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The Nadal formula, also called Nadal's formula, is an equation in railway design that relates the downward force exerted by a train's wheels upon the rail, with the lateral force of the wheel's flange against the face of the rail. This relationship is significant in railway design, as a wheel-climb derailment may occur if the lateral and vertical forces are not properly considered.
The Nadal formula is represented by:
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{\displaystyle \left({\frac {L}{V}}\right){=}\left({\frac {\tan(\delta )-\mu }{1+\mu *\tan(\delta )}}\right)}
In this equation, L and V refer to the lateral and vertical forces acting upon the rail and wheel, δ is the angle made when the wheel flange is in contact with the rail face, and μ is the coefficient of friction between the wheel and the rail.
Typically, the axle load for a railway vehicle should be such that the lateral forces of the wheel against the rail should not exceed 50% of the vertical down-force of the vehicle on the rail. Put another way, there should be twice as much downward force holding the wheel to the rail, as there is lateral force which will tend to cause the wheel to climb in turns. This ratio is accomplished by matching the wheelset with the appropriate rail profile to achieve the L/V ratio desired. If the L/V ratio gets too high, the wheel flange will be pressing against the rail face, and during a turn this will cause the wheel to climb the face of the rail, potentially derailing the railcar.
== Wagner Formula ==
The Nadal formula assumes the wheel remains perpendicular to the rail—it does not take into account hunting oscillation of the wheelset, or the movement of the wheel flange contact point against the rail.
A variation of the Nadal formula, which does take these factors into consideration, is the Wagner formula. As the wheelset yaws relative to the rail, the vertical force V is no longer completely vertical, but is now acting at an angle to the vertical, β. When this angle is factored into the Nadal formula, the result is the Wagner formula:
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{\displaystyle \left({\frac {L}{V}}\right){=}\left({\frac {\tan(\delta )-\mu *\cos \beta }{(1+\mu *\tan(\delta ))*\cos \beta )}}\right)}
When the vertical force is truly vertical (that is, β=0 and therefore cos(β)=1), the Wagner formula equals the Nadal formula.
== References ==

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Nanoelectromechanical systems (NEMS) are a class of devices integrating electrical and mechanical functionality on the nanoscale. NEMS form the next logical miniaturization step from so-called microelectromechanical systems, or MEMS devices. NEMS typically integrate transistor-like nanoelectronics with mechanical actuators, pumps, or motors, and may thereby form physical, biological, and chemical sensors. The name derives from typical device dimensions in the nanometer range, leading to low mass, high mechanical resonance frequencies, potentially large quantum mechanical effects such as zero point motion, and a high surface-to-volume ratio useful for surface-based sensing mechanisms. Applications include accelerometers and sensors to detect chemical substances in the air.
== History ==
=== Background ===
As noted by Richard Feynman in his famous talk in 1959, "There's Plenty of Room at the Bottom," there are many potential applications of machines at smaller and smaller sizes; by building and controlling devices at smaller scales, all technology benefits. The expected benefits include greater efficiencies and reduced size, decreased power consumption and lower costs of production in electromechanical systems.
The first silicon dioxide field effect transistors were built by Frosch and Derick in 1957 at Bell Labs. In 1960, Atalla and Kahng at Bell Labs fabricated a MOSFET with a gate oxide thickness of 100 nm. In 1962, Atalla and Kahng fabricated a nanolayer-base metal–semiconductor junction (M–S junction) transistor that used gold (Au) thin films with a thickness of 10 nm. In 1987, Bijan Davari led an IBM research team that demonstrated the first MOSFET with a 10 nm oxide thickness. Multi-gate MOSFETs enabled scaling below 20 nm channel length, starting with the FinFET. The FinFET originates from the research of Digh Hisamoto at Hitachi Central Research Laboratory in 1989. At UC Berkeley, a group led by Hisamoto and TSMC's Chenming Hu fabricated FinFET devices down to 17 nm channel length in 1998.
