behaviour exhibited by entities, particularly animals, of similar size which aggregate together, perhaps milling about the same spot or perhaps moving en masse or migrating in some direction. It is a highly interdisciplinary topic. As a term, swarming is applied particularly to insects, but can also be applied to any other entity or animal that exhibits swarm behaviour. The term flocking or murmuration can refer specifically to swarm behaviour in birds, herding to refer to swarm behaviour in tetrapods, and shoaling or schooling to refer to swarm behaviour in fish. Phytoplankton also gather in huge swarms called blooms, although these organisms are algae and are not self-propelled the way most animals are. By extension, the term "swarm" is applied also to inanimate entities which exhibit parallel behaviours, as in a robot swarm, an earthquake swarm or a star swarm. From a more abstract point of view, swarm behaviour is the collective motion of a large number of self-propelled entities. From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination. Swarm behaviour is also studied by


id: swarm-behaviour-20260505-1
file: data/en.wikipedia.org/wiki/Swarm_behaviour-1.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
A further key concept in the field of swarm intelligence is stigmergy. Stigmergy is a mechanism of indirect coordination between agents or actions. The principle is that the trace left in the environment by an action stimulates the performance of a next action, by the same or a different agent. In that way, subsequent actions tend to reinforce and build on each other, leading to the spontaneous emergence of coherent, apparently systematic activity. Stigmergy is a form of self-organization. It produces complex, seemingly intelligent structures, without need for any planning, control, or even direct communication between the agents. As such it supports efficient collaboration between extremely simple agents, who lack any memory, intelligence or even awareness of each other. === Swarm intelligence === Swarm intelligence is the collective behaviour of decentralized, self-organized systems, natural or artificial. The concept is employed in work on artificial intelligence. The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems. Swarm intelligence systems are typically made up of a population of simple agents such as boids interacting locally with one another and with their environment. The agents follow very simple rules, and although there is no


id: swarm-behaviour-20260505-2
file: data/en.wikipedia.org/wiki/Swarm_behaviour-2.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
Particle swarm optimization is another algorithm widely used to solve problems related to swarms. It was developed in 1995 by Kennedy and Eberhart and was first aimed at simulating the social behaviour and choreography of bird flocks and fish schools. The algorithm was simplified and it was observed to be performing optimization. The system initially seeds a population with random solutions. It then searches in the problem space through successive generations using stochastic optimization to find the best solutions. The solutions it finds are called particles. Each particle stores its position as well as the best solution it has achieved so far. The particle swarm optimizer tracks the best local value obtained so far by any particle in the local neighbourhood. The remaining particles then move through the problem space following the lead of the optimum particles. At each time iteration, the particle swarm optimiser accelerates each particle toward its optimum locations according to simple mathematical rules. In a related approach, Shvalb et al. (2024) introduced a statistical-physics-based framework for controlling large-scale multi-robot systems. By modeling robots as particles within a statistical ensemble, the study leverages macroscopic parameters—such as density and flow fields—to guide collective behavior without the need for


id: swarm-behaviour-20260505-3
file: data/en.wikipedia.org/wiki/Swarm_behaviour-3.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
In temperate climates, honey bees usually form swarms in late spring. A swarm typically contains about half the workers together with the old queen, while the new queen stays back with the remaining workers in the original hive. When honey bees emerge from a hive to form a swarm, they may gather on a branch of a tree or on a bush only a few meters from the hive. The bees cluster about the queen and send out 20–50 scouts to find suitable new nest locations. The scouts are the most experienced foragers in the cluster. If a scout finds a suitable location, she returns to the cluster and promotes it by dancing a version of the waggle dance. This dance conveys information about the quality, direction, and distance of the new site. The more excited she is about her findings, the more vigorously she dances. If she can convince others they may take off and check the site she found. If they approve they may promote it as well. In this decision-making process, scouts check several sites, often abandoning their own original site to promote the superior site of another scout. Several different sites may be promoted by different


id: swarm-behaviour-20260505-4
file: data/en.wikipedia.org/wiki/Swarm_behaviour-4.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
Locusts are the swarming phase of the short-horned grasshoppers of the family Acrididae. Some species can breed rapidly under suitable conditions and subsequently become gregarious and migratory. They form bands as nymphs and swarms as adults—both of which can travel great distances, rapidly stripping fields and greatly damaging crops. The largest swarms can cover hundreds of square miles and contain billions of locusts. A locust can eat its own weight (about 2 grams) in plants every day. That means one million locusts can eat more than one tonne of food each day, and the largest swarms can consume over 100,000 tonnes each day. Swarming in locusts has been found to be associated with increased levels of serotonin which causes the locust to change colour, eat much more, become mutually attracted, and breed much more easily. Researchers propose that swarming behaviour is a response to overcrowding and studies have shown that increased tactile stimulation of the hind legs or, in some species, simply encountering other individuals causes an increase in levels of serotonin. The transformation of the locust to the swarming variety can be induced by several contacts per minute over a four-hour period. Notably, an innate predisposition to aggregate has


id: swarm-behaviour-20260505-5
file: data/en.wikipedia.org/wiki/Swarm_behaviour-5.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
Other animals may use similar drafting techniques when migrating. Lobsters, for example, migrate in close single-file formation "lobster trains", sometimes for hundreds of miles. The Mediterranean and other seas present a major obstacle to soaring birds, which must cross at the narrowest points. Massive numbers of large raptors and storks pass through areas such as Gibraltar, Falsterbo, and the Bosphorus at migration times. More common species, such as the European honey buzzard, can be counted in hundreds of thousands in autumn. Other barriers, such as mountain ranges, can also cause funnelling, particularly of large diurnal migrants. This is a notable factor in the Central American migratory bottleneck. This concentration of birds during migration can put species at risk. Some spectacular migrants have already gone extinct, the most notable being the passenger pigeon. During migration the flocks were a mile (1.6 km) wide and 300 miles (500 km) long, taking several days to pass and containing up to a billion birds. === Marine life === ==== Fish ==== The term "shoal" can be used to describe any group of fish, including mixed-species groups, while "school" is used for more closely knit groups of the same species swimming in a highly synchronised


id: swarm-behaviour-20260505-6
file: data/en.wikipedia.org/wiki/Swarm_behaviour-6.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
Copepods are a group of tiny crustaceans found in the sea and lakes. Many species are planktonic (drifting in sea waters), and others are benthic (living on the ocean floor). Copepods are typically 1 to 2 millimetres (0.04 to 0.08 in) long, with a teardrop shaped body and large antennae. Although like other crustaceans they have an armoured exoskeleton, they are so small that in most species this thin armour, and the entire body, is almost totally transparent. Copepods have a compound, median single eye, usually bright red, in the centre of the transparent head. Copepods also swarm. For example, monospecific swarms have been observed regularly around coral reefs and sea grass, and in lakes. Swarms densities were about one million copepods per cubic metre. Typical swarms were one or two metres in diameter, but some exceeded 30 cubic metres. Copepods need visual contact to keep together, and they disperse at night. Spring produces blooms of swarming phytoplankton which provide food for copepods. Planktonic copepods are usually the dominant members of the zooplankton, and are in turn major food organisms for many other marine animals. In particular, copepods are prey to forage fish and jellyfish, both of which can assemble


id: swarm-behaviour-20260505-7
file: data/en.wikipedia.org/wiki/Swarm_behaviour-7.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
A collection of people can also exhibit swarm behaviour, such as pedestrians or soldiers swarming the parapets. In Cologne, Germany, two biologists from the University of Leeds demonstrated flock like behaviour in humans. The group of people exhibited similar behavioural pattern to a flock, where if five percent of the flock changed direction the others would follow. If one person was designated as a predator and everyone else was to avoid him, the flock behaved very much like a school of fish. Understanding how humans interact in crowds is important if crowd management is to effectively avoid casualties at football grounds, music concerts and subway stations. The mathematical modelling of flocking behaviour is a common technology, and has found uses in animation. Flocking simulations have been used in many films to generate crowds which move realistically. Tim Burton's Batman Returns was the first movie to make use of swarm technology for rendering, realistically depicting the movements of a group of bats using the boids system. The Lord of the Rings film trilogy made use of similar technology, known as Massive, during battle scenes. Swarm technology is particularly attractive because it is cheap, robust, and simple. An ant-based computer simulation using


id: swarm-behaviour-20260505-8
file: data/en.wikipedia.org/wiki/Swarm_behaviour-8.md
category: reference
title: Swarm behaviour
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Swarm_behaviour
date_saved: 2026-05-05T10:54:25.436021+00:00
instance: kb-cron
parent: swarm-behaviour-20260505-0
summary:
Military swarming is a behaviour where autonomous or partially autonomous units of action attack an enemy from several different directions and then regroup. Pulsing, where the units shift the point of attack, is also a part of military swarming. Military swarming involves the use of a decentralized force against an opponent, in a manner that emphasizes mobility, communication, unit autonomy and coordination or synchronization. Historically military forces used principles of swarming without really examining them explicitly, but now active research consciously examines military doctrines that draw ideas from swarming. Merely because multiple units converge on a target, they are not necessarily swarming. Siege operations do not involve swarming, because there is no manoeuvre; there is convergence but on the besieged fortification. Nor do guerrilla ambushes constitute swarms, because they are "hit-and-run". Even though the ambush may have several points of attack on the enemy, the guerillas withdraw when they either have inflicted adequate damage, or when they are endangered. In 2014 the U. S. Office of Naval Research released a video showing tests of a swarm of small autonomous drone attack boats that can steer and take coordinated offensive action as a group. == Gallery == == Myths == There


id: time-loop-20260505-0
file: data/en.wikipedia.org/wiki/Time_loop-0.md
category: reference
title: Time loop
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Time_loop
date_saved: 2026-05-05T10:54:26.798374+00:00
instance: kb-cron
parent: time-loop-20260505-0
summary:
The time loop or temporal loop is a plot device in fiction whereby characters re-experience a span of time which is repeated, sometimes more than once, with some hope of breaking out of the cycle of repetition. Time loops are constantly resetting; when a certain condition is met, such as a death of a character or a certain point in time, the loop starts again, possibly with one or more characters retaining the memories from the previous loop. A time loop is also sometimes used to describe a scenario involving time travel where events form a circular chain of causality. In this context, actions in the past lead to future events, which then trigger the original journey back in time, creating a self-contained loop without a clear starting point. This concept challenges the conventional linear view of time and is often explored in science fiction and theories of temporal physics, such as those involving closed timelike curves. == History == An early example of a time loop is the 1915 Russian novel Strange Life of Ivan Osokin, where the main character gets to live his life over again but struggles to change it the second time around. The episode "The


id: acoustic-attenuation-20260505-0
file: data/en.wikipedia.org/wiki/Acoustic_attenuation-0.md
category: reference
title: Acoustic attenuation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Acoustic_attenuation
date_saved: 2026-05-05T10:54:29.602856+00:00
instance: kb-cron
parent: acoustic-attenuation-20260505-0
summary:
In acoustics, acoustic attenuation is a measure of the energy loss of sound propagation through an acoustic transmission medium. Most media have viscosity and are therefore not ideal media. When sound propagates in such media, there is always thermal consumption of energy caused by viscosity. This effect can be quantified through the Stokes's law of sound attenuation. Sound attenuation may also be a result of heat conductivity in the media as has been shown by G. Kirchhoff in 1868. The Stokes-Kirchhoff attenuation formula takes into account both viscosity and thermal conductivity effects. For heterogeneous media, besides media viscosity, acoustic scattering is another main reason for removal of acoustic energy. Acoustic attenuation in a lossy medium plays an important role in many scientific researches and engineering fields, such as medical ultrasonography, vibration and noise reduction. == Power-law frequency-dependent acoustic attenuation == Many experimental and field measurements show that the acoustic attenuation coefficient of a wide range of viscoelastic materials, such as soft tissue, polymers, soil, and porous rock, can be expressed as the following power law with respect to frequency: P ( x + Δ x ) = P ( x ) e − α ( ω ) Δ x ,


id: aharonov-bohm-effect-20260505-0
file: data/en.wikipedia.org/wiki/Aharonov–Bohm_effect-0.md
category: reference
title: Aharonov–Bohm effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aharonov–Bohm_effect
date_saved: 2026-05-05T10:54:30.845762+00:00
instance: kb-cron
parent: aharonov-bohm-effect-20260505-0
summary:
The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum-mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic potential ( φ {\displaystyle \varphi } , A {\displaystyle \mathbf {A} } ), despite being confined to a region in which both the magnetic field B {\displaystyle \mathbf {B} } and electric field E {\displaystyle \mathbf {E} } are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wave function, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments. The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid. This phase shift has been observed experimentally. There are also magnetic Aharonov–Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested. An electric Aharonov–Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different


id: aharonov-bohm-effect-20260505-1
file: data/en.wikipedia.org/wiki/Aharonov–Bohm_effect-1.md
category: reference
title: Aharonov–Bohm effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aharonov–Bohm_effect
date_saved: 2026-05-05T10:54:30.845762+00:00
instance: kb-cron
parent: aharonov-bohm-effect-20260505-0
summary:
=== Global action vs. local forces === Similarly, the Aharonov–Bohm effect illustrates that the Lagrangian approach to dynamics, based on energies, is not just a computational aid to the Newtonian approach, based on forces. Thus the Aharonov–Bohm effect validates the view that forces are an incomplete way to formulate physics, and potential energies must be used instead. In fact Richard Feynman complained that he had been taught electromagnetism from the perspective of electromagnetic fields, and he wished later in life he had been taught to think in terms of the electromagnetic potential instead, as this would be more fundamental. In Feynman's path-integral view of dynamics, the potential field directly changes the phase of an electron wave function, and it is these changes in phase that lead to measurable quantities. === Locality of electromagnetic effects === The Aharonov–Bohm effect shows that the local E and B fields do not contain full information about the electromagnetic field, and the electromagnetic four-potential, (Φ, A), must be used instead. By Stokes' theorem, the magnitude of the Aharonov–Bohm effect can be calculated using the electromagnetic fields alone, or using the four-potential alone. But when using just the electromagnetic fields, the effect depends on the field


id: aharonov-bohm-effect-20260505-2
file: data/en.wikipedia.org/wiki/Aharonov–Bohm_effect-2.md
category: reference
title: Aharonov–Bohm effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aharonov–Bohm_effect
date_saved: 2026-05-05T10:54:30.845762+00:00
instance: kb-cron
parent: aharonov-bohm-effect-20260505-0
summary:
In quantum mechanics the same particle can travel between two points by a variety of paths. Therefore, this phase difference can be observed by placing a solenoid between the slits of a double-slit experiment (or equivalent). An ideal solenoid (i.e. infinitely long and with a perfectly uniform current distribution) encloses a magnetic field B {\displaystyle \mathbf {B} } , but does not produce any magnetic field outside of its cylinder, and thus the charged particle (e.g. an electron) passing outside experiences no magnetic field B {\displaystyle \mathbf {B} } . (This idealization simplifies the analysis but it's important to realize that the Aharonov–Bohm effect does not rely on it, provided the magnetic flux returns outside the electron paths, for example if one path goes through a toroidal solenoid and the other around it, and the solenoid is shielded so that it produces no external magnetic field.) However, there is a (curl-free) vector potential A {\displaystyle \mathbf {A} } outside the solenoid with an enclosed flux, and so the relative phase of particles passing through one slit or the other is altered by whether the solenoid current is turned on or off. This corresponds to an observable shift of the interference


id: aharonov-bohm-effect-20260505-3
file: data/en.wikipedia.org/wiki/Aharonov–Bohm_effect-3.md
category: reference
title: Aharonov–Bohm effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aharonov–Bohm_effect
date_saved: 2026-05-05T10:54:30.845762+00:00
instance: kb-cron
parent: aharonov-bohm-effect-20260505-0
summary:
== Electric effect == Just as the phase of the wave function depends upon the magnetic vector potential, it also depends upon the scalar electric potential. By constructing a situation in which the electrostatic potential varies for two paths of a particle, through regions of zero electric field, an observable Aharonov–Bohm interference phenomenon from the phase shift has been predicted; again, the absence of an electric field means that, classically, there would be no effect. From the Schrödinger equation, the phase of an eigenfunction with energy E {\displaystyle E} goes as e − i E t / ℏ {\displaystyle e^{-iEt/\hbar }} . The energy, however, will depend upon the electrostatic potential V {\displaystyle V} for a particle with charge q {\displaystyle q} . In particular, for a region with constant potential V {\displaystyle V} (zero field), the electric potential energy q V {\displaystyle qV} is simply added to E {\displaystyle E} , resulting in a phase shift: Δ φ = − q V t ℏ , {\displaystyle \Delta \varphi =-{\frac {qVt}{\hbar }},} where t is the time spent in the potential. For example, we may have a pair of large flat conductors, connected to a battery of voltage Δ V


id: aharonov-bohm-effect-20260505-4
file: data/en.wikipedia.org/wiki/Aharonov–Bohm_effect-4.md
category: reference
title: Aharonov–Bohm effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aharonov–Bohm_effect
date_saved: 2026-05-05T10:54:30.845762+00:00
instance: kb-cron
parent: aharonov-bohm-effect-20260505-0
summary:
The Aharonov–Bohm effect can be understood from the fact that one can only measure absolute values of the wave function. While this allows for measurement of phase differences through quantum interference experiments, there is no way to specify a wavefunction with constant absolute phase. In the absence of an electromagnetic field one can come close by declaring the eigenfunction of the momentum operator with zero momentum to be the function "1" (ignoring normalization problems) and specifying wave functions relative to this eigenfunction "1". In this representation the i-momentum operator is (up to a factor ℏ / i {\displaystyle \hbar /i} ) the differential operator ∂ i = ∂ ∂ x i {\displaystyle \partial _{i}={\frac {\partial }{\partial x^{i}}}} . However, by gauge invariance, it is equally valid to declare the zero momentum eigenfunction to be e − i ϕ ( x ) {\displaystyle e^{-i\phi (x)}} at the cost of representing the i-momentum operator (up to a factor) as ∇ i = ∂ i + i ( ∂ i ϕ ) {\displaystyle \nabla _{i}=\partial _{i}+i(\partial _{i}\phi )} i.e. with a pure gauge vector potential A = d ϕ {\displaystyle A=d\phi } . There is no real asymmetry because representing the former in


id: aharonov-casher-effect-20260505-0
file: data/en.wikipedia.org/wiki/Aharonov–Casher_effect-0.md
category: reference
title: Aharonov–Casher effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Aharonov–Casher_effect
date_saved: 2026-05-05T10:54:32.083006+00:00
instance: kb-cron
parent: aharonov-casher-effect-20260505-0
summary:
The Aharonov–Casher effect is a quantum mechanical phenomenon predicted in 1984 by Yakir Aharonov and Aharon Casher, in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It was observed in a gravitational neutron interferometer in 1989 and later by fluxon interference of magnetic vortices in Josephson junctions. It has also been seen with electrons and atoms. In both effects the particle acquires a phase shift ( φ {\displaystyle \varphi } ) while traveling along some path P. In the Aharonov–Bohm effect it is φ A B = q ℏ ∫ P A ⋅ d x {\displaystyle \varphi _{\rm {AB}}={\frac {q}{\hbar }}\int _{P}\mathbf {A} \cdot d\mathbf {x} } While for the Aharonov–Casher effect it is φ A C = 1 ℏ c 2 ∫ P ( E × μ ) ⋅ d x {\displaystyle \varphi _{\rm {AC}}={\frac {1}{\hbar c^{2}}}\int _{P}(\mathbf {E} \times {\boldsymbol {\mu }})\cdot d\mathbf {x} } where q {\displaystyle q} is its


id: andreev-reflection-20260505-0
file: data/en.wikipedia.org/wiki/Andreev_reflection-0.md
category: reference
title: Andreev reflection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Andreev_reflection
date_saved: 2026-05-05T10:54:33.330992+00:00
instance: kb-cron
parent: andreev-reflection-20260505-0
summary:
Andreev reflection, named after the Russian physicist Alexander F. Andreev, is a type of particle scattering which occurs at interfaces between a superconductor (S) and a normal state material (N). It is a charge-transfer process by which normal current in N is converted to supercurrent in S. Each Andreev reflection transfers a charge 2e across the interface, avoiding the forbidden single-particle transmission within the superconducting energy gap. This effect is generally called Andreev reflection but is sometimes called Andreev–Saint-James reflection, as it was predicted independently by Saint-James and de Gennes and by Andreev in the early sixties. == Overview == The process involves an electron incident on the interface from the normal state material at energies less than the superconducting energy gap. The incident electron forms a Cooper pair in the superconductor with the retroreflection of a hole of opposite spin and velocity but equal momentum to the incident electron, as seen in the figure. The barrier transparency is assumed to be high, with no oxide or tunnel layer which reduces instances of normal electron-electron or hole-hole scattering at the interface. Since the pair consists of an up and down spin electron, a second electron of opposite spin to the


id: antiferromagnetism-20260505-0
file: data/en.wikipedia.org/wiki/Antiferromagnetism-0.md
category: reference
title: Antiferromagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Antiferromagnetism
date_saved: 2026-05-05T10:54:34.556757+00:00
instance: kb-cron
parent: antiferromagnetism-20260505-0
summary:
Antiferromagnetism is a type of magnetic ordering, just like ferromagnetism and ferrimagnetism. In antiferromagnets the individual magnetic dipoles are oriented in a way such that the bulk of the material has a vanishing total magnetization. In the simplest model, as shown in the picture on the right, neighboring moments in an ordered lattice are oriented antiparallel to one another. Since there are multiple ways of arranging magnetic moments on a lattice (especially in three dimensions), there exist various types of antiferromagnetic ordering. The phenomenon of antiferromagnetism was first introduced by Lev Landau in 1933. Generally, antiferromagnetic order may exist at sufficiently low temperatures, but vanishes at and above the Néel temperature – named after Louis Néel, who had first identified this type of magnetic ordering. Above the Néel temperature, the material is typically paramagnetic. == Measurement == When no external field is applied, the antiferromagnetic structure corresponds to a vanishing total magnetization. In an external magnetic field, a kind of ferrimagnetic behavior may be displayed in the antiferromagnetic phase, with the absolute value of one of the sublattice magnetizations differing from that of the other sublattice, resulting in a nonzero net magnetization. Although the net magnetization should be zero at


id: arago-s-rotations-20260505-0
file: data/en.wikipedia.org/wiki/Arago's_rotations-0.md
category: reference
title: Arago's rotations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Arago's_rotations
date_saved: 2026-05-05T10:54:35.884320+00:00
instance: kb-cron
parent: arago-s-rotations-20260505-0
summary:
Arago's rotations is an observable magnetic phenomenon that involves the interactions between a magnetized needle and a moving metal disk. The effect was discovered by François Arago in 1824. At the time of their discovery, Arago's rotations were surprising effects that were difficult to explain. In 1831, Michael Faraday introduced the theory of electromagnetic induction, which explained how the effects happen in detail. == History == === Early observations and publications === As has so often occurred in other branches of science, the discovery of the magnetic rotations was made nearly simultaneously by several persons, for all of whom priority has been claimed. About 1824, Gambey the celebrated instrument-maker of Paris, had made the casual observation that a compass-needle, when disturbed and set oscillating around its pivot, comes to rest sooner if the bottom of the compass-box is of copper than if it is of wood or other material. Barlow and Marsh, at Woolwich, had at the same time been observing the effect on a magnetic needle of rotating in its neighborhood a sphere of iron. Arago the astronomer, who is said to have learned of the phenomenon from Gambey, but who is also said to have independently discovered it


id: arago-s-rotations-20260505-1
file: data/en.wikipedia.org/wiki/Arago's_rotations-1.md
category: reference
title: Arago's rotations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Arago's_rotations
date_saved: 2026-05-05T10:54:35.884320+00:00
instance: kb-cron
parent: arago-s-rotations-20260505-0
summary:
=== Investigations of the phenomena by other scientists === At this stage the phenomenon was investigated by several English experimenters, by Babbage and Herschel, by Christie, and, later, by Sturgeon and by Faraday. Babbage and Herschel measured the amount of retarding force exerted on the needle by different materials, and found the most powerful to be silver and copper (which are the two best conductors of electricity), after them gold and zinc, whilst lead, mercury and bismuth were very inferior in power. In 1825 they announced the successful reversal of Arago's experiment; for by spinning the magnet underneath a pivoted copper disk (Fig. 2) they had caused the latter to rotate briskly. They also made the notable observation that slits cut radially in a copper disk (Fig. 3) diminished its tendency to be rotated by the spinning magnet. If the rotatory force of the unslit disk be reckoned as 100, one radial slit reduced it to 88, two radial slits to 77, four to 48, and eight to 24. Amperè, in 1826, showed that a rotating disk of copper also exercises a turning moment upon a neighbouring copper wire through which a current is flowing. Seebeck in Germany, Prévost and


id: arago-s-rotations-20260505-2
file: data/en.wikipedia.org/wiki/Arago's_rotations-2.md
category: reference
title: Arago's rotations
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Arago's_rotations
date_saved: 2026-05-05T10:54:35.884320+00:00
instance: kb-cron
parent: arago-s-rotations-20260505-0
summary:
With the explanation given by Faraday of the Arago rotations, as being merely due to induced eddy-currents, the peculiar interest which they excited whilst their cause was unknown, seems almost to have died out. True, a few years later some interest was revived when Foucault showed that they were capable of heating the metal disk, if in spite of the drag the rotation was forcibly continued in the magnetic field. Why this observation should have caused the eddy-currents discovered by Faraday as the explanation of Arago's phenomenon to be dubbed Foucault's currents is not clear. If anyone is entitled to the honour of having the eddy-currents named after him, it is obviously Faraday or Arago, not Foucault. A little later, Le Roux produced the paradox that a copper disk rotated between concentric magnet poles is not heated thereby, and does not suffer any drag. The explanation of this is as follows. If there is an annular north pole in front of one face of the disk, and an annular south pole in front of the other face, though there is a magnetic field produced right through the disk, there are no eddy-currents. For if all round the disk there are


id: askaryan-radiation-20260505-0
file: data/en.wikipedia.org/wiki/Askaryan_radiation-0.md
category: reference
title: Askaryan radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Askaryan_radiation
date_saved: 2026-05-05T10:54:37.138257+00:00
instance: kb-cron
parent: askaryan-radiation-20260505-0
summary:
The Askaryan radiation also known as Askaryan effect is the phenomenon whereby a particle traveling faster than the phase velocity of light in a dense dielectric (such as salt, ice or the lunar regolith) produces a shower of secondary charged particles which contains a charge anisotropy and emits a cone of coherent radiation in the radio or microwave part of the electromagnetic spectrum. The signal is a result of the Cherenkov radiation from individual particles in the shower. Wavelengths greater than the extent of the shower interfere constructively and thus create a radio or microwave signal which is strongest at the Cherenkov angle. The effect is named after Gurgen Askaryan, a Soviet-Armenian physicist who postulated it in 1962. The radiation was first observed experimentally in 2000, 38 years after its theoretical prediction. So far the effect has been observed in silica sand, rock salt, ice, and Earth's atmosphere. The effect is of primary interest in using bulk matter to detect ultra-high energy neutrinos. The Antarctic Impulse Transient Antenna (ANITA) experiment uses antennas attached to a balloon flying over Antarctica to detect the Askaryan radiation produced by showers of particles when cosmic neutrinos interact in the ice. Several experiments have also


id: attenuation-20260505-0
file: data/en.wikipedia.org/wiki/Attenuation-0.md
category: reference
title: Attenuation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Attenuation
date_saved: 2026-05-05T10:54:38.322362+00:00
instance: kb-cron
parent: attenuation-20260505-0
summary:
In physics, attenuation is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates. Hearing protectors help reduce acoustic flux from flowing into the ears. This phenomenon is called acoustic attenuation and is measured in decibels (dBs). In electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibers, and in air. Electrical attenuators and optical attenuators are commonly manufactured components in this field. == Background == In many cases, attenuation is an exponential function of the path length through the medium. In optics and in chemical spectroscopy, this is known as the Beer–Lambert law. In engineering, attenuation is usually measured in units of decibels per unit length of medium (dB/cm, dB/km, etc.) and is represented by the attenuation coefficient of the medium in question. Attenuation also occurs in earthquakes; when the seismic waves move farther away from the hypocenter, they grow smaller as they are attenuated by the ground. == Ultrasound == One area of research in which attenuation plays a prominent role is in ultrasound physics. Attenuation in ultrasound is


id: attenuation-20260505-1
file: data/en.wikipedia.org/wiki/Attenuation-1.md
category: reference
title: Attenuation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Attenuation
date_saved: 2026-05-05T10:54:38.322362+00:00
instance: kb-cron
parent: attenuation-20260505-0
summary:
where P 1 {\displaystyle P_{1}} is the input power into a 100 m long cable terminated with the nominal value of its characteristic impedance, and P 2 {\displaystyle P_{2}} is the output power at the far end of this cable. Attenuation in a coaxial cable is a function of the materials and the construction. === Radiography === The beam of X-ray is attenuated when photons are absorbed when the x-ray beam passes through the tissue. Interaction with matter varies between high energy photons and low energy photons. Photons travelling at higher energy are more capable of travelling through a tissue specimen as they have less chances of interacting with matter. This is mainly due to the photoelectric effect which states that "the probability of photoelectric absorption is approximately proportional to (Z/E)3, where Z is the atomic number of the tissue atom and E is the photon energy. In context of this, an increase in photon energy (E) will result in a rapid decrease in the interaction with matter. In CT imaging, attenuation describes the density or darkness of the image. === Optics === Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the light


id: attenuation-20260505-2
file: data/en.wikipedia.org/wiki/Attenuation-2.md
category: reference
title: Attenuation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Attenuation
date_saved: 2026-05-05T10:54:38.322362+00:00
instance: kb-cron
parent: attenuation-20260505-0
summary:
=== Applications === In optical fibers, attenuation is the rate at which the signal light decreases in intensity. For this reason, glass fiber (which has a low attenuation) is used for long-distance fiber optic cables; plastic fiber has a higher attenuation and, hence, shorter range. There also exist optical attenuators that decrease the signal in a fiber optic cable intentionally. Attenuation of light is also important in physical oceanography. This same effect is an important consideration in weather radar, as raindrops absorb a part of the emitted beam that is more or less significant, depending on the wavelength used. Due to the damaging effects of high-energy photons, it is necessary to know how much energy is deposited in tissue during diagnostic treatments involving such radiation. In addition, gamma radiation is used in cancer treatments where it is important to know how much energy will be deposited in healthy and in tumorous tissue. In computer graphics attenuation defines the local or global influence of light sources and force fields. === Radio === Attenuation is an important consideration in the modern world of wireless telecommunications. Attenuation limits the range of radio signals and is affected by the materials a signal must travel


id: biefeld-brown-effect-20260505-0
file: data/en.wikipedia.org/wiki/Biefeld–Brown_effect-0.md
category: reference
title: Biefeld–Brown effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Biefeld–Brown_effect
date_saved: 2026-05-05T10:54:39.546162+00:00
instance: kb-cron
parent: biefeld-brown-effect-20260505-0
summary:
The Biefeld–Brown effect () is an electrical phenomenon, first noticed by inventor Thomas Townsend Brown in the 1920s, where high voltage applied to the electrodes of an asymmetric capacitor causes a net propulsive force toward the smaller electrode. Brown believed this effect was an anti-gravity force, and referred to it as electrogravitics based on it being an electricity/gravity phenomenon. Detailed studies in vacuum chambers failed to replicate Brown's observations and follow-up studies attribute the force measure to corona wind from electrical discharge. == Overview == It is generally assumed that the Biefeld–Brown effect produces an ionic wind that transfers its momentum to surrounding neutral particles. It describes a force observed on an asymmetric capacitor when high voltage is applied to the capacitor's electrodes. Once suitably charged up to high DC potentials, a thrust at the negative terminal, pushing it away from the positive terminal, is generated. The use of an asymmetric capacitor, with the negative electrode being larger than the positive electrode, allowed for more thrust to be produced in the direction from the low-flux to the high-flux region compared to a conventional capacitor. These asymmetric capacitors became known as Asymmetrical Capacitor Thrusters (ACT). These devices can be observed in


id: biefeld-brown-effect-20260505-1
file: data/en.wikipedia.org/wiki/Biefeld–Brown_effect-1.md
category: reference
title: Biefeld–Brown effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Biefeld–Brown_effect
date_saved: 2026-05-05T10:54:39.546162+00:00
instance: kb-cron
parent: biefeld-brown-effect-20260505-0
summary:
The effect is generally believed to rely on corona discharge, which allows air molecules to become ionized near sharp points and edges. Usually, two electrodes are used with a high voltage between them, ranging from a few kilovolts and up to megavolt levels, where one electrode is small or sharp, and the other larger and smoother. The most effective distance between electrodes occurs at an electric potential gradient of about 10 kV/cm, which is just below the nominal breakdown voltage of air between two sharp points, at a current density level usually referred to as the saturated corona current condition. This creates a high field gradient around the smaller, positively charged electrode. Around this electrode, ionization occurs, that is, electrons are stripped from the atoms in the surrounding medium; they are literally pulled right off by the electrode's charge. This leaves a cloud of positively charged ions in the medium, which are attracted to the negative smooth electrode by Coulomb's law, where they are neutralized again. This produces an equally scaled opposing force in the lower electrode. This effect can be used for propulsion (see EHD thruster), fluid pumps and recently also in EHD cooling systems. The velocity achievable by


id: breath-figure-self-assembly-20260505-0
file: data/en.wikipedia.org/wiki/Breath-figure_self-assembly-0.md
category: reference
title: Breath-figure self-assembly
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Breath-figure_self-assembly
date_saved: 2026-05-05T10:54:40.829980+00:00
instance: kb-cron
parent: breath-figure-self-assembly-20260505-0
summary:
Breath-figure self-assembly is the self-assembly process of the formation of honeycomb micro-scaled polymer patterns by the condensation of water droplets. "Breath-figure" refers to the fog that forms when water vapor contacts a cold surface. In the modern era systematic study of the process of breath-figures water condensation was carried out by Aitken and Rayleigh, among others. Half a century later the interest in the breath-figure formation was revived in a view of study of atmospheric processes, and in particular the extended study of a dew formation which turned out to be a complicated physical process. The experimental and theoretical study of dew formation has been carried out by Beysens. Thermodynamic and kinetic aspects of dew formation, which are crucial for understanding of formation of breath-figures inspired polymer patterns will be addressed further in detail. Breakthrough in the application of the breath-figures patterns was achieved in 1994–1995 when Widawski, François and Pitois reported manufacturing of polymer films with a self-organized, micro-scaled, honeycomb morphology using the breath-figures condensation process. The reported process was based on the rapidly evaporated polymer solutions exerted to humidity. The introduction to experimental techniques involved in manufacturing of micropatterned surfaces is supplied in reference 1; image representing typical


id: buttered-toast-phenomenon-20260505-0
file: data/en.wikipedia.org/wiki/Buttered_toast_phenomenon-0.md
category: reference
title: Buttered toast phenomenon
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Buttered_toast_phenomenon
date_saved: 2026-05-05T10:54:42.080554+00:00
instance: kb-cron
parent: buttered-toast-phenomenon-20260505-0
summary:
The buttered toast phenomenon is an observation that buttered toast tends to land butter-side down after it falls. It is used as an idiom representing pessimistic outlooks. Various people have attempted to determine whether there is an actual tendency for bread to fall in this fashion, with varying results. == Origins == Written accounts can be traced to the mid-19th century. The phenomenon is often attributed to a parodic poem of James Payn from 1884: I never had a slice of bread, Particularly large and wide, That did not fall upon the floor, And always on the buttered side! In the past, this has often been considered just a pessimistic belief. A 1991 study by the BBC's television series Q.E.D. found that when toast is tossed into the air, it lands butter-side down just one-half of the time (as would be predicted by chance). However, several scientific studies have found that when toast is dropped from a table (as opposed to being thrown in the air), it more often falls butter-side down. A study on this subject by Robert Matthews won the Ig Nobel Prize for physics in 1996. == Explanation == The problem has been studied modelling the toast


id: butterfly-effect-20260505-0
file: data/en.wikipedia.org/wiki/Butterfly_effect-0.md
category: reference
title: Butterfly effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Butterfly_effect
date_saved: 2026-05-05T10:54:43.276736+00:00
instance: kb-cron
parent: butterfly-effect-20260505-0
summary:
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972. He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome. The idea that small causes may have large effects in weather was earlier acknowledged by the French mathematician and physicist Henri Poincaré. The American


id: butterfly-effect-20260505-1
file: data/en.wikipedia.org/wiki/Butterfly_effect-1.md
category: reference
title: Butterfly effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Butterfly_effect
date_saved: 2026-05-05T10:54:43.276736+00:00
instance: kb-cron
parent: butterfly-effect-20260505-0
summary:
Following proposals from colleagues, in later speeches and papers, Lorenz used the more poetic butterfly. According to Lorenz, when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly's wings in Brazil set off a tornado in Texas? as a title. Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely. The phrase refers to the effect of a butterfly's wings creating tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate, or even prevent the occurrence of a tornado in another location. The butterfly does not power or directly create the tornado, but the term is intended to imply that the flap of the butterfly's wings can cause the tornado: in the sense that the flap of the wings is a part of the initial conditions of an interconnected complex web; one set of conditions leads to a tornado, while the other set of


id: butterfly-effect-20260505-2
file: data/en.wikipedia.org/wiki/Butterfly_effect-2.md
category: reference
title: Butterfly effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Butterfly_effect
date_saved: 2026-05-05T10:54:43.276736+00:00
instance: kb-cron
parent: butterfly-effect-20260505-0
summary:
which, unlike most chaotic maps, has a closed-form solution: x n = sin 2 ⁡ ( 2 n θ π ) {\displaystyle x_{n}=\sin ^{2}(2^{n}\theta \pi )} where the initial condition parameter θ {\displaystyle \theta } is given by θ = 1 π sin − 1 ⁡ ( x 0 1 / 2 ) {\displaystyle \theta ={\tfrac {1}{\pi }}\sin ^{-1}(x_{0}^{1/2})} . For rational θ {\displaystyle \theta } , after a finite number of iterations x n {\displaystyle x_{n}} maps into a periodic sequence. But almost all θ {\displaystyle \theta } are irrational, and, for irrational θ {\displaystyle \theta } , x n {\displaystyle x_{n}} never repeats itself – it is non-periodic. This solution equation clearly demonstrates the two key features of chaos – stretching and folding: the factor 2n shows the exponential growth of stretching, which results in sensitive dependence on initial conditions (the butterfly effect), while the squared sine function keeps x n {\displaystyle x_{n}} folded within the range [0, 1]. == In physical systems == === In weather === ==== Overview ==== The butterfly effect is most familiar in terms of weather; it can easily be demonstrated in standard weather prediction models, for example. The climate scientists James Annan