=== NEMS ===
In 2000, the first very-large-scale integration (VLSI) NEMS device was demonstrated by researchers at IBM. Its premise was an array of AFM tips which can heat/sense a deformable substrate in order to function as a memory device (Millipede memory). Further devices have been described by Stefan de Haan. In 2007, the International Technical Roadmap for Semiconductors (ITRS) contains NEMS memory as a new entry for the Emerging Research Devices section.
== Atomic force microscopy ==
A key application of NEMS is atomic force microscope tips. The increased sensitivity achieved by NEMS leads to smaller and more efficient sensors to detect stresses, vibrations, forces at the atomic level, and chemical signals. AFM tips and other detection at the nanoscale rely heavily on NEMS.
== Approaches to miniaturization ==
Two complementary approaches to fabrication of NEMS can be found, the top-down approach and the bottom-up approach.
The top-down approach uses the traditional microfabrication methods, i.e. optical, electron-beam lithography and thermal treatments, to manufacture devices. While being limited by the resolution of these methods, it allows a large degree of control over the resulting structures. In this manner devices such as nanowires, nanorods, and patterned nanostructures are fabricated from metallic thin films or etched semiconductor layers. For top-down approaches, increasing surface area to volume ratio enhances the reactivity of nanomaterials.
Bottom-up approaches, in contrast, use the chemical properties of single molecules to cause single-molecule components to self-organize or self-assemble into some useful conformation, or rely on positional assembly. These approaches utilize the concepts of molecular self-assembly and/or molecular recognition. This allows fabrication of much smaller structures, albeit often at the cost of limited control of the fabrication process. Furthermore, while there are residue materials removed from the original structure for the top-down approach, minimal material is removed or wasted for the bottom-up approach.
A combination of these approaches may also be used, in which nanoscale molecules are integrated into a top-down framework. One such example is the carbon nanotube nanomotor.
== Materials ==
=== Carbon allotropes ===
Many of the commonly used materials for NEMS technology have been carbon based, specifically diamond, carbon nanotubes and graphene. This is mainly because of the useful properties of carbon based materials which directly meet the needs of NEMS. The mechanical properties of carbon (such as large Young's modulus) are fundamental to the stability of NEMS while the metallic and semiconductor conductivities of carbon based materials allow them to function as transistors.
Both graphene and diamond exhibit high Young's modulus, low density, low friction, exceedingly low mechanical dissipation, and large surface area. The low friction of CNTs, allow practically frictionless bearings and has thus been a huge motivation towards practical applications of CNTs as constitutive elements in NEMS, such as nanomotors, switches, and high-frequency oscillators. Carbon nanotubes and graphene's physical strength allows carbon based materials to meet higher stress demands, when common materials would normally fail and thus further support their use as a major materials in NEMS technological development.
Along with the mechanical benefits of carbon based materials, the electrical properties of carbon nanotubes and graphene allow it to be used in many electrical components of NEMS. Nanotransistors have been developed for both carbon nanotubes as well as graphene. Transistors are one of the basic building blocks for all electronic devices, so by effectively developing usable transistors, carbon nanotubes and graphene are both very crucial to NEMS.
Nanomechanical resonators are frequently made of graphene. As NEMS resonators are scaled down in size, there is a general trend for a decrease in quality factor in inverse proportion to surface area to volume ratio. However, despite this challenge, it has been experimentally proven to reach a quality factor as high as 2400. The quality factor describes the purity of tone of the resonator's vibrations. Furthermore, it has been theoretically predicted that clamping graphene membranes on all sides yields increased quality numbers. Graphene NEMS can also function as mass, force, and position sensors.
==== Metallic carbon nanotubes ====

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Carbon nanotubes (CNTs) are allotropes of carbon with a cylindrical nanostructure. They can be considered a rolled up graphene. When rolled at specific and discrete ("chiral") angles, and the combination of the rolling angle and radius decides whether the nanotube has a bandgap (semiconducting) or no bandgap (metallic).