id: butterfly-effect-20260505-3
file: data/en.wikipedia.org/wiki/Butterfly_effect-3.md
category: reference
title: Butterfly effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Butterfly_effect
date_saved: 2026-05-05T10:54:43.276736+00:00
instance: kb-cron
parent: butterfly-effect-20260505-0
summary:
=== In quantum mechanics === The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics, including atoms in strong fields and the anisotropic Kepler problem. Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments; however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller and John B. Delos and co-workers. The random matrix theory and simulations with quantum computers prove that some versions of the butterfly effect in quantum mechanics do not exist. Other authors suggest that the butterfly effect can be observed in quantum systems. Zbyszek P. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians. David Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect". Whereas the classical


id: casimir-effect-20260505-0
file: data/en.wikipedia.org/wiki/Casimir_effect-0.md
category: reference
title: Casimir effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Casimir_effect
date_saved: 2026-05-05T10:54:44.616020+00:00
instance: kb-cron
parent: casimir-effect-20260505-0
summary:
In quantum field theory, the Casimir effect (or Casimir force) is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of a field. The term Casimir pressure is sometimes used when it is described in units of force per unit area. It is named after the Dutch physicist Hendrik Casimir, who predicted the effect for electromagnetic systems in 1948. In the same year Casimir, together with Dirk Polder, described a similar effect experienced by a neutral atom in the vicinity of a macroscopic interface which is called the Casimir–Polder force. Their result is a generalization of the London–van der Waals force and includes retardation due to the finite speed of light. The fundamental principles leading to the London–van der Waals force, the Casimir force, and the Casimir–Polder force can be formulated on the same footing. In 1997, a direct experiment by Steven K. Lamoreaux quantitatively measured the Casimir force to be within 5% of the value predicted by the theory. The Casimir effect can be understood by the idea that the presence of macroscopic material interfaces, such as electrical conductors and dielectrics, alters the vacuum expectation value of the energy of


id: casimir-effect-20260505-1
file: data/en.wikipedia.org/wiki/Casimir_effect-1.md
category: reference
title: Casimir effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Casimir_effect
date_saved: 2026-05-05T10:54:44.616020+00:00
instance: kb-cron
parent: casimir-effect-20260505-0
summary:
The causes of the Casimir effect are described by quantum field theory, which states that all of the various fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space. In a simplified view, a "field" in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field can be visualized as the displacement of a ball from its rest position. Vibrations in this field propagate and are governed by the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength of the field be quantized at each point in space. At the most basic level, the field at each point in space is a simple harmonic oscillator, and its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. However, even the vacuum has a vastly complex structure, so all calculations of quantum field theory must be made in relation to this model of the vacuum. The vacuum has, implicitly, all of the


id: casimir-effect-20260505-2
file: data/en.wikipedia.org/wiki/Casimir_effect-2.md
category: reference
title: Casimir effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Casimir_effect
date_saved: 2026-05-05T10:54:44.616020+00:00
instance: kb-cron
parent: casimir-effect-20260505-0
summary:
F ( p ) = − δ ⟨ E ( s ) ⟩ δ s | p . {\displaystyle F(p)=-\left.{\frac {\delta \langle E(s)\rangle }{\delta s}}\right\vert _{p}\,.} This value is finite in many practical calculations. Attraction between the plates can be easily understood by focusing on the one-dimensional situation. Suppose that a moveable conductive plate is positioned at a short distance a from one of two widely separated plates (distance l apart). With a ≪ l, the states within the slot of width a are highly constrained so that the energy E of any one mode is widely separated from that of the next. This is not the case in the large region l where there is a large number of states (about ⁠l/a⁠) with energy evenly spaced between E and the next mode in the narrow slot, or in other words, all slightly larger than E. Now on shortening a by an amount da (which is negative), the mode in the narrow slot shrinks in wavelength and therefore increases in energy proportional to −⁠da/a⁠, whereas all the ⁠l/a⁠ states that lie in the large region lengthen and correspondingly decrease their energy by an amount proportional to −⁠da/l⁠ (note the different


id: casimir-effect-20260505-3
file: data/en.wikipedia.org/wiki/Casimir_effect-3.md
category: reference
title: Casimir effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Casimir_effect
date_saved: 2026-05-05T10:54:44.616020+00:00
instance: kb-cron
parent: casimir-effect-20260505-0
summary:
⟨ E ⟩ A = lim s → 0 ⟨ E ( s ) ⟩ A = − ℏ c π 2 6 a 3 ζ ( − 3 ) . {\displaystyle {\frac {\langle E\rangle }{A}}=\lim _{s\to 0}{\frac {\langle E(s)\rangle }{A}}=-{\frac {\hbar c\pi ^{2}}{6a^{3}}}\zeta (-3)\,.} But ζ(−3) = ⁠1/120⁠ and so one obtains ⟨ E ⟩ A = − ℏ c π 2 720 a 3 . {\displaystyle {\frac {\langle E\rangle }{A}}=-{\frac {\hbar c\pi ^{2}}{720a^{3}}}\,.} The analytic continuation has evidently lost an additive positive infinity, somehow exactly accounting for the zero-point energy (not included above) outside the slot between the plates, but which changes upon plate movement within a closed system. The Casimir force per unit area ⁠Fc/A⁠ for idealized, perfectly conducting plates with vacuum between them is F c A = − d d a ⟨ E ⟩ A = − ℏ c π 2 240 a 4 {\displaystyle {\frac {F_{\mathrm {c} }}{A}}=-{\frac {d}{da}}{\frac {\langle E\rangle }{A}}=-{\frac {\hbar c\pi ^{2}}{240a^{4}}}} where ħ is the reduced Planck constant, c is the speed of light, a is the distance between the two plates The force is negative, indicating that the force is attractive: by moving the two plates closer together, the


id: casimir-effect-20260505-4
file: data/en.wikipedia.org/wiki/Casimir_effect-4.md
category: reference
title: Casimir effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Casimir_effect
date_saved: 2026-05-05T10:54:44.616020+00:00
instance: kb-cron
parent: casimir-effect-20260505-0
summary:
⟨ E ( t ) ⟩ = 1 2 ∑ n ℏ | ω n | exp ⁡ ( − t | ω n | ) , {\displaystyle \langle E(t)\rangle ={\frac {1}{2}}\sum _{n}\hbar |\omega _{n}|\exp {\bigl (}-t|\omega _{n}|{\bigr )}\,,} where the limit t → 0+ is taken in the end. The divergence of the sum is typically manifested as ⟨ E ( t ) ⟩ = C t 3 + finite {\displaystyle \langle E(t)\rangle ={\frac {C}{t^{3}}}+{\textrm {finite}}\,} for three-dimensional cavities. The infinite part of the sum is associated with the bulk constant C which does not depend on the shape of the cavity. The interesting part of the sum is the finite part, which is shape-dependent. The Gaussian regulator ⟨ E ( t ) ⟩ = 1 2 ∑ n ℏ | ω n | exp ⁡ ( − t 2 | ω n | 2 ) {\displaystyle \langle E(t)\rangle ={\frac {1}{2}}\sum _{n}\hbar |\omega _{n}|\exp \left(-t^{2}|\omega _{n}|^{2}\right)} is better suited to numerical calculations because of its superior convergence properties, but is more difficult to use in theoretical calculations. Other, suitably smooth, regulators may be used as well. The zeta function regulator ⟨ E ( s ) ⟩ = 1 2


id: casimir-effect-20260505-5
file: data/en.wikipedia.org/wiki/Casimir_effect-5.md
category: reference
title: Casimir effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Casimir_effect
date_saved: 2026-05-05T10:54:44.616020+00:00
instance: kb-cron
parent: casimir-effect-20260505-0
summary:
== Repulsive forces == There are a few instances where the Casimir effect can give rise to repulsive forces between uncharged objects. Evgeny Lifshitz showed (theoretically) that in certain circumstances (most commonly involving liquids), repulsive forces can arise. This has sparked interest in applications of the Casimir effect toward the development of levitating devices. An experimental demonstration of the Casimir-based repulsion predicted by Lifshitz was carried out by Munday et al. who described it as "quantum levitation". Other scientists have also suggested the use of gain media to achieve a similar levitation effect, though this is controversial because these materials seem to violate fundamental causality constraints and the requirement of thermodynamic equilibrium (Kramers–Kronig relations). Casimir and Casimir–Polder repulsion can in fact occur for sufficiently anisotropic electrical bodies; for a review of the issues involved with repulsion see Milton et al. A notable recent development on repulsive Casimir forces relies on using chiral materials. Q.-D. Jiang at Stockholm University and Nobel Laureate Frank Wilczek at MIT show that chiral "lubricant" can generate repulsive, enhanced, and tunable Casimir interactions. Timothy Boyer showed in his work published in 1968 that a conductor with spherical symmetry will also show this repulsive force, and the


id: cavitation-20260505-0
file: data/en.wikipedia.org/wiki/Cavitation-0.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
Cavitation in fluid mechanics and engineering normally is the phenomenon in which the static pressure of a liquid reduces to below the liquid's vapor pressure, leading to the formation of small vapor-filled cavities in the liquid. When subjected to higher pressure, these cavities, called "bubbles" or "voids", collapse and can generate shock waves that may damage machinery. As a concrete propeller example: The pressure on the suction side of the propeller blades can be very low and when the pressure falls to that of the vapour pressure of the working liquid, cavities filled with gas vapour can form. The process of the formation of these cavities is referred to as cavitation. If the cavities move into the regions of higher pressure (lower velocity), they will implode or collapse. These shock waves are strong when they are very close to the imploded bubble, but rapidly weaken as they propagate away from the implosion. Cavitation collapse is therefore a significant cause of wear in some engineering contexts. Collapsing voids that implode near to a hard surface cause cyclic stress through repeated implosion. This results in surface fatigue of the material, causing a type of damage also called "cavitation damage" or "cavitation erosion".


id: cavitation-20260505-1
file: data/en.wikipedia.org/wiki/Cavitation-1.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
=== Inertial cavitation === Inertial cavitation was first observed in the late 19th century, considering the collapse of a spherical void within a liquid. When a volume of liquid is subjected to a sufficiently low pressure, it may rupture and form a cavity. This phenomenon is coined cavitation inception and may occur behind the blade of a rapidly rotating propeller or on any surface vibrating in the liquid with sufficient amplitude and acceleration. A fast-flowing river can cause cavitation on rock surfaces, particularly when there is a drop-off, such as on a waterfall. Vapor gases evaporate into the cavity from the surrounding medium; thus, the cavity is not a vacuum at all, but rather a low-pressure vapor (gas) bubble. Once the conditions which caused the bubble to form are no longer present, such as when the bubble moves downstream, the surrounding liquid begins to implode due its higher pressure, building up momentum as it moves inward. As the bubble finally collapses, the inward momentum of the surrounding liquid causes a sharp increase of pressure and temperature of the vapor within. The bubble eventually collapses to a minute fraction of its original size, at which point the gas within dissipates into


id: cavitation-20260505-2
file: data/en.wikipedia.org/wiki/Cavitation-2.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
=== Hydrodynamic cavitation === Hydrodynamic cavitation is the process of vaporisation, bubble generation and bubble implosion which occurs in a flowing liquid as a result of a decrease and subsequent increase in local pressure. Cavitation will only occur if the local pressure declines to some point below the saturated vapor pressure of the liquid and subsequent recovery above the vapor pressure. If the recovery pressure is not above the vapor pressure then flashing is said to have occurred. In pipe systems, cavitation typically occurs either as the result of an increase in the kinetic energy (through an area constriction) or an increase in the pipe elevation. Hydrodynamic cavitation can be produced by passing a liquid through a constricted channel at a specific flow velocity or by mechanical rotation of an object through a liquid. In the case of the constricted channel and based on the specific (or unique) geometry of the system, the combination of pressure and kinetic energy can create the hydrodynamic cavitation cavern downstream of the local constriction generating high energy cavitation bubbles. Based on the thermodynamic phase change diagram, an increase in temperature could initiate a known phase change mechanism known as boiling. However, a decrease in


id: cavitation-20260505-3
file: data/en.wikipedia.org/wiki/Cavitation-3.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
=== Acoustic cavitation and ultrasonic cavitation === Inertial cavitation can also occur in the presence of an acoustic field. Microscopic gas bubbles that are generally present in a liquid will be forced to oscillate due to an applied acoustic field. If the acoustic intensity is sufficiently high, the bubbles will first grow in size and then rapidly collapse. Hence, inertial cavitation can occur even if the rarefaction in the liquid is insufficient for a Rayleigh-like void to occur. Ultrasonic cavitation inception will occur when the acceleration of the ultrasound source is enough to produce the needed pressure drop. This pressure drop depends on the value of the acceleration and the size of the affected volume by the pressure wave. The dimensionless number that predicts ultrasonic cavitation is the Garcia-Atance number. High power ultrasonic horns produce accelerations high enough to create a cavitating region that can be used for homogenization, dispersion, deagglomeration, erosion, cleaning, milling, emulsification, extraction, disintegration, and sonochemistry. == Applications == === Water transport === In supercavitation, cavitation is intentionally induced around high-speed submerged objects to reduce skin drag. === Chemical engineering === In industry, cavitation is often used to homogenize, or mix and break down, suspended particles in


id: cavitation-20260505-4
file: data/en.wikipedia.org/wiki/Cavitation-4.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
Cavitation is usually an undesirable occurrence. In devices such as propellers and pumps, cavitation causes a great deal of noise, damage to components, vibrations, and a loss of efficiency. Noise caused by cavitation can be particularly undesirable in naval vessels where such noise may render them more easily detectable by passive sonar. Cavitation has also become a concern in the renewable energy sector as it may occur on the blade surface of tidal stream turbines. When the cavitation bubbles collapse, they force energetic liquid into very small volumes, thereby creating spots of high temperature and emitting shock waves, the latter of which are a source of noise. The noise created by cavitation is a particular problem for military submarines, as it increases the chances of being detected by passive sonar. Although the collapse of a small cavity is a relatively low-energy event, highly localized collapses can erode metals, such as steel, over time. The pitting caused by the collapse of cavities produces great wear on components and can dramatically shorten a propeller's or pump's lifetime. After a surface is initially affected by cavitation, it tends to erode at an accelerating pace. The cavitation pits increase the turbulence of the fluid


id: cavitation-20260505-5
file: data/en.wikipedia.org/wiki/Cavitation-5.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
==== Cavitation solutions ==== Since all pumps require well-developed inlet flow to meet their potential, a pump may not perform or be as reliable as expected due to a faulty suction piping layout such as a close-coupled elbow on the inlet flange. When poorly developed flow enters the pump impeller, it strikes the vanes and is unable to follow the impeller passage. The liquid then separates from the vanes causing mechanical problems due to cavitation, vibration and performance problems due to turbulence and poor filling of the impeller. This results in premature seal, bearing and impeller failure, high maintenance costs, high power consumption, and less-than-specified head and/or flow. To have a well-developed flow pattern, pump manufacturer's manuals recommend about (10 diameters?) of straight pipe run upstream of the pump inlet flange. Unfortunately, piping designers and plant personnel must contend with space and equipment layout constraints and usually cannot comply with this recommendation. Instead, it is common to use an elbow close-coupled to the pump suction which creates a poorly developed flow pattern at the pump suction. With a double-suction pump tied to a close-coupled elbow, flow distribution to the impeller is poor and causes reliability and performance shortfalls. The elbow


id: cavitation-20260505-6
file: data/en.wikipedia.org/wiki/Cavitation-6.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
=== Engines === Some larger diesel engines suffer from cavitation due to high compression and undersized cylinder walls. Vibrations of the cylinder wall induce alternating low and high pressure in the coolant against the cylinder wall. The result is pitting of the cylinder wall, which will eventually let cooling fluid leak into the cylinder and combustion gases to leak into the coolant. It is possible to prevent this from happening with the use of chemical additives in the cooling fluid that form a protective layer on the cylinder wall. This layer will be exposed to the same cavitation, but rebuilds itself. Additionally a regulated overpressure in the cooling system (regulated and maintained by the coolant filler cap spring pressure) prevents the forming of cavitation. From about the 1980s, new designs of smaller gasoline engines also displayed cavitation phenomena. One answer to the need for smaller and lighter engines was a smaller coolant volume and a correspondingly higher coolant flow velocity. This gave rise to rapid changes in flow velocity and therefore rapid changes of static pressure in areas of high heat transfer. Where resulting vapor bubbles collapsed against a surface, they had the effect of first disrupting protective oxide layers


id: cavitation-20260505-7
file: data/en.wikipedia.org/wiki/Cavitation-7.md
category: reference
title: Cavitation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cavitation
date_saved: 2026-05-05T10:54:45.984996+00:00
instance: kb-cron
parent: cavitation-20260505-0
summary:
== History == As early as 1754, the Swiss mathematician Leonhard Euler (1707–1783) speculated about the possibility of cavitation. In 1859, the English mathematician William Henry Besant (1828–1917) published a solution to the problem of the dynamics of the collapse of a spherical cavity in a fluid, which had been presented by the Anglo-Irish mathematician George Stokes (1819–1903) as one of the Cambridge University Senate-house problems and riders for the year 1847. In 1894, Irish fluid dynamicist Osborne Reynolds (1842–1912) studied the formation and collapse of vapor bubbles in boiling liquids and in constricted tubes. The term cavitation first appeared in 1895 in a paper by John Isaac Thornycroft (1843–1928) and Sydney Walker Barnaby (1855–1925)—son of Sir Nathaniel Barnaby (1829 – 1915), who had been Chief Constructor of the Royal Navy—to whom it had been suggested by the British engineer Robert Edmund Froude (1846–1924), third son of the English hydrodynamicist William Froude (1810–1879). Early experimental studies of cavitation were conducted in 1894–5 by Thornycroft and Barnaby and by the Anglo-Irish engineer Charles Algernon Parsons (1854–1931), who constructed a stroboscopic apparatus to study the phenomenon. Thornycroft and Barnaby were the first researchers to observe cavitation on the back sides of propeller


id: cherenkov-radiation-20260505-0
file: data/en.wikipedia.org/wiki/Cherenkov_radiation-0.md
category: reference
title: Cherenkov radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cherenkov_radiation
date_saved: 2026-05-05T10:54:47.273838+00:00
instance: kb-cron
parent: cherenkov-radiation-20260505-0
summary:
Cherenkov radiation () is an electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium. A classic example of Cherenkov radiation is the characteristic blue glow of an underwater nuclear reactor. Its cause is similar to the cause of a sonic boom, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist Pavel Cherenkov. == History == The radiation is named after the Soviet scientist Pavel Cherenkov, the 1958 Nobel Prize winner, who was the first to detect it experimentally under the supervision of Sergey Vavilov at the Lebedev Institute in 1934. Therefore, it is also known as Vavilov–Cherenkov radiation. Cherenkov saw a faint bluish light around a radioactive preparation in water during experiments. His doctorate thesis was on luminescence of uranium salt solutions that were excited by gamma rays instead of less energetic visible light, as done commonly. He discovered the anisotropy of the radiation and came to the conclusion that the bluish glow was not a fluorescent phenomenon. A theory of


id: cherenkov-radiation-20260505-1
file: data/en.wikipedia.org/wiki/Cherenkov_radiation-1.md
category: reference
title: Cherenkov radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cherenkov_radiation
date_saved: 2026-05-05T10:54:47.273838+00:00
instance: kb-cron
parent: cherenkov-radiation-20260505-0
summary:
In their original work on the theoretical foundations of Cherenkov radiation, Tamm and Frank wrote, "This peculiar radiation can evidently not be explained by any common mechanism such as the interaction of the fast electron with individual atom or as radiative scattering of electrons on atomic nuclei. On the other hand, the phenomenon can be explained both qualitatively and quantitatively if one takes into account the fact that an electron moving in a medium does radiate light even if it is moving uniformly provided that its velocity is greater than the velocity of light in the medium." === Emission angle === In the figure on the geometry, the particle (red arrow) travels in a medium with speed v p {\displaystyle v_{\text{p}}} such that c n < v p < c , {\displaystyle {\frac {c}{n}}<v_{\text{p}}<c,} where c {\displaystyle c} is speed of light in vacuum, and n {\displaystyle n} is the refractive index of the medium. If the medium is water, the condition is 0.75 c < v p < c {\displaystyle 0.75c<v_{\text{p}}<c} , since n ≈ 1.33 {\displaystyle n\approx 1.33} for water at 20 °C. We define the ratio between the speed of the particle and the speed of light


id: cherenkov-radiation-20260505-2
file: data/en.wikipedia.org/wiki/Cherenkov_radiation-2.md
category: reference
title: Cherenkov radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cherenkov_radiation
date_saved: 2026-05-05T10:54:47.273838+00:00
instance: kb-cron
parent: cherenkov-radiation-20260505-0
summary:
The Frank–Tamm formula describes the amount of energy E {\displaystyle E} emitted from Cherenkov radiation, per unit length traveled x {\displaystyle x} and per frequency ω {\displaystyle \omega } . μ ( ω ) {\displaystyle \mu (\omega )} is the permeability and n ( ω ) {\displaystyle n(\omega )} is the index of refraction of the material the charged particle moves through. q {\displaystyle q} is the electric charge of the particle, v {\displaystyle v} is the speed of the particle, and c {\displaystyle c} is the speed of light in vacuum. Unlike fluorescence or emission spectra that have characteristic spectral peaks, Cherenkov radiation is continuous. Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency, with higher frequencies (shorter wavelengths) being more intense in Cherenkov radiation. Visible Cherenkov radiation is observed to be brilliant blue because while most Cherenkov radiation is in the ultraviolet spectrum, it is only with sufficiently accelerated charges that it even becomes visible; the sensitivity of the human eye peaks at green, and is very low in the violet portion of the spectrum. There is a cut-off frequency above which the equation cos ⁡ θ = 1 / (


id: cherenkov-radiation-20260505-3
file: data/en.wikipedia.org/wiki/Cherenkov_radiation-3.md
category: reference
title: Cherenkov radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cherenkov_radiation
date_saved: 2026-05-05T10:54:47.273838+00:00
instance: kb-cron
parent: cherenkov-radiation-20260505-0
summary:
Cherenkov radiation is commonly used in experimental particle physics for particle identification. One could measure (or put limits on) the velocity of an electrically charged elementary particle by the properties of the Cherenkov light it emits in a certain medium. If the momentum of the particle is measured independently, one could compute the mass of the particle by its momentum and velocity (see four-momentum), and hence identify the particle. The simplest type of particle identification device based on a Cherenkov radiation technique is the threshold counter, which answers whether the velocity of a charged particle is lower or higher than a certain value ( v 0 = c / n {\displaystyle v_{0}=c/n} , where c {\displaystyle c} is the speed of light, and n {\displaystyle n} is the refractive index of the medium) by looking at whether this particle emits Cherenkov light in a certain medium. Knowing particle momentum, one can separate particles lighter than a certain threshold from those heavier than the threshold. The most advanced type of a detector is the RICH, or ring-imaging Cherenkov detector, developed in the 1980s. In a RICH detector, a cone of Cherenkov light is produced when a high-speed charged particle traverses a


id: coand-effect-20260505-0
file: data/en.wikipedia.org/wiki/Coandă_effect-0.md
category: reference
title: Coandă effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coandă_effect
date_saved: 2026-05-05T10:54:48.580764+00:00
instance: kb-cron
parent: coand-effect-20260505-0
summary:
The Coandă effect ( or ) is the tendency of a fluid jet to stay attached to a surface of any form. Merriam-Webster describes it as "the tendency of a jet of fluid emerging from an orifice to follow an adjacent flat or curved surface and to entrain fluid from the surroundings so that a region of lower pressure develops." It is named after Romanian inventor Henri Coandă, who was the first to recognize the practical application of the phenomenon in aircraft design around 1910. It was first documented explicitly in two patents issued in 1936. == History == A description of this phenomenon was provided by Thomas Young in a lecture to The Royal Society in 1800: The lateral pressure which urges the flame of a candle towards the stream of air from a blowpipe is probably exactly similar to that pressure which eases the inflection of a current of air near an obstacle. Mark the dimple which a slender stream of air makes on the surface of water. Bring a convex body into contact with the side of the stream and the place of the dimple will immediately show the current is deflected towards the body; and if


id: coand-effect-20260505-1
file: data/en.wikipedia.org/wiki/Coandă_effect-1.md
category: reference
title: Coandă effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coandă_effect
date_saved: 2026-05-05T10:54:48.580764+00:00
instance: kb-cron
parent: coand-effect-20260505-0
summary:
With a much smaller radius (12 centimeters in the image on the right) a transverse difference arises between external and wall surface pressures of the jet, creating a pressure gradient depending upon ⁠h/r⁠, the relative curvature. This pressure gradient can appear in a zone before and after the origin of the jet where it gradually arises, and disappear at the point where the jet boundary layer separates from the wall, where the wall pressure reaches atmospheric pressure (and the transverse gradient becomes zero). Experiments made in 1956 with turbulent air jets at a Reynolds number of 106 at various jet widths (h) show the pressures measured along a circularly curved wall radius (r) at a series of horizontal distance from the origin of the jet (see the diagram on the right). Above a critical ⁠h/r⁠ ratio of 0.5 only local effects at the origin of the jet are seen extending over a small angle of 18° along the curved wall. The jet then immediately separates from the curved wall. A Coandă effect is therefore not seen here but only a local attachment: a pressure smaller than atmospheric pressure appears on the wall along a distance corresponding to a small angle


id: coand-effect-20260505-2
file: data/en.wikipedia.org/wiki/Coandă_effect-2.md
category: reference
title: Coandă effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coandă_effect
date_saved: 2026-05-05T10:54:48.580764+00:00
instance: kb-cron
parent: coand-effect-20260505-0
summary:
An image of the surface pressure distribution of the jet round the cylindrical surface using the same values of the relative curvature ⁠h/r⁠, and the same angle θ as those found for the wall jet reported in the image on the right side here has been established: it may be found in reference (15) p. 104 and both images are quite similar: the Coandă effect of a free jet is inertial, the same as Coandă effect of a wall jet. However, an experimental measurement of the corresponding surface pressure distribution is not known. Experiments in 1959 by Bourque and Newmann concerning the reattachment of a two-dimensional turbulent jet to an offset parallel plate after enclosing a separation bubble where a low pressure vortex is confined (as in the image 5 in the preceding section) and also for a two-dimensional jet followed by a single flat plate inclined at an angle instead of the circularly curved wall in the diagram on the right here describing the experience of a wall jet: the jet separates from the plate, then curves towards the plate when the surrounding fluid is entrained and pressure lowered, and eventually reattaches to it, enclosing a separation bubble. The


id: coand-effect-20260505-3
file: data/en.wikipedia.org/wiki/Coandă_effect-3.md
category: reference
title: Coandă effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coandă_effect
date_saved: 2026-05-05T10:54:48.580764+00:00
instance: kb-cron
parent: coand-effect-20260505-0
summary:
The experimental McDonnell Douglas YC-15 and its production derivative, the Boeing C-17 Globemaster III, also employ the effect. The NOTAR helicopter replaces the conventional propeller tail rotor with a Coandă effect tail (diagram on the left). A better understanding of Coandă effect was provided by the scientific literature produced by ACHEON EU FP7 project. This project utilized a particular symmetric nozzle to produce an effective modeling of the Coandă effect, and determined innovative STOL aircraft configurations based on the effect. This activity has been expanded by Dragan in the turbomachinery sector, with the objective of better optimizing the shape of rotating blades by Romanian Comoti Research Centre's work on turbomachinery. A practical use of the Coandă effect is for inclined hydropower screens, which separate debris, fish, etc., otherwise in the input flow to the turbines. Due to the slope, the debris falls from the screens without mechanical clearing, and due to the wires of the screen optimizing the Coandă effect, the water flows through the screen to the penstocks leading the water to the turbines. The Coandă effect is used in dual-pattern fluid dispensers in automobile windshield washers. The operation principle of oscillatory flowmeters also relies on the Coandă phenomenon.


id: coand-effect-20260505-4
file: data/en.wikipedia.org/wiki/Coandă_effect-4.md
category: reference
title: Coandă effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coandă_effect
date_saved: 2026-05-05T10:54:48.580764+00:00
instance: kb-cron
parent: coand-effect-20260505-0
summary:
== Demonstration == The Coandă effect can be demonstrated by directing a small jet of air upwards at an angle over a ping pong ball. The jet is drawn to and follows the upper surface of the ball curving around it, due to the (radial) acceleration (slowing and turning) of the air around the ball. With enough airflow, this change in momentum is balanced by the equal and opposite force on the ball supporting its weight. This demonstration can be performed using a hairdryer on the lowest setting or a vacuum cleaner if the outlet can be attached to the pipe and aimed upwards at an angle. A common misconception is that the Coandă effect is demonstrated when a stream of tap water flows over the back of a spoon held lightly in the stream and the spoon is pulled into the stream (for example, Massey 1979, Fig 3.12 uses the Coandă effect to explain the deflection of water around a cylinder). While the flow looks very similar to the air flow over the ping pong ball above (if one could see the air flow), the cause is not really the Coandă effect. Here, because it is a flow of


id: coffee-ring-effect-20260505-0
file: data/en.wikipedia.org/wiki/Coffee_ring_effect-0.md
category: reference
title: Coffee ring effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coffee_ring_effect
date_saved: 2026-05-05T10:54:49.911756+00:00
instance: kb-cron
parent: coffee-ring-effect-20260505-0
summary:
In physics, a "coffee ring" is a pattern left by a puddle of particle-laden liquid after it evaporates. The phenomenon is named for the characteristic ring-like deposit along the perimeter of a spill of coffee. It is also commonly seen after spilling red wine. The mechanism behind the formation of these and similar rings is known as the coffee ring effect or in some instances, the coffee stain effect, or simply ring stain. == Flow mechanism == The coffee-ring pattern originates from the capillary flow induced by the evaporation of the drop: liquid evaporating from the edge is replenished by liquid from the interior. The resulting current can carry nearly all the dispersed material to the edge. As a function of time, this process exhibits a "rush-hour" effect, that is, a rapid acceleration of the flow towards the edge at the final stage of the drying process. Evaporation induces a Marangoni flow inside a droplet. The flow, if strong, redistributes particles back to the center of the droplet. Thus, for particles to accumulate at the edges, the liquid must have a weak Marangoni flow, or something must occur to disrupt the flow. For example, surfactants can be added to reduce


id: condensation-cloud-20260505-0
file: data/en.wikipedia.org/wiki/Condensation_cloud-0.md
category: reference
title: Condensation cloud
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Condensation_cloud
date_saved: 2026-05-05T10:54:51.182419+00:00
instance: kb-cron
parent: condensation-cloud-20260505-0
summary:
A transient condensation cloud, also called a Wilson cloud, is observable surrounding large explosions in humid air. When a nuclear weapon or high explosive is detonated in sufficiently humid air, the "negative phase" of the shock wave causes a rarefaction of the air surrounding the explosion but not of the air contained within it. The rarefied air is temporarily cooled, which causes condensation of some of the water vapor within the rarefied air. When the pressure and temperature return to normal, the Wilson cloud dissipates. == Mechanism == Since heat does not leave the affected air mass, the change of pressure following a detonation is adiabatic, with an associated change of temperature. In humid air, the drop in temperature in the most rarefied portion of the shock wave can bring the air temperature below its dew point, at which moisture condenses to form a visible cloud of microscopic water droplets. Since the pressure effect of the wave is reduced by its expansion (the same pressure effect is spread over a larger radius), the vapor effect also has a limited radius. Such vapor can also be seen in low pressure regions during high–g subsonic maneuvers of aircraft in humid conditions. ==


id: convection-20260505-0
file: data/en.wikipedia.org/wiki/Convection-0.md
category: reference
title: Convection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convection
date_saved: 2026-05-05T10:54:52.394392+00:00
instance: kb-cron
parent: convection-20260505-0
summary:
Convection is the transfer of heat through the physical movement of fluids (liquids or gases), where warmer, less-dense material rises and cooler, denser material sinks. It is a single-phase or multiphase fluid flow that occurs spontaneously through the combined effects of material property heterogeneity and body forces on a fluid. When the cause of the convection is unspecified, convection due to the effects of thermal expansion (change in density) and gravity/buoyancy can be assumed (see convection in heat transfer). Convective flow may be transient (such as when a multiphase mixture of oil and water separates) or steady state (see convection cell). The convection may be due to gravitational, electromagnetic or fictitious body forces. Heat transfer by natural convection plays a role in the structure of Earth's atmosphere, its oceans, and its mantle. Discrete convective cells in the atmosphere can be identified by clouds, with stronger convection resulting in thunderstorms. Natural convection also plays a role in stellar physics. Convection is often categorised or described by the main effect causing the convective flow; for example, thermal convection. Convection may also take place in soft solids or mixtures where particles can flow. Convection cannot take place in most solids because neither bulk


id: convection-20260505-1
file: data/en.wikipedia.org/wiki/Convection-1.md
category: reference
title: Convection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convection
date_saved: 2026-05-05T10:54:52.394392+00:00
instance: kb-cron
parent: convection-20260505-0
summary:
Natural convection is a flow whose motion is caused by some parts of a fluid being heavier than other parts. In most cases this leads to natural circulation: the ability of a fluid in a system to circulate continuously under gravity, with transfer of heat energy. The driving force for natural convection is gravity. In a column of fluid, pressure increases with depth from the weight of the overlying fluid. The pressure at the bottom of a submerged object then exceeds that at the top, resulting in a net upward buoyancy force equal to the weight of the displaced fluid. Objects of higher density than that of the displaced fluid then sink. For example, regions of warmer low-density air rise, while those of colder high-density air sink. This creates a circulating flow: convection. Gravity drives natural convection. Without gravity, convection does not occur, so there is no convection in free-fall (inertial) environments, such as that of the orbiting International Space Station. Natural convection can occur when there are hot and cold regions of either air or water, because both water and air become less dense as they are heated. But, for example, in the world's oceans it also occurs due


id: convection-20260505-2
file: data/en.wikipedia.org/wiki/Convection-2.md
category: reference
title: Convection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convection
date_saved: 2026-05-05T10:54:52.394392+00:00
instance: kb-cron
parent: convection-20260505-0
summary:
== Examples and applications == Systems of natural circulation include tornadoes and other weather systems, ocean currents, and household ventilation. Some solar water heaters use natural circulation. The Gulf Stream circulates as a result of the evaporation of water. In this process, the water increases in salinity and density. In the North Atlantic Ocean, the water becomes so dense that it begins to sink down. Convection occurs on a large scale in atmospheres, oceans, planetary mantles, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of the Sun and all stars. Fluid movement during convection may be invisibly slow, or it may be obvious and rapid, as in a hurricane. On astronomical scales, convection of gas and dust is thought to occur in the accretion disks of black holes, at speeds which may closely approach that of light. === Demonstration experiments === Thermal convection in liquids can be demonstrated by placing a heat source (for example, a Bunsen burner) at the side of a container with a liquid. Adding a dye to the water (such as food colouring) will enable visualisation of the flow. Another common experiment to demonstrate thermal convection in liquids


id: convection-20260505-3
file: data/en.wikipedia.org/wiki/Convection-3.md
category: reference
title: Convection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convection
date_saved: 2026-05-05T10:54:52.394392+00:00
instance: kb-cron
parent: convection-20260505-0
summary:
Warm air has a lower density than cool air, so warm air rises within cooler air, similar to hot air balloons. Clouds form as relatively warmer air carrying moisture rises within cooler air. As the moist air rises, it cools, causing some of the water vapor in the rising packet of air to condense. When the moisture condenses, it releases energy known as latent heat of condensation which allows the rising packet of air to cool less than its surrounding air, continuing the cloud's ascension. If enough instability is present in the atmosphere, this process will continue long enough for cumulonimbus clouds to form, which support lightning and thunder. Generally, thunderstorms require three conditions to form: moisture, an unstable airmass, and a lifting force (heat). All thunderstorms, regardless of type, go through three stages: the developing stage, the mature stage, and the dissipation stage. The average thunderstorm has a 24 km (15 mi) diameter. Depending on the conditions present in the atmosphere, these three stages take an average of 30 minutes to go through. === Oceanic circulation === Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the poles, while cold polar water heads towards


id: convection-20260505-4
file: data/en.wikipedia.org/wiki/Convection-4.md
category: reference
title: Convection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convection
date_saved: 2026-05-05T10:54:52.394392+00:00
instance: kb-cron
parent: convection-20260505-0
summary:
The convection zone of a star is the range of radii in which energy is transported outward from the core region primarily by convection rather than radiation. This occurs at radii which are sufficiently opaque that convection is more efficient than radiation at transporting energy. Granules on the photosphere of the Sun are the visible tops of convection cells in the photosphere, caused by convection of plasma in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours. === Water convection at freezing temperatures === Water is a fluid that does not obey the Boussinesq approximation. This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures. The density of water reaches a maximum at 4 °C and decreases as the temperature deviates. This


id: convection-20260505-5
file: data/en.wikipedia.org/wiki/Convection-5.md
category: reference
title: Convection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convection
date_saved: 2026-05-05T10:54:52.394392+00:00
instance: kb-cron
parent: convection-20260505-0
summary:
Δ ρ = ρ 0 β Δ T {\displaystyle \Delta \rho =\rho _{0}\beta \Delta T} where ρ 0 {\displaystyle \rho _{0}} is the reference density, typically picked to be the average density of the medium, β {\displaystyle \beta } is the coefficient of thermal expansion, and Δ T {\displaystyle \Delta T} is the temperature difference across the medium. The general diffusivity, D {\displaystyle D} , is redefined as a thermal diffusivity, α {\displaystyle \alpha } . D = α {\displaystyle D=\alpha } Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection. Ra = ρ 0 g β Δ T L 3 α μ {\displaystyle {\textbf {Ra}}={\frac {\rho _{0}g\beta \Delta TL^{3}}{\alpha \mu }}} === Turbulence === The tendency of a particular naturally convective system towards turbulence relies on the Grashof number (Gr). G r = g β Δ T L 3 ν 2 {\displaystyle Gr={\frac {g\beta \Delta TL^{3}}{\nu ^{2}}}} In very sticky, viscous fluids (large ν), fluid motion is restricted, and natural convection will be non-turbulent. Following the treatment of the previous subsection, the typical fluid velocity is of the order of g Δ ρ L 2 / μ {\displaystyle g\Delta \rho L^{2}/\mu } ,


id: convection-20260505-6
file: data/en.wikipedia.org/wiki/Convection-6.md
category: reference
title: Convection
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Convection
date_saved: 2026-05-05T10:54:52.394392+00:00
instance: kb-cron
parent: convection-20260505-0
summary:
Convection, especially Rayleigh–Bénard convection, where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a pattern-forming system. When heat is fed into the system from one direction (usually below), at small values it merely diffuses (conducts) from below upward, without causing fluid flow. As the heat flow is increased, above a critical value of the Rayleigh number, the system undergoes a bifurcation from the stable conducting state to the convecting state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is symmetric, with the same volume of fluid rising as falling. This is known as Boussinesq convection. As the temperature difference between the top and bottom of the fluid becomes higher, significant differences in fluid parameters other than density may develop in the fluid due to temperature. An example of such a parameter is viscosity, which may begin to significantly vary horizontally across layers of fluid. This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen in the illustration. Such hexagons are one example of


id: coriolis-force-20260505-0
file: data/en.wikipedia.org/wiki/Coriolis_force-0.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
In physics, the Coriolis force is a pseudo-force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology. On Earth, the Coriolis force will affect the movement of air and water over long distance. Because of Earth's rotation, the moving object does not travel in a straight line relative to the Earth's surface but follows a curved path. This deflection, to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, significantly influences large-scale circulation of winds and ocean currents. Newton's laws of motion describe the motion of an object in an inertial


id: coriolis-force-20260505-1
file: data/en.wikipedia.org/wiki/Coriolis_force-1.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
Italian scientist Giovanni Battista Riccioli and his assistant Francesco Maria Grimaldi described the effect in connection with artillery in the 1651 Almagestum Novum, writing that rotation of the Earth should cause a cannonball fired to the north to deflect to the east. In 1674, Claude François Milliet Dechales described in his Cursus seu Mundus Mathematicus how the rotation of the Earth should cause a deflection in the trajectories of both falling bodies and projectiles aimed toward one of the planet's poles. Riccioli, Grimaldi, and Dechales all described the effect as part of an argument against the heliocentric system of Copernicus. In other words, they argued that the Earth's rotation should create the effect, and so failure to detect the effect was evidence for an immobile Earth. Their arguments were correct, but the effect of Coriolis force is so small that it was not measured until the 19th century. The Coriolis acceleration equation was derived by Euler in 1749, and the effect was described in the tidal equations of Pierre-Simon Laplace in 1778. Gaspard-Gustave de Coriolis published a paper in 1835 on the energy yield of machines with rotating parts, such as waterwheels. That paper considered the supplementary forces that are


id: coriolis-force-20260505-2
file: data/en.wikipedia.org/wiki/Coriolis_force-2.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
if the velocity is parallel to the rotation axis, the Coriolis force is zero. For example, on Earth, this situation occurs for a body at the equator moving north or south relative to the Earth's surface. (At any latitude other than the equator, however, the north–south motion would have a component perpendicular to the rotation axis and a force specified by the inward or outward cases mentioned below). if the velocity is straight inward to the axis, the Coriolis force is in the direction of local rotation. For example, on Earth, this situation occurs for a body at the equator falling downward, as in the Dechales illustration above, where the falling ball travels further to the east than does the tower. Note also that heading north in the Northern Hemisphere would have a velocity component toward the rotation axis, resulting in a Coriolis force to the east (more pronounced the further north one is). if the velocity is straight outward from the axis, the Coriolis force is against the direction of local rotation. In the tower example, a ball launched upward would move toward the west. if the velocity is in the direction of rotation, the Coriolis force is outward


id: coriolis-force-20260505-3
file: data/en.wikipedia.org/wiki/Coriolis_force-3.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
The figure describes a more complex situation where the tossed ball on a turntable bounces off the edge of the carousel and then returns to the tosser, who catches the ball. The effect of Coriolis force on its trajectory is shown again as seen by two observers: an observer (referred to as the "camera") that rotates with the carousel, and an inertial observer. The figure shows a bird's-eye view based upon the same ball speed on forward and return paths. Within each circle, plotted dots show the same time points. In the left panel, from the camera's viewpoint at the center of rotation, the tosser (smiley face) and the rail both are at fixed locations, and the ball makes a very considerable arc on its travel toward the rail, and takes a more direct route on the way back. From the ball tosser's viewpoint, the ball seems to return more quickly than it went (because the tosser is rotating toward the ball on the return flight). On the carousel, instead of tossing the ball straight at a rail to bounce back, the tosser must throw the ball toward the right of the target and the ball then seems to the


id: coriolis-force-20260505-4
file: data/en.wikipedia.org/wiki/Coriolis_force-4.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
a C = − 2 Ω × v = 2 ω ( − v u 0 v e ) . {\displaystyle \mathbf {a} _{\mathrm {C} }=-2{\boldsymbol {\Omega }}\times \mathbf {v} =2\,\omega \,{\begin{pmatrix}-v_{\mathrm {u} }\\0\\v_{\mathrm {e} }\end{pmatrix}}\ .} Ω in this case is parallel to the north–south axis. Accordingly, an eastward motion (that is, in the same direction as the rotation of the sphere) provides an upward acceleration known as the Eötvös effect, and an upward motion produces an acceleration due west. === Meteorology and oceanography === Perhaps the most important impact of the Coriolis effect is in the large-scale dynamics of the oceans and the atmosphere. In meteorology and oceanography, it is convenient to postulate a rotating frame of reference wherein the Earth is stationary. In accommodation of that provisional postulation, the centrifugal and Coriolis forces are introduced. Their relative importance is determined by the applicable Rossby numbers. Tornadoes have high Rossby numbers, so, while tornado-associated centrifugal forces are quite substantial, Coriolis forces associated with tornadoes are for practical purposes negligible. Because surface ocean currents are driven by the movement of wind over the water's surface, the Coriolis force also affects the movement of ocean currents and cyclones as well.


id: coriolis-force-20260505-5
file: data/en.wikipedia.org/wiki/Coriolis_force-5.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
The practical impact of the "Coriolis effect" is mostly caused by the horizontal acceleration component produced by horizontal motion. There are other components of the Coriolis effect. Westward-traveling objects are deflected downwards, while eastward-traveling objects are deflected upwards. This is known as the Eötvös effect. This aspect of the Coriolis effect is greatest near the equator. The force produced by the Eötvös effect is similar to the horizontal component, but the much larger vertical forces due to gravity and pressure suggest that it is unimportant in the hydrostatic equilibrium. However, in the atmosphere, winds are associated with small deviations of pressure from the hydrostatic equilibrium. In the tropical atmosphere, the order of magnitude of the pressure deviations is so small that the contribution of the Eötvös effect to the pressure deviations is considerable. In addition, objects traveling upwards (i.e. out) or downwards (i.e. in) are deflected to the west or east respectively. This effect is also the greatest near the equator. Since vertical movement is usually of limited extent and duration, the size of the effect is smaller and requires precise instruments to detect. For example, idealized numerical modeling studies suggest that this effect can directly affect tropical large-scale wind


id: coriolis-force-20260505-6
file: data/en.wikipedia.org/wiki/Coriolis_force-6.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
The train travels toward the west: In that case, it moves against the direction of rotation. Therefore, on the Earth's rotating frame the Coriolis term is pointed inwards towards the axis of rotation (down). This additional force downwards should cause the train to be heavier while moving in that direction.If one looks at this train from the fixed non-rotating frame on top of the center of the Earth, at that speed it remains stationary as the Earth spins beneath it. Hence, the only force acting on it is gravity and the reaction from the track. This force is greater (by 0.34%) than the force that the passengers and the train experience when at rest (rotating along with Earth). This difference is what the Coriolis effect accounts for in the rotating frame of reference. The train comes to a stop: From the point of view on the Earth's rotating frame, the velocity of the train is zero, thus the Coriolis force is also zero and the train and its passengers recuperate their usual weight.From the fixed inertial frame of reference above Earth, the train now rotates along with the rest of the Earth. 0.34% of the force of gravity provides the


id: coriolis-force-20260505-7
file: data/en.wikipedia.org/wiki/Coriolis_force-7.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
==== Laboratory testing of draining water under atypical conditions ==== In 1962, Ascher Shapiro performed an experiment at MIT to test the Coriolis force on a large basin of water, 2 meters (6 ft 7 in) across, with a small wooden cross above the plug hole to display the direction of rotation, covering it and waiting for at least 24 hours for the water to settle. Under these precise laboratory conditions, he demonstrated the effect and consistent counterclockwise rotation. The experiment required extreme precision, since the acceleration due to Coriolis effect is only 3 × 10 − 7 {\displaystyle 3\times 10^{-7}} that of gravity. The vortex was measured by a cross made of two slivers of wood pinned above the draining hole. It takes 20 minutes to drain, and the cross starts turning only around 15 minutes. At the end it is turning at 1 rotation every 3 to 4 seconds. He reported that, Both schools of thought are in some sense correct. For the everyday observations of the kitchen sink and bath-tub variety, the direction of the vortex seems to vary in an unpredictable manner with the date, the time of day, and the particular household of the experimenter.


id: coriolis-force-20260505-8
file: data/en.wikipedia.org/wiki/Coriolis_force-8.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
To demonstrate the Coriolis effect, a parabolic turntable can be used. On a flat turntable, the inertia of a co-rotating object forces it off the edge. However, if the turntable surface has the correct paraboloid (parabolic bowl) shape (see the figure) and rotates at the corresponding rate, the force components shown in the figure make the component of gravity tangential to the bowl surface exactly equal to the centripetal force necessary to keep the object rotating at its velocity and radius of curvature (assuming no friction). (See banked turn.) This carefully contoured surface allows the Coriolis force to be displayed in isolation. Discs cut from cylinders of dry ice can be used as pucks, moving around almost frictionlessly over the surface of the parabolic turntable, allowing effects of Coriolis on dynamic phenomena to show themselves. To get a view of the motions as seen from the reference frame rotating with the turntable, a video camera is attached to the turntable so as to co-rotate with the turntable, with results as shown in the figure. In the left panel of the figure, which is the viewpoint of a stationary observer, the gravitational force in the inertial frame pulling the object toward


id: coriolis-force-20260505-9
file: data/en.wikipedia.org/wiki/Coriolis_force-9.md
category: reference
title: Coriolis force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Coriolis_force
date_saved: 2026-05-05T10:54:53.676521+00:00
instance: kb-cron
parent: coriolis-force-20260505-0
summary:
The definition of the Coriolis effect from the Glossary of Meteorology The Coriolis Effect — a conflict between common sense and mathematics PDF-file. 20 pages. A general discussion by Anders Persson of various aspects of the coriolis effect, including Foucault's Pendulum and Taylor columns. The coriolis effect in meteorology PDF-file. 5 pages. A detailed explanation by Mats Rosengren of how the gravitational force and the rotation of the Earth affect the atmospheric motion over the Earth surface. 2 figures 10 Coriolis Effect Videos and Games- from the About.com Weather Page Coriolis Force – from ScienceWorld Coriolis Effect and Drains An article from the NEWTON web site hosted by the Argonne National Laboratory. Catalog of Coriolis videos Coriolis Effect: A graphical animation, a visual Earth animation with precise explanation An introduction to fluid dynamics SPINLab Educational Film explains the Coriolis effect with the aid of lab experiments Do bathtubs drain counterclockwise in the Northern Hemisphere? Archived 15 May 2008 at the Wayback Machine by Cecil Adams. Bad Coriolis. An article uncovering misinformation about the Coriolis effect. By Alistair B. Fraser, emeritus professor of meteorology at Pennsylvania State University The Coriolis Effect: A (Fairly) Simple Explanation, an explanation for the layperson Observe


id: critical-phenomena-20260505-0
file: data/en.wikipedia.org/wiki/Critical_phenomena-0.md
category: reference
title: Critical phenomena
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Critical_phenomena
date_saved: 2026-05-05T10:54:54.979917+00:00
instance: kb-cron
parent: critical-phenomena-20260505-0
summary:
In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking. Critical phenomena take place in second order phase transitions, although not exclusively. The critical behavior is usually different from the mean-field approximation which is valid away from the phase transition, since the latter neglects correlations, which become increasingly important as the system approaches the critical point where the correlation length diverges. Many properties of the critical behavior of a system can be derived in the framework of the renormalization group. In order to explain the physical origin of these phenomena, we shall use the Ising model as a pedagogical example. == Critical point of the 2D Ising model == Consider a 2 D {\displaystyle 2D} square array of classical spins which may only take two positions: +1 and −1, at a certain temperature T {\displaystyle T} , interacting through the Ising classical Hamiltonian: H =


id: critical-phenomena-20260505-1
file: data/en.wikipedia.org/wiki/Critical_phenomena-1.md
category: reference
title: Critical phenomena
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Critical_phenomena
date_saved: 2026-05-05T10:54:54.979917+00:00
instance: kb-cron
parent: critical-phenomena-20260505-0
summary:
== Mathematical tools == The main mathematical tools to study critical points are renormalization group, which takes advantage of the Russian dolls picture or the self-similarity to explain universality and predict numerically the critical exponents, and variational perturbation theory, which converts divergent perturbation expansions into convergent strong-coupling expansions relevant to critical phenomena. In two-dimensional systems, conformal field theory is a powerful tool which has discovered many new properties of 2D critical systems, employing the fact that scale invariance, along with a few other requisites, leads to an infinite symmetry group. == Critical point in renormalization group theory == The critical point is described by a conformal field theory. According to the renormalization group theory, the defining property of criticality is that the characteristic length scale of the structure of the physical system, also known as the correlation length ξ, becomes infinite. This can happen along critical lines in phase space. This effect is the cause of the critical opalescence that can be observed as a binary fluid mixture approaches its liquid–liquid critical point. In systems in equilibrium, the critical point is reached only by precisely tuning a control parameter. However, in some non-equilibrium systems, the critical point is an attractor


id: cross-ventilation-20260505-0
file: data/en.wikipedia.org/wiki/Cross_ventilation-0.md
category: reference
title: Cross ventilation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cross_ventilation
date_saved: 2026-05-05T10:54:56.230155+00:00
instance: kb-cron
parent: cross-ventilation-20260505-0
summary:
Cross ventilation is a natural phenomenon where wind enters an opening, such as a window, flows directly through the space, and exits through an opening on the opposite side of the building (where the air pressure is lower). This produces a cool stream of air and a current across the room from the exposed area to the sheltered area. Cross ventilation is powered by the wind and thus requires no energy input, in addition to being the most effective method of wind ventilation. A commonly used technique to remove pollutants and heat in an indoor environment, cross ventilation can also decrease or even obviate the need for air conditioning and can improve indoor air quality. Other terms used for the effect include cross-breeze, cross-draft, wind effect ventilation and cross-flow ventilation. In Germany they have been called lüften and Stoßlüften. == Process == The phenomenon occurs when openings in an environment (including vehicles) or building (houses, factories, sheds, etc) are set on opposite or adjoining walls, which allow air to enter and exit, thus creating a current of air across the interior environment. Windows or vents positioned on opposite sides of the room allow passive breezes a pathway through the structure,


id: cross-ventilation-20260505-1
file: data/en.wikipedia.org/wiki/Cross_ventilation-1.md
category: reference
title: Cross ventilation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Cross_ventilation
date_saved: 2026-05-05T10:54:56.230155+00:00
instance: kb-cron
parent: cross-ventilation-20260505-0
summary:
Single-sided ventilation: This method depends on the pressure contrasts between different openings within the occupied space. For rooms that only feature a single opening, the ventilation is impelled by turbulence, thereby creating a pumping activity on that lone opening, causing small inflows and outflows. Single-sided ventilation has a weak effect. It is preferable when cross ventilation is not achievable, where it uses windows or vents at the other side of the space to control air pressure. Cross ventilation (single spaces): Being unsophisticated and efficacious, this type of ventilation is a horizontal process that is driven by pressure differences between the windward and leeward sides of the occupied indoor environment. Ventilation here is generally provided using windows and vents at either side of a building where the variation in pressure draw air in and out. Cross ventilation (double-banked spaces): Involving banked rooms, this method features openings in the hallway structure. The openings allow a way for noise to move between spaces. It can provide a much higher air-exchange rate in comparison with single-sided ventilation. Stack ventilation: This ventilation is a vertical process and it's beneficiary for taller buildings with central atriums. It draws cooler air in at a lower level, whereby


id: diffraction-20260505-0
file: data/en.wikipedia.org/wiki/Diffraction-0.md
category: reference
title: Diffraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Diffraction
date_saved: 2026-05-05T10:54:57.453682+00:00
instance: kb-cron
parent: diffraction-20260505-0
summary:
Diffraction is the deviation of waves from straight-line propagation due to an obstacle or through an aperture, without any change in their energy. Diffraction is the same physical effect as interference, but interference is typically used for the superposition of a few waves, while the term diffraction is used when many waves are superposed. The term diffraction pattern is used to refer to an image or map of the different directions of the waves after they have been diffracted. Diffraction patterns are pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture as shown in the first image. In classical physics, diffraction is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The patterns are due to the summation over different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the registering surface. If there are multiple closely spaced openings, a complex pattern of varying intensity can result. Other types of apertures or obstacles lead to different patterns, some of which are described later on this page. These effects occur when a light wave travels through a


id: diffraction-20260505-1
file: data/en.wikipedia.org/wiki/Diffraction-1.md
category: reference
title: Diffraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Diffraction
date_saved: 2026-05-05T10:54:57.453682+00:00
instance: kb-cron
parent: diffraction-20260505-0
summary:
== Basics == Diffraction is a general phenomenon of waves, occurring whenever a wave encounters some form of obstruction. The obstruction may be solidly blocking the wave, or transparent and shifting the phase of the wave without any change in energy (elastic scattering). The waves beyond the obstacle interfere leading to a diffraction pattern. The diffraction pattern cannot be predicted by the straight line trajectories of geometrical optics. For a simple example, a strong light source blocked by a solid object does not show a crisp dark shadow when examined carefully. The appropriate model for diffraction depends upon the character of the waves and the obstructions. The simplest model uses the Huygens–Fresnel principle. The Huygens part visualizes propagation of a wave by considering every point on a wavefront as a source for a secondary spherical wave, these being called Huygens wavelets. The Fresnel part is the superposition (linear sum) of these secondary waves and their consequent interference. In the absence of obstacles, the Huygens's principle alone predicts wavefront propagation. When some of the secondary waves are blocked by an obstacle, the remainder will create both wavefront propagation in the unblocked direction and waves behind the obstacle which form the diffraction


id: diffraction-20260505-2
file: data/en.wikipedia.org/wiki/Diffraction-2.md
category: reference
title: Diffraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Diffraction
date_saved: 2026-05-05T10:54:57.453682+00:00
instance: kb-cron
parent: diffraction-20260505-0
summary:
An illuminated slit that is wider than a wavelength produces interference effects in the space downstream of the slit. Assuming that the slit behaves as though it has a large number of point sources spaced evenly across the width of the slit, the interference effects can be calculated. If the incident light is a single wavelength and coherent, these sources all have the same phase. Light in the space downstream of the slit is made up of contributions from each of these point sources. If the relative phases of contributions from each point source vary due to differences in the path lengths, the resulting intensity will vary. Imagining the slit as the y axis with the z across the slit and x pointing downstream, intensity minima and maxima can be seen along z for large values of x. For points very close to x {\displaystyle x} all the point sources are in phase. This is the undiffracted beam, forming a maximum. Moving away fom the x {\displaystyle x} axis, the path length from the point sources in the center and those on the edges of the slit differ. When the path difference equals λ / 2 {\displaystyle \lambda /2} ,


id: diffraction-20260505-3
file: data/en.wikipedia.org/wiki/Diffraction-3.md
category: reference
title: Diffraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Diffraction
date_saved: 2026-05-05T10:54:57.453682+00:00
instance: kb-cron
parent: diffraction-20260505-0
summary:
where θ i {\displaystyle \theta _{i}} is the angle at which the light is incident, d {\displaystyle d} is the separation of grating elements, and m {\displaystyle m} is an integer which can be positive or negative. The light diffracted by a grating is found by summing the light diffracted from each of the elements, and is essentially a convolution of diffraction and interference patterns. The figure shows the light diffracted by 2-element and 5-element gratings where the grating spacings are the same; it can be seen that the maxima are in the same position, but the detailed structures of the intensities are different. === General case for far field === A more mathematical approach involves treating the problem as a summation over spherical waves derived from the relevant wave equation; see for instance Born and Wolf for details. The wave that emerges from a point source has an amplitude ψ {\displaystyle \psi } at location r {\displaystyle \mathbf {r} } that is given by the solution of the frequency domain wave equation for a point source (the Helmholtz equation), ∇ 2 ψ + k 2 ψ = δ ( r ) , {\displaystyle \nabla ^{2}\psi +k^{2}\psi =\delta (\mathbf {r}


id: diffraction-20260505-4
file: data/en.wikipedia.org/wiki/Diffraction-4.md
category: reference
title: Diffraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Diffraction
date_saved: 2026-05-05T10:54:57.453682+00:00
instance: kb-cron
parent: diffraction-20260505-0
summary:
== Bragg diffraction == Diffraction from a large three-dimensional periodic structure such as many thousands of atoms in a crystal is called Bragg diffraction. It is similar to what occurs when waves are scattered from a diffraction grating. Bragg diffraction is a consequence of interference between waves reflecting from many different crystal planes. The condition of constructive interference is given by Bragg's law: m λ = 2 d sin ⁡ θ , {\displaystyle m\lambda =2d\sin \theta ,} where λ {\displaystyle \lambda } is the wavelength, d {\displaystyle d} is the distance between crystal planes, θ {\displaystyle \theta } is the angle of the diffracted wave, and m {\displaystyle m} is an integer known as the order of the diffracted beam. Bragg diffraction may be carried out using either electromagnetic radiation of very short wavelength like X-rays or matter waves like neutrons whose wavelength is on the order of (or much smaller than) the atomic spacing. The pattern produced gives information of the separations of crystallographic planes d {\displaystyle d} , allowing one to deduce the crystal structure. For completeness, Bragg diffraction is a limit for a large number of atoms with X-rays or neutrons, and is rarely valid for electron


id: dislon-20260505-0
file: data/en.wikipedia.org/wiki/Dislon-0.md
category: reference
title: Dislon
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Dislon
date_saved: 2026-05-05T10:54:58.714495+00:00
instance: kb-cron
parent: dislon-20260505-0
summary:
A dislon is a quantized field associated with the quantization of the lattice displacement in crystalline solids. It is a localized collective excitation of a crystal dislocation. == Description == Dislons are special quasiparticles that emerge from the quantization of the lattice displacement field around a dislocation in a crystal. They exhibit unique particle statistics depending on the dimension of quantization. In one-dimensional quantization, dislons behave as bosonic quasiparticles. However, in three-dimensional quantization, the topological constraint of the dislocation leads to a breakdown of the canonical commutation relation, resulting in the emergence of two independent bosonic fields known as the d-field and f-field. == Interaction == Dislons interact with other particles such as electrons and phonons. In the presence of multiple dislocations, the electron-dislon interaction can affect the electrical conductivity of the system. The distance-dependent interaction between electrons and dislocations leads to oscillations in the electron self-energy away from the dislocation core. == Applications == The study of dislons provides insights into various phenomena in materials science, including the variation of superconducting transition temperatures in dislocated crystals. Dislons play a role in understanding the interaction between dislocations and phonons, affecting thermal transport properties in the presence of dislocations. == See


id: doppler-broadening-20260505-0
file: data/en.wikipedia.org/wiki/Doppler_broadening-0.md
category: reference
title: Doppler broadening
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Doppler_broadening
date_saved: 2026-05-05T10:54:59.980028+00:00
instance: kb-cron
parent: doppler-broadening-20260505-0
summary:
In atomic physics, Doppler broadening is broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting (or absorbing) particles result in different Doppler shifts, the cumulative effect of which is the emission (absorption) line broadening. This resulting line profile is known as a Doppler profile. A particular case is the thermal Doppler broadening due to the thermal motion of the particles. Then, the broadening depends only on the frequency of the spectral line, the mass of the emitting particles, and their temperature, and therefore can be used for inferring the temperature of an emitting (or absorbing) body being spectroscopically investigated. == Derivation (non-relativistic case) == When a particle moves (e.g., due to the thermal motion) towards the observer, the emitted radiation is shifted to a higher frequency. Likewise, when the emitter moves away, the frequency is lowered. In the non-relativistic limit, the Doppler shift is f = f 0 ( 1 + v c ) , {\displaystyle f=f_{0}\left(1+{\frac {v}{c}}\right),} where f {\displaystyle f} is the observed frequency, f 0 {\displaystyle f_{0}} is the frequency in the rest frame, v {\displaystyle v} is the velocity of the


id: dresselhaus-effect-20260505-0
file: data/en.wikipedia.org/wiki/Dresselhaus_effect-0.md
category: reference
title: Dresselhaus effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Dresselhaus_effect
date_saved: 2026-05-05T10:55:01.257959+00:00
instance: kb-cron
parent: dresselhaus-effect-20260505-0
summary:
The Dresselhaus effect is a phenomenon in solid-state physics in which spin–orbit interaction causes energy bands to split. It is usually present in crystal systems lacking inversion symmetry. The effect is named after Gene Dresselhaus, who discovered this splitting in 1955. Spin–orbit interaction is a relativistic coupling between the electric field produced by an ion-core and the resulting dipole moment arising from the relative motion of the electron, and its intrinsic magnetic dipole proportional to the electron spin. In an atom, the coupling weakly splits an orbital energy state into two states: one state with the spin aligned to the orbital field and one anti-aligned. In a solid crystalline material, the motion of the conduction electrons in the lattice can be altered by a complementary effect due to the coupling between the potential of the lattice and the electron spin. If the crystalline material is not centro-symmetric, the asymmetry in the potential can favour one spin orientation over the opposite and split the energy bands into spin aligned and anti-aligned subbands. The Rashba spin–orbit coupling has a similar energy band splitting, but the asymmetry comes either from the bulk asymmetry of uniaxial crystals (e.g. of wurtzite type) or the spatial


id: droplet-cluster-20260505-0
file: data/en.wikipedia.org/wiki/Droplet_cluster-0.md
category: reference
title: Droplet cluster
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Droplet_cluster
date_saved: 2026-05-05T10:55:02.492156+00:00
instance: kb-cron
parent: droplet-cluster-20260505-0
summary:
Droplet cluster is a self-assembled levitating monolayer of microdroplets usually arranged into a hexagonally ordered structure over a locally heated thin (about 1 mm) layer of water. The droplet cluster is typologically similar to colloidal crystals. The phenomenon was observed for the first time in 2004, and it has been extensively studied after that. Growing condensing droplets with a typical diameter of 0.01 mm – 0.2 mm levitate at an equilibrium height, where their weight is equilibrated by the drag force of the ascending air-vapor jet rising over the heated spot. At the same time, the droplets are dragged towards the center of the heated spot; however, they do not merge, forming an ordered hexagonal (densest packed) pattern due to an aerodynamic repulsive pressure force from gas flow between the droplets. The spot is usually heated by a laser beam or another source of heat to 60 °C – 95 °C, although the phenomenon was observed also at temperatures slightly above 20 °C. The height of levitation and the distance between the droplets are of the same order as their diameters. Due to complex nature of aerodynamic forces between the microdroplets in an ascending jet, the droplets do not coalesce


id: dynamic-scaling-20260505-0
file: data/en.wikipedia.org/wiki/Dynamic_scaling-0.md
category: reference
title: Dynamic scaling
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Dynamic_scaling
date_saved: 2026-05-05T10:55:03.760471+00:00
instance: kb-cron
parent: dynamic-scaling-20260505-0
summary:
Dynamic scaling (sometimes known as Family–Vicsek scaling) is a litmus test that shows whether an evolving system exhibits self-similarity. In general a function is said to exhibit dynamic scaling if it satisfies: f ( x , t ) ∼ t θ φ ( x t z ) . {\displaystyle f(x,t)\sim t^{\theta }\varphi \left({\frac {x}{t^{z}}}\right).} Here the exponent θ {\displaystyle \theta } is fixed by the dimensional requirement [ f ] = [ t θ ] {\displaystyle [f]=[t^{\theta }]} . The numerical value of f / t θ {\displaystyle f/t^{\theta }} should remain invariant despite the unit of measurement of t {\displaystyle t} is changed by some factor since φ {\displaystyle \varphi } is a dimensionless quantity. Many of these systems evolve in a self-similar fashion in the sense that data obtained from the snapshot at any fixed time is similar to the respective data taken from the snapshot of any earlier or later time. That is, the system is similar to itself at different times. The litmus test of such self-similarity is provided by the dynamic scaling. == History == The term "dynamic scaling" as one of the essential concepts to describe the dynamics of critical phenomena seems to originate


id: electrofreezing-20260505-0
file: data/en.wikipedia.org/wiki/Electrofreezing-0.md
category: reference
title: Electrofreezing
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Electrofreezing
date_saved: 2026-05-05T10:55:05.009538+00:00
instance: kb-cron
parent: electrofreezing-20260505-0
summary:
Electrofreezing is the tendency of a material to solidify upon being exposed to an external electric field. Electrofreezing was initially introduced by Dufour in 1892. Examples are the electrofreezing of liquid ammonia supposed to be naturally occurring during electrical storms in Jupiter-like planets, and ice χ supposedly being a form of high pressure ice. Depending on the material, freezing occur only at certain field intensities, above which electric fields are strong enough to induce chemical reactions. == References ==


id: electromagnetic-induction-20260505-0
file: data/en.wikipedia.org/wiki/Electromagnetic_induction-0.md
category: reference
title: Electromagnetic induction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Electromagnetic_induction
date_saved: 2026-05-05T10:55:06.297489+00:00
instance: kb-cron
parent: electromagnetic-induction-20260505-0
summary:
Electromagnetic induction or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism. Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators. == History == Electromagnetic induction was discovered by Michael Faraday, published in 1831. It was discovered independently by Joseph Henry in 1832. In Faraday's first experimental demonstration, on August 29, 1831, he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer). Based on his understanding of electromagnets, he expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other


id: electromagnetic-induction-20260505-1
file: data/en.wikipedia.org/wiki/Electromagnetic_induction-1.md
category: reference
title: Electromagnetic induction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Electromagnetic_induction
date_saved: 2026-05-05T10:55:06.297489+00:00
instance: kb-cron
parent: electromagnetic-induction-20260505-0
summary:
=== Faraday's law and relativity === Faraday's law describes two different phenomena: the motional emf generated by a magnetic force on a moving wire (see Lorentz force), and the transformer emf that is generated by an electric force due to a changing magnetic field (due to the differential form of the Maxwell–Faraday equation). James Clerk Maxwell drew attention to the separate physical phenomena in 1861. This is believed to be a unique example in physics of where such a fundamental law is invoked to explain two such different phenomena. Albert Einstein noticed that the two situations both corresponded to a relative movement between a conductor and a magnet, and the outcome was unaffected by which one was moving. This was one of the principal paths that led him to develop special relativity. == Applications == The principles of electromagnetic induction are applied in many devices and systems, including: === Electrical generator === The emf generated by Faraday's law of induction due to relative movement of a circuit and a magnetic field is the phenomenon underlying electrical generators. When a permanent magnet is moved relative to a conductor, or vice versa, an electromotive force is created. If the wire is connected


id: electromagnetic-induction-20260505-2
file: data/en.wikipedia.org/wiki/Electromagnetic_induction-2.md
category: reference
title: Electromagnetic induction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Electromagnetic_induction
date_saved: 2026-05-05T10:55:06.297489+00:00
instance: kb-cron
parent: electromagnetic-induction-20260505-0
summary:
Only five laminations or plates are shown in this example, so as to show the subdivision of the eddy currents. In practical use, the number of laminations or punchings ranges from 40 to 66 per inch (16 to 26 per centimetre), and brings the eddy current loss down to about one percent. While the plates can be separated by insulation, the voltage is so low that the natural rust/oxide coating of the plates is enough to prevent current flow across the laminations. This is a rotor approximately 20 mm in diameter from a DC motor used in a CD player. Note the laminations of the electromagnet pole pieces, used to limit parasitic inductive losses. === Parasitic induction within conductors === In this illustration, a solid copper bar conductor on a rotating armature is just passing under the tip of the pole piece N of the field magnet. Note the uneven distribution of the lines of force across the copper bar. The magnetic field is more concentrated and thus stronger on the left edge of the copper bar (a,b) while the field is weaker on the right edge (c,d). Since the two edges of the bar move with the same velocity,


id: electron-emission-20260505-0
file: data/en.wikipedia.org/wiki/Electron_emission-0.md
category: reference
title: Electron emission
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Electron_emission
date_saved: 2026-05-05T10:55:07.536321+00:00
instance: kb-cron
parent: electron-emission-20260505-0
summary:
In physics, electron emission is the ejection of an electron from the surface of matter, or, in beta decay (β− decay), where a beta particle (a fast energetic electron or positron) is emitted from an atomic nucleus transforming the original nuclide to an isobar. == Radioactive decay == In Beta decay (β− decay), radioactive decay results in a beta particle (fast energetic electron or positron in β+ decay) being emitted from the nucleus == Surface emission == Thermionic emission, the liberation of electrons from an electrode by virtue of its temperature Schottky emission, due to the: Schottky effect or field enhanced thermionic emission Field electron emission, emission of electrons induced by an electrostatic field === Devices === An electron gun or electron emitter, is an electrical component in some vacuum tubes that uses surface emission == Others == Exoelectron emission, a weak electron emission, appearing only from pretreated objects Photoelectric effect, the emission of electrons when electromagnetic radiation, such as light, hits a material == See also == Positron emission, (of a positron or "antielectron") is one aspect of β+ decay Electron excitation, the transfer of an electron to a higher atomic orbital == References ==


id: ergosphere-20260505-0
file: data/en.wikipedia.org/wiki/Ergosphere-0.md
category: reference
title: Ergosphere
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ergosphere
date_saved: 2026-05-05T10:55:08.890537+00:00
instance: kb-cron
parent: ergosphere-20260505-0
summary:
In astrophysics, the ergosphere is a region located just outside a rotating black hole, between its event horizon and a further external surface predicted by the Kerr metric which describes these objects. Its name was proposed by Remo Ruffini and John Archibald Wheeler during the Les Houches lectures in 1971 and is derived from Ancient Greek ἔργον (ergon) 'work'. It received this name because it is theoretically possible to extract energy and mass from this region. The ergosphere touches the event horizon at the poles of a rotating black hole and extends to a greater radius at the equator. A black hole with modest angular momentum has an ergosphere with a shape approximated by an oblate spheroid, while faster spins produce a more pumpkin-shaped ergosphere. The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole. == Rotation == As a black hole rotates, it twists spacetime in the direction of the rotation at a speed that decreases with distance from the event


id: event-horizon-20260505-0
file: data/en.wikipedia.org/wiki/Event_horizon-0.md
category: reference
title: Event horizon
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Event_horizon
date_saved: 2026-05-05T10:55:10.114290+00:00
instance: kb-cron
parent: event-horizon-20260505-0
summary:
In astrophysics, an event horizon is a boundary in spacetime beyond which no signal can ever reach a given observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact objects that even light cannot escape. At that time, the Newtonian theory of gravitation and the so-called corpuscular theory of light were dominant. In these theories, if the escape velocity of the gravitational influence of a massive object exceeds the speed of light, then light originating inside or from it can escape temporarily but will return. In 1958, David Finkelstein used general relativity to introduce a stricter definition of a local black hole event horizon as a boundary beyond which events of any kind cannot affect an outside observer, leading to information and firewall paradoxes, encouraging the re-examination of the concept of local event horizons and the notion of black holes. Several theories were subsequently developed, some with and some without event horizons. One of the leading developers of theories to describe black holes, Stephen Hawking, suggested that an apparent horizon should be used instead of an event horizon, saying, "Gravitational collapse produces apparent horizons


id: event-horizon-20260505-1
file: data/en.wikipedia.org/wiki/Event_horizon-1.md
category: reference
title: Event horizon
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Event_horizon
date_saved: 2026-05-05T10:55:10.114290+00:00
instance: kb-cron
parent: event-horizon-20260505-0
summary:
=== Interacting with a cosmic horizon === In the case of a horizon perceived by a uniformly accelerating observer in empty space, the horizon seems to remain a fixed distance from the observer no matter how its surroundings move. Varying the observer's acceleration may cause the horizon to appear to move over time or may prevent an event horizon from existing, depending on the acceleration function chosen. The observer never touches the horizon and never passes a location where it appeared to be. In the case of a horizon perceived by an occupant of a de Sitter universe, the horizon always appears to be a fixed distance away for a non-accelerating observer. It is never contacted, even by an accelerating observer. == Event horizon of a black hole == One of the best-known examples of an event horizon derives from general relativity's description of a black hole, a celestial object so dense that no nearby matter or radiation can escape its gravitational field. Often, this is described as the boundary within which the black hole's escape velocity is greater than the speed of light. However, a more detailed description is that within this horizon, all lightlike paths (paths that light


id: event-horizon-20260505-2
file: data/en.wikipedia.org/wiki/Event_horizon-2.md
category: reference
title: Event horizon
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Event_horizon
date_saved: 2026-05-05T10:55:10.114290+00:00
instance: kb-cron
parent: event-horizon-20260505-0
summary:
=== Interacting with black hole horizons === A misconception concerning event horizons, especially black hole event horizons, is that they represent an immutable surface that destroys objects that approach them. In practice, all event horizons appear to be some distance away from any observer, and objects sent towards an event horizon never appear to cross it from the sending observer's point of view (as the horizon-crossing event's light cone never intersects the observer's world line). Attempting to make an object near the horizon remain stationary with respect to an observer requires applying a force whose magnitude increases unboundedly (becoming infinite) the closer it gets. In the case of the horizon around a black hole, observers stationary with respect to a distant object will all agree on where the horizon is. While this seems to allow an observer lowered towards the hole on a rope (or rod) to contact the horizon, in practice this cannot be done. The proper distance to the horizon is finite, so the length of rope needed would be finite as well, but if the rope were lowered slowly (so that each point on the rope was approximately at rest in Schwarzschild coordinates), the proper acceleration (G-force)


id: fermat-s-principle-20260505-0
file: data/en.wikipedia.org/wiki/Fermat's_principle-0.md
category: reference
title: Fermat's principle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fermat's_principle
date_saved: 2026-05-05T10:55:11.341862+00:00
instance: kb-cron
parent: fermat-s-principle-20260505-0
summary:
Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time. First proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the ordinary law of refraction of light (Fig. 1), Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature. Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves. If points A and B are given, a wavefront expanding from A sweeps all possible ray paths radiating from A, whether they pass through B or not. If the wavefront reaches point B, it sweeps not only the ray path(s) from A to B, but also an infinitude of nearby paths with the same endpoints. Fermat's principle describes any ray that happens to reach point B; there is no implication that the ray "knew" the quickest path or "intended" to take that path. In its original "strong" form, Fermat's principle states that the path


id: fermat-s-principle-20260505-1
file: data/en.wikipedia.org/wiki/Fermat's_principle-1.md
category: reference
title: Fermat's principle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fermat's_principle
date_saved: 2026-05-05T10:55:11.341862+00:00
instance: kb-cron
parent: fermat-s-principle-20260505-0
summary:
If the corridor of paths reinforcing a ray path from A to B is substantially obstructed, this will significantly affect the energy reaching B from A – unlike a similar-sized obstruction outside any such corridor. Thus the ray path marks an energy path – as does a beam. Suppose that a wavefront expanding from point A passes point P, which lies on a ray path from point A to point B. By definition, all points on the wavefront have the same propagation time from A. Now let the wavefront be blocked except for a window, centered on P, and small enough to lie within the corridor of paths that reinforce the ray path from A to B. Then all points on the unobstructed portion of the wavefront will have, nearly enough, equal propagation times to B, but not to points in other directions, so that B will be in the direction of peak intensity of the beam admitted through the window. So the ray path marks the beam. And in optical experiments, a beam is routinely considered as a collection of rays or (if it is narrow) as an approximation to a ray (Fig. 3). === Analogies === According to


id: fermat-s-principle-20260505-2
file: data/en.wikipedia.org/wiki/Fermat's_principle-2.md
category: reference
title: Fermat's principle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fermat's_principle
date_saved: 2026-05-05T10:55:11.341862+00:00
instance: kb-cron
parent: fermat-s-principle-20260505-0
summary:
By (i), the ray path is a path of stationary traversal time from P to W′; and by (ii), it is a path of stationary traversal time from a point on W to P′. So Huygens's construction implicitly defines a ray path as a path of stationary traversal time between successive positions of a wavefront, the time being reckoned from a point-source on the earlier wavefront. This conclusion remains valid if the secondary wavefronts are reflected or refracted by surfaces of discontinuity in the properties of the medium, provided that the comparison is restricted to the affected paths and the affected portions of the wavefronts. Fermat's principle, however, is conventionally expressed in point-to-point terms, not wavefront-to-wavefront terms. Accordingly, the example may be modified by supposing that the wavefront which becomes surface W at time t, and which becomes surface W′ at the later time t + Δt, is emitted from point A at time 0. Let P be a point on W (as before), and B a point on W′. And let A, W, W′, and B be given, so that the problem is to find P. If P satisfies Huygens's construction, so that the secondary wavefront from P is


id: fermat-s-principle-20260505-3
file: data/en.wikipedia.org/wiki/Fermat's_principle-3.md
category: reference
title: Fermat's principle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fermat's_principle
date_saved: 2026-05-05T10:55:11.341862+00:00
instance: kb-cron
parent: fermat-s-principle-20260505-0
summary:
where n r = c / v r {\displaystyle \,n_{\mathrm {r} }=c/v_{\mathrm {r} }\,} is the ray index – that is, the refractive index calculated on the ray velocity instead of the usual phase velocity (wave-normal velocity). For an infinitesimal path, d S = n r d s , {\displaystyle dS=n_{\mathrm {r} \,}ds\,,\,} indicating that the optical length is the physical length multiplied by the ray index: the OPL is a notional geometric quantity, from which time has been factored out. In terms of OPL, the condition for Γ to be a ray path (Fermat's principle) becomes This has the form of Maupertuis's principle in classical mechanics (for a single particle), with the ray index in optics taking the role of momentum or velocity in mechanics. In an isotropic medium, for which the ray velocity is also the phase velocity, the usual refractive index n may be substituted for nr. === Relation to Hamilton's principle === If x, y, z are Cartesian coordinates and an overdot denotes differentiation with respect to s, Fermat's principle (2) may be written δ S = δ ∫ A B n r d x 2 + d y 2 + d z 2 = δ


id: fermat-s-principle-20260505-4
file: data/en.wikipedia.org/wiki/Fermat's_principle-4.md
category: reference
title: Fermat's principle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fermat's_principle
date_saved: 2026-05-05T10:55:11.341862+00:00
instance: kb-cron
parent: fermat-s-principle-20260505-0
summary:
1. The principle that you take as the basis of your demonstration, namely that nature always acts in the shortest and simplest ways, is merely a moral principle and not a physical one; it is not, and cannot be, the cause of any effect in nature .... For otherwise we would attribute knowledge to nature; but here, by "nature", we understand only this order and this law established in the world as it is, which acts without foresight, without choice, and by a necessary determination. 2. This same principle would make nature irresolute ... For I ask you ... when a ray of light must pass from a point in a rare medium to a point in a dense one, is there not reason for nature to hesitate if, by your principle, it must choose the straight line as soon as the bent one, since if the latter proves shorter in time, the former is shorter and simpler in length? Who will decide and who will pronounce? Fermat, being unaware of the mechanistic foundations of his own principle, was not well placed to defend it, except as a purely geometric and kinematic proposition. The wave theory of light, first proposed


id: fermat-s-principle-20260505-5
file: data/en.wikipedia.org/wiki/Fermat's_principle-5.md
category: reference
title: Fermat's principle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fermat's_principle
date_saved: 2026-05-05T10:55:11.341862+00:00
instance: kb-cron
parent: fermat-s-principle-20260505-0
summary:
In fact Laplace was aware that Fermat's principle follows from Huygens's construction in the case of refraction from an isotropic medium to an anisotropic one; a geometric proof was contained in the long version of Laplace's report, printed in 1810. Young's claim was more general than Laplace's, and likewise upheld Fermat's principle even in the case of extraordinary refraction, in which the rays are generally not perpendicular to the wavefronts. Unfortunately, however, the omitted middle sentence of the quoted paragraph by Young began "The motion of every undulation must necessarily be in a direction perpendicular to its surface ..." (emphasis added), and was therefore bound to sow confusion rather than clarity. No such confusion subsists in Augustin-Jean Fresnel's "Second Memoir" on double refraction (Fresnel, 1827), which addresses Fermat's principle in several places (without naming Fermat), proceeding from the special case in which rays are normal to wavefronts, to the general case in which rays are paths of least time or stationary time. (In the following summary, page numbers refer to Alfred W. Hobson's translation.) For refraction of a plane wave at parallel incidence on one face of an anisotropic crystalline wedge (pp. 291–2), in order to find the "first ray


id: ferromagnetism-20260505-0
file: data/en.wikipedia.org/wiki/Ferromagnetism-0.md
category: reference
title: Ferromagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ferromagnetism
date_saved: 2026-05-05T10:55:12.614744+00:00
instance: kb-cron
parent: ferromagnetism-20260505-0
summary:
Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. For example, this temporary magnetization inside a steel plate accounts for the plate's attraction to a magnet. Whether or not that steel plate then acquires permanent magnetization depends on both the strength of the applied field and on the coercivity of that particular piece of steel (which varies with the steel's chemical composition and any heat treatment it may have undergone). In physics, multiple types of material magnetism have been distinguished. Ferromagnetism (along with the similar effect ferrimagnetism) is the strongest type and is responsible for the common phenomenon of everyday magnetism. A common example of a permanent magnet is a refrigerator magnet. Substances respond weakly to magnetic fields by three other types of magnetism—paramagnetism, diamagnetism, and antiferromagnetism—but the forces are usually so weak that they can only be detected by


id: ferromagnetism-20260505-1
file: data/en.wikipedia.org/wiki/Ferromagnetism-1.md
category: reference
title: Ferromagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ferromagnetism
date_saved: 2026-05-05T10:55:12.614744+00:00
instance: kb-cron
parent: ferromagnetism-20260505-0
summary:
=== Unusual materials === Most ferromagnetic materials are metals, since the conducting electrons are often responsible for mediating the ferromagnetic interactions. It is therefore a challenge to develop ferromagnetic insulators, especially multiferroic materials, which are both ferromagnetic and ferroelectric. A number of actinide compounds are ferromagnets at room temperature or exhibit ferromagnetism upon cooling. PuP is a paramagnet with cubic symmetry at room temperature, but which undergoes a structural transition into a tetragonal state with ferromagnetic order when cooled below its TC = 125 K. In its ferromagnetic state, PuP's easy axis is in the ⟨100⟩ direction. In NpFe2 the easy axis is ⟨111⟩. Above TC ≈ 500 K, NpFe2 is also paramagnetic and cubic. Cooling below the Curie temperature produces a rhombohedral distortion wherein the rhombohedral angle changes from 60° (cubic phase) to 60.53°. An alternate description of this distortion is to consider the length c along the unique trigonal axis (after the distortion has begun) and a as the distance in the plane perpendicular to c. In the cubic phase this reduces to c/a = 1.00. Below the Curie temperature, the lattice acquires a distortion c a − 1 = − ( 120 ± 5 ) × 10


id: ferromagnetism-20260505-2
file: data/en.wikipedia.org/wiki/Ferromagnetism-2.md
category: reference
title: Ferromagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ferromagnetism
date_saved: 2026-05-05T10:55:12.614744+00:00
instance: kb-cron
parent: ferromagnetism-20260505-0
summary:
When two nearby atoms have unpaired electrons, whether the electron spins are parallel or antiparallel affects whether the electrons can share the same orbit as a result of the quantum mechanical effect called the exchange interaction. This in turn affects the electron location and the Coulomb (electrostatic) interaction and thus the energy difference between these states. The exchange interaction is related to the Pauli exclusion principle, which says that two electrons with the same spin cannot also be in the same spatial state (orbital). This is a consequence of the spin–statistics theorem and that electrons are fermions. Therefore, under certain conditions, when the orbitals of the unpaired outer valence electrons from adjacent atoms overlap, the distributions of their electric charge in space are farther apart when the electrons have parallel spins than when they have opposite spins. This reduces the electrostatic energy of the electrons when their spins are parallel compared to their energy when the spins are antiparallel, so the parallel-spin state is more stable. This difference in energy is called the exchange energy. In simple terms, the outer electrons of adjacent atoms, which repel each other, can move further apart by aligning their spins in the same direction.


id: ferromagnetism-20260505-3
file: data/en.wikipedia.org/wiki/Ferromagnetism-3.md
category: reference
title: Ferromagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ferromagnetism
date_saved: 2026-05-05T10:55:12.614744+00:00
instance: kb-cron
parent: ferromagnetism-20260505-0
summary:
Thus, a piece of iron in its lowest energy state ("unmagnetized") generally has little or no net magnetic field. However, the magnetic domains in a material are not fixed in place; they are simply regions where the spins of the electrons have aligned spontaneously due to their magnetic fields, and thus can be altered by an external magnetic field. If a strong-enough external magnetic field is applied to the material, the domain walls will move via a process in which the spins of the electrons in atoms near the wall in one domain turn under the influence of the external field to face in the same direction as the electrons in the other domain, thus reorienting the domains so more of the dipoles are aligned with the external field. The domains will remain aligned when the external field is removed, and sum to create a magnetic field of their own extending into the space around the material, thus creating a "permanent" magnet. The domains do not go back to their original minimum energy configuration when the field is removed because the domain walls tend to become 'pinned' or 'snagged' on defects in the crystal lattice, preserving their parallel orientation. This


id: field-effect-semiconductor-20260505-0
file: data/en.wikipedia.org/wiki/Field_effect_(semiconductor)-0.md
category: reference
title: Field effect (semiconductor)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Field_effect_(semiconductor)
date_saved: 2026-05-05T10:55:13.888296+00:00
instance: kb-cron
parent: field-effect-semiconductor-20260505-0
summary:
In physics, the field effect refers to the modulation of the electrical conductivity of a material by the application of an external electric field. In a metal, the electron density that responds to applied fields is so large that an external electric field can penetrate only a very short distance into the material. However, in a semiconductor the lower density of electrons (and possibly holes) that can respond to an applied field is sufficiently small that the field can penetrate quite far into the material. This field penetration alters the conductivity of the semiconductor near its surface, and is called the field effect. The field effect underlies the operation of the Schottky diode and of field-effect transistors, notably the MOSFET, the JFET and the MESFET. == Surface conductance and band bending == The change in surface conductance occurs because the applied field alters the energy levels available to electrons to considerable depths from the surface, and that in turn changes the occupancy of the energy levels in the surface region. A typical treatment of such effects is based upon a band-bending diagram showing the positions in energy of the band edges as a function of depth into the material. An


id: flowability-20260505-0
file: data/en.wikipedia.org/wiki/Flowability-0.md
category: reference
title: Flowability
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Flowability
date_saved: 2026-05-05T10:55:15.173423+00:00
instance: kb-cron
parent: flowability-20260505-0
summary:
Flowability, also known as powder flow is a property that defines an ability of a powdered material to flow, related to cohesion. Powder flowability depends on many traits: the shape and size of the powder particles due to intermolecular force, porosity electrostatic activity hygroscopy bulk density angle of repose presence of glidants oxidation rate (of a metallic powder) humidity ISO 4490:2018 norm (and its precedent, ISO 4490:2014) standardizes a method for determining the flow rate of metallic powders. It uses a normalized/calibrated funnel, named Hall flowmeter. == See also == Fluid mechanics Soil mechanics Cohesion (geology) angle of repose == References ==


id: free-neutron-decay-20260505-0
file: data/en.wikipedia.org/wiki/Free_neutron_decay-0.md
category: reference
title: Free neutron decay
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Free_neutron_decay
date_saved: 2026-05-05T10:55:16.386179+00:00
instance: kb-cron
parent: free-neutron-decay-20260505-0
summary:
A free neutron refers to a neutron that is not bound to an atomic nucleus. When embedded in a stable nuclide, neutrons have not been observed to decay. Free neutrons decay with a mean lifetime of 878.4±0.5 s (nearly 15 minutes), which corresponds with a half-life of around 608 seconds. The free neutron decays via the weak interaction and may be called the simplest example of beta decay. The decay results in the stable resultant products of a proton, electron and an electron antineutrino. This is expressed as a decay equation: The decay parameters of such a common baryon are of significance across multiple areas of physics, in particular particle physics and cosmology. Highly precise quantitative measurements of the free neutron mean lifetime by two different methods vary by more than the errors in the measurement techniques. This issue has been called the neutron lifetime puzzle. == History == The neutron was discovered in 1932. In a 1935 article, James Chadwick and Maurice Goldhaber speculated that the free neutron would be unstable, due to its estimated mass being larger than that of a hydrogen atom. In 1948 free neutron decay was first observed, along with a rudimentary estimation of its


id: free-neutron-decay-20260505-1
file: data/en.wikipedia.org/wiki/Free_neutron_decay-1.md
category: reference
title: Free neutron decay
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Free_neutron_decay
date_saved: 2026-05-05T10:55:16.386179+00:00
instance: kb-cron
parent: free-neutron-decay-20260505-0
summary:
=== Neutron lifetime puzzle === While the neutron lifetime has been studied for decades, there is currently a lack of agreement on its exact value, due to different results from two experimental methods, "bottle" versus "beam" methods. This has been called variously the neutron lifetime puzzle, neutron lifetime problem, or neutron lifetime anomaly. The neutron lifetime puzzle was realized after the refinement of experiments with ultracold neutrons. The error margins of the two methods previously overlapped, but increasing refinement in technique has failed to demonstrate convergence to a single value. The difference in mean lifetime values obtained as of 2014 was approximately 9 s. Further, a 2018 lattice QCD calculation of the lifetime value was not sufficiently precise to support one over the other. To give a concrete example of the discrepancy for two specific experiments, in 2013 a beam method experiment found a lifetime of τ n = 887.7 ± 1.2 s t a t ± 1.8 s y s t s . {\displaystyle \ \tau _{n}=887.7\pm 1.2_{\mathsf {stat}}\ \pm {1.8}_{\mathsf {syst}}\ {\mathsf {s}}~.} In 2021 a bottle method experiment found a lifetime of τ n = 877.75 ± 0.28 s t a t − 0.16 + 0.22 s


id: fundamental-interaction-20260505-0
file: data/en.wikipedia.org/wiki/Fundamental_interaction-0.md
category: reference
title: Fundamental interaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fundamental_interaction
date_saved: 2026-05-05T10:55:17.649266+00:00
instance: kb-cron
parent: fundamental-interaction-20260505-0
summary:
In physics, the fundamental interactions or fundamental forces are interactions in nature that appear not to be reducible to more basic interactions. There are four fundamental interactions known to exist: gravity, electromagnetism, weak interaction, and strong interaction. The gravitational and electromagnetic interactions produce long-range forces whose effects can be seen directly in everyday life. The strong and weak interactions produce forces at subatomic scales and govern nuclear interactions inside atoms. Some scientists hypothesize that a fifth force might exist, but these hypotheses remain speculative. Each of the known fundamental interactions can be described mathematically as a field. The gravitational interaction is attributed to the curvature of spacetime, described by Einstein's general theory of relativity. The other three are discrete quantum fields, and their interactions are mediated by elementary particles described by the Standard Model of particle physics. Within the Standard Model, the strong interaction is carried by a particle called the gluon and is responsible for quarks binding together to form hadrons, such as protons and neutrons. As a residual effect, it creates the nuclear force that binds the latter particles to form atomic nuclei. The weak interaction is carried by particles called W and Z bosons, and also acts


id: fundamental-interaction-20260505-1
file: data/en.wikipedia.org/wiki/Fundamental_interaction-1.md
category: reference
title: Fundamental interaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fundamental_interaction
date_saved: 2026-05-05T10:55:17.649266+00:00
instance: kb-cron
parent: fundamental-interaction-20260505-0
summary:
Two fermions go in → interaction by boson exchange → two changed fermions go out. The exchange of bosons always carries energy and momentum between the fermions, thereby changing their speed and direction. The exchange may also transport a charge between the fermions, changing the charges of the fermions in the process (e.g., turn them from one type of fermion to another). Since bosons carry one unit of angular momentum, the fermion's spin direction will flip from +1⁄2 to −1⁄2 (or vice versa) during such an exchange (in units of the reduced Planck constant). Since such interactions result in a change in momentum, they can give rise to classical Newtonian forces. In quantum mechanics, physicists often use the terms "force" and "interaction" interchangeably; for example, the weak interaction is sometimes referred to as the "weak force". According to the present understanding, there are four fundamental interactions or forces: gravitation, electromagnetism, the weak interaction, and the strong interaction. Their magnitude and behaviour vary greatly, as described in the table below. Modern physics attempts to explain every observed physical phenomenon by these fundamental interactions. The fundamental interactions can be compared using dimensionless coupling constants that characterize the intensity or "strength" of the


id: fundamental-interaction-20260505-2
file: data/en.wikipedia.org/wiki/Fundamental_interaction-2.md
category: reference
title: Fundamental interaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fundamental_interaction
date_saved: 2026-05-05T10:55:17.649266+00:00
instance: kb-cron
parent: fundamental-interaction-20260505-0
summary:
Electromagnetism is the force that acts between electrically charged particles. This phenomenon includes the electrostatic force acting between charged particles at rest, and the combined effect of electric and magnetic forces acting between charged particles moving relative to each other. Electromagnetism has an infinite range, as gravity does, but is vastly stronger. It is the force that binds electrons to atoms, and it holds molecules together. It is responsible for everyday phenomena like light, magnets, electricity, and friction. Electromagnetism fundamentally determines all macroscopic, and many atomic-level, properties of the chemical elements. In a four kilogram (~1 gallon) jug of water, there is of total electron charge. Thus, if we place two such jugs a meter apart, the electrons in one of the jugs repel those in the other jug with a force of This force is many times larger than the weight of the planet Earth. The atomic nuclei in one jug also repel those in the other with the same force. However, these repulsive forces are canceled by the attraction of the electrons in jug A with the nuclei in jug B and the attraction of the nuclei in jug A with the electrons in jug B, resulting in


id: fundamental-interaction-20260505-3
file: data/en.wikipedia.org/wiki/Fundamental_interaction-3.md
category: reference
title: Fundamental interaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fundamental_interaction
date_saved: 2026-05-05T10:55:17.649266+00:00
instance: kb-cron
parent: fundamental-interaction-20260505-0
summary:
The pions were understood to be oscillations of vacuum condensates; Jun John Sakurai proposed the rho and omega vector bosons to be force carrying particles for approximate symmetries of isospin and hypercharge; Geoffrey Chew, Edward K. Burdett and Steven Frautschi grouped the heavier hadrons into families that could be understood as vibrational and rotational excitations of strings. While each of these approaches offered insights, no approach led directly to a fundamental theory. Murray Gell-Mann along with George Zweig first proposed fractionally charged quarks in 1961. Throughout the 1960s, different authors considered theories similar to the modern fundamental theory of quantum chromodynamics (QCD) as simple models for the interactions of quarks. The first to hypothesize the gluons of QCD were Moo-Young Han and Yoichiro Nambu, who introduced the quark color charge. Han and Nambu hypothesized that it might be associated with a force-carrying field. At that time, however, it was difficult to see how such a model could permanently confine quarks. Han and Nambu also assigned each quark color an integer electrical charge, so that the quarks were fractionally charged only on average, and they did not expect the quarks in their model to be permanently confined. In 1971, Murray Gell-Mann


id: fundamental-interaction-20260505-4
file: data/en.wikipedia.org/wiki/Fundamental_interaction-4.md
category: reference
title: Fundamental interaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Fundamental_interaction
date_saved: 2026-05-05T10:55:17.649266+00:00
instance: kb-cron
parent: fundamental-interaction-20260505-0
summary:
== Unification == The fundamental forces may become unified into a single force at very high energies and on a minuscule scale, the Planck scale. Particle accelerators cannot produce the enormous energies required to experimentally probe this regime. The weak and electromagnetic forces have already been unified with the electroweak theory of Sheldon Glashow, Abdus Salam, and Steven Weinberg, for which they received the 1979 Nobel Prize in physics. Numerous theoretical efforts have been made to systematize the existing four fundamental interactions on the model of electroweak unification. Grand Unified Theories (GUTs) are proposals to show that each of the three fundamental interactions described by the Standard Model is a different manifestation of a single interaction with symmetries that break down and create separate interactions below some extremely high level of energy. GUTs are also expected to predict some of the relationships between constants of nature that the Standard Model treats as unrelated and gauge coupling unification for the relative strengths of the electromagnetic, weak, and strong forces. (GUT). Some attempts at GUTs hypothesize "shadow" particles, such that every known matter particle associates with an undiscovered force particle, and vice versa, altogether supersymmetry (SUSY). Other theorists seek to quantize the


id: gravitational-singularity-20260505-0
file: data/en.wikipedia.org/wiki/Gravitational_singularity-0.md
category: reference
title: Gravitational singularity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gravitational_singularity
date_saved: 2026-05-05T10:55:18.898698+00:00
instance: kb-cron
parent: gravitational-singularity-20260505-0
summary:
A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the best theory of gravity available, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete. General relativity predicts that any object collapsing beyond its Schwarzschild radius would form a black hole, inside which a singularity will form. A black hole singularity is, however, covered by an event horizon, so it is never in the causal past of any outside observer, and at no time can it be objectively said to have formed. General relativity also predicts that the initial state of the universe, at the beginning of the Big


id: gravitational-singularity-20260505-1
file: data/en.wikipedia.org/wiki/Gravitational_singularity-1.md
category: reference
title: Gravitational singularity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gravitational_singularity
date_saved: 2026-05-05T10:55:18.898698+00:00
instance: kb-cron
parent: gravitational-singularity-20260505-0
summary:
Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity once they cross the event horizon. As they fall further into the black hole, they will be torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the noodle effect. Eventually, they will reach the singularity and be crushed into an infinitely small point. Although in theory, the interior of a Schwarzschild black hole curves inwards towards a sharp point at the singularity, this model is only true when the spacetime inside the black hole had not been perturbed. Any perturbations, such as those caused by matter or radiation falling in, would cause space to oscillate chaotically near the singularity. Any matter falling in would experience intense tidal forces rapidly changing in direction, all while being compressed into an increasingly small volume. In the case of a charged or rotating black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole. The possibility of travelling to another universe is,


id: gravitational-singularity-20260505-2
file: data/en.wikipedia.org/wiki/Gravitational_singularity-2.md
category: reference
title: Gravitational singularity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Gravitational_singularity
date_saved: 2026-05-05T10:55:18.898698+00:00
instance: kb-cron
parent: gravitational-singularity-20260505-0
summary:
Until the early 1990s, it was widely believed that general relativity hides every singularity behind an event horizon, making naked singularities impossible. This is referred to as the cosmic censorship hypothesis. However, in 1991, physicists Stuart Shapiro and Saul Teukolsky performed computer simulations of a rotating plane of dust that indicated that general relativity might allow for "naked" singularities. What these objects would actually look like in such a model is unknown. Nor is it known whether singularities would still arise if the simplifying assumptions used to make the simulation were removed. However, it is hypothesized that light entering a singularity would similarly have its geodesics terminated, thus making the naked singularity look like a black hole. Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum, if the angular momentum ( J {\displaystyle J} ) is high enough. Transforming the Kerr metric to Boyer–Lindquist coordinates, it can be shown that the coordinate (which is not the radius) of the event horizon is, r ± = μ ± ( μ 2 − a 2 ) 1 / 2 {\displaystyle r_{\pm }=\mu \pm \left(\mu ^{2}-a^{2}\right)^{1/2}} , where μ = G M / c 2


id: group-velocity-dispersion-20260505-0
file: data/en.wikipedia.org/wiki/Group-velocity_dispersion-0.md
category: reference
title: Group-velocity dispersion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group-velocity_dispersion
date_saved: 2026-05-05T10:55:20.281680+00:00
instance: kb-cron
parent: group-velocity-dispersion-20260505-0
summary:
In optics, group-velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium affects the duration of an optical pulse traveling through it. Formally, GVD is defined as the derivative of the inverse of group velocity of light in a material with respect to angular frequency, GVD ( ω 0 ) ≡ ∂ ∂ ω ( 1 v g ( ω ) ) ω = ω 0 , {\displaystyle {\text{GVD}}(\omega _{0})\equiv {\frac {\partial }{\partial \omega }}\left({\frac {1}{v_{g}(\omega )}}\right)_{\omega =\omega _{0}},} where ω {\displaystyle \omega } and ω 0 {\displaystyle \omega _{0}} are angular frequencies, and the group velocity v g ( ω ) {\displaystyle v_{g}(\omega )} is defined as v g ( ω ) ≡ ∂ ω / ∂ k {\displaystyle v_{g}(\omega )\equiv \partial \omega /\partial k} . The units of group-velocity dispersion are [time]2/[distance], often expressed in fs2/mm. Equivalently, group-velocity dispersion can be defined in terms of the medium-dependent wave vector k ( ω ) {\displaystyle k(\omega )} according to GVD ( ω 0 ) ≡ ( ∂ 2 k ∂ ω 2 ) ω = ω 0 , {\displaystyle {\text{GVD}}(\omega _{0})\equiv \left({\frac {\partial ^{2}k}{\partial \omega ^{2}}}\right)_{\omega =\omega _{0}},} or in terms


id: group-velocity-dispersion-20260505-1
file: data/en.wikipedia.org/wiki/Group-velocity_dispersion-1.md
category: reference
title: Group-velocity dispersion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Group-velocity_dispersion
date_saved: 2026-05-05T10:55:20.281680+00:00
instance: kb-cron
parent: group-velocity-dispersion-20260505-0
summary:
Δ T = d ( 1 v g ( ω 2 ) − 1 v g ( ω 1 ) ) . {\displaystyle \Delta T=d\left({\frac {1}{v_{g}(\omega _{2})}}-{\frac {1}{v_{g}(\omega _{1})}}\right).} The expression can be approximated as a Taylor expansion, giving Δ T = d ( 1 v g ( ω 1 ) + ∂ ∂ ω ( 1 v g ( ω ′ ) ) ω ′ = ω 1 ( ω 2 − ω 1 ) − 1 v g ( ω 1 ) ) , {\displaystyle \Delta T=d\left({\frac {1}{v_{g}(\omega _{1})}}+{\frac {\partial }{\partial \omega }}\left({\frac {1}{v_{g}(\omega ')}}\right)_{\omega '=\omega _{1}}(\omega _{2}-\omega _{1})-{\frac {1}{v_{g}(\omega _{1})}}\right),} or Δ T = d × GVD ( ω 1 ) × ( ω 2 − ω 1 ) . {\displaystyle \Delta T=d\times {\textrm {GVD}}(\omega _{1})\times (\omega _{2}-\omega _{1}).} From here it is possible to imagine scaling this expression up two pulses to infinitely many. The frequency difference ω 2 − ω 1 {\displaystyle \omega _{2}-\omega _{1}} must be replaced by the bandwidth, and the time delay Δ T {\displaystyle \Delta T} evolves into the induced chirp. == Group-delay dispersion == A closely related yet independent quantity is the group-delay dispersion (GDD), defined such that group-velocity dispersion


id: hanle-effect-20260505-0
file: data/en.wikipedia.org/wiki/Hanle_effect-0.md
category: reference
title: Hanle effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Hanle_effect
date_saved: 2026-05-05T10:55:21.498118+00:00
instance: kb-cron
parent: hanle-effect-20260505-0
summary:
The Hanle effect (also known as zero-field level crossing) is a reduction in the polarization of light emitted by atoms excited by polarized light, when subjected to a magnetic field. Typically, when atoms are excited by linearly polarized light, the emitted fluorescence is also polarized. If a weak transverse magnetic field is applied, the emitted light becomes depolarized (or its polarization rotates). This effect can be utilized in experiments to measure the lifetime of excited states and detect the presence of magnetic fields. == History == The first experimental evidence for the effect came from Robert W. Wood, and Lord Rayleigh. The effect is named after Wilhelm Hanle, who was the first to explain the effect, in terms of classical physics, in Zeitschrift für Physik in 1924. Initially, the causes of the effect were controversial, and many theorists mistakenly thought it was a version of the Faraday effect. Attempts to understand the phenomenon were important in the subsequent development of quantum physics. An early theoretical treatment of level crossing effect was given by Gregory Breit. == Theory == === Classical model === The classical explanation for this effect involves the Lorentz oscillator model, which treats the electron bound to the


id: heat-treating-20260505-0
file: data/en.wikipedia.org/wiki/Heat_treating-0.md
category: reference
title: Heat treating
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Heat_treating
date_saved: 2026-05-05T10:55:22.810075+00:00
instance: kb-cron
parent: heat-treating-20260505-0
summary:
Heat treating (or heat treatment) is a group of industrial, thermal and metalworking processes used to alter the physical, and sometimes chemical properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass. Heat treatment involves the use of heating or chilling, normally to extreme temperatures, to achieve the desired result, such as the softening or hardening of a material. Heat treatment techniques include annealing, case hardening, precipitation strengthening, tempering, carburizing, normalizing and quenching. Although the term heat treatment applies only to processes where the heating and cooling are done for the specific purpose of altering properties intentionally, heating and cooling often occur incidentally during other manufacturing processes, such as hot forming or welding. == Physical processes == Metallic materials consist of a microstructure of small crystals called "grains" or crystallites. The nature of the grains (i.e. grain size and composition) is one of the most effective factors that can determine the overall mechanical behavior of the metal. Heat treatment provides an efficient way to manipulate the properties of the metal by controlling the rate of diffusion and the rate of cooling within the microstructure. Heat


id: heat-treating-20260505-1
file: data/en.wikipedia.org/wiki/Heat_treating-1.md
category: reference
title: Heat treating
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Heat_treating
date_saved: 2026-05-05T10:55:22.810075+00:00
instance: kb-cron
parent: heat-treating-20260505-0
summary:
=== Hypoeutectoid alloys === A hypoeutectic alloy has two separate melting points. Both are above the eutectic melting point for the system but are below the melting points of any constituent forming the system. Between these two melting points, the alloy will exist as part solid and part liquid. The constituent with the higher melting point will solidify first. When completely solidified, a hypoeutectic alloy will often be in a solid solution. Similarly, a hypoeutectoid alloy has two critical temperatures, called "arrests". Between these two temperatures, the alloy will exist partly as the solution and partly as a separate crystallizing phase, called the "pro eutectoid phase". These two temperatures are called the upper (A3) and lower (A1) transformation temperatures. As the solution cools from the upper transformation temperature toward an insoluble state, the excess base metal will often be forced to "crystallize-out", becoming the pro eutectoid. This will occur until the remaining concentration of solutes reaches the eutectoid level, which will then crystallize as a separate microstructure. For example, a hypoeutectoid steel contains less than 0.77% carbon. Upon cooling a hypoeutectoid steel from the austenite transformation temperature, small islands of proeutectoid-ferrite will form. These will continue to grow and the


id: heat-treating-20260505-2
file: data/en.wikipedia.org/wiki/Heat_treating-2.md
category: reference
title: Heat treating
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Heat_treating
date_saved: 2026-05-05T10:55:22.810075+00:00
instance: kb-cron
parent: heat-treating-20260505-0
summary:
Proper heat treating requires precise control over temperature, time held at a certain temperature and cooling rate. With the exception of stress-relieving, tempering, and aging, most heat treatments begin by heating an alloy beyond a certain transformation, or arrest (A), temperature. This temperature is referred to as an "arrest" because at the A temperature the metal experiences a period of hysteresis. At this point, all of the heat energy is used to cause the crystal change, so the temperature stops rising for a short time (arrests) and then continues climbing once the change is complete. Therefore, the alloy must be heated above the critical temperature for a transformation to occur. The alloy will usually be held at this temperature long enough for the heat to completely penetrate the alloy, thereby bringing it into a complete solid solution. Iron, for example, has four critical-temperatures, depending on carbon content. Pure iron in its alpha (room temperature) state changes to nonmagnetic gamma-iron at its A2 temperature, and weldable delta-iron at its A4 temperature. However, as carbon is added, becoming steel, the A2 temperature splits into the A3 temperature, also called the austenitizing temperature (all phases become austenite, a solution of gamma iron and


id: heat-treating-20260505-3
file: data/en.wikipedia.org/wiki/Heat_treating-3.md
category: reference
title: Heat treating
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Heat_treating
date_saved: 2026-05-05T10:55:22.810075+00:00
instance: kb-cron
parent: heat-treating-20260505-0
summary:
Annealing consists of heating a metal to a specific temperature and then cooling at a rate that will produce a refined microstructure, either fully or partially separating the constituents. The rate of cooling is generally slow. Annealing is most often used to soften a metal for cold working, to improve machinability, or to enhance properties like electrical conductivity. In ferrous alloys, annealing is usually accomplished by heating the metal beyond the upper critical temperature and then cooling very slowly, resulting in the formation of pearlite. In both pure metals and many alloys that cannot be heat treated, annealing is used to remove the hardness caused by cold working. The metal is heated to a temperature where recrystallization can occur, thereby repairing the defects caused by plastic deformation. In these metals, the rate of cooling will usually have little effect. Most non-ferrous alloys that are heat-treatable are also annealed to relieve the hardness of cold working. These may be slowly cooled to allow full precipitation of the constituents and produce a refined microstructure. Ferrous alloys are usually either "full annealed" or "process annealed". Full annealing requires very slow cooling rates, in order to form coarse pearlite. In process annealing, the cooling


id: heat-treating-20260505-4
file: data/en.wikipedia.org/wiki/Heat_treating-4.md
category: reference
title: Heat treating
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Heat_treating
date_saved: 2026-05-05T10:55:22.810075+00:00
instance: kb-cron
parent: heat-treating-20260505-0
summary:
Untempered martensitic steel, while very hard, is too brittle to be useful for most applications. A method for alleviating this problem is called tempering. Most applications require that quenched parts be tempered. Tempering consists of heating steel below the lower critical temperature, (often from 400˚F to 1105˚F or 205˚C to 595˚C, depending on the desired results), to impart some toughness. Higher tempering temperatures (maybe up to 1,300˚F or 700˚C, depending on the alloy and application) are sometimes used to impart further ductility, although some yield strength is lost. Tempering may also be performed on normalized steels. Other methods of tempering consist of quenching to a specific temperature, which is above the martensite start temperature, and then holding it there until pure bainite can form or internal stresses can be relieved. These include austempering and martempering. ==== Tempering colors ==== Steel that has been freshly ground or polished will form oxide layers when heated. At a very specific temperature, the iron oxide will form a layer with a very specific thickness, causing thin-film interference. This causes colors to appear on the surface of the steel. As the temperature is increased, the iron oxide layer grows in thickness, changing the color. These


id: heat-treating-20260505-5
file: data/en.wikipedia.org/wiki/Heat_treating-5.md
category: reference
title: Heat treating
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Heat_treating
date_saved: 2026-05-05T10:55:22.810075+00:00
instance: kb-cron
parent: heat-treating-20260505-0
summary:
=== Decarburization === The heating of steel is sometimes used as a method to alter the carbon content. When steel is heated in an oxidizing environment, the oxygen combines with the iron to form an iron-oxide layer, which protects the steel from decarburization. When the steel turns to austenite, however, the oxygen combines with iron to form a slag, which provides no protection from decarburization. The formation of slag and scale actually increases decarburization, because the iron oxide keeps oxygen in contact with the decarburization zone even after the steel is moved into an oxygen-free environment, such as the coals of a forge. Thus, the carbon atoms begin combining with the surrounding scale and slag to form both carbon monoxide and carbon dioxide, which is released into the air. Steel contains a relatively small percentage of carbon, which can migrate freely within the gamma iron. When austenitized steel is exposed to air for long periods of time, the carbon content in the steel can be lowered. This is the opposite from what happens when steel is heated in a reducing environment, in which carbon slowly diffuses further into the metal. In an oxidizing environment, the carbon can readily diffuse outwardly,


id: heat-treating-20260505-6
file: data/en.wikipedia.org/wiki/Heat_treating-6.md
category: reference
title: Heat treating
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Heat_treating
date_saved: 2026-05-05T10:55:22.810075+00:00
instance: kb-cron
parent: heat-treating-20260505-0
summary:
=== Salt bath furnaces === Salt baths are used in a wide variety of heat treatment processes including neutral hardening, liquid carburising, liquid nitriding, austempering, martempering and tempering. Parts are loaded into a pot of molten salt where they are heated by conduction, giving a very readily available source of heat. The core temperature of a part rises in temperature at approximately the same rate as its surface in a salt bath. Salt baths utilize a variety of salts for heat treatment, with cyanide salts being the most extensively used. Concerns about associated occupation health and safety, and expensive waste management and disposal due to their environmental effects have made the use of salt baths less attractive in recent years. Consequently, many salt baths are being replaced by more environmentally friendly fluidized bed furnaces. === Fluidised bed furnaces === A fluidised bed consists of a cylindrical retort made from high-temperature alloy, filled with sand-like aluminum oxide particulate. Gas (air or nitrogen) is bubbled through the oxide and the sand moves in such a way that it exhibits fluid-like behavior, hence the term fluidized. The solid-solid contact of the oxide gives very high thermal conductivity and excellent temperature uniformity throughout the


id: kondo-effect-20260505-0
file: data/en.wikipedia.org/wiki/Kondo_effect-0.md
category: reference
title: Kondo effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Kondo_effect
date_saved: 2026-05-05T10:55:24.098887+00:00
instance: kb-cron
parent: kondo-effect-20260505-0
summary:
In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature. The cause of the effect was first explained by Jun Kondo, who applied third-order perturbation theory to the problem to account for scattering of s-orbital conduction electrons off d-orbital electrons localized at impurities (Kondo model). Kondo's calculation predicted that the scattering rate and the resulting part of the resistivity should increase logarithmically as the temperature approaches 0 K. Extended to a lattice of magnetic impurities, the Kondo effect likely explains the formation of heavy fermions and Kondo insulators in intermetallic compounds, especially those involving rare earth elements such as cerium, praseodymium, and ytterbium, and actinide elements such as uranium. The Kondo effect has also been observed in quantum dot systems. == Theory == The dependence of the resistivity ρ {\displaystyle \rho } on temperature T {\displaystyle T} , including the Kondo effect, is written as ρ ( T ) = ρ 0 + a T 2 + c m ln ⁡ μ T + b T 5 , {\displaystyle \rho (T)=\rho _{0}+aT^{2}+c_{m}\ln {\frac {\mu }{T}}+bT^{5},} where ρ 0 {\displaystyle


id: latent-heat-20260505-0
file: data/en.wikipedia.org/wiki/Latent_heat-0.md
category: reference
title: Latent heat
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latent_heat
date_saved: 2026-05-05T10:55:25.319832+00:00
instance: kb-cron
parent: latent-heat-20260505-0
summary:
Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process—usually a first-order phase transition, like melting or condensation. Latent heat can be understood as hidden energy which is supplied or extracted to change the state of a substance without changing its temperature or pressure. This includes the latent heat of fusion (solid to liquid), the latent heat of vaporization (liquid to gas) and the latent heat of sublimation (solid to gas). The term was introduced around 1762 by Scottish chemist Joseph Black. Black used the term in the context of calorimetry where a heat transfer caused a volume change in a body while its temperature was constant. In contrast to latent heat, sensible heat is energy transferred as heat, with a resultant temperature change in a body. == Usage == The terms sensible heat and latent heat refer to energy transferred between a body and its surroundings, defined by the occurrence or non-occurrence of temperature change; they depend on the properties of the body. Sensible heat is sensed or felt in a process as a change in the body's temperature. Latent heat is


id: latent-heat-20260505-1
file: data/en.wikipedia.org/wiki/Latent_heat-1.md
category: reference
title: Latent heat
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Latent_heat
date_saved: 2026-05-05T10:55:25.319832+00:00
instance: kb-cron
parent: latent-heat-20260505-0
summary:
The English word latent comes from Latin latēns, meaning lying hidden. The term latent heat was introduced into calorimetry around 1750 by Joseph Black, commissioned by producers of Scotch whisky in search of ideal quantities of fuel and water for their distilling process to study system changes, such as of volume and pressure, when the thermodynamic system was held at constant temperature in a thermal bath. It was known that when the air temperature rises above freezing—air then becoming the obvious heat source—snow melts very slowly and the temperature of the melted snow is close to its freezing point. In 1757, Black started to investigate if heat, therefore, was required for the melting of a solid, independent of any rise in temperature. As far Black knew, the general view at that time was that melting was inevitably accompanied by a small increase in temperature, and that no additional heat was needed beyond what this increase in temperature would require in itself. Soon, however, Black was able to show that much more heat was required during melting than could be explained by the increase in temperature alone. He was also able to show that heat is released by a liquid during


id: leidenfrost-effect-20260505-0
file: data/en.wikipedia.org/wiki/Leidenfrost_effect-0.md
category: reference
title: Leidenfrost effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Leidenfrost_effect
date_saved: 2026-05-05T10:55:26.560991+00:00
instance: kb-cron
parent: leidenfrost-effect-20260505-0
summary:
The Leidenfrost effect or film boiling is a physical phenomenon in which a liquid, close to a solid surface of another body that is significantly hotter than the liquid's boiling point, produces an insulating vapor layer that keeps the liquid from boiling rapidly. Because of this repulsive force, a droplet hovers over the surface, rather than making physical contact with it. The effect is named after the German doctor Johann Gottlob Leidenfrost, who described it in A Tract About Some Qualities of Common Water. This is most commonly seen when cooking, when drops of water are sprinkled onto a hot pan. If the pan's temperature is at or above the Leidenfrost point, which is approximately 193 °C (379 °F) for water, the water skitters across the pan and takes longer to evaporate than it would take if the water droplets had been sprinkled onto a cooler pan. == Details == The Leidenfrost effect can be seen as drops of water are sprinkled onto a pan at various times as it heats up. Initially, as the temperature of the pan is just below 100 °C (212 °F), the water flattens out and slowly evaporates, or if the temperature of the pan


id: leidenfrost-effect-20260505-1
file: data/en.wikipedia.org/wiki/Leidenfrost_effect-1.md
category: reference
title: Leidenfrost effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Leidenfrost_effect
date_saved: 2026-05-05T10:55:26.560991+00:00
instance: kb-cron
parent: leidenfrost-effect-20260505-0
summary:
== Heat transfer correlations == The heat transfer coefficient may be approximated using Bromley's equation, h = C [ k v 3 ρ v g ( ρ L − ρ v ) ( h f g + 0.4 c p v ( T s − T s a t ) ) D o μ v ( T s − T s a t ) ] 1 ╱ 4 {\displaystyle h=C{{\left[{\frac {k_{v}^{3}{{\rho }_{v}}g\left({{\rho }_{L}}-{{\rho }_{v}}\right)\left({{h}_{fg}}+0.4{{c}_{pv}}\left({{T}_{s}}-{{T}_{sat}}\right)\right)}{{{D}_{o}}{{\mu }_{v}}\left({{T}_{s}}-{{T}_{sat}}\right)}}\right]}^{{}^{1}\!\!\diagup \!\!{}_{4}\;}}} where D o {\displaystyle {{D}_{o}}} is the outside diameter of the tube. The correlation constant C is 0.62 for horizontal cylinders and vertical plates, and 0.67 for spheres. Vapor properties are evaluated at film temperature. For stable film boiling on a horizontal surface, Berenson has modified Bromley's equation to yield, h = 0.425 [ k v f 3 ρ v f g ( ρ L − ρ v ) ( h f g + 0.4 c p v ( T s − T s a t ) ) μ v f ( T s − T s a t ) σ / g ( ρ L − ρ v ) ] 1 ╱ 4 {\displaystyle h=0.425{{\left[{\frac {k_{vf}^{3}{{\rho }_{vf}}g\left({{\rho }_{L}}-{{\rho }_{v}}\right)\left({{h}_{fg}}+0.4{{c}_{pv}}\left({{T}_{s}}-{{T}_{sat}}\right)\right)}{{{\mu }_{vf}}\left({{T}_{s}}-{{T}_{sat}}\right){\sqrt {\sigma /g\left({{\rho }_{L}}-{{\rho


id: leidenfrost-effect-20260505-2
file: data/en.wikipedia.org/wiki/Leidenfrost_effect-2.md
category: reference
title: Leidenfrost effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Leidenfrost_effect
date_saved: 2026-05-05T10:55:26.560991+00:00
instance: kb-cron
parent: leidenfrost-effect-20260505-0
summary:
Non-volatile materials were discovered in 2015 to also exhibit a 'reactive Leidenfrost effect', whereby solid particles were observed to float above hot surfaces and skitter around erratically. Detailed characterization of the reactive Leidenfrost effect was completed for small particles of cellulose (~0.5 mm) on high temperature polished surfaces by high speed photography. Cellulose was shown to decompose to short-chain oligomers which melt and wet smooth surfaces with increasing heat transfer associated with increasing surface temperature. Above 675 °C (1,247 °F), cellulose was observed to exhibit transition boiling with violent bubbling and associated reduction in heat transfer. Liftoff of the cellulose droplet (depicted at the right) was observed to occur above about 750 °C (1,380 °F), associated with a dramatic reduction in heat transfer. High speed photography of the reactive Leidenfrost effect of cellulose on porous surfaces (macroporous alumina) was also shown to suppress the reactive Leidenfrost effect and enhance overall heat transfer rates to the particle from the surface. The new phenomenon of a 'reactive Leidenfrost (RL) effect' was characterized by a dimensionless quantity, (φRL= τconv/τrxn), which relates the time constant of solid particle heat transfer to the time constant of particle reaction, with the reactive Leidenfrost effect occurring for


id: linearity-20260505-0
file: data/en.wikipedia.org/wiki/Linearity-0.md
category: reference
title: Linearity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Linearity
date_saved: 2026-05-05T10:55:27.962652+00:00
instance: kb-cron
parent: linearity-20260505-0
summary:
In mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping); linearity of a polynomial. An example of a linear function is the function defined by f ( x ) = ( a x , b x ) {\displaystyle f(x)=(ax,bx)} that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables X , {\displaystyle X,} Y {\displaystyle Y} and Z {\displaystyle Z} is a X + b Y + c Z + d . {\displaystyle aX+bY+cZ+d.} Linearity of a mapping is closely related to proportionality. Examples in physics include the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships, such as between velocity and kinetic energy, are nonlinear. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. Linearity of a polynomial means that its degree is less than two. The use of the term for polynomials stems from the fact


id: linearity-20260505-1
file: data/en.wikipedia.org/wiki/Linearity-1.md
category: reference
title: Linearity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Linearity
date_saved: 2026-05-05T10:55:27.962652+00:00
instance: kb-cron
parent: linearity-20260505-0
summary:
In every row in which the truth value of the function is T, there are an odd number of Ts assigned to the arguments, and in every row in which the function is F there is an even number of Ts assigned to arguments. Specifically, f(F, F, ..., F) = F, and these functions correspond to linear maps over the Boolean vector space. In every row in which the value of the function is T, there is an even number of Ts assigned to the arguments of the function; and in every row in which the truth value of the function is F, there are an odd number of Ts assigned to arguments. In this case, f(F, F, ..., F) = T. Another way to express this is that each variable always makes a difference in the truth value of the operation or it never makes a difference. Negation, Logical biconditional, exclusive or, tautology, and contradiction are linear functions. == Physics == In physics, linearity is a property of the differential equations governing many systems; for instance, the Maxwell equations or the diffusion equation. Linearity of a homogeneous differential equation means that if two functions f and g are solutions


id: liquid-rope-coil-effect-20260505-0
file: data/en.wikipedia.org/wiki/Liquid_rope_coil_effect-0.md
category: reference
title: Liquid rope coil effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Liquid_rope_coil_effect
date_saved: 2026-05-05T10:55:29.255017+00:00
instance: kb-cron
parent: liquid-rope-coil-effect-20260505-0
summary:
The liquid rope coil effect or liquid rope coiling is a fluid mechanics phenomenon characterized by the steadily rotating helical structure formed when pouring a thin stream of viscous fluid from a sufficient height onto a surface, resulting from a buckling instability in which the initially vertical fluid stream becomes unstable to bending deformation under axial compressive stress. The rope can change shape in three ways: stretching, bending, and twisting. Each deformation faces resistance in the form of viscous forces. The rope's shape is influenced by the balance between these forces and the fluid's inertia. Surface tension, usually significant in fluid dynamics, plays only a minor role. == Further reading == Barnes, George; Woodcock, Richard (1958-04-01). "Liquid Rope-Coil Effect". American Journal of Physics. 26 (4): 205–209. doi:10.1119/1.1996110. ISSN 0002-9505. == References ==


id: liquid-slugging-20260505-0
file: data/en.wikipedia.org/wiki/Liquid_slugging-0.md
category: reference
title: Liquid slugging
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Liquid_slugging
date_saved: 2026-05-05T10:55:30.467230+00:00
instance: kb-cron
parent: liquid-slugging-20260505-0
summary:
Liquid slugging is the phenomenon of liquid entering the cylinder of a reciprocating compressor, a common cause of failure. Under normal conditions, the intake and output of a compressor cylinder is entirely vapor or gas, when a liquid accumulates at the suction port liquid slugging can occur. As more of the practically incompressible liquid enters, strain is placed upon the system leading to a variety of failures. == References ==


id: lorentz-force-20260505-0
file: data/en.wikipedia.org/wiki/Lorentz_force-0.md
category: reference
title: Lorentz force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lorentz_force
date_saved: 2026-05-05T10:55:31.743490+00:00
instance: kb-cron
parent: lorentz-force-20260505-0
summary:
In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation of electric motors and particle accelerators to the behavior of plasmas. The Lorentz force has two components. The electric force acts in the direction of the electric field for positive charges and opposite to it for negative charges, tending to accelerate the particle in a straight line. The magnetic force is perpendicular to both the particle's velocity and the magnetic field, and it causes the particle to move along a curved trajectory, often circular or helical in form, depending on the directions of the fields. Variations on the force law describe the magnetic force on a current-carrying wire (sometimes called Laplace force), and the electromotive force in a wire loop moving through a magnetic field, as described by Faraday's law of induction. Together with Maxwell's equations, which describe how electric and magnetic fields are generated by charges and currents, the Lorentz force law forms the foundation of classical electrodynamics. While the law remains valid in special relativity, it breaks down at small scales where quantum


id: lorentz-force-20260505-1
file: data/en.wikipedia.org/wiki/Lorentz_force-1.md
category: reference
title: Lorentz force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lorentz_force
date_saved: 2026-05-05T10:55:31.743490+00:00
instance: kb-cron
parent: lorentz-force-20260505-0
summary:
=== Continuous charge distribution === The Lorentz force law can also be given in terms of continuous charge distributions, such as those found in conductors or plasmas. For a small element of a moving charge distribution with charge d q {\displaystyle \mathrm {d} q} , the infinitesimal force is given by: d F = d q ( E + v × B ) {\displaystyle \mathrm {d} \mathbf {F} =\mathrm {d} q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right)} Dividing both sides by the volume d V {\displaystyle \mathrm {d} V} of the charge element gives the force density f = ρ ( E + v × B ) , {\displaystyle \mathbf {f} =\rho \left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right),} where ρ {\displaystyle \rho } is the charge density and f {\displaystyle \mathbf {f} } is the force per unit volume. Introducing the current density J = ρ v {\textstyle \mathbf {J} =\rho \mathbf {v} } , this can be rewritten as: The total force is the volume integral over the charge distribution: F = ∫ ( ρ E + J × B ) d V . {\displaystyle \mathbf {F} =\int \left(\rho \mathbf {E} +\mathbf {J} \times \mathbf {B}


id: lorentz-force-20260505-2
file: data/en.wikipedia.org/wiki/Lorentz_force-2.md
category: reference
title: Lorentz force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lorentz_force
date_saved: 2026-05-05T10:55:31.743490+00:00
instance: kb-cron
parent: lorentz-force-20260505-0
summary:
F = N F q = q v B n ℓ A sin ⁡ θ = B I ℓ sin ⁡ θ , {\displaystyle F=NF_{q}=qvBn\ell A\sin \theta =BI\ell \sin \theta ,} where the current, I = nqvA. This is the same as the equation above using the definition of the cross product. If the wire is not straight or the magnetic field is non-uniform, the total force can be computed by applying the formula to each infinitesimal segment of wire d ℓ {\displaystyle \mathrm {d} {\boldsymbol {\ell }}} , then adding up all these forces by integration. In this case, the net force on a stationary wire carrying a steady current is F = I ∫ ( d ℓ × B ) . {\displaystyle \mathbf {F} =I\int (\mathrm {d} {\boldsymbol {\ell }}\times \mathbf {B} ).} One application of this is Ampère's force law, which describes the attraction or repulsion between two current-carrying wires. Each wire generates a magnetic field, described by the Biot–Savart law, which exerts a Lorentz force on the other wire. If the currents flow in the same direction, the wires attract; if the currents flow in opposite directions, they repel. This interaction provided the basis of the


id: lorentz-force-20260505-3
file: data/en.wikipedia.org/wiki/Lorentz_force-3.md
category: reference
title: Lorentz force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lorentz_force
date_saved: 2026-05-05T10:55:31.743490+00:00
instance: kb-cron
parent: lorentz-force-20260505-0
summary:
=== Transformer emf === A complementary case is transformer emf, which occurs when the conducting loop remains stationary but the magnetic flux through it changes due to a time-varying magnetic field. This can happen in two ways: either the source of the magnetic field moves, altering the field distribution through the fixed loop, or the strength of the magnetic field changes over time at a fixed location, as in the case of a powered electromagnet.. In either situation, no magnetic force acts on the charges, and the emf is entirely due to the electric component (qE) of the Lorentz force. According to the Maxwell–Faraday equation, a time-varying magnetic field produces a circulating electric field, which drives current in the loop. This phenomenon underlies the operation of electrical machines such as synchronous generators. The electric field induced in this way is non-conservative, meaning its line integral around a closed loop is not zero. === Relativity === From the viewpoint of special relativity, the distinction between motional and transformer emf is frame-dependent. In the laboratory frame, a moving loop in a static field generates emf via magnetic forces. But in a frame moving with the loop, the magnetic field appears time-dependent, and


id: lorentz-force-20260505-4
file: data/en.wikipedia.org/wiki/Lorentz_force-4.md
category: reference
title: Lorentz force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lorentz_force
date_saved: 2026-05-05T10:55:31.743490+00:00
instance: kb-cron
parent: lorentz-force-20260505-0
summary:
(Notice that the coordinates and the velocity components should be treated as independent variables, so the del operator acts only on A {\displaystyle \mathbf {A} } , not on v {\displaystyle \mathbf {v} } ; thus, there is no need to use Feynman's subscript notation in the equation above.) Using the chain rule, the convective derivative of A {\displaystyle \mathbf {A} } is: d A d t = ∂ A ∂ t + ( v ⋅ ∇ ) A {\displaystyle {\frac {\mathrm {d} \mathbf {A} }{\mathrm {d} t}}={\frac {\partial \mathbf {A} }{\partial t}}+(\mathbf {v} \cdot \nabla )\mathbf {A} } so that the above expression becomes: F = q [ − ∇ ( ϕ − v ⋅ A ) − d A d t ] . {\displaystyle \mathbf {F} =q\left[-\nabla (\phi -\mathbf {v} \cdot \mathbf {A} )-{\frac {\mathrm {d} \mathbf {A} }{\mathrm {d} t}}\right].} With v = ẋ and d d t [ ∂ ∂ x ˙ ( ϕ − x ˙ ⋅ A ) ] = − d A d t , {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left[{\frac {\partial }{\partial {\dot {\mathbf {x} }}}}\left(\phi -{\dot {\mathbf {x} }}\cdot \mathbf {A} \right)\right]=-{\frac {\mathrm {d} \mathbf {A} }{\mathrm {d} t}},} we


id: lorentz-force-20260505-5
file: data/en.wikipedia.org/wiki/Lorentz_force-5.md
category: reference
title: Lorentz force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lorentz_force
date_saved: 2026-05-05T10:55:31.743490+00:00
instance: kb-cron
parent: lorentz-force-20260505-0
summary:
d p 1 d τ = q U β F 1 β = q ( U 0 F 10 + U 1 F 11 + U 2 F 12 + U 3 F 13 ) . {\displaystyle {\frac {\mathrm {d} p^{1}}{\mathrm {d} \tau }}=qU_{\beta }F^{1\beta }=q\left(U_{0}F^{10}+U_{1}F^{11}+U_{2}F^{12}+U_{3}F^{13}\right).} Substituting the components of the covariant electromagnetic tensor F yields d p 1 d τ = q [ U 0 ( E x c ) + U 2 ( − B z ) + U 3 ( B y ) ] . {\displaystyle {\frac {\mathrm {d} p^{1}}{\mathrm {d} \tau }}=q\left[U_{0}\left({\frac {E_{x}}{c}}\right)+U_{2}(-B_{z})+U_{3}(B_{y})\right].} Using the components of covariant four-velocity yields d p 1 d τ = q γ [ c ( E x c ) + ( − v y ) ( − B z ) + ( − v z ) ( B y ) ] = q γ ( E x + v y B z − v z B y ) = q γ [ E x + ( v × B ) x ] . {\displaystyle {\begin{aligned}{\frac {\mathrm {d} p^{1}}{\mathrm {d} \tau }}&=q\gamma \left[c\left({\frac {E_{x}}{c}}\right)+(-v_{y})(-B_{z})+(-v_{z})(B_{y})\right]\\[1ex]&=q\gamma \left(E_{x}+v_{y}B_{z}-v_{z}B_{y}\right)=q\gamma \left[E_{x}+\left(\mathbf {v} \times \mathbf {B} \right)_{x}\right]\,.\end{aligned}}} The calculation for α = 2, 3 (force components in


id: lorentz-force-20260505-6
file: data/en.wikipedia.org/wiki/Lorentz_force-6.md
category: reference
title: Lorentz force
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Lorentz_force
date_saved: 2026-05-05T10:55:31.743490+00:00
instance: kb-cron
parent: lorentz-force-20260505-0
summary:
H ^ = 1 2 m [ p ^ − q A ( r , t ) ] 2 + q Φ ( r , t ) , {\displaystyle {\hat {H}}={\frac {1}{2m}}\left[{\hat {\mathbf {p} }}-q\mathbf {A} (\mathbf {r} ,t)\right]^{2}+q\Phi (\mathbf {r} ,t),} This expression is a direct generalization of the classical Hamiltonian that leads to the Lorentz force law. The key difference is that in quantum mechanics, position r {\displaystyle \mathbf {r} } and momentum p ^ {\displaystyle {\hat {\mathbf {p} }}} are operators that do not commute. As a result, quantum dynamics incorporate fundamentally different behavior such as wave interference and quantization. Unlike in classical physics, where only electric and magnetic fields influence particle motion, quantum mechanics allows the electromagnetic potentials themselves to produce observable effects. This is exemplified by the Aharonov–Bohm effect, in which a charged particle passes through a region with zero electric and magnetic fields but encircles a magnetic flux confined to an inaccessible area. Although the classical Lorentz force is zero along the particle's path, the interference pattern observed on a screen shifts depending on the enclosed magnetic flux, revealing the physical significance of the vector potential in quantum mechanics. Nevertheless, the classical Lorentz force


id: magnetic-braking-astronomy-20260505-0
file: data/en.wikipedia.org/wiki/Magnetic_braking_(astronomy)-0.md
category: reference
title: Magnetic braking (astronomy)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_braking_(astronomy)
date_saved: 2026-05-05T10:55:33.039720+00:00
instance: kb-cron
parent: magnetic-braking-astronomy-20260505-0
summary:
Magnetic braking is the process by which a star loses angular momentum due to a coupling between its solar wind and magnetic field. Magnetic braking plays an important role in the formation and evolution of stars, particularly binaries. == Stellar formation == Magnetic braking is integral to explaining angular momentum loss during stellar formation. Consider some fragment of a star-forming molecular cloud with angular momentum derived from the observed galactic turbulence. Current theories of star formation state that such a cloud should flatten and contract, conserving angular momentum L {\displaystyle L} in the process. As the cloud contracts and its density increases, the angular velocity must increase, causing the cloud to spin faster. Without considering magnetic braking, an angular momentum problem emerges where the large angular momentum of the cloud causes very high centrifugal forces limiting star formation. In such a scenario the observed cloud angular momentum would be orders of magnitude larger than observed in young stars. This angular momentum problem is resolved, however, when considering the effects of magnetic braking. In a protostellar cloud, both gravitational and magnetic effects are significant, and magnetic braking acts as a torque, transporting angular momentum from the infalling material to the interstellar


id: magnetic-braking-astronomy-20260505-1
file: data/en.wikipedia.org/wiki/Magnetic_braking_(astronomy)-1.md
category: reference
title: Magnetic braking (astronomy)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_braking_(astronomy)
date_saved: 2026-05-05T10:55:33.039720+00:00
instance: kb-cron
parent: magnetic-braking-astronomy-20260505-0
summary:
This leads to a critical radius r c = 15 R ⊙ {\displaystyle r_{c}=15R_{\odot }} . This means that the ionized plasma will rotate together with the Sun as a solid body until it reaches a distance of nearly 15 times the radius of the Sun; from there the material will break off and stop affecting the Sun. The amount of solar mass needed to be thrown out along the field lines to make the Sun completely stop rotating can then be calculated using the specific angular momentum: j ⊙ j c = ( R ⊙ r c ) 2 ≈ 0.5 % {\displaystyle {\frac {j_{\odot }}{j_{c}}}=\left({\frac {R_{\odot }}{r_{c}}}\right)^{2}\approx 0.5\%} It has been suggested that the Sun lost a comparable amount of material over the course of its lifetime. == Weakened magnetic braking == In 2016 scientists at Carnegie Observatories published a research suggesting that stars at a similar stage of life as the Sun were spinning faster than magnetic braking theories predicted. To calculate this they pinpointed the dark spots on the surface of stars and tracked them as they moved with the stars' spin. While this method has been successful for measuring the spin of younger stars, the


id: magnetic-resonance-20260505-0
file: data/en.wikipedia.org/wiki/Magnetic_resonance-0.md
category: reference
title: Magnetic resonance
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnetic_resonance
date_saved: 2026-05-05T10:55:34.341025+00:00
instance: kb-cron
parent: magnetic-resonance-20260505-0
summary:
Magnetic resonance is a process by which a physical excitation (resonance) is set up via magnetism. This process was used to develop magnetic resonance imaging (MRI) and nuclear magnetic resonance spectroscopy (NMRS) technology. It is also being used to develop nuclear magnetic resonance quantum computers. == History == The first observation of electron-spin resonance was in 1944 by Y. K. Zavosky, a Soviet physicist then teaching at Kazan State University (now Kazan Federal University). Nuclear magnetic resonance was first observed in 1946 in the US by a team led by Felix Bloch at the same time as a separate team led by Edward Mills Purcell, the two of whom would later be the 1952 Nobel Laureates in Physics. == Resonant and non-resonant methods == A natural way to measure the separation between two energy levels is to find a measurable quantity defined by this separation and measure it. However, the precision of this method is limited by measurement precision and thus may be poor. Alternatively, we can set up an experiment in which the system's behavior depends on the energy level. If we apply an external field of controlled frequency, we can measure the level separation by noting at which


id: magnus-effect-20260505-0
file: data/en.wikipedia.org/wiki/Magnus_effect-0.md
category: reference
title: Magnus effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnus_effect
date_saved: 2026-05-05T10:55:35.900656+00:00
instance: kb-cron
parent: magnus-effect-20260505-0
summary:
The Magnus effect is a phenomenon that occurs when a spinning object is moving through a fluid. A lift force acts on the spinning object and its path may be deflected in a manner not present when it is not spinning. The strength and direction of the Magnus force is dependent on the speed and direction of the rotation of the object. The Magnus effect is named after Heinrich Gustav Magnus, the German physicist who investigated it. The force on a rotating cylinder is an example of Kutta–Joukowski lift, named after Martin Kutta and Nikolay Zhukovsky (or Joukowski), mathematicians who contributed to the knowledge of how lift is generated in a fluid flow. == Description == The most readily observable case of the Magnus effect is when a spinning sphere (or cylinder) curves away from the arc it would follow if it were not spinning. It is often used in football (soccer), volleyball, baseball pitching, cricket bowling, tennis and table tennis, and other ball sports, and is important in studying the physics of these sports. It is also an important factor in the study of the effects of spinning on guided missiles, and has some engineering uses, such as in


id: magnus-effect-20260505-1
file: data/en.wikipedia.org/wiki/Magnus_effect-1.md
category: reference
title: Magnus effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnus_effect
date_saved: 2026-05-05T10:55:35.900656+00:00
instance: kb-cron
parent: magnus-effect-20260505-0
summary:
Streamlines are closer spaced immediately above the cylinder than below, so the air flows faster past the upper surface than past the lower surface. Bernoulli's principle shows that the pressure adjacent to the upper surface is lower than the pressure adjacent to the lower surface. The Magnus force acts vertically upwards on the cylinder. Streamlines immediately above the cylinder are curved with radius little more than the radius of the cylinder. This means there is low pressure close to the upper surface of the cylinder. Streamlines immediately below the cylinder are curved with a larger radius than streamlines above the cylinder. This means there is higher pressure acting on the lower surface than on the upper. Air immediately above and below the cylinder is curving downwards, accelerated by the pressure gradient. A downwards force is acting on the air. Newton's third law predicts that the Magnus force and the downwards force acting on the air are equal in magnitude and opposite in direction. == History == The effect is named after German physicist Heinrich Gustav Magnus, who demonstrated the effect with a rapidly rotating brass cylinder and an air blower in 1852. Isaac Newton was the first to observe and


id: magnus-effect-20260505-2
file: data/en.wikipedia.org/wiki/Magnus_effect-2.md
category: reference
title: Magnus effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Magnus_effect
date_saved: 2026-05-05T10:55:35.900656+00:00
instance: kb-cron
parent: magnus-effect-20260505-0
summary:
== In external ballistics == The Magnus effect can also be found in advanced external ballistics. First, a spinning bullet in flight is often subject to a crosswind, which can be simplified as blowing from either the left or the right. In addition to this, even in completely calm air a bullet experiences a small sideways wind component due to its yawing motion. This yawing motion along the bullet's flight path means that the nose of the bullet points in a slightly different direction from the direction the bullet travels. In other words, the bullet "skids" sideways at any given moment, and thus experiences a small sideways wind component in addition to any crosswind component. The combined sideways wind component of these two effects causes a Magnus force to act on the bullet, which is perpendicular both to the direction the bullet is pointing and the combined sideways wind. In a very simple case where we ignore various complicating factors, the Magnus force from the crosswind would cause an upward or downward force to act on the spinning bullet (depending on the left or right wind and rotation), causing deflection of the bullet's flight path up or down, thus influencing


id: marangoni-effect-20260505-0
file: data/en.wikipedia.org/wiki/Marangoni_effect-0.md
category: reference
title: Marangoni effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Marangoni_effect
date_saved: 2026-05-05T10:55:37.291932+00:00
instance: kb-cron
parent: marangoni-effect-20260505-0
summary:
The Marangoni effect (also called the Gibbs–Marangoni effect) is the mass transfer along an interface between two phases due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermo-capillary convection or Bénard–Marangoni convection. == History == This phenomenon was first identified in the so-called "tears of wine" by physicist James Thomson (Lord Kelvin's brother) in 1855. The general effect is named after Italian physicist Carlo Marangoni, who studied it for his doctoral dissertation at the University of Pavia and published his results in 1865. A complete theoretical treatment of the subject was given by J. Willard Gibbs in his work On the Equilibrium of Heterogeneous Substances (1875–1878). == Mechanism == Since a liquid with a high surface tension pulls more strongly on the surrounding liquid than one with a low surface tension, the presence of a gradient in surface tension will naturally cause the liquid to flow away from regions of low surface tension. The surface tension gradient can be caused by concentration gradient or by a temperature gradient (surface tension is an inversely proportional function of temperature). In simple cases, the speed of the flow u ≈ Δ γ /


id: marangoni-effect-20260505-1
file: data/en.wikipedia.org/wiki/Marangoni_effect-1.md
category: reference
title: Marangoni effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Marangoni_effect
date_saved: 2026-05-05T10:55:37.291932+00:00
instance: kb-cron
parent: marangoni-effect-20260505-0
summary:
As an example, wine may exhibit a visible effect called "tears of wine". The effect is a consequence of the fact that alcohol has a lower surface tension and higher volatility than water. The water/alcohol solution rises up the surface of the glass lowering the surface energy of the glass. Alcohol evaporates from the film leaving behind liquid with a higher surface tension (more water, less alcohol). This region with a lower concentration of alcohol (greater surface tension) pulls on the surrounding fluid more strongly than the regions with a higher alcohol concentration (lower in the glass). The result is the liquid is pulled up until its own weight exceeds the force of the effect, and the liquid drips back down the vessel's walls. This can also be easily demonstrated by spreading a thin film of water on a smooth surface and then allowing a drop of alcohol to fall on the center of the film. The liquid will rush out of the region where the drop of alcohol fell. == Significance to transport phenomena == Under earth conditions, the effect of gravity causing natural convection in a system with a temperature gradient along a fluid/fluid interface is usually much


id: m-ssbauer-effect-20260505-0
file: data/en.wikipedia.org/wiki/Mössbauer_effect-0.md
category: reference
title: Mössbauer effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mössbauer_effect
date_saved: 2026-05-05T10:55:38.633939+00:00
instance: kb-cron
parent: m-ssbauer-effect-20260505-0
summary:
The Mössbauer effect, or recoilless nuclear resonance fluorescence, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of gamma radiation by atomic nuclei bound in a solid. Its main application is in Mössbauer spectroscopy. In the Mössbauer effect, a narrow resonance for nuclear gamma emission and absorption results from the momentum of recoil being delivered to a surrounding crystal lattice rather than to the emitting or absorbing nucleus alone. When this occurs, no gamma energy is lost to the kinetic energy of recoiling nuclei at either the emitting or absorbing end of a gamma transition: emission and absorption occur at the same energy, resulting in strong, resonant absorption. == History == The interaction of X-rays with gases, particularly their attenuation and scattering, had been studied since the early years of X-ray research, and element-specific X-ray absorption phenomena had been established in the early 20th century. It was expected that a similar phenomenon would be found for gamma rays, which are created by nuclear transitions (as opposed to X-rays, which are typically produced by electronic transitions). However, attempts to observe nuclear resonance produced by gamma rays in gases failed due to


id: mpemba-effect-20260505-0
file: data/en.wikipedia.org/wiki/Mpemba_effect-0.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T10:55:40.016392+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
The Mpemba effect is the observation that very hot liquids or colloids (such as ice cream) can freeze more quickly than colder ones, for similar volumes and surrounding conditions. Physicists remain divided on the effect's reproducibility, precise definition, and underlying mechanisms. It is named after Erasto Mpemba, a Tanzanian teenager who studied it scientifically in the 1960s for the first time, along with Denis Osborne. The Mpemba effect was initially observed in only ice cream and water, and later in other colloids. It has been studied extensively in water, with mixed results, and some experiments finding no reproducible effect. It has also been studied in magnetic alloys, nanomechanical systems, and quantum systems. == Definition == The definition of the Mpemba effect used in theoretical studies varies, making it difficult to compare experiments. Monwhea Jeng proposed this definition for the effect in water: "There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will freeze sooner." Even this definition does not specify whether "freezing" refers to the point at which a visible surface layer of ice has formed,


id: mpemba-effect-20260505-1
file: data/en.wikipedia.org/wiki/Mpemba_effect-1.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T10:55:40.016392+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
=== Studies of the effect in water === Modern studies using freezers with well-understood properties have observed the Mpemba effect where water supercools before freezing. Water that starts out cooler tends to reach a lower supercooled temperature before freezing. Some studies measure the time it takes for a sample to begin to freeze (the start of recalescence, the moment where the heat of freezing first starts to be released) the time it takes to completely freeze, or the difference: the time from the onset of recalescence to the completion of freezing. Some also measure the time it takes for a sample to reach the freezing point of the fluid, before any freezing has begun. In 1995, David Auerbach studied glass beakers placed into a liquid cooling bath, where the water supercooled to −6 to −18 °C (21 to 0 °F; 267 to 255 K) before freezing. In some cases water which started off hotter began freezing first. Considerable random variation was observed in the time required for spontaneous freezing to start, and Auerbach observed the Mpemba effect more frequently when the ambient temperature was between −6 and −12 °C (21 and 10 °F). James Brownridge later studied a variety of


id: mpemba-effect-20260505-2
file: data/en.wikipedia.org/wiki/Mpemba_effect-2.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T10:55:40.016392+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
== Theoretical explanations == While the definition of the Mpemba effect used in theoretical studies varies, several explanations have been offered for its occurrence. In 2017, two research groups independently and simultaneously found a theoretical Mpemba effect and also predicted a new "inverse" Mpemba effect in which heating a cooled, far-from-equilibrium system takes less time than another system that is initially closer to equilibrium. Zhiyue Lu and Oren Raz yielded a general criterion based on Markovian statistical mechanics, predicting the appearance of the inverse Mpemba effect in the Ising model and diffusion dynamics. Antonio Lasanta and co-authors also predicted the direct and inverse Mpemba effects for a granular gas in a far-from-equilibrium initial state. Lasanta's paper also suggested that a very generic mechanism leading to both Mpemba effects is due to a particle velocity distribution function that significantly deviates from the Maxwell–Boltzmann distribution. In 2024, building on Kumar's work, Isha Malhotra simulated single colloids placed in a different, double-well potential, and predicted conditions under which two specific ranges of hotter starting temperatures lead to faster freezing, but not temperatures in between those ranges. Supercooling is a component of many theoretical explanations, particularly the tendency of hot liquids that are cooled


id: mpemba-effect-20260505-3
file: data/en.wikipedia.org/wiki/Mpemba_effect-3.md
category: reference
title: Mpemba effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Mpemba_effect
date_saved: 2026-05-05T10:55:40.016392+00:00
instance: kb-cron
parent: mpemba-effect-20260505-0
summary:
"Heat questions". HyperPhysics. Georgia State University. "Mpemba effect: Why hot water can freeze faster than cold". A possible explanation of the Mpemba Effect Tyrovolas, Ilias J. (2019). "New Explanation for the Mpemba Effect". The 5th International Electronic Conference on Entropy and Its Applications. p. 2. doi:10.3390/ecea-5-06658. "The Mpemba effect: Hot Water may Freeze Faster than Cold Water". An analysis of the Mpemba effect London South Bank University "The Mpemba Effect". Archived from the original on 9 October 2011. – History and analysis of the Mpemba effect "The story of the Mpemba effect told by the protagonists". YouTube. 10 January 2013. Archived from the original on 12 December 2021. An historical interview with Erasto B. Mpemba, Dr Denis G. Osborne and Ray deSouza "Which freezes quicker, hot or cold water?". Retrieved 25 August 2021. High school experiment description, with link to experimental results Adams, Cecil; M. Q. C., Mary (1996). "Which freezes faster, hot water or cold water?". The Straight Dope. Chicago Reader, Inc. Brownridge, James (2010). "A search for the Mpemba effect: When hot water freezes faster than cold water". arXiv:1003.3185 [physics.pop-ph]. Jeng, Monwhea (November 1998). "Can hot water freeze faster than cold water?". in the University of California Usenet


id: negative-air-ions-20260505-0
file: data/en.wikipedia.org/wiki/Negative_air_ions-0.md
category: reference
title: Negative air ions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Negative_air_ions
date_saved: 2026-05-05T10:55:41.275232+00:00
instance: kb-cron
parent: negative-air-ions-20260505-0
summary:
Negative air ions (NAI) are negatively charged single gas molecules or ion clusters in the air. They play a role in maintaining the charge balance of the atmosphere. The main components of air are molecular nitrogen and oxygen. Due to the strong electronegativity of oxygen and oxygen-containing molecules, they can easily capture electrons to form negatively charged air ions, most of which are superoxide radicals ·O2−, so NAI are mainly composed of negative oxygen ions, also called air negative oxygen ions. The ions can be produced by natural means such as lightning, or artificially by methods such as a corona discharge. They can play a role in electrostatic removal of air particulates both for industrial applications and with indoor air, and there are claims that they have a beneficial health effect although the evidence for this is weak. == Generation mechanism == Various negative air ions are formed by combining active neutral molecules and electrons in the gas through a series of ion-molecule reactions. In the air, due to the presence of many water molecules, the negative air ions typically combine with water to form hydrated negative air ions, such as O−·(H2O)n, O2−·(H2O)n, O3−·(H2O)n, OH−·(H2O)n, CO3−·(H2O)n, HCO3−·(H2O)n, CO4−·(H2O)n, NO2−·(H2O)n, NO3−·(H2O)n,


id: negative-air-ions-20260505-1
file: data/en.wikipedia.org/wiki/Negative_air_ions-1.md
category: reference
title: Negative air ions
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Negative_air_ions
date_saved: 2026-05-05T10:55:41.275232+00:00
instance: kb-cron
parent: negative-air-ions-20260505-0
summary:
==== The water vapour method ==== The water vapour method refers to the use of artificial technology and modern instruments to simulate the process of charging via the waterfall effect, using high-speed airflow to collide with water droplets, dispersing larger water droplets into a large number of microdroplets. As the water droplet dispersion occurs, the Leonard effect is active, generating negative ions. The air moving past the water droplets may also lead to triboelectric charging, similar to aircraft "precipitation static" or "P-static"; aircraft typically have one or more static wicks to remove this. == Detection == Detection of negative air ions is divided into measurement and identification. NAI measurement can be achieved by measuring the change in atmospheric conductivity when NAI pass through a conductive tube. NAI identification is typically performed by mass spectrometry, which can effectively identify a variety of negative ions, including O−,O2−,O3−,CO3−,HCO3−,NO3−, etc. == Application of negative air ions == === Environmental improvement === Negative air ions are a component of electrostatic filters which are used to remove dust and particulate pollutants (PM) both in industry and for indoor pollutants. One area that has been studied is the use of a corona-negative ions generator in experiments on


id: negative-refraction-20260505-0
file: data/en.wikipedia.org/wiki/Negative_refraction-0.md
category: reference
title: Negative refraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Negative_refraction
date_saved: 2026-05-05T10:55:42.649705+00:00
instance: kb-cron
parent: negative-refraction-20260505-0
summary:
In optics, negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for electric permittivity (ε) and magnetic permeability (μ); in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials. Negative refraction occurs at interfaces between materials at which one has an ordinary positive phase velocity (i.e., a positive refractive index), and the other has the more exotic negative phase velocity (a negative refractive index). == Negative phase velocity == Negative phase velocity (NPV) is a property of light propagation in a medium. There are different definitions of NPV; the most common is Victor Veselago's original proposal of opposition of the wave vector and (Abraham) the Poynting vector. Other definitions include the opposition of wave vector to group velocity, and energy to velocity. "Phase velocity" is used conventionally, as phase velocity has the same sign as the wave vector. A typical criterion used to determine Veselago's NPV is that the dot product of the Poynting vector and


id: nuclear-fusion-20260505-0
file: data/en.wikipedia.org/wiki/Nuclear_fusion-0.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
Nuclear fusion is a reaction in which two or more atomic nuclei combine to form a larger nucleus. The difference in mass between the reactants and products is manifested as either the release or the absorption of energy. This difference in mass arises as a result of the difference in nuclear binding energy between the atomic nuclei before and after the fusion reaction. Nuclear fusion is the process that powers all active stars, via many reaction pathways. Fusion processes require an extremely large triple product of temperature, density, and confinement time. These conditions occur only in stellar cores, advanced nuclear weapons, and are approached in fusion power experiments. A nuclear fusion process that produces atomic nuclei lighter than nickel-62 is generally exothermic, due to the positive gradient of the nuclear binding energy curve. The most fusible nuclei are among the lightest, especially deuterium, tritium, and helium-3. The opposite process, nuclear fission, is most energetic for very heavy nuclei, especially the actinides. Applications of fusion include fusion power, thermonuclear weapons, boosted fission weapons, neutron sources, and superheavy element production. == History == === Theory === American chemist William Draper Harkins was the first to propose the concept of nuclear fusion in


id: nuclear-fusion-20260505-1
file: data/en.wikipedia.org/wiki/Nuclear_fusion-1.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
While fusion bomb detonations were loosely considered for energy production, the possibility of controlled and sustained reactions remained the scientific focus for peaceful fusion power. Research into developing controlled fusion inside fusion reactors has been ongoing since the 1930s, with Los Alamos National Laboratory's Scylla I device producing the first laboratory thermonuclear fusion in 1958, but the technology is still in its developmental phase. The first experiments producing large amounts of controlled fusion power were the experiments with mixes of deuterium and tritium in Tokamaks. Experiments in the TFTR at the PPPL in Princeton University Princeton NJ, USA during 1993–1996 produced 1.6 GJ of fusion energy. The peak fusion power was 10.3 MW from 3.7×1018 reactions per second, and peak fusion energy created in one discharge was 7.6 MJ. Subsequent experiments in the JET in 1997 achieved a peak fusion power of 16 MW (5.8×1018/s). The central Q, defined as the local fusion power produced to the local applied heating power, is computed to be 1.3. A JET experiment in 2024 produced 69 MJ of fusion power, consuming 0.2 mgm of D and T. The US National Ignition Facility, which uses laser-driven inertial confinement fusion, was designed with a goal


id: nuclear-fusion-20260505-2
file: data/en.wikipedia.org/wiki/Nuclear_fusion-2.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
== In astrophysics == Fusion is responsible for the astrophysical production of the majority of elements lighter than iron. This includes most types of Big Bang nucleosynthesis and stellar nucleosynthesis. Non-fusion processes that contribute include the s-process and r-process in neutron merger and supernova nucleosynthesis, responsible for elements heavier than iron. === Stars === An important fusion process is the stellar nucleosynthesis that powers stars, including the Sun. In the 20th century, it was recognized that the energy released from nuclear fusion reactions accounts for the longevity of stellar heat and light. The fusion of nuclei in a star, starting from its initial hydrogen and helium abundance, provides that energy and synthesizes new nuclei. Different reaction chains are involved, depending on the mass of the star (and therefore the pressure and temperature in its core). Around 1920, Arthur Eddington anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper The Internal Constitution of the Stars. At that time, the source of stellar energy was unknown; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation E = mc2. This was a particularly remarkable development since at that


id: nuclear-fusion-20260505-3
file: data/en.wikipedia.org/wiki/Nuclear_fusion-3.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
A substantial energy barrier of electrostatic forces must be overcome before fusion can occur. At large distances, two naked nuclei repel one another because of the repulsive electrostatic force between their positively charged protons. If two nuclei can be brought close enough together, however, the electrostatic repulsion can be overcome by the quantum effect in which nuclei can tunnel through coulomb forces. When a nucleon such as a proton or neutron is added to a nucleus, the nuclear force attracts it to all the other nucleons of the nucleus (if the atom is small enough), but primarily to its immediate neighbors due to the short range of the force. The nucleons in the interior of a nucleus have more neighboring nucleons than those on the surface. Since smaller nuclei have a larger surface-area-to-volume ratio, the binding energy per nucleon due to the nuclear force generally increases with the size of the nucleus but approaches a limiting value corresponding to that of a nucleus with a diameter of about four nucleons. It is important to keep in mind that nucleons are quantum objects. So, for example, since two neutrons in a nucleus are identical to each other, the goal of distinguishing


id: nuclear-fusion-20260505-4
file: data/en.wikipedia.org/wiki/Nuclear_fusion-4.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
⟨ σ v ⟩ {\displaystyle \langle \sigma v\rangle } increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of 10–100 keV/kB. At these temperatures, well above typical ionization energies (13.6 eV in the hydrogen case), the fusion reactants exist in a plasma state. The significance of ⟨ σ v ⟩ {\displaystyle \langle \sigma v\rangle } as a function of temperature in a device with a particular energy confinement time is found by considering the Lawson criterion. This is an extremely challenging barrier to overcome on Earth, which explains why fusion research has taken many years to reach the current advanced technical state. == Artificial fusion == === Thermonuclear fusion === Thermonuclear fusion is the process of atomic nuclei combining or "fusing" using high temperatures to drive them close enough together for this to become possible. Such temperatures cause the matter to become a plasma and, if confined, fusion reactions may occur due to collisions with extreme thermal kinetic energies of the particles. There are two forms of thermonuclear fusion: uncontrolled, in which the resulting energy is released in an uncontrolled manner, as it is in thermonuclear weapons ("hydrogen bombs") and in most stars; and controlled, where


id: nuclear-fusion-20260505-5
file: data/en.wikipedia.org/wiki/Nuclear_fusion-5.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
=== Muon-catalyzed fusion === Muon-catalyzed fusion is a fusion process that occurs at ordinary temperatures. It was studied in detail by Steven Jones in the early 1980s. Net energy production from this reaction has been unsuccessful because of the high energy required to create muons, their short 2.2 μs half-life, and the high chance that a muon will bind to the new alpha particle and thus stop catalyzing fusion. === Other principles === Some other confinement principles have been investigated. Antimatter-initialized fusion uses small amounts of antimatter to trigger a tiny fusion explosion. This has been studied primarily in the context of making nuclear pulse propulsion, and pure fusion bombs feasible. This is not near becoming a practical power source, due to the cost of manufacturing antimatter alone. Pyroelectric fusion was reported in April 2005 by a team at UCLA. The scientists used a pyroelectric crystal heated from −34 to 7 °C (−29 to 45 °F), combined with a tungsten needle to produce an electric field of about 25 gigavolts per meter to ionize and accelerate deuterium nuclei into an erbium deuteride target. At the estimated energy levels, the D–D fusion reaction may occur, producing helium-3 and a 2.45 MeV


id: nuclear-fusion-20260505-6
file: data/en.wikipedia.org/wiki/Nuclear_fusion-6.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
A third confinement principle is to apply a rapid pulse of energy to a large part of the surface of a pellet of fusion fuel, causing it to simultaneously "implode" and heat to very high pressure and temperature. If the fuel is dense enough and hot enough, the fusion reaction rate will be high enough to burn a significant fraction of the fuel before it has dissipated. To achieve these extreme conditions, the initially cold fuel must be explosively compressed. Inertial confinement is used in the hydrogen bomb, where the driver is x-rays created by a fission bomb. Inertial confinement is also attempted in "controlled" nuclear fusion, where the driver is a laser, ion, or electron beam, or a Z-pinch. Another method is to use conventional high explosive material to compress a fuel to fusion conditions. The UTIAS explosive-driven-implosion facility was used to produce stable, centred and focused hemispherical implosions to generate neutrons from D–D reactions. The simplest and most direct method proved to be in a predetonated stoichiometric mixture of deuterium–oxygen. The other successful method was using a miniature Voitenko compressor, where a plane diaphragm was driven by the implosion wave into a secondary small spherical cavity that contained


id: nuclear-fusion-20260505-7
file: data/en.wikipedia.org/wiki/Nuclear_fusion-7.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
The latter of the two equations was unknown when the U.S. conducted the Castle Bravo fusion bomb test in 1954. Being just the second fusion bomb ever tested (and the first to use lithium), the designers of the Castle Bravo "Shrimp" had understood the usefulness of 6Li in tritium production, but had failed to recognize that 7Li fission would greatly increase the yield of the bomb. While 7Li has a small neutron cross-section for low neutron energies, it has a higher cross section above 5 MeV. The 15 Mt yield was 150% greater than the predicted 6 Mt and caused unexpected exposure to fallout. To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the energy released, one needs to know something about the nuclear cross section. Any given fusion device has a maximum plasma pressure it can sustain, and an economical device would always operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is chosen so that ⟨σv⟩/T2 is a maximum. This is also the temperature at which the value of the triple product nTτ required for ignition is a minimum, since that required value is inversely


id: nuclear-fusion-20260505-8
file: data/en.wikipedia.org/wiki/Nuclear_fusion-8.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
The last column is the neutronicity of the reaction, the fraction of the fusion energy released as neutrons. This is an important indicator of the magnitude of the problems associated with neutrons like radiation damage, biological shielding, remote handling, and safety. For the first two reactions it is calculated as (Efus − Ech)/Efus. For the last two reactions, where this calculation would give zero, the values quoted are rough estimates based on side reactions that produce neutrons in a plasma in thermal equilibrium. Of course, the reactants should also be mixed in the optimal proportions. This is the case when each reactant ion plus its associated electrons accounts for half the pressure. Assuming that the total pressure is fixed, this means that particle density of the non-hydrogenic ion is smaller than that of the hydrogenic ion by a factor 2/(Z + 1). Therefore, the rate for these reactions is reduced by the same factor, on top of any differences in the values of ⟨σv⟩/T2. On the other hand, because the 21D–21D reaction has only one reactant, its rate is twice as high as when the fuel is divided between two different hydrogenic species, thus creating a more efficient reaction. Thus


id: nuclear-fusion-20260505-9
file: data/en.wikipedia.org/wiki/Nuclear_fusion-9.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
The actual ratios of fusion to Bremsstrahlung power will likely be significantly lower for several reasons. For one, the calculation assumes that the energy of the fusion products is transmitted completely to the fuel ions, which then lose energy to the electrons by collisions, which in turn lose energy by Bremsstrahlung. However, because the fusion products move much faster than the fuel ions, they will give up a significant fraction of their energy directly to the electrons. Secondly, the ions in the plasma are assumed to be purely fuel ions. In practice, there will be a significant proportion of impurity ions, which will then lower the ratio. In particular, the fusion products themselves must remain in the plasma until they have given up their energy, and will remain for some time after that in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung have been neglected. The last two factors are related. On theoretical and experimental grounds, particle and energy confinement seem to be closely related. In a confinement scheme that does a good job of retaining energy, fusion products will build up. If the fusion products are efficiently ejected, then energy confinement will be poor,


id: nuclear-fusion-20260505-10
file: data/en.wikipedia.org/wiki/Nuclear_fusion-10.md
category: reference
title: Nuclear fusion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_fusion
date_saved: 2026-05-05T10:55:43.941196+00:00
instance: kb-cron
parent: nuclear-fusion-20260505-0
summary:
Bosch-Hale also reports a R-matrix calculated cross sections fitting observation data with Padé rational approximating coefficients. With energy in units of keV and cross sections in units of millibarn, the factor has the form: S Bosch-Hale ( ϵ ) = A 1 + ϵ ( A 2 + ϵ ( A 3 + ϵ ( A 4 + ϵ A 5 ) ) ) 1 + ϵ ( B 1 + ϵ ( B 2 + ϵ ( B 3 + ϵ B 4 ) ) ) {\displaystyle S^{\text{Bosch-Hale}}(\epsilon )={\frac {A_{1}+\epsilon {\bigg (}A_{2}+\epsilon {\big (}A_{3}+\epsilon (A_{4}+\epsilon A_{5}){\big )}{\bigg )}}{1+\epsilon {\bigg (}B_{1}+\epsilon {\big (}B_{2}+\epsilon (B_{3}+\epsilon B_{4}){\big )}{\bigg )}}}} , with the coefficient values: where σ Bosch-Hale ( ϵ ) = S Bosch-Hale ( ϵ ) ϵ exp ⁡ ( ϵ G / ϵ ) {\displaystyle \sigma ^{\text{Bosch-Hale}}(\epsilon )={\frac {S^{\text{Bosch-Hale}}(\epsilon )}{\epsilon \exp(\epsilon _{G}/{\sqrt {\epsilon }})}}} === Maxwell-averaged nuclear cross sections === In fusion systems that are in thermal equilibrium, the particles are in a Maxwell–Boltzmann distribution, meaning the particles have a range of energies centered around the plasma temperature. The sun, magnetically confined plasmas and inertial confinement fusion systems are well modeled to be in thermal equilibrium. In these cases, the value


id: nuclear-reaction-20260505-0
file: data/en.wikipedia.org/wiki/Nuclear_reaction-0.md
category: reference
title: Nuclear reaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_reaction
date_saved: 2026-05-05T10:55:45.173780+00:00
instance: kb-cron
parent: nuclear-reaction-20260505-0
summary:
In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. If a nucleus interacts with another nucleus or particle, and they then separate without changing the nature of any nuclide, the process is simply referred to as a type of nuclear scattering, rather than a nuclear reaction. In principle, a reaction can involve more than two particles colliding, but because the probability of three or more nuclei to meet at the same time at the same place is much less than for two nuclei, such an event is exceptionally rare (see triple alpha process for an example very close to a three-body nuclear reaction). The term "nuclear reaction" may refer either to a change in a nuclide induced by collision with another particle or to a spontaneous change of a nuclide without collision. Natural nuclear reactions occur in the interaction between cosmic rays and matter, and nuclear reactions can be employed artificially to obtain nuclear energy, at an adjustable rate, on-demand. Nuclear chain


id: nuclear-reaction-20260505-1
file: data/en.wikipedia.org/wiki/Nuclear_reaction-1.md
category: reference
title: Nuclear reaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_reaction
date_saved: 2026-05-05T10:55:45.173780+00:00
instance: kb-cron
parent: nuclear-reaction-20260505-0
summary:
kinetic energy of the product particles (fraction of the kinetic energy of the charged nuclear reaction products can be directly converted into electrostatic energy); emission of very high energy photons, called gamma rays; some energy may remain in the nucleus, as a metastable energy level. When the product nucleus is metastable, this is indicated by placing an asterisk ("*") next to its atomic number. This energy is eventually released through nuclear decay. A small amount of energy may also emerge in the form of X-rays. Generally, the product nucleus has a different atomic number, and thus the configuration of its electron shells is wrong. As the electrons rearrange themselves and drop to lower energy levels, internal transition X-rays (X-rays with precisely defined emission lines) may be emitted. == Q-value and energy balance == In writing down the reaction equation, in a way analogous to a chemical equation, one may, in addition, give the reaction energy on the right side: For the particular case discussed above, the reaction energy has already been calculated as Q = 22.2 MeV. Hence: The reaction energy (the "Q-value") is positive for exothermal reactions and negative for endothermal reactions, opposite to the similar expression in chemistry.


id: nuclear-reaction-20260505-2
file: data/en.wikipedia.org/wiki/Nuclear_reaction-2.md
category: reference
title: Nuclear reaction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Nuclear_reaction
date_saved: 2026-05-05T10:55:45.173780+00:00
instance: kb-cron
parent: nuclear-reaction-20260505-0
summary:
(α,n) and (α,p) reactions. Some of the earliest nuclear reactions studied involved an alpha particle produced by alpha decay, knocking a nucleon from a target nucleus. (d,n) and (d,p) reactions. A deuteron beam impinges on a target; the target nuclei absorb either the neutron or proton from the deuteron. The deuteron is so loosely bound that this is almost the same as proton or neutron capture. A compound nucleus may be formed, leading to additional neutrons being emitted more slowly. (d,n) reactions are used to generate energetic neutrons. The strangeness exchange reaction (K, π) has been used to study hypernuclei. The reaction 14N(α,p)17O performed by Rutherford in 1917 (reported 1919), is generally regarded as the first nuclear transmutation experiment. ==== Reactions with neutrons ==== Reactions with neutrons are important in nuclear reactors and nuclear weapons. While the best-known neutron reactions are neutron scattering, neutron capture, and nuclear fission, for some light nuclei (especially odd-odd nuclei) the most probable reaction with a thermal neutron is a transfer reaction: Some reactions are only possible with fast neutrons: (n,2n) reactions produce small amounts of protactinium-231 and uranium-232 in the thorium cycle which is otherwise relatively free of highly radioactive actinide products. 9Be +


id: observer-effect-physics-20260505-0
file: data/en.wikipedia.org/wiki/Observer_effect_(physics)-0.md
category: reference
title: Observer effect (physics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Observer_effect_(physics)
date_saved: 2026-05-05T10:55:46.414538+00:00
instance: kb-cron
parent: observer-effect-physics-20260505-0
summary:
In physics, the observer effect is the disturbance of a system by the act of observation. This is often the result of utilising instruments that, by necessity, alter the state of what they measure in some manner. A common example is checking the pressure in an automobile tire, which causes some of the air to escape, thereby changing the amount of pressure one observes. Similarly, seeing non-luminous objects requires light hitting the object to cause it to reflect that light. While the effects of observation are often negligible, the object still experiences a change. This effect can be found in many domains of physics, but can usually be reduced to insignificance by using various instruments or observation techniques. A notable example of the observer effect occurs in quantum mechanics, as demonstrated by the double-slit experiment. Physicists have found that observation of quantum phenomena by a detector or an instrument can change the measured results of this experiment. Despite the "observer effect" in the double-slit experiment being caused by the presence of an electronic detector, the experiment's results have been interpreted by some to suggest that a conscious mind can directly affect reality. However, the need for the "observer" to be


id: optogalvanic-effect-20260505-0
file: data/en.wikipedia.org/wiki/Optogalvanic_effect-0.md
category: reference
title: Optogalvanic effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Optogalvanic_effect
date_saved: 2026-05-05T10:55:47.865472+00:00
instance: kb-cron
parent: optogalvanic-effect-20260505-0
summary:
The Optogalvanic effect is the change in the conductivity of a gas discharge induced by a light source (typically a laser). This effect has found many applications in atomic spectroscopy and laser stabilization. == Introduction == In general, neutral atoms/molecules are generated in a gas discharge, and some of these neutral particles will be subsequently ionized, thereby creating a plasma. Incoming light will excite electronic transitions if the energy difference between pairs of atomic/molecular levels is in resonance with a frequency component of this light. Now, the probability and the cross-section to ionize one neutral particle depends on its initial energetic state. This means that light can change the rate at which neutral particles are ionised. Since the medium contains charged particles, it is not surprising that also the electrical properties of the gas discharge can change. == References ==


id: paramagnetism-20260505-0
file: data/en.wikipedia.org/wiki/Paramagnetism-0.md
category: reference
title: Paramagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paramagnetism
date_saved: 2026-05-05T10:55:49.100672+00:00
instance: kb-cron
parent: paramagnetism-20260505-0
summary:
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer. Paramagnetism is due to the presence of unpaired electrons in the material, so most atoms with incompletely filled atomic orbitals are paramagnetic, although exceptions such as copper exist. Due to their spin, unpaired electrons have a magnetic dipole moment and act like tiny magnets. An external magnetic field causes the electrons' spins to align parallel to the field, causing a net attraction. Paramagnetic materials include aluminium, oxygen,


id: paramagnetism-20260505-1
file: data/en.wikipedia.org/wiki/Paramagnetism-1.md
category: reference
title: Paramagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paramagnetism
date_saved: 2026-05-05T10:55:49.100672+00:00
instance: kb-cron
parent: paramagnetism-20260505-0
summary:
==== d and f electrons ==== Stronger magnetic effects are typically only observed when d or f electrons are involved. Particularly the latter are usually strongly localized. Moreover, the size of the magnetic moment on a lanthanide atom can be quite large as it can carry up to 7 unpaired electrons in the case of gadolinium(III) (hence its use in MRI). The high magnetic moments associated with lanthanides is one reason why superstrong magnets are typically based on elements like neodymium or samarium. ==== Molecular localization ==== The above picture is a generalization as it pertains to materials with an extended lattice rather than a molecular structure. Molecular structure can also lead to localization of electrons. Although there are usually energetic reasons why a molecular structure results such that it does not exhibit partly filled orbitals (i.e. unpaired spins), some non-closed shell moieties do occur in nature. Molecular oxygen is a good example. Even in the frozen solid it contains di-radical molecules resulting in paramagnetic behavior. The unpaired spins reside in orbitals derived from oxygen p wave functions, but the overlap is limited to the one neighbor in the O2 molecules. The distances to other oxygen atoms in the lattice


id: paramagnetism-20260505-2
file: data/en.wikipedia.org/wiki/Paramagnetism-2.md
category: reference
title: Paramagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paramagnetism
date_saved: 2026-05-05T10:55:49.100672+00:00
instance: kb-cron
parent: paramagnetism-20260505-0
summary:
n ↑ ≈ n e 2 − μ 0 μ B 2 g ( E F ) H ; ( n ↓ ≈ n e 2 + μ 0 μ B 2 g ( E F ) H ) , {\displaystyle n_{\uparrow }\approx {\frac {n_{\text{e}}}{2}}-{\frac {\mu _{0}\mu _{\mathrm {B} }}{2}}g(E_{\mathrm {F} })H\quad ;\quad \left(n_{\downarrow }\approx {\frac {n_{\text{e}}}{2}}+{\frac {\mu _{0}\mu _{\mathrm {B} }}{2}}g(E_{\mathrm {F} })H\right),} with n e {\displaystyle n_{\text{e}}} the total free-electron density and g ( E F ) {\displaystyle g(E_{\mathrm {F} })} the electronic density of states (number of states per energy per volume) at the Fermi energy E F {\displaystyle E_{\mathrm {F} }} . In this approximation the magnetization is given as the magnetic moment of one electron times the difference in densities: M = μ B ( n ↓ − n ↑ ) = μ 0 μ B 2 g ( E F ) H , {\displaystyle M=\mu _{\mathrm {B} }(n_{\downarrow }-n_{\uparrow })=\mu _{0}\mu _{\mathrm {B} }^{2}g(E_{\mathrm {F} })H,} which yields a positive paramagnetic susceptibility independent of temperature: χ P = μ 0 μ B 2 g ( E F ) . {\displaystyle \chi _{\mathrm {P} }=\mu _{0}\mu _{\mathrm {B} }^{2}g(E_{\mathrm {F} }).} The Pauli paramagnetic susceptibility


id: paramagnetism-20260505-3
file: data/en.wikipedia.org/wiki/Paramagnetism-3.md
category: reference
title: Paramagnetism
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Paramagnetism
date_saved: 2026-05-05T10:55:49.100672+00:00
instance: kb-cron
parent: paramagnetism-20260505-0
summary:
As stated above, many materials that contain d- or f-elements do retain unquenched spins. Salts of such elements often show paramagnetic behavior but at low enough temperatures the magnetic moments may order. It is not uncommon to call such materials 'paramagnets', when referring to their paramagnetic behavior above their Curie or Néel-points, particularly if such temperatures are very low or have never been properly measured. Even for iron it is not uncommon to say that iron becomes a paramagnet above its relatively high Curie-point. In that case the Curie-point is seen as a phase transition between a ferromagnet and a 'paramagnet'. The word paramagnet now merely refers to the linear response of the system to an applied field, the temperature dependence of which requires an amended version of Curie's law, known as the Curie–Weiss law: M = C T − θ H {\displaystyle \mathbf {M} ={\frac {C}{T-\theta }}\mathbf {H} } This amended law includes a term θ that describes the exchange interaction that is present albeit overcome by thermal motion. The sign of θ depends on whether ferro- or antiferromagnetic interactions dominate and it is seldom exactly zero, except in the dilute, isolated cases mentioned above. Obviously, the paramagnetic Curie–Weiss


id: phase-transition-20260505-0
file: data/en.wikipedia.org/wiki/Phase_transition-0.md
category: reference
title: Phase transition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_transition
date_saved: 2026-05-05T10:55:50.323304+00:00
instance: kb-cron
parent: phase-transition-20260505-0
summary:
In physics, chemistry and biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. == Types == === States of matter === Phase transitions commonly refer to when a substance transforms between one of the four states of matter to another. At the phase transition point for a substance, for instance the boiling point, the two phases involved - liquid and vapor, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is


id: phase-transition-20260505-1
file: data/en.wikipedia.org/wiki/Phase_transition-1.md
category: reference
title: Phase transition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_transition
date_saved: 2026-05-05T10:55:50.323304+00:00
instance: kb-cron
parent: phase-transition-20260505-0
summary:
Transition to a mesophase between solid and liquid, such as one of the "liquid crystal" phases. The dependence of the adsorption geometry on coverage and temperature, such as for hydrogen on iron (110). The emergence of superconductivity in certain metals and ceramics when cooled below a critical temperature. The emergence of metamaterial properties in artificial photonic media as their parameters are varied. Quantum condensation of bosonic fluids (Bose–Einstein condensation). The superfluid transition in liquid helium is an example of this. The breaking of symmetries in the laws of physics during the early history of the universe as its temperature cooled. Isotope fractionation occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. When water vapor condenses (an equilibrium fractionation), the heavier water isotopes (18O and 2H) become enriched in the liquid phase while the lighter isotopes (16O and 1H) tend toward the vapor phase. Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables (cf. phases). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are small. Phase transitions can


id: phase-transition-20260505-2
file: data/en.wikipedia.org/wiki/Phase_transition-2.md
category: reference
title: Phase transition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_transition
date_saved: 2026-05-05T10:55:50.323304+00:00
instance: kb-cron
parent: phase-transition-20260505-0
summary:
In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes: First-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water. (Water does not instantly turn into vapor, but forms a turbulent mixture of liquid water and vapor bubbles.) Related primary research reports have suggested that quenched disorder can broaden a first-order transition: that while transformation is completed over a finite range of temperatures, phenomena like supercooling and superheating survive, and hysteresis is observed on thermal cycling. Second-order phase transitions, also called "continuous phase transitions", are characterized by a divergent susceptibility—the change of an extensive property under variation of an intensive property), an infinite correlation length, and a power law decay of correlations near criticality. Examples of second-order phase transitions are the ferromagnetic


id: phase-transition-20260505-3
file: data/en.wikipedia.org/wiki/Phase_transition-3.md
category: reference
title: Phase transition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_transition
date_saved: 2026-05-05T10:55:50.323304+00:00
instance: kb-cron
parent: phase-transition-20260505-0
summary:
=== Order parameters === An order parameter is a measure of the degree of order across the boundaries in a phase transition system; it normally takes on the value of zero in one phase (usually above the critical point) and nonzero in the other. At the critical point, the order parameter susceptibility (the change of an extensive property under variation of an intensive property) will usually diverge. An example of an order parameter is the net magnetization in a ferromagnetic system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities. From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the ferromagnetic phase, one must provide the net magnetization, whose direction was spontaneously chosen when the system cooled below the Curie point. However, note that order parameters can also be defined for non-symmetry-breaking transitions. Some phase transitions, such as superconducting and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even


id: phase-transition-20260505-4
file: data/en.wikipedia.org/wiki/Phase_transition-4.md
category: reference
title: Phase transition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_transition
date_saved: 2026-05-05T10:55:50.323304+00:00
instance: kb-cron
parent: phase-transition-20260505-0
summary:
It can be shown that there are only two independent exponents, e.g. ν and η. It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as universality. For example, the critical exponents at the liquid–gas critical point have been found to be independent of the chemical composition of the fluid. More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the correlation length is the essential point. === Critical phenomena === There are also other critical phenomena; e.g., besides static functions there is also critical dynamics. As a consequence, at a phase transition one may observe critical slowing down or speeding up. Connected to the previous phenomenon is also


id: phase-transition-20260505-5
file: data/en.wikipedia.org/wiki/Phase_transition-5.md
category: reference
title: Phase transition
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Phase_transition
date_saved: 2026-05-05T10:55:50.323304+00:00
instance: kb-cron
parent: phase-transition-20260505-0
summary:
== Further reading == Nishimori, Hidetoshi; Ortiz, Gerardo (2010). Elements of Phase Transitions and Critical Phenomena. Oxford University Press. ISBN 9780191722943. Faghri, A., and Zhang, Y., Fundamentals of Multiphase Heat Transfer and Flow Archived 14 June 2021 at the Wayback Machine, Springer Nature Switzerland AG, 2020. Fisher, M.E. (1974). "The renormalization group in the theory of critical behavior". Rev. Mod. Phys. 46 (4): 597–616. Bibcode:1974RvMP...46..597F. doi:10.1103/revmodphys.46.597. Goldenfeld, N., Lectures on Phase Transitions and the Renormalization Group, Perseus Publishing (1992). Ivancevic, Vladimir G; Ivancevic, Tijana T (2008), Chaos, Phase Transitions, Topology Change and Path Integrals, Berlin: Springer, ISBN 978-3-540-79356-4, retrieved 14 March 2013 M.R. Khoshbin-e-Khoshnazar, Ice Phase Transition as a sample of finite system phase transition, (Physics Education (India) Volume 32. No. 2, Apr - Jun 2016) Archived 29 April 2025 at the Wayback Machine Kleinert, H., Gauge Fields in Condensed Matter, Vol. I, "Superfluidity and Vortex lines; Disorder Fields, Phase Transitions", pp. 1–742, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0 (physik.fu-berlin.de readable online Archived 27 May 2008 at the Wayback Machine) Kleinert, Hagen; Verena Schulte-Frohlinde (2001). Critical Properties of φ4-Theories. World Scientific. ISBN 981-02-4659-5. Archived from the original on 26 February 2008. (readable online Archived 29 June 2008 at the


id: photon-polarization-20260505-0
file: data/en.wikipedia.org/wiki/Photon_polarization-0.md
category: reference
title: Photon polarization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Photon_polarization
date_saved: 2026-05-05T10:55:51.584316+00:00
instance: kb-cron
parent: photon-polarization-20260505-0
summary:
Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two. The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well. Polarization is an example of a qubit degree of freedom, which forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations in the description. The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave. Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through lossless media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations


id: photon-polarization-20260505-1
file: data/en.wikipedia.org/wiki/Photon_polarization-1.md
category: reference
title: Photon polarization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Photon_polarization
date_saved: 2026-05-05T10:55:51.584316+00:00
instance: kb-cron
parent: photon-polarization-20260505-0
summary:
| ψ ⟩ = d e f ( ψ x ψ y ) = ( cos ⁡ θ exp ⁡ ( i α x ) sin ⁡ θ exp ⁡ ( i α y ) ) . {\displaystyle |\psi \rangle \ {\stackrel {\mathrm {def} }{=}}\ {\begin{pmatrix}\psi _{x}\\\psi _{y}\end{pmatrix}}={\begin{pmatrix}\cos \theta \exp \left(i\alpha _{x}\right)\\\sin \theta \exp \left(i\alpha _{y}\right)\end{pmatrix}}.} ==== Geometric visualization of an arbitrary polarization state ==== To get an understanding of what a polarization state looks like, one can observe the orbit that is made if the polarization state is multiplied by a phase factor of e i ω t {\displaystyle e^{i\omega t}} and then having the real parts of its components interpreted as x and y coordinates respectively. That is: ( x ( t ) y ( t ) ) = ( ℜ ( e i ω t ψ x ) ℜ ( e i ω t ψ y ) ) = ℜ [ e i ω t ( ψ x ψ y ) ] = ℜ ( e i ω t | ψ ⟩ ) . {\displaystyle {\begin{pmatrix}x(t)\\y(t)\end{pmatrix}}={\begin{pmatrix}\Re (e^{i\omega t}\psi _{x})\\\Re (e^{i\omega t}\psi _{y})\end{pmatrix}}=\Re \left[e^{i\omega t}{\begin{pmatrix}\psi _{x}\\\psi _{y}\end{pmatrix}}\right]=\Re \left(e^{i\omega t}|\psi \rangle \right).} If only the traced out shape and


id: photon-polarization-20260505-2
file: data/en.wikipedia.org/wiki/Photon_polarization-2.md
category: reference
title: Photon polarization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Photon_polarization
date_saved: 2026-05-05T10:55:51.584316+00:00
instance: kb-cron
parent: photon-polarization-20260505-0
summary:
A linear filter transmits one component of a plane wave and absorbs the perpendicular component. In that case, if the filter is polarized in the x direction, the fraction of energy passing through the filter is f x = ψ x ∗ ψ x = cos 2 ⁡ θ . {\displaystyle f_{x}=\psi _{x}^{*}\psi _{x}=\cos ^{2}\theta .\,} === Example of energy conservation: Passage of a classical wave through a birefringent crystal === An ideal birefringent crystal transforms the polarization state of an electromagnetic wave without loss of wave energy. Birefringent crystals therefore provide an ideal test bed for examining the conservative transformation of polarization states. Even though this treatment is still purely classical, standard quantum tools such as unitary and Hermitian operators that evolve the state in time naturally emerge. ==== Initial and final states ==== A birefringent crystal is a material that has an optic axis with the property that the light has a different index of refraction for light polarized parallel to the axis than it has for light polarized perpendicular to the axis. Light polarized parallel to the axis are called "extraordinary rays" or "extraordinary photons", while light polarized perpendicular to the axis are called "ordinary rays" or


id: photon-polarization-20260505-3
file: data/en.wikipedia.org/wiki/Photon_polarization-3.md
category: reference
title: Photon polarization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Photon_polarization
date_saved: 2026-05-05T10:55:51.584316+00:00
instance: kb-cron
parent: photon-polarization-20260505-0
summary:
The photon energy can be related to classical fields through the correspondence principle that states that for a large number of photons, the quantum and classical treatments must agree. Thus, for very large N {\displaystyle N} , the quantum energy density must be the same as the classical energy density N ℏ ω V = E c = | E | 2 8 π . {\displaystyle {N\hbar \omega \over V}={\mathcal {E}}_{c}={\frac {\vert \mathbf {E} \vert ^{2}}{8\pi }}.} The number of photons in the box is then N = V 8 π ℏ ω | E | 2 . {\displaystyle N={\frac {V}{8\pi \hbar \omega }}\vert \mathbf {E} \vert ^{2}.} ==== Momentum ==== The correspondence principle also determines the momentum and angular momentum of the photon. For momentum P z = N ℏ ω c V = N ℏ k z V {\displaystyle {\mathcal {P}}_{z}={N\hbar \omega \over cV}={N\hbar k_{z} \over V}} where k z {\displaystyle k_{z}} is the wave number. This implies that the momentum of a photon is p z = ℏ k z . {\displaystyle p_{z}=\hbar k_{z}.\,} ==== Angular momentum and spin ==== Similarly for the spin angular momentum L = 1 ω E c ( | ψ R |


id: photon-polarization-20260505-4
file: data/en.wikipedia.org/wiki/Photon_polarization-4.md
category: reference
title: Photon polarization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Photon_polarization
date_saved: 2026-05-05T10:55:51.584316+00:00
instance: kb-cron
parent: photon-polarization-20260505-0
summary:
To see this, note S ^ d exp ⁡ ( i α x − i s θ ) | s ⟩ → i ∂ ∂ θ exp ⁡ ( i α x − i s θ ) | s ⟩ = s [ exp ⁡ ( i α x − i s θ ) | s ⟩ ] . {\displaystyle {\hat {S}}_{d}\exp \left(i\alpha _{x}-is\theta \right)|s\rangle \rightarrow i{\partial \over \partial \theta }\exp \left(i\alpha _{x}-is\theta \right)|s\rangle =s\left[\exp \left(i\alpha _{x}-is\theta \right)|s\rangle \right].} The spin angular momentum operator is l ^ z = ℏ S ^ d . {\displaystyle {\hat {l}}_{z}=\hbar {\hat {S}}_{d}.} === Nature of probability in quantum mechanics === ==== Probability for a single photon ==== There are two ways in which probability can be applied to the behavior of photons; probability can be used to calculate the probable number of photons in a particular state, or probability can be used to calculate the likelihood of a single photon to be in a particular state. The former interpretation violates energy conservation. The latter interpretation is the viable, if nonintuitive, option. Dirac explains this in the context of the double-slit experiment: Some time before the discovery of quantum mechanics people realized that the


id: photon-polarization-20260505-5
file: data/en.wikipedia.org/wiki/Photon_polarization-5.md
category: reference
title: Photon polarization
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Photon_polarization
date_saved: 2026-05-05T10:55:51.584316+00:00
instance: kb-cron
parent: photon-polarization-20260505-0
summary:
==== Application to angular momentum ==== The connection to physics can be made if we identify the operators with physical operators such as the angular momentum and the polarization angle. We have then Δ ψ L ^ z Δ ψ θ ≥ ℏ 2 , {\displaystyle \Delta _{\psi }{\hat {L}}_{z}\,\Delta _{\psi }{\theta }\geq {\frac {\hbar }{2}},} which means that angular momentum and the polarization angle cannot be measured simultaneously with infinite accuracy. (The polarization angle can be measured by checking whether the photon can pass through a polarizing filter oriented at a particular angle, or a polarizing beam splitter. This results in a yes/no answer that, if the photon was plane-polarized at some other angle, depends on the difference between the two angles.) === States, probability amplitudes, unitary and Hermitian operators, and eigenvectors === Much of the mathematical apparatus of quantum mechanics appears in the classical description of a polarized sinusoidal electromagnetic wave. The Jones vector for a classical wave, for instance, is identical with the quantum polarization state vector for a photon. The right and left circular components of the Jones vector can be interpreted as probability amplitudes of spin states of the photon. Energy conservation requires that the


id: photophoresis-20260505-0
file: data/en.wikipedia.org/wiki/Photophoresis-0.md
category: reference
title: Photophoresis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Photophoresis
date_saved: 2026-05-05T10:55:52.870083+00:00
instance: kb-cron
parent: photophoresis-20260505-0
summary:
Photophoresis denotes the phenomenon that small particles suspended in gas (aerosols) or liquids (hydrocolloids) start to migrate when illuminated by a sufficiently intense beam of light. The existence of this phenomenon is owed to a non-uniform distribution of temperature of an illuminated particle in a fluid medium. Separately from photophoresis, in a fluid mixture of different kinds of particles, the migration of some kinds of particles may be due to differences in their absorptions of thermal radiation and other thermal effects collectively known as thermophoresis. In laser photophoresis, particles migrate once they have a refractive index different from their surrounding medium. The migration of particles is usually possible when the laser is slightly or not focused. A particle with a higher refractive index compared to its surrounding molecule moves away from the light source due to momentum transfer from absorbed and scattered light photons. This is referred to as a radiation pressure force. This force depends on light intensity and particle size but has nothing to do with the surrounding medium. Just like in Crookes radiometer, light can heat up one side and gas molecules bounce from that surface with greater velocity, hence push the particle to the other side.


id: physical-change-20260505-0
file: data/en.wikipedia.org/wiki/Physical_change-0.md
category: reference
title: Physical change
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physical_change
date_saved: 2026-05-05T10:55:54.160341+00:00
instance: kb-cron
parent: physical-change-20260505-0
summary:
Physical changes are changes affecting the form of a chemical substance, but not its chemical composition. Physical changes are used to separate mixtures into their component compounds, but can not usually be used to separate compounds into chemical elements or simpler compounds. Physical changes occur when objects or substances undergo a change that does not change their chemical composition. This contrasts with the concept of chemical change in which the composition of a substance changes or one or more substances combine or break up to form new substances. In general a physical change is reversible using physical means. For example, salt dissolved in water can be recovered by allowing the water to evaporate. A physical change involves a change in physical properties. Examples of physical properties include melting, transition to a gas, change of strength, change of durability, changes to crystal form, textural change, shape, size, color, volume and density. An example of a physical change is the process of tempering steel to form a knife blade. A steel blank is repeatedly heated and hammered which changes the hardness of the steel, its flexibility and its ability to maintain a sharp edge. Many physical changes also involve the rearrangement of


id: physical-property-20260505-0
file: data/en.wikipedia.org/wiki/Physical_property-0.md
category: reference
title: Physical property
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Physical_property
date_saved: 2026-05-05T10:55:55.382806+00:00
instance: kb-cron
parent: physical-property-20260505-0
summary:
A physical property is any property of a physical system that is measurable. The changes in the physical properties of a system can be used to describe its changes between momentary states. A quantifiable physical property is called physical quantity. Measurable physical quantities are often referred to as observables. Some physical properties are qualitative, such as shininess, brittleness, etc.; some general qualitative properties admit more specific related quantitative properties, such as in opacity, hardness, ductility, viscosity, etc. Physical properties are often characterized as intensive and extensive properties. An intensive property does not depend on the size or extent of the system, nor on the amount of matter in the object, while an extensive property shows an additive relationship. These classifications are in general only valid in cases when smaller subdivisions of the sample do not interact in some physical or chemical process when combined. Properties may also be classified with respect to the directionality of their nature. For example, isotropic properties do not change with the direction of observation, and anisotropic properties do have directional variance. It may be difficult to determine whether a given property is a material property or not. Color, for example, can be seen and measured;


id: piston-effect-20260505-0
file: data/en.wikipedia.org/wiki/Piston_effect-0.md
category: reference
title: Piston effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Piston_effect
date_saved: 2026-05-05T10:55:56.703725+00:00
instance: kb-cron
parent: piston-effect-20260505-0
summary:
Piston effect refers to the forced-air flow inside a tunnel or shaft caused by moving vehicles. It is one of numerous phenomena that engineers and designers must consider when developing a range of structures. == Cause == In open air, when a vehicle travels along, air pushed aside can move in any direction except into the ground. Inside a tunnel, air is confined by the tunnel walls to move along the tunnel. Behind the moving vehicle, as air has been pushed away, suction is created, and air is pulled to flow into the tunnel. In addition, because of fluid viscosity, the surface of the vehicle drags the air to flow with vehicle, a force experienced as skin drag by the vehicle. This movement of air by the vehicle is analogous to the operation of a mechanical piston as inside a reciprocating compressor gas pump, hence the name "piston effect". The effect is also similar to the pressure fluctuations inside drainage pipes as waste water pushes air in front of it. The piston effect is very pronounced in railway tunnels, because the cross sectional area of trains is large and in many cases almost completely fills the tunnel cross section. The


id: pouillet-effect-20260505-0
file: data/en.wikipedia.org/wiki/Pouillet_effect-0.md
category: reference
title: Pouillet effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pouillet_effect
date_saved: 2026-05-05T10:55:57.966508+00:00
instance: kb-cron
parent: pouillet-effect-20260505-0
summary:
In physics and chemical engineering, the term Pouillet effect refers to an exothermic reaction that takes place when a liquid is added to a powder. Strictly speaking, the heat generated is caused by adhesion of the liquid to the surface of the particles rather than by a chemical reaction. It was first observed in 1802 by physicist John Leslie, who noted that heat was evolved when dry sawdust was wetted with water. Claude Pouillet later described this phenomenon in 1822, and it subsequently became known as the Pouillet effect in France, and then elsewhere. == Negative Pouillet effect == Under certain conditions, a negative Pouillet effect is possible, i.e., heat can be absorbed instead of being released. G. Schwalbe showed that in the case of water below 4 degrees Celsius, the temperature of the system decreases. Joseph Mellor argued that this is due to the negative thermal expansion coefficient of water between 0 and 4 degrees Celsius, with the temperature change Δ T {\displaystyle \Delta T} given by Δ T = α T C p D Δ P {\displaystyle \Delta T={{\alpha T} \over {C_{p}D}}\Delta P} where α {\displaystyle \alpha } is the thermal expansion coefficient, C P {\displaystyle C_{P}} is


id: prandtl-glauert-singularity-20260505-0
file: data/en.wikipedia.org/wiki/Prandtl–Glauert_singularity-0.md
category: reference
title: Prandtl–Glauert singularity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Prandtl–Glauert_singularity
date_saved: 2026-05-05T10:55:59.299675+00:00
instance: kb-cron
parent: prandtl-glauert-singularity-20260505-0
summary:
The Prandtl–Glauert singularity is a theoretical construct in flow physics, often incorrectly used to explain vapor cones in transonic flows. It is the prediction by the Prandtl–Glauert transformation that infinite pressures would be experienced by an aircraft as it approaches the speed of sound. Because it is invalid to apply the transformation at these speeds, the predicted singularity does not emerge. The incorrect association is related to the early-20th-century misconception of the impenetrability of the sound barrier. == Reasons of invalidity around Mach 1 == The Prandtl–Glauert transformation assumes linearity (i.e. a small change will have a small effect that is proportional to its size). This assumption becomes inaccurate toward Mach 1 and is entirely invalid in places where the flow reaches supersonic speeds, since sonic shock waves are instantaneous (and thus manifestly non-linear) changes in the flow. Indeed, one assumption in the Prandtl–Glauert transformation is approximately constant Mach number throughout the flow, and the increasing slope in the transformation indicates that very small changes will have a very strong effect at higher Mach numbers, thus violating the assumption, which breaks down entirely at the speed of sound. This means that the singularity featured by the transformation near the sonic


id: pulse-physics-20260505-0
file: data/en.wikipedia.org/wiki/Pulse_(physics)-0.md
category: reference
title: Pulse (physics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Pulse_(physics)
date_saved: 2026-05-05T10:56:00.562549+00:00
instance: kb-cron
parent: pulse-physics-20260505-0
summary:
In physics, a pulse is an individual disturbance that propagates through a transmission medium. This medium may be vacuum (in the case of electromagnetic radiation) or matter, and may be indefinitely large or finite. Pulse movement and changes can often be described by a partial differential equation (PDE), such as a hyperbolic PDE or a parabolic PDE, which corresponds to the specific type of disturbance. == Reflection of a wave-like pulse == Consider a deformation pulse moving through an elastic medium - perhaps through a rope or a slinky. When the pulse reaches the end of that medium, what happens to it depends on whether the medium is fixed in space or free to move at its end. For example, if the pulse is moving through a rope and the end of the rope is held firmly by a person, then it is said that the pulse is approaching a fixed end. On the other hand, if the end of the rope is fixed to a stick such that it is free to move up or down along the stick when the pulse reaches its end, then it is said that the pulse is approaching a free end. === Free


id: quantization-physics-20260505-0
file: data/en.wikipedia.org/wiki/Quantization_(physics)-0.md
category: reference
title: Quantization (physics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantization_(physics)
date_saved: 2026-05-05T10:56:01.873549+00:00
instance: kb-cron
parent: quantization-physics-20260505-0
summary:
Quantization (in British English quantisation) is the systematic transition procedure from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. It is a procedure for constructing quantum mechanics from classical mechanics. A generalization involving infinite degrees of freedom is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance as light quanta). This procedure is basic to theories of atomic physics, chemistry, particle physics, nuclear physics, condensed matter physics, and quantum optics. == Historical overview == In 1901, when Max Planck was developing the distribution function of statistical mechanics to solve the ultraviolet catastrophe problem, he realized that the properties of blackbody radiation can be explained by the assumption that the amount of energy must be in countable fundamental units, i.e. amount of energy is not continuous but discrete. That is, a minimum unit of energy exists and the following relationship holds E = h ν {\displaystyle E=h\nu } for the frequency ν {\displaystyle \nu } . Here, h {\displaystyle h} is called the Planck constant, which represents the amount of the quantum mechanical effect. It means a fundamental change of mathematical model of physical quantities. In


id: quantization-physics-20260505-1
file: data/en.wikipedia.org/wiki/Quantization_(physics)-1.md
category: reference
title: Quantization (physics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quantization_(physics)
date_saved: 2026-05-05T10:56:01.873549+00:00
instance: kb-cron
parent: quantization-physics-20260505-0
summary:
In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest. For example, the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics should be built in. A more geometric approach to quantization, in which the classical phase space can be a general symplectic manifold, was developed in the 1970s by Bertram Kostant and Jean-Marie Souriau. The method proceeds in two stages. First, once constructs a "prequantum Hilbert space" consisting of square-integrable functions (or, more properly, sections of a line bundle) over the phase space. Here one can construct operators satisfying commutation relations corresponding exactly to the classical Poisson-bracket relations. On the other hand, this prequantum Hilbert space is too big to be physically meaningful. One then restricts to functions (or sections) depending on half the variables on the phase space, yielding the quantum Hilbert space. == Path integral quantization == A classical mechanical theory is given by an


id: quasiparticle-20260505-0
file: data/en.wikipedia.org/wiki/Quasiparticle-0.md
category: reference
title: Quasiparticle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quasiparticle
date_saved: 2026-05-05T10:56:03.122412+00:00
instance: kb-cron
parent: quasiparticle-20260505-0
summary:
In condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely related phenomena that arise when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For example, as an electron travels through a semiconductor, its motion is disturbed in a complex way by its interactions with other electrons and with atomic nuclei. The electron behaves as though it has a different effective mass travelling unperturbed in vacuum. Such an electron is called an electron quasiparticle. In another example, the aggregate motion of electrons in the valence band of a semiconductor or a hole band in a metal behave as though the material instead contained positively charged quasiparticles called electron holes. Other quasiparticles or collective excitations include the phonon, a quasiparticle derived from the vibrations of atoms in a solid, and the plasmon, a particle derived from plasma oscillation. These phenomena are typically called quasiparticles if they are related to fermions, and called collective excitations if they are related to bosons, although the precise


id: quasiparticle-20260505-1
file: data/en.wikipedia.org/wiki/Quasiparticle-1.md
category: reference
title: Quasiparticle
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Quasiparticle
date_saved: 2026-05-05T10:56:03.122412+00:00
instance: kb-cron
parent: quasiparticle-20260505-0
summary:
=== Distinction between quasiparticles and collective excitations === Usually, an elementary excitation is called a "quasiparticle" if it is a fermion and a "collective excitation" if it is a boson. However, the precise distinction is not universally agreed upon. There is a difference in the way that quasiparticles and collective excitations are intuitively envisioned. A quasiparticle is usually thought of as being like a dressed particle: it is built around a real particle at its "core", but the behavior of the particle is affected by the environment. A standard example is the "electron quasiparticle": an electron in a crystal behaves as if it had an effective mass which differs from its real mass. On the other hand, a collective excitation is usually imagined to be a reflection of the aggregate behavior of the system, with no single real particle at its "core". A standard example is the phonon, which characterizes the vibrational motion of every atom in the crystal. However, these two visualizations leave some ambiguity. For example, a magnon in a ferromagnet can be considered in one of two perfectly equivalent ways: (a) as a mobile defect (a misdirected spin) in a perfect alignment of magnetic moments or (b)


id: radiation-20260505-0
file: data/en.wikipedia.org/wiki/Radiation-0.md
category: reference
title: Radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Radiation
date_saved: 2026-05-05T10:56:04.366371+00:00
instance: kb-cron
parent: radiation-20260505-0
summary:
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: electromagnetic radiation consisting of photons, such as radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation (γ) particle radiation consisting of particles of non-zero rest energy, such as alpha radiation (α), beta radiation (β), proton radiation and neutron radiation acoustic radiation, such as ultrasound, sound, and seismic waves, all dependent on a physical transmission medium gravitational radiation, in the form of gravitational waves, ripples in spacetime Radiation is often categorized as either ionizing or non-ionizing depending on the energy of the radiated particles. Ionizing radiation carries more than 10 electron volts (eV), which is enough to ionize atoms and molecules and break chemical bonds. This is an important distinction due to the large difference in harmfulness to living organisms. A common source of ionizing radiation is radioactive materials that emit α, β, or γ radiation, consisting of helium nuclei, electrons or positrons, and photons, respectively. Other sources include X-rays from medical radiography examinations and muons, mesons, positrons, neutrons and other particles that constitute the secondary cosmic rays that are produced after primary cosmic


id: radiation-20260505-1
file: data/en.wikipedia.org/wiki/Radiation-1.md
category: reference
title: Radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Radiation
date_saved: 2026-05-05T10:56:04.366371+00:00
instance: kb-cron
parent: radiation-20260505-0
summary:
Ionizing radiation has many practical uses in medicine, research, and construction, but presents a health hazard if used improperly. Exposure to radiation causes damage to living tissue; high doses result in Acute radiation syndrome (ARS), with skin burns, hair loss, internal organ failure, and death, while any dose may result in an increased chance of cancer and genetic damage; a particular form of cancer, thyroid cancer, often occurs when nuclear weapons and reactors are the radiation source because of the biological proclivities of the radioactive iodine fission product, iodine-131. However, calculating the exact risk and chance of cancer forming in cells caused by ionizing radiation is still not well understood, and currently estimates are loosely determined by population-based data from the atomic bombings of Hiroshima and Nagasaki and from follow-up of reactor accidents, such as the Chernobyl disaster. The International Commission on Radiological Protection states that "The Commission is aware of uncertainties and lack of precision of the models and parameter values", "Collective effective dose is not intended as a tool for epidemiological risk assessment, and it is inappropriate to use it in risk projections" and "in particular, the calculation of the number of cancer deaths based on collective effective


id: radiation-20260505-2
file: data/en.wikipedia.org/wiki/Radiation-2.md
category: reference
title: Radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Radiation
date_saved: 2026-05-05T10:56:04.366371+00:00
instance: kb-cron
parent: radiation-20260505-0
summary:
Alpha particles are helium-4 nuclei (two protons and two neutrons). They interact with matter strongly due to their charges and combined mass, and at their usual velocities only penetrate a few centimetres of air, or a few millimetres of low density material (such as the thin mica material which is specially placed in some Geiger counter tubes to allow alpha particles in). This means that alpha particles from ordinary alpha decay do not penetrate the outer layers of dead skin cells and cause no damage to the live tissues below. Some very high energy alpha particles compose about 10% of cosmic rays, and these are capable of penetrating the body and even thin metal plates. However, they are of danger only to astronauts, since they are deflected by the Earth's magnetic field and then stopped by its atmosphere. Alpha radiation is dangerous when alpha-emitting radioisotopes are inhaled or ingested (breathed or swallowed). This brings the radioisotope close enough to sensitive live tissue for the alpha radiation to damage cells. Per unit of energy, alpha particles are at least 20 times more effective at cell-damage than gamma rays and X-rays. See relative biological effectiveness for a discussion of this. Examples of


id: radiation-20260505-3
file: data/en.wikipedia.org/wiki/Radiation-3.md
category: reference
title: Radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Radiation
date_saved: 2026-05-05T10:56:04.366371+00:00
instance: kb-cron
parent: radiation-20260505-0
summary:
There are two sources of high energy particles entering the Earth's atmosphere from outer space: the sun and deep space. The sun continuously emits particles, primarily free protons, in the solar wind, and occasionally augments the flow hugely with coronal mass ejections (CME). The particles from deep space (inter- and extra-galactic) are much less frequent, but of much higher energies. These particles are also mostly protons, with much of the remainder consisting of helions (alpha particles). A few completely ionized nuclei of heavier elements are present. The origin of these galactic cosmic rays is not yet well understood, but they seem to be remnants of supernovae and especially gamma-ray bursts (GRB), which feature magnetic fields capable of the huge accelerations measured from these particles. They may also be generated by quasars, which are galaxy-wide jet phenomena similar to GRBs but known for their much larger size, and which seem to be a violent part of the universe's early history. == Non-ionizing radiation == The kinetic energy of particles of non-ionizing radiation is too small to produce charged ions when passing through matter. For non-ionizing electromagnetic radiation (see types below), the associated particles (photons) have only sufficient energy to change the


id: radiation-20260505-4
file: data/en.wikipedia.org/wiki/Radiation-4.md
category: reference
title: Radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Radiation
date_saved: 2026-05-05T10:56:04.366371+00:00
instance: kb-cron
parent: radiation-20260505-0
summary:
=== Very low frequency === Very low frequency (VLF) refers to a frequency range of 30 Hz to 3 kHz which corresponds to wavelengths of 100000 to 10000 m respectively. Since there is not much bandwidth in this range of the radio spectrum, only the very simplest signals can be transmitted, such as for radio navigation. Also known as the myriametre band or myriametre wave as the wavelengths range from 100 km to 10 km (an obsolete metric unit equal to 10 km). === Extremely low frequency === Extremely low frequency (ELF) is radiation frequencies from 3 to 30 Hz (108 to 107 m respectively). In atmosphere science, an alternative definition is usually given, from 3 Hz to 3 kHz. In the related magnetosphere science, the lower frequency electromagnetic oscillations (pulsations occurring below ~3 Hz) are considered to lie in the ULF range, which is thus also defined differently from the ITU Radio Bands. A massive military ELF antenna in Michigan radiates very slow messages to otherwise unreachable receivers, such as submerged submarines. === Thermal radiation (heat) === Thermal radiation is a common synonym for infrared radiation emitted by objects at temperatures often encountered on Earth. Thermal radiation refers not


id: radiation-20260505-5
file: data/en.wikipedia.org/wiki/Radiation-5.md
category: reference
title: Radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Radiation
date_saved: 2026-05-05T10:56:04.366371+00:00
instance: kb-cron
parent: radiation-20260505-0
summary:
Electromagnetic radiation of wavelengths other than visible light were discovered in the early 19th century. The discovery of infrared radiation is ascribed to William Herschel, the astronomer. Herschel published his results in 1800 before the Royal Society of London. Herschel, like Ritter, used a prism to refract light from the Sun and detected the infrared (beyond the red part of the spectrum), through an increase in the temperature recorded by a thermometer. In 1801, the German physicist Johann Wilhelm Ritter made the discovery of ultraviolet by noting that the rays from a prism darkened silver chloride preparations more quickly than violet light. Ritter's experiments were an early precursor to what would become photography. Ritter noted that the UV rays were capable of causing chemical reactions. The first radio waves detected were not from a natural source, but were produced deliberately and artificially by the German scientist Heinrich Hertz in 1887, using electrical circuits calculated to produce oscillations in the radio frequency range, following formulas suggested by the equations of James Clerk Maxwell. Wilhelm Röntgen discovered and named X-rays. While experimenting with high voltages applied to an evacuated tube on 8 November 1895, he noticed a fluorescence on a nearby plate


id: radiation-20260505-6
file: data/en.wikipedia.org/wiki/Radiation-6.md
category: reference
title: Radiation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Radiation
date_saved: 2026-05-05T10:56:04.366371+00:00
instance: kb-cron
parent: radiation-20260505-0
summary:
Radiation is not always dangerous, and not all types of radiation are equally dangerous, contrary to several common medical myths. For example, although bananas contain naturally occurring radioactive isotopes, particularly potassium-40 (40K), which emit ionizing radiation when undergoing radioactive decay, the levels of such radiation are far too low to induce radiation poisoning, and bananas are not a radiation hazard. It would not be physically possible to eat enough bananas to cause radiation poisoning, as the radiation dose from bananas is non-cumulative. Radiation is ubiquitous on Earth, and humans are adapted to survive at the normal low-to-moderate levels of radiation found on Earth's surface. The relationship between dose and toxicity is often non-linear, and many substances that are toxic at very high doses actually have neutral or positive health effects, or are biologically essential, at moderate or low doses. There is some evidence to suggest that this is true for ionizing radiation: normal levels of ionizing radiation may serve to stimulate and regulate the activity of DNA repair mechanisms. High enough levels of any kind of radiation will eventually become lethal, however. Ionizing radiation in certain conditions can damage living organisms, causing cancer or genetic damage. Non-ionizing radiation in certain


id: ramsauer-townsend-effect-20260505-0
file: data/en.wikipedia.org/wiki/Ramsauer–Townsend_effect-0.md
category: reference
title: Ramsauer–Townsend effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Ramsauer–Townsend_effect
date_saved: 2026-05-05T10:56:05.733364+00:00
instance: kb-cron
parent: ramsauer-townsend-effect-20260505-0
summary:
The Ramsauer–Townsend effect, also sometimes called the Ramsauer effect or the Townsend effect, is a physical phenomenon involving the scattering of low-energy electrons by atoms of a noble gas. This effect is a result of quantum mechanics. The effect is named for Carl Ramsauer and John Sealy Townsend, who each independently studied the collisions between atoms and low-energy electrons in 1921. == Definitions == When an electron moves through a gas, its interactions with the gas atoms cause scattering to occur. These interactions are classified as inelastic if they cause excitation or ionization of the atom to occur or elastic if they do not. The probability of scattering in such a system is defined as the number of electrons scattered, per unit electron current, per unit path length, per unit pressure at 0 °C, per unit solid angle. The number of collisions equals the total number of electrons scattered elastically and inelastically in all angles, and the probability of collision is the total number of collisions, per unit electron current, per unit path length, per unit pressure at 0 °C. Because noble gas atoms have a relatively high first ionization energy and the electrons do not carry enough energy to


id: rayleigh-scattering-20260505-0
file: data/en.wikipedia.org/wiki/Rayleigh_scattering-0.md
category: reference
title: Rayleigh scattering
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Rayleigh_scattering
date_saved: 2026-05-05T10:56:07.297744+00:00
instance: kb-cron
parent: rayleigh-scattering-20260505-0
summary:
Rayleigh scattering ( RAY-lee) is the scattering or deflection of light, or other electromagnetic radiation, by particles with a size much smaller than the wavelength of the radiation. For light frequencies well below the resonance frequency of the scattering medium (normal dispersion regime), the amount of scattering is inversely proportional to the fourth power of the wavelength (e.g., a blue color is scattered much more than a red color as light propagates through air). The phenomenon is named after the 19th-century British physicist Lord Rayleigh (John William Strutt). Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle, therefore, becomes a small radiating dipole whose radiation we see as scattered light. The particles may be individual atoms or molecules; it can occur when light travels through transparent solids and liquids, but is most prominently seen in gases. Rayleigh scattering of sunlight in Earth's atmosphere causes diffuse sky radiation. Since blue light wavelengths scatter more, the diffuse sky seen in daytime is blue. At twilight the sunlight on the horizon is missing the scattered blue light


id: rayleigh-scattering-20260505-1
file: data/en.wikipedia.org/wiki/Rayleigh_scattering-1.md
category: reference
title: Rayleigh scattering
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Rayleigh_scattering
date_saved: 2026-05-05T10:56:07.297744+00:00
instance: kb-cron
parent: rayleigh-scattering-20260505-0
summary:
I s = I 0 π 2 α 2 ε 0 2 λ 4 R 2 1 + cos 2 ⁡ θ 2 . {\displaystyle I_{s}=I_{0}{\frac {\pi ^{2}\alpha ^{2}}{{\varepsilon _{0}}^{2}\lambda ^{4}R^{2}}}{\frac {1+\cos ^{2}\theta }{2}}.} == Effect of fluctuations == When the dielectric constant ϵ {\displaystyle \epsilon } of a certain region of volume V {\displaystyle V} is different from the average dielectric constant of the medium ϵ ¯ {\displaystyle {\bar {\epsilon }}} , then any incident light will be scattered according to the following equation I = I 0 π 2 V 2 σ ϵ 2 2 λ 4 R 2 ( 1 + cos 2 ⁡ θ ) {\displaystyle I=I_{0}{\frac {\pi ^{2}V^{2}\sigma _{\epsilon }^{2}}{2\lambda ^{4}R^{2}}}{\left(1+\cos ^{2}\theta \right)}} where σ ϵ 2 {\displaystyle \sigma _{\epsilon }^{2}} represents the variance of the fluctuation in the dielectric constant ϵ {\displaystyle \epsilon } . == Cause of the blue color of the sky == The blue color of the sky is a consequence of three factors: the blackbody spectrum of sunlight coming into the Earth's atmosphere, Rayleigh scattering of that light off oxygen and nitrogen molecules, and the response of the human visual system. The strong wavelength dependence of the Rayleigh scattering (~λ−4)


id: recovery-effect-20260505-0
file: data/en.wikipedia.org/wiki/Recovery_effect-0.md
category: reference
title: Recovery effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Recovery_effect
date_saved: 2026-05-05T10:56:08.762744+00:00
instance: kb-cron
parent: recovery-effect-20260505-0
summary:
The recovery effect is a phenomenon observed in battery usage where the available energy is less than the difference between energy charged and energy consumed. == Mechanism == Intuitively, this is because the energy has been consumed from the edge of the battery and the charge has not yet diffused evenly around the battery. When power is extracted continuously voltage decreases in a smooth curve, but the recovery effect can result in the voltage partially increasing if the current is interrupted. == In non-lead-acid batteries == The KiBaM battery model describes the recovery effect for lead-acid batteries and is also a good approximation to the observed effects in Li-ion batteries. In some batteries, the gains from the recovery life can extend battery life by up to 45% by alternating discharging and inactive periods rather than constantly discharging. The size of the recovery effect depends on the battery load, recovery time and depth of discharge. Even though the recovery effect phenomenon is prominent in the lead acid battery chemistry, its existence in alkaline, Ni-MH and Li-Ion batteries is still questionable. For instance, a systematic experimental case study shows that an intermittent discharge current in case of alkaline, Ni-MH and Li-ion batteries


id: reflection-physics-20260505-0
file: data/en.wikipedia.org/wiki/Reflection_(physics)-0.md
category: reference
title: Reflection (physics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Reflection_(physics)
date_saved: 2026-05-05T10:56:09.994224+00:00
instance: kb-cron
parent: reflection-physics-20260505-0
summary:
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection (for example at a mirror) the angle at which the wave is incident on the surface equals the angle at which it is reflected. In acoustics, reflection causes echoes and is used in sonar. In geology, it is important in the study of seismic waves. Reflection is observed with surface waves in bodies of water. Reflection is observed with many types of electromagnetic wave, besides visible light. Reflection of VHF and higher frequencies is important for radio transmission and for radar. Even hard X-rays and gamma rays can be reflected at shallow angles with special "grazing" mirrors. == Reflection of light == Reflection of light is either specular (mirror-like) or diffuse (retaining the energy, but losing the image) depending on the nature of the interface. In specular reflection the phase of the reflected waves depends on the choice of the origin of coordinates, but the relative phase between s and p (TE


id: reflection-physics-20260505-1
file: data/en.wikipedia.org/wiki/Reflection_(physics)-1.md
category: reference
title: Reflection (physics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Reflection_(physics)
date_saved: 2026-05-05T10:56:09.994224+00:00
instance: kb-cron
parent: reflection-physics-20260505-0
summary:
In classical electrodynamics, light is considered as an electromagnetic wave, which is described by Maxwell's equations. Light waves incident on a material induce small oscillations of polarisation in the individual atoms (or oscillation of electrons, in metals), causing each particle to radiate a small secondary wave in all directions, like a dipole antenna. All these waves add up to give specular reflection and refraction, according to the Huygens–Fresnel principle. In the case of dielectrics such as glass, the electric field of the light acts on the electrons in the material, and the moving electrons generate fields and become new radiators. The refracted light in the glass is the combination of the forward radiation of the electrons and the incident light. The reflected light is the combination of the backward radiation of all of the electrons. In metals, electrons with no binding energy are called free electrons. When these electrons oscillate with the incident light, the phase difference between their radiation field and the incident field is π radians (180°), so the forward radiation cancels the incident light, and backward radiation is just the reflected light. Light–matter interaction in terms of photons is a topic of quantum electrodynamics, and is described


id: reflection-physics-20260505-2
file: data/en.wikipedia.org/wiki/Reflection_(physics)-2.md
category: reference
title: Reflection (physics)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Reflection_(physics)
date_saved: 2026-05-05T10:56:09.994224+00:00
instance: kb-cron
parent: reflection-physics-20260505-0
summary:
When a longitudinal sound wave strikes a flat surface, sound is reflected in a coherent manner provided that the dimension of the reflective surface is large compared to the wavelength of the sound. Note that audible sound has a very wide frequency range (from 20 to about 17000 Hz), and thus a very wide range of wavelengths (from about 20 mm to 17 m). As a result, the overall nature of the reflection varies according to the texture and structure of the surface. For example, porous materials will absorb some energy, and rough materials (where rough is relative to the wavelength) tend to reflect in many directions—to scatter the energy, rather than to reflect it coherently. This leads into the field of architectural acoustics, because the nature of these reflections is critical to the auditory feel of a space. In the theory of exterior noise mitigation, reflective surface size mildly detracts from the concept of a noise barrier by reflecting some of the sound into the opposite direction. Sound reflection can affect the acoustic space. === Seismic reflection === Seismic waves produced by earthquakes or other sources (such as explosions) may be reflected by layers within the Earth. Study of


id: refraction-20260505-0
file: data/en.wikipedia.org/wiki/Refraction-0.md
category: reference
title: Refraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Refraction
date_saved: 2026-05-05T10:56:11.224500+00:00
instance: kb-cron
parent: refraction-20260505-0
summary:
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed. Optical prisms and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light, and thus the angle of the refraction also varies correspondingly. This is called dispersion and allows certain prisms and raindrops in rainbows to divide white light into its constituent spectral colors. == Law == For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence θ 1 {\displaystyle {\theta _{1}}} and angle of refraction θ 2 {\displaystyle {\theta _{2}}} is equal to the ratio of phase velocities v 1 v 2 {\textstyle {\frac {v_{1}}{v_{2}}}} in


id: refraction-20260505-1
file: data/en.wikipedia.org/wiki/Refraction-1.md
category: reference
title: Refraction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Refraction
date_saved: 2026-05-05T10:56:11.224500+00:00
instance: kb-cron
parent: refraction-20260505-0
summary:
The phenomenon of refraction can in a more fundamental way be derived from the 2 or 3-dimensional wave equation. The boundary condition at the interface will then require the tangential component of the wave vector to be identical on the two sides of the interface. Since the magnitude of the wave vector depend on the wave speed this requires a change in direction of the wave vector. The relevant wave speed in the discussion above is the phase velocity of the wave. This is typically close to the group velocity which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction. A wave traveling perpendicular to a boundary, i.e. having its wavefronts parallel to the boundary, will not change direction even if the speed of the wave changes. === Dispersion of light === Refraction is also responsible for rainbows and for the splitting of white light into a rainbow-spectrum as it passes through a glass prism. Glass and water have higher refractive indexes than air. When a beam of white light passes from air into a material having an index of refraction


id: revolving-rivers-20260505-0
file: data/en.wikipedia.org/wiki/Revolving_rivers-0.md
category: reference
title: Revolving rivers
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Revolving_rivers
date_saved: 2026-05-05T10:56:12.432363+00:00
instance: kb-cron
parent: revolving-rivers-20260505-0
summary:
Revolving rivers are a surprising, uncommon way of sand pile growth that can be found in a few sands around the world, but has been studied in detail only for one Cuban sand from a place called Santa Teresa (Pinar del Rio province). == Description == When pouring "revolving" sand on a flat surface from a fixed position, the growth of a conical pile does not occur by the common avalanche mechanism, where sand slides down the pile in a more or less random fashion. What happens is that a relatively thin "river" of flowing sand travels from the pouring point at the apex of the pile to its base, while the rest of the sand at the surface is static. In addition, the river "revolves" around the pile either in clockwise or counter-clockwise directions (looking from top) depending on the initial conditions. Actually the river constitutes the "cutting edge" of a layer of sand that deposits as a helix on the conical pile, and makes it grow. For small sandpiles, rivers are continuous, but they become intermittent for larger piles. == History and state of the art == The phenomenon was observed first by E. Altshuler at the University


id: scattering-20260505-0
file: data/en.wikipedia.org/wiki/Scattering-0.md
category: reference
title: Scattering
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Scattering
date_saved: 2026-05-05T10:56:13.653453+00:00
instance: kb-cron
parent: scattering-20260505-0
summary:
In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays (electron beams) and X-rays was observed and discussed. With the discovery of subatomic particles (e.g. Ernest Rutherford in 1911) and the development of quantum theory in the 20th century,


id: scattering-20260505-1
file: data/en.wikipedia.org/wiki/Scattering-1.md
category: reference
title: Scattering
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Scattering
date_saved: 2026-05-05T10:56:13.653453+00:00
instance: kb-cron
parent: scattering-20260505-0
summary:
Scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a boundary condition, and then propagate away "to the distant future". The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles scattered from the object. === Attenuation due to scattering === When the target is a set of many scattering centers


id: scattering-20260505-2
file: data/en.wikipedia.org/wiki/Scattering-2.md
category: reference
title: Scattering
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Scattering
date_saved: 2026-05-05T10:56:13.653453+00:00
instance: kb-cron
parent: scattering-20260505-0
summary:
In mathematical physics, scattering theory is a framework for studying and understanding the interaction or scattering of solutions to partial differential equations. In acoustics, the differential equation is the wave equation, and scattering studies how its solutions, the sound waves, scatter from solid objects or propagate through non-uniform media (such as sound waves, in sea water, coming from a submarine). In the case of classical electrodynamics, the differential equation is again the wave equation, and the scattering of light or radio waves is studied. In particle physics, the equations are those of Quantum electrodynamics, Quantum chromodynamics and the Standard Model, the solutions of which correspond to fundamental particles. In regular quantum mechanics, which includes quantum chemistry, the relevant equation is the Schrödinger equation, although equivalent formulations, such as the Lippmann-Schwinger equation and the Faddeev equations, are also largely used. The solutions of interest describe the long-term motion of free atoms, molecules, photons, electrons, and protons. The scenario is that several particles come together from an infinite distance away. These reagents then collide, optionally reacting, getting destroyed or creating new particles. The products and unused reagents then fly away to infinity again. (The atoms and molecules are effectively particles for our


id: scattering-20260505-3
file: data/en.wikipedia.org/wiki/Scattering-3.md
category: reference
title: Scattering
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Scattering
date_saved: 2026-05-05T10:56:13.653453+00:00
instance: kb-cron
parent: scattering-20260505-0
summary:
α ≪ 1: Rayleigh scattering (small particle compared to wavelength of light); α ≈ 1: Mie scattering (particle about the same size as wavelength of light, valid only for spheres); α ≫ 1: geometric scattering (particle much larger than wavelength of light). Rayleigh scattering is a process in which electromagnetic radiation (including light) is scattered by a small spherical volume of variant refractive indexes, such as a particle, bubble, droplet, or even a density fluctuation. This effect was first modeled successfully by Lord Rayleigh, from whom it gets its name. In order for Rayleigh's model to apply, the sphere must be much smaller in diameter than the wavelength (λ) of the scattered wave; typically the upper limit is taken to be about 1/10 the wavelength. In this size regime, the exact shape of the scattering center is usually not very significant and can often be treated as a sphere of equivalent volume. The inherent scattering that radiation undergoes passing through a pure gas is due to microscopic density fluctuations as the gas molecules move around, which are normally small enough in scale for Rayleigh's model to apply. This scattering mechanism is the primary cause of the blue color of the


id: self-oscillation-20260505-0
file: data/en.wikipedia.org/wiki/Self-oscillation-0.md
category: reference
title: Self-oscillation
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Self-oscillation
date_saved: 2026-05-05T10:56:14.848602+00:00
instance: kb-cron
parent: self-oscillation-20260505-0
summary:
Self-oscillation is the generation and maintenance of a periodic motion by a source of power that lacks any corresponding periodicity. The oscillator itself controls the phase with which the external power acts on it. Self-oscillators are therefore distinct from forced and parametric resonators, in which the power that sustains the motion must be modulated externally. In linear systems, self-oscillation appears as an instability associated with a negative damping term, which causes small perturbations to grow exponentially in amplitude. This negative damping is due to a positive feedback between the oscillation and the modulation of the external source of power. The amplitude and waveform of steady self-oscillations are determined by the nonlinear characteristics of the system. Self-oscillations are important in physics, engineering, biology, and economics. == History of the subject == The study of self-oscillators dates back to the early 1830s, with the work of Robert Willis and George Biddell Airy on the mechanism by which the vocal cords produce the human voice. Another instance of self-oscillation, associated with the unstable operation of centrifugal governors, was studied mathematically by James Clerk Maxwell in 1867. In the second edition of his treatise on The Theory of Sound, published in 1896, Lord Rayleigh


id: shock-diamond-20260505-0
file: data/en.wikipedia.org/wiki/Shock_diamond-0.md
category: reference
title: Shock diamond
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Shock_diamond
date_saved: 2026-05-05T10:56:16.046807+00:00
instance: kb-cron
parent: shock-diamond-20260505-0
summary:
Shock diamonds (also known as Mach diamonds or thrust diamonds, and less commonly Mach disks) are a formation of standing wave patterns that appear in the supersonic exhaust plume of an aerospace propulsion system, such as a supersonic jet engine, rocket, ramjet, or scramjet, when it is operated in an atmosphere. The "diamonds" are actually a complex flow field made visible by abrupt changes in local density and pressure as the exhaust passes through a series of standing shock waves and expansion fans. The physicist Ernst Mach was the first to describe a strong shock perpendicular to the direction of fluid flow, the presence of which causes the diamond pattern. == Mechanism == Shock diamonds form when the supersonic exhaust from a propelling nozzle is slightly over-expanded, meaning that the static pressure of the gases exiting the nozzle is less than the ambient air pressure. The higher ambient pressure compresses the flow, and since the resulting pressure increase in the exhaust gas stream is adiabatic, a reduction in velocity causes its static temperature to be substantially increased. The exhaust is typically over-expanded at low altitudes where air pressure is higher. As the flow exits the nozzle, ambient air pressure will


id: shower-curtain-effect-20260505-0
file: data/en.wikipedia.org/wiki/Shower-curtain_effect-0.md
category: reference
title: Shower-curtain effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Shower-curtain_effect
date_saved: 2026-05-05T10:56:17.236300+00:00
instance: kb-cron
parent: shower-curtain-effect-20260505-0
summary:
The shower-curtain effect in physics describes the phenomenon of a shower curtain being blown inward when a shower is running. The problem of identifying the cause of this effect has been featured in Scientific American magazine, with several hypotheses given to explain the phenomenon but no definite conclusion. == Hypotheses == === Buoyancy hypothesis === Also called chimney effect or stack effect, observes that warm air (from the hot shower) rises out over the shower curtain as cooler air (near the floor) pushes in under the curtain to replace the rising air. By pushing the curtain in towards the shower, the (short range) vortex and Coandă effects become more significant. However, the shower-curtain effect persists when cold water is used, implying that this is not the sole mechanism. === Bernoulli effect hypothesis === The most popular explanation given for the shower-curtain effect is Bernoulli's principle. Bernoulli's principle states that an increase in velocity results in a decrease in pressure. This theory presumes that the water flowing out of a shower head causes the air through which the water moves to start flowing in the same direction as the water. This movement would be parallel to the plane of the shower


id: singing-sand-20260505-0
file: data/en.wikipedia.org/wiki/Singing_sand-0.md
category: reference
title: Singing sand
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Singing_sand
date_saved: 2026-05-05T10:56:18.398176+00:00
instance: kb-cron
parent: singing-sand-20260505-0
summary:
Singing sand, also called whistling sand, barking sand, booming sand or singing dune, is sand that produces sound. The sound emission may be caused by wind passing over dunes or by walking on the sand. Certain conditions have to come together to create singing sand: The sand grains have to be round and between 0.1 and 0.5 mm in diameter. The sand has to contain silica. The sand needs to be at a certain humidity. The most common frequency emitted seems to be close to 450 Hz. There are various theories about the singing sand mechanism. It has been proposed that the sound frequency is controlled by the shear rate. Others have suggested that the frequency of vibration is related to the thickness of the dry surface layer of sand. The sound waves bounce back and forth between the surface of the dune and the surface of the moist layer, creating a resonance that increases the sound's volume. The noise may be generated by friction between the grains or by the compression of air between them. Other sounds that can be emitted by sand have been described as "roaring" or "booming". == In dunes == Singing sand dunes, an example


id: singing-sand-20260505-1
file: data/en.wikipedia.org/wiki/Singing_sand-1.md
category: reference
title: Singing sand
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Singing_sand
date_saved: 2026-05-05T10:56:18.398176+00:00
instance: kb-cron
parent: singing-sand-20260505-0
summary:
== Literature == Nori, Franco; Sholtz, Paul; Bretz, Michael (1997). "Booming Sand". Scientific American. 277 (3): 84–89. Bibcode:1997SciAm.277c..84N. doi:10.1038/scientificamerican0997-84. JSTOR 24995915. Sholtz, Paul; Bretz, Michael; Nori, Franco (1997). "Sound-producing sand avalanches" (PDF). Contemporary Physics. 38 (5): 329–342. Bibcode:1997ConPh..38..329S. doi:10.1080/001075197182306. Ridgeway, K.; Scotton, J. B. (1973). "Whistling sand beaches in the British Isles". Sedimentology. 20 (2). Wiley: 263–279. Bibcode:1973Sedim..20..263R. doi:10.1111/j.1365-3091.1973.tb02049.x. ISSN 0037-0746. Andreotti, B. (2004-12-01). "The Song of Dunes as a Wave-Particle Mode Locking". Physical Review Letters. 93 (23) 238001. American Physical Society (APS). Bibcode:2004PhRvL..93w8001A. doi:10.1103/physrevlett.93.238001. ISSN 0031-9007. PMID 15601204. Douady, S.; Manning, A.; Hersen, P.; Elbelrhiti, H.; Protière, S.; Daerr, A.; Kabbachi, B. (2006-07-07). "Song of the Dunes as a Self-Synchronized Instrument". Physical Review Letters. 97 (1) 018002. American Physical Society (APS). arXiv:nlin/0412047. Bibcode:2006PhRvL..97a8002D. doi:10.1103/physrevlett.97.018002. ISSN 0031-9007. PMID 16907409. S2CID 19628505. Bonneau, L.; Andreotti, B.; Clément, E. (2007-01-08). "Surface elastic waves in granular media under gravity and their relation to booming avalanches". Physical Review E. 75 (1) 016602. American Physical Society (APS). Bibcode:2007PhRvE..75a6602B. doi:10.1103/physreve.75.016602. ISSN 1539-3755. PMID 17358270. Vriend, Nathalie M.; Hunt, Melany L.; Clayton, Robert W.; Brennen, Christopher Earls; Brantley, Katherine S.; Ruiz-Angulo, Angel (2007-08-23). "Solving the mystery of booming sand dunes". Geophysical Research Letters. 34 (16). American Geophysical


id: singing-sand-dunes-dunhuang-20260505-0
file: data/en.wikipedia.org/wiki/Singing_Sand_Dunes_(Dunhuang)-0.md
category: reference
title: Singing Sand Dunes (Dunhuang)
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Singing_Sand_Dunes_(Dunhuang)
date_saved: 2026-05-05T10:56:19.612042+00:00
instance: kb-cron
parent: singing-sand-dunes-dunhuang-20260505-0
summary:
The Singing Sand Dunes (Chinese: 鳴沙山 Pinyin: míng shā shān) in Dunhuang, China, are the sand dunes that, when the wind blows, give out a singing or drumming sound. They are part of the Kumtag Desert. The Singing Sand Dunes were originally known as the "Gods' Sand Dunes" (Chinese: 神沙山). In the Records of the Grand Historian, Sima Qian described the sound "as if listening to music when the weather is fine." During the Ming Dynasty, they came to be called by the current name. The dunes are also where a crescent-shaped lake called Yueyaquan or Crescent Lake is located. There are four better-known singing sand dunes in China, that include those of Hami, which are usually said to give the best sound among the four, and those of Dunhuang. The tourist area at the site offers various facilities and activities such as ATV riding, paragliding, camel rides and sandboarding. == See also == Singing sand Mogao Caves: nearby == References ==


id: sommerfeld-effect-20260505-0
file: data/en.wikipedia.org/wiki/Sommerfeld_effect-0.md
category: reference
title: Sommerfeld effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sommerfeld_effect
date_saved: 2026-05-05T10:56:20.820359+00:00
instance: kb-cron
parent: sommerfeld-effect-20260505-0
summary:
In mechanics, Sommerfeld effect is a phenomenon arising from feedback in the energy exchange between vibrating systems: for example, when for the rocking table, under given conditions, energy transmitted to the motor resulted not in higher revolutions but in stronger vibrations of the table. It is named after Arnold Sommerfeld. In 1902, A. Sommerfeld analyzed the vibrations caused by a motor driving an unbalanced weight and wrote that "This experiment corresponds roughly to the case in which a factory owner has a machine set on a poor foundation running at 30 horsepower. He achieves an effective level of just 1/3, however, because only 10 horsepower are doing useful work, while 20 horsepower are transferred to the foundational masonry". First mathematical descriptions of Sommerfeld effect were suggested by I. Blekhman and V. Kononenko. == Hidden attractors in Sommerfeld effect == In the theory of hidden oscillations, Sommerfeld effect is explained by the multistability and presence in the phase space of dynamical model without stationary states of two coexisting hidden attractors, one of which attracts trajectories from vicinity of zero initial data (which correspond to the typical start up of the motor), and the other attractor corresponds to the desired mode of


id: sonochemical-synthesis-20260505-0
file: data/en.wikipedia.org/wiki/Sonochemical_synthesis-0.md
category: reference
title: Sonochemical synthesis
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonochemical_synthesis
date_saved: 2026-05-05T10:56:22.002477+00:00
instance: kb-cron
parent: sonochemical-synthesis-20260505-0
summary:
Sonochemical synthesis is the process which utilizes the principles of sonochemistry to make molecules undergo a chemical reaction with the application of powerful ultrasound radiation (20 kHz–10 MHz). Sonochemistry generates hot spots that can achieve very high temperatures (5000–25.000 K), pressures of more than 1000 atmospheres, and rates of heating and cooling that can exceed 10^11 K/s. High intensity ultrasound produces chemical and physical effects that can be used for the production or modification of a wide range of nanostructured materials. The principle that causes the modification of nanostructures in the sonochemical process is acoustic cavitation. == References ==


id: sonochemistry-20260505-0
file: data/en.wikipedia.org/wiki/Sonochemistry-0.md
category: reference
title: Sonochemistry
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonochemistry
date_saved: 2026-05-05T10:56:23.217039+00:00
instance: kb-cron
parent: sonochemistry-20260505-0
summary:
In chemistry, the study of sonochemistry is concerned with understanding the effect of ultrasound in forming acoustic cavitation in liquids, resulting in the initiation or enhancement of the chemical activity in the solution. Therefore, the chemical effects of ultrasound do not come from a direct interaction of the ultrasonic sound wave with the molecules in the solution. == History == The influence of sonic waves travelling through liquids was first reported by Robert Williams Wood (1868–1955) and Alfred Lee Loomis (1887–1975) in 1927. The experiment was about the frequency of the energy that it took for sonic waves to "penetrate" the barrier of water. He came to the conclusion that sound does travel faster in water, but because of the water's density compared to Earth's atmosphere it was incredibly hard to get the sonic waves to couple their energy into the water. Due to the sudden density change, much of the energy is lost, similar to shining a flashlight towards a piece of glass; some of the light is transmitted into the glass, but much of it is lost to reflection outwards. Similarly with an air-water interface, almost all of the sound is reflected off the water, instead of being


id: sonoluminescence-20260505-0
file: data/en.wikipedia.org/wiki/Sonoluminescence-0.md
category: reference
title: Sonoluminescence
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonoluminescence
date_saved: 2026-05-05T10:56:24.486325+00:00
instance: kb-cron
parent: sonoluminescence-20260505-0
summary:
Sonoluminescence is luminescence induced by sound waves, such as in the emission of light from imploding bubbles in a liquid when excited by sound. Sonoluminescence is sometimes considered a kind of mechanoluminescence. However, mechanoluminescence is typically defined as pertaining to solids, while sonoluminescence usually pertains to liquids. The related terms acoustoluminescence and sonotriboluminescence have been used to describe sound-induced luminescence in solids (e.g., crystals suspended in slurries). Sonoluminescence was first discovered in 1934 at the University of Cologne. It occurs when a sound wave of sufficient intensity induces a gaseous cavity within a liquid to collapse quickly, emitting a burst of light. The phenomenon can be observed in stable single-bubble sonoluminescence (SBSL) and multi-bubble sonoluminescence (MBSL). In 1960, Peter Jarman proposed that sonoluminescence is thermal in origin and might arise from microshocks within collapsing cavities. Later experiments revealed that the temperature inside the bubble during SBSL could reach up to 12,000 kelvins (11,700 °C; 21,100 °F). The exact mechanism behind sonoluminescence remains unknown, with various hypotheses including hotspot, bremsstrahlung, and collision-induced radiation. Some researchers have even speculated that temperatures in sonoluminescing systems could reach millions of kelvins, potentially causing thermonuclear fusion; this idea, however, has been met with skepticism by


id: sonoluminescence-20260505-1
file: data/en.wikipedia.org/wiki/Sonoluminescence-1.md
category: reference
title: Sonoluminescence
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonoluminescence
date_saved: 2026-05-05T10:56:24.486325+00:00
instance: kb-cron
parent: sonoluminescence-20260505-0
summary:
R R ¨ + 3 2 R ˙ 2 = 1 ρ ( P ∞ ( t ) − P 0 ( t ) − 4 μ R ˙ R − 2 γ R ) {\displaystyle R{\ddot {R}}+{\frac {3}{2}}{\dot {R}}^{2}={\frac {1}{\rho }}\left(P_{\infty }(t)-P_{0}(t)-4\mu {\frac {\dot {R}}{R}}-{\frac {2\gamma }{R}}\right)} This is an approximate equation that is derived from the Navier–Stokes equations (written in spherical coordinate system) and describes the motion of the radius of the bubble R as a function of time t. Here, μ is the viscosity, P ∞ ( t ) {\displaystyle P_{\infty }(t)} is the external pressure infinitely far from the bubble, P 0 ( t ) {\displaystyle P_{0}(t)} is the internal pressure of the bubble, ρ {\displaystyle \rho } is the liquid density, and γ is the surface tension. The over-dots represent time derivatives. This equation, though approximate, has been shown to give good estimates on the motion of the bubble under the acoustically driven field except during the final stages of collapse. Both simulation and experimental measurement show that during the critical final stages of collapse, the bubble wall velocity exceeds the speed of sound of the gas inside the bubble. Thus a more detailed analysis


id: sonoluminescence-20260505-2
file: data/en.wikipedia.org/wiki/Sonoluminescence-2.md
category: reference
title: Sonoluminescence
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Sonoluminescence
date_saved: 2026-05-05T10:56:24.486325+00:00
instance: kb-cron
parent: sonoluminescence-20260505-0
summary:
== Biological sonoluminescence == Pistol shrimp (also called snapping shrimp) produce a type of cavitation luminescence from a collapsing bubble caused by quickly snapping its claw. The animal snaps a specialized claw shut to create a cavitation bubble that generates acoustic pressures of up to 80 kPa at a distance of 4 cm from the claw. As it extends out from the claw, the bubble reaches speeds of 60 miles per hour (97 km/h) and releases a sound reaching 218 decibels. The pressure is strong enough to kill small fish. The light produced is of lower intensity than the light produced by typical sonoluminescence and is not visible to the naked eye. The light and heat produced by the bubble may have no direct significance, as it is the shockwave produced by the rapidly collapsing bubble which these shrimp use to stun or kill prey. However, it is the first known instance of an animal producing light by this effect and was whimsically dubbed "shrimpoluminescence" upon its discovery in 2001. It has subsequently been discovered that another group of crustaceans, the mantis shrimp, contains species whose club-like forelimbs can strike so quickly and with such force as to induce sonoluminescent


id: spatial-dispersion-20260505-0
file: data/en.wikipedia.org/wiki/Spatial_dispersion-0.md
category: reference
title: Spatial dispersion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spatial_dispersion
date_saved: 2026-05-05T10:56:25.759895+00:00
instance: kb-cron
parent: spatial-dispersion-20260505-0
summary:
In the physics of continuous media, spatial dispersion is a phenomenon where material parameters such as the permittivity or conductivity have dependence on wavevector. Normally such a dependence is assumed to be absent for simplicity, however spatial dispersion exists to varying degrees in all materials. The underlying physical reason for the wavevector dependence is often that the material has some spatial structure smaller than the wavelength of any signals (such as light or sound) being considered. Since these small spatial structures cannot be resolved by the waves, only indirect effects (e.g. wavevector dependence) remain detectable. In such a case, although the light cannot resolve the individual atoms, they nevertheless can as an aggregate affect how the light propagates. Another common mechanism is that the (e.g.) light is coupled to an excitation of the material, such as a plasmon. Spatial dispersion can be compared to temporal dispersion, the latter often just called dispersion. Temporal dispersion represents memory effects in systems, commonly seen in optics and electronics. Spatial dispersion on the other hand represents spreading effects and is usually significant only at microscopic length scales. Spatial dispersion contributes relatively small perturbations to optics, providing weak effects such as optical activity. Spatial dispersion


id: spatial-dispersion-20260505-1
file: data/en.wikipedia.org/wiki/Spatial_dispersion-1.md
category: reference
title: Spatial dispersion
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spatial_dispersion
date_saved: 2026-05-05T10:56:25.759895+00:00
instance: kb-cron
parent: spatial-dispersion-20260505-0
summary:
ω 2 μ 0 ϵ ( k → , ω ) E → − ( k → ⋅ k → ) E → + ( k → ⋅ E → ) k → = 0. {\displaystyle \omega ^{2}\mu _{0}\epsilon ({\vec {k}},\omega ){\vec {E}}-({\vec {k}}\cdot {\vec {k}}){\vec {E}}+({\vec {k}}\cdot {\vec {E}}){\vec {k}}=0.} Spatial dispersion in ϵ ( k → , ω ) {\displaystyle \epsilon ({\vec {k}},\omega )} can lead to strange phenomena, such as the existence of multiple modes at the same frequency and wavevector direction, but with different wavevector magnitudes. Nearby crystal surfaces and boundaries, it is no longer valid to describe system response in terms of wavevectors. For a full description it is necessary to return to a full nonlocal response function (without translational symmetry), however the end effect can sometimes be described by "additional boundary conditions" (ABC's). === In isotropic media === In materials that have no relevant crystalline structure, spatial dispersion can be important. Although symmetry demands that the permittivity is isotropic for zero wavevector, this restriction does not apply for nonzero wavevector. The non-isotropic permittivity for nonzero wavevector leads to effects such as optical activity in solutions of chiral molecules. In isotropic materials without optical activity,


id: spontaneous-emission-20260505-0
file: data/en.wikipedia.org/wiki/Spontaneous_emission-0.md
category: reference
title: Spontaneous emission
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spontaneous_emission
date_saved: 2026-05-05T10:56:26.913707+00:00
instance: kb-cron
parent: spontaneous-emission-20260505-0
summary:
Spontaneous emission is the process in which a quantum mechanical system (such as a molecule, an atom or a subatomic particle) transitions from an excited energy state to a lower energy state (e.g., its ground state) and emits a quantized amount of energy in the form of a photon. If the system in question is excited by some means other than heating, the spontaneous emission is called luminescence. There are different sub-categories of luminescence depending on how excited atoms are produced (electroluminescence, chemiluminescence etc.). If the excitation is affected by the absorption of radiation the spontaneous emission is called fluorescence. Some systems have a metastable level and continue to fluoresce long after the exciting radiation is turned off; this is called phosphorescence. Lasers start via spontaneous emission, then during continuous operation work by stimulated emission. Spontaneous emission cannot be explained by classical electromagnetic theory and is fundamentally a quantum process. Albert Einstein first predicted the phenomenon of spontaneous emission in a series of papers starting in 1916, culminating in what is now called the Einstein A Coefficient. Einstein's quantum theory of radiation anticipated ideas later expressed in quantum electrodynamics and quantum optics by several decades. Later, after the formal discovery


id: spontaneous-emission-20260505-1
file: data/en.wikipedia.org/wiki/Spontaneous_emission-1.md
category: reference
title: Spontaneous emission
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spontaneous_emission
date_saved: 2026-05-05T10:56:26.913707+00:00
instance: kb-cron
parent: spontaneous-emission-20260505-0
summary:
== Theory == Spontaneous transitions cannot be modeled with a classical electromagnetic field, even with quantum-mechanical treatment of the atom. The stationary quantum states of an atom are orthogonal: the overlap of the wavefunctions between an excited state and the ground state of the atom is zero. Thus, in the absence of a quantized electromagnetic field operator, the excited state atom cannot decay to the ground state. In order to explain spontaneous transitions, quantum mechanics must be extended to a quantum field theory, wherein the electromagnetic field is quantized at every point in space. The quantum field theory of electrons and electromagnetic fields is known as quantum electrodynamics. In quantum electrodynamics (or QED), the electromagnetic field has a ground state, the QED vacuum, which can mix with the excited stationary states of the atom. As a result of this interaction, the stationary state of the atom is no longer a eigenstate of the combined system of the atom plus electromagnetic field. The transition from the electronic excited state to the electronic ground state mixes with the transition of the electromagnetic field from the ground state to an excited state, a field state with one photon in it. Spontaneous emission in


id: spontaneous-emission-20260505-2
file: data/en.wikipedia.org/wiki/Spontaneous_emission-2.md
category: reference
title: Spontaneous emission
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Spontaneous_emission
date_saved: 2026-05-05T10:56:26.913707+00:00
instance: kb-cron
parent: spontaneous-emission-20260505-0
summary:
where ω {\displaystyle \omega } is the emission frequency, n {\displaystyle n} is the index of refraction, μ 12 {\displaystyle \mu _{12}} is the transition dipole moment, ε 0 {\displaystyle \varepsilon _{0}} is the vacuum permittivity, ℏ {\displaystyle \hbar } is the reduced Planck constant, c {\displaystyle c} is the vacuum speed of light, and α {\displaystyle \alpha } is the fine-structure constant. The expression | ⟨ 1 | r | 2 ⟩ | {\displaystyle |\langle 1|\mathbf {r} |2\rangle |} stands for the definition of the transition dipole moment | μ 12 | = | ⟨ 1 | d | 2 ⟩ | {\displaystyle |\mu _{12}|=|\langle 1|\mathbf {d} |2\rangle |} for dipole moment operator d = q r {\displaystyle \mathbf {d} =q\mathbf {r} } , where q {\displaystyle q} is the elementary charge and r {\displaystyle \mathbf {r} } stands for position operator. (This approximation breaks down in the case of inner shell electrons in high-Z atoms.) The above equation clearly shows that the rate of spontaneous emission in free space increases proportionally to ω 3 {\displaystyle \omega ^{3}} . In contrast with atoms, which have a discrete emission spectrum, quantum dots can be tuned continuously by changing their size.


id: stark-effect-20260505-0
file: data/en.wikipedia.org/wiki/Stark_effect-0.md
category: reference
title: Stark effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stark_effect
date_saved: 2026-05-05T10:56:28.115020+00:00
instance: kb-cron
parent: stark-effect-20260505-0
summary:
The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several components due to the presence of the magnetic field. Although initially coined for the static case, it is also used in the wider context to describe the effect of time-dependent electric fields. In particular, the Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles in plasmas. For most spectral lines, the Stark effect is either linear (proportional to the applied electric field) or quadratic with a high accuracy. The Stark effect can be observed both for emission and absorption lines. The latter was sometimes called the inverse Stark effect, but this term is no longer used in the modern literature. == History == The effect is named after the German physicist Johannes Stark, who discovered it in 1913. It was independently discovered in the same year by the Italian physicist Antonino Lo Surdo. The discovery of this effect contributed importantly to the development of quantum theory and Stark was awarded with the


id: stark-effect-20260505-1
file: data/en.wikipedia.org/wiki/Stark_effect-1.md
category: reference
title: Stark effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stark_effect
date_saved: 2026-05-05T10:56:28.115020+00:00
instance: kb-cron
parent: stark-effect-20260505-0
summary:
where q {\displaystyle q} and μ {\displaystyle {\boldsymbol {\mu }}} are, respectively, the total charge (zero moment) and the dipole moment of the charge distribution. Classical macroscopic objects are usually neutral or quasi-neutral ( q = 0 {\displaystyle q=0} ), so the first, monopole, term in the expression above is identically zero. This is also the case for a neutral atom or molecule. However, for an ion this is no longer true. Nevertheless, it is often justified to omit it in this case, too. Indeed, the Stark effect is observed in spectral lines, which are emitted when an electron "jumps" between two bound states. Since such a transition only alters the internal degrees of freedom of the radiator but not its charge, the effects of the monopole interaction on the initial and final states exactly cancel each other. === Perturbation theory === Turning now to quantum mechanics an atom or a molecule can be thought of as a collection of point charges (electrons and nuclei), so that the second definition of the dipole applies. The interaction of atom or molecule with a uniform external field is described by the operator V i n t = − F ⋅ μ .


id: stark-effect-20260505-2
file: data/en.wikipedia.org/wiki/Stark_effect-2.md
category: reference
title: Stark effect
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stark_effect
date_saved: 2026-05-05T10:56:28.115020+00:00
instance: kb-cron
parent: stark-effect-20260505-0
summary:
E k ( 2 ) = ∑ k ′ ≠ k ⟨ ψ k 0 | V i n t | ψ k ′ 0 ⟩ ⟨ ψ k ′ 0 | V i n t | ψ k 0 ⟩ E k ( 0 ) − E k ′ ( 0 ) ≡ − 1 2 ∑ i , j = 1 3 α i j F i F j {\displaystyle E_{k}^{(2)}=\sum _{k'\neq k}{\frac {\langle \psi _{k}^{0}|V_{\mathrm {int} }|\psi _{k^{\prime }}^{0}\rangle \langle \psi _{k'}^{0}|V_{\mathrm {int} }|\psi _{k}^{0}\rangle }{E_{k}^{(0)}-E_{k'}^{(0)}}}\equiv -{\frac {1}{2}}\sum _{i,j=1}^{3}\alpha _{ij}F_{i}F_{j}} with the components of the polarizability tensor α defined by α i j = − 2 ∑ k ′ ≠ k ⟨ ψ k 0 | μ i | ψ k ′ 0 ⟩ ⟨ ψ k ′ 0 | μ j | ψ k 0 ⟩ E k ( 0 ) − E k ′ ( 0 ) . {\displaystyle \alpha _{ij}=-2\sum _{k'\neq k}{\frac {\langle \psi _{k}^{0}|\mu _{i}|\psi _{k'}^{0}\rangle \langle \psi _{k'}^{0}|\mu _{j}|\psi _{k}^{0}\rangle }{E_{k}^{(0)}-E_{k'}^{(0)}}}.} The energy E(2) gives the quadratic Stark effect. Neglecting the hyperfine structure (which is often justified — unless extremely weak electric fields are considered), the polarizability tensor of atoms is isotropic,


id: stimulated-emission-20260505-0
file: data/en.wikipedia.org/wiki/Stimulated_emission-0.md
category: reference
title: Stimulated emission
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stimulated_emission
date_saved: 2026-05-05T10:56:29.293495+00:00
instance: kb-cron
parent: stimulated-emission-20260505-0
summary:
Stimulated emission is the process by which an incoming photon of a specific frequency can interact with an excited atomic electron (or other excited molecular state), causing it to drop to a lower energy level. The liberated energy transfers to the electromagnetic field, creating a new photon with a frequency, polarization, and direction of travel that are all identical to the photons of the incident wave. This is in contrast to spontaneous emission, which occurs at a characteristic rate for each of the atoms/oscillators in the upper energy state regardless of the external electromagnetic field. According to the American Physical Society, the first person to correctly predict the phenomenon of stimulated emission was Albert Einstein in a series of papers starting in 1916, culminating in what is now called the Einstein B Coefficient. Einstein's work became the theoretical foundation of the maser and the laser. The process is identical in form to atomic absorption in which the energy of an absorbed photon causes an identical but opposite atomic transition: from the lower level to a higher energy level. In normal media at thermal equilibrium, absorption exceeds stimulated emission because there are more electrons in the lower energy states than in


id: stimulated-emission-20260505-1
file: data/en.wikipedia.org/wiki/Stimulated_emission-1.md
category: reference
title: Stimulated emission
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stimulated_emission
date_saved: 2026-05-05T10:56:29.293495+00:00
instance: kb-cron
parent: stimulated-emission-20260505-0
summary:
where the proportionality constant B21 is known as the Einstein B coefficient for that particular transition, and ρ(ν) is the radiation density of the incident field at frequency ν. The rate of emission is thus proportional to the number of atoms in the excited state N2, and to the density of incident photons. At the same time, there will be a process of atomic absorption which removes energy from the field while raising electrons from the lower state to the upper state. Its rate is precisely the negative of the stimulated emission rate, ∂ N 2 ∂ t = − ∂ N 1 ∂ t = B 12 ρ ( ν ) N 1 . {\displaystyle {\frac {\partial N_{2}}{\partial t}}=-{\frac {\partial N_{1}}{\partial t}}=B_{12}\,\rho (\nu )\,N_{1}.} The rate of absorption is thus proportional to the number of atoms in the lower state, N1. The B coefficients can be calculated using dipole approximation and time dependent perturbation theory in quantum mechanics as: B a b = e 2 6 ϵ 0 ℏ 2 | ⟨ a | r → | b ⟩ | 2 {\displaystyle B_{ab}={\frac {e^{2}}{6\epsilon _{0}\hbar ^{2}}}|\langle a|{\vec {r}}|b\rangle |^{2}} where B corresponds to energy distribution in terms of frequency


id: stimulated-emission-20260505-2
file: data/en.wikipedia.org/wiki/Stimulated_emission-2.md
category: reference
title: Stimulated emission
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Stimulated_emission
date_saved: 2026-05-05T10:56:29.293495+00:00
instance: kb-cron
parent: stimulated-emission-20260505-0
summary:
== Optical amplification == Stimulated emission can provide a physical mechanism for optical amplification. If an external source of energy stimulates more than 50% of the atoms in the ground state to transition into the excited state, then what is called a population inversion is created. When light of the appropriate frequency passes through the inverted medium, the photons are either absorbed by the atoms that remain in the ground state or the photons stimulate the excited atoms to emit additional photons of the same frequency, phase, and direction. Since more atoms are in the excited state than in the ground state then an amplification of the input intensity results. The population inversion, in units of atoms per cubic metre, is Δ N 21 = N 2 − g 2 g 1 N 1 {\displaystyle \Delta N_{21}=N_{2}-{g_{2} \over g_{1}}N_{1}} where g1 and g2 are the degeneracies of energy levels 1 and 2, respectively. === Small signal gain equation === The intensity (in watts per square metre) of the stimulated emission is governed by the following differential equation: d I d z = σ 21 ( ν ) ⋅ Δ N 21 ⋅ I ( z ) {\displaystyle {dI \over dz}=\sigma


id: suction-20260505-0
file: data/en.wikipedia.org/wiki/Suction-0.md
category: reference
title: Suction
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Suction
date_saved: 2026-05-05T10:56:30.451492+00:00
instance: kb-cron
parent: suction-20260505-0
summary:
Suction is the day-to-day term for the movement of gases or liquids along a pressure gradient with the implication that the movement occurs because the lower pressure pulls the gas or liquid. However, the forces acting in this case do not originate from just the lower pressure side, but instead from the side of the higher pressure, as a reaction to the pressure difference. When the pressure in one part of a physical system is reduced relative to another, the fluid or gas in the higher pressure region will exert a force relative to the region of lowered pressure, referred to as pressure-gradient force. If all gas or fluid is removed the result is a perfect vacuum in which the pressure is zero. Hence, no negative pressure forces can be generated. Accordingly, from a physics point of view, the objects are not pulled but pushed. == Examples == Pressure reduction may be static, as in a piston and cylinder arrangement, or dynamic, as in the case of a vacuum cleaner when air flow results in a reduced pressure region. When animals breathe, the diaphragm and muscles around the rib cage cause a change of volume in the lungs. With increasing


id: superconductivity-20260505-0
file: data/en.wikipedia.org/wiki/Superconductivity-0.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T10:56:31.658062+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source. The superconductivity phenomenon was discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes. Like ferromagnetism and atomic spectral lines, superconductivity is a phenomenon which can only be explained by quantum mechanics. It is characterized by the Meissner effect, the complete cancellation of the magnetic field in the interior of the superconductor during its transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics. In 1986, it was discovered that some cuprate-perovskite ceramic materials have a critical temperature above 35 K (−238 °C). It was shortly found (by Ching-Wu Chu) that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K (−181 °C), which was


id: superconductivity-20260505-1
file: data/en.wikipedia.org/wiki/Superconductivity-1.md
category: reference
title: Superconductivity
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Superconductivity
date_saved: 2026-05-05T10:56:31.658062+00:00
instance: kb-cron
parent: superconductivity-20260505-0
summary:
=== Niobium === The first practical application of superconductivity was developed in 1954 with Dudley Allen Buck's invention of the cryotron. Two superconductors with greatly different values of the critical magnetic field are combined to produce a fast, simple switch for computer elements. Soon after discovering superconductivity in 1911, Kamerlingh Onnes attempted to make an electromagnet with superconducting windings but found that relatively low magnetic fields destroyed superconductivity in the materials he investigated. Much later, in 1955, G. B. Yntema succeeded in constructing a small 0.7-tesla iron-core electromagnet with superconducting niobium wire windings. Then, in 1961, J. E. Kunzler, E. Buehler, F. S. L. Hsu, and J. H. Wernick made the startling discovery that, at 4.2 kelvin, niobium–tin, a compound consisting of three parts niobium and one part tin, was capable of supporting a current density of more than 100,000 amperes per square centimeter in a magnetic field of 8.8 tesla. The alloy was brittle and difficult to fabricate, but niobium–tin proved useful for generating magnetic fields as high as 20 tesla. In 1962, T. G. Berlincourt and R. R. Hake discovered that more ductile alloys of niobium and titanium are suitable for applications up to 10 tesla. Commercial production