Metallic carbon nanotubes have also been proposed for nanoelectronic interconnects since they can carry high current densities. This is a useful property as wires to transfer current are another basic building block of any electrical system. Carbon nanotubes have specifically found so much use in NEMS that methods have already been discovered to connect suspended carbon nanotubes to other nanostructures. This allows carbon nanotubes to form complicated nanoelectric systems. Because carbon based products can be properly controlled and act as interconnects as well as transistors, they serve as a fundamental material in the electrical components of NEMS.
==== CNT-based NEMS switches ====
A major disadvantage of MEMS switches over NEMS switches are limited microsecond range switching speeds of MEMS, which impedes performance for high speed applications. Limitations on switching speed and actuation voltage can be overcome by scaling down devices from micro to nanometer scale. A comparison of performance parameters between carbon nanotube (CNT)-based NEMS switches with its counterpart CMOS revealed that CNT-based NEMS switches retained performance at lower levels of energy consumption and had a subthreshold leakage current several orders of magnitude smaller than that of CMOS switches. CNT-based NEMS with doubly clamped structures are being further studied as potential solutions for floating gate nonvolatile memory applications.
==== Difficulties ====
Despite all of the useful properties of carbon nanotubes and graphene for NEMS technology, both of these products face several hindrances to their implementation. One of the main problems is carbon's response to real life environments. Carbon nanotubes exhibit a large change in electronic properties when exposed to oxygen. Similarly, other changes to the electronic and mechanical attributes of carbon based materials must fully be explored before their implementation, especially because of their high surface area which can easily react with surrounding environments. Carbon nanotubes were also found to have varying conductivities, being either metallic or semiconducting depending on their helicity when processed. Because of this, special treatment must be given to the nanotubes during processing to assure that all of the nanotubes have appropriate conductivities. Graphene also has complicated electric conductivity properties compared to traditional semiconductors because it lacks an energy band gap and essentially changes all the rules for how electrons move through a graphene based device. This means that traditional constructions of electronic devices will likely not work and completely new architectures must be designed for these new electronic devices.
==== Nanoelectromechanical accelerometer ====
Graphene's mechanical and electronic properties have made it favorable for integration into NEMS accelerometers, such as small sensors and actuators for heart monitoring systems and mobile motion capture. The atomic scale thickness of graphene provides a pathway for accelerometers to be scaled down from micro to nanoscale while retaining the system's required sensitivity levels.
By suspending a silicon proof mass on a double-layer graphene ribbon, a nanoscale spring-mass and piezoresistive transducer can be made with the capability of currently produced transducers in accelerometers. The spring mass provides greater accuracy, and the piezoresistive properties of graphene converts the strain from acceleration to electrical signals for the accelerometer. The suspended graphene ribbon simultaneously forms the spring and piezoresistive transducer, making efficient use of space in while improving performance of NEMS accelerometers.
=== Polydimethylsiloxane (PDMS) ===
Failures arising from high adhesion and friction are of concern for many NEMS. NEMS frequently utilize silicon due to well-characterized micromachining techniques; however, its intrinsic stiffness often hinders the capability of devices with moving parts.
A study conducted by Ohio State researchers compared the adhesion and friction parameters of a single crystal silicon with native oxide layer against PDMS coating. PDMS is a silicone elastomer that is highly mechanically tunable, chemically inert, thermally stable, permeable to gases, transparent, non-fluorescent, biocompatible, and nontoxic. Inherent to polymers, the Young's Modulus of PDMS can vary over two orders of magnitude by manipulating the extent of crosslinking of polymer chains, making it a viable material in NEMS and biological applications. PDMS can form a tight seal with silicon and thus be easily integrated into NEMS technology, optimizing both mechanical and electrical properties. Polymers like PDMS are beginning to gain attention in NEMS due to their comparatively inexpensive, simplified, and time-efficient prototyping and manufacturing.
Rest time has been characterized to directly correlate with adhesive force, and increased relative humidity lead to an increase of adhesive forces for hydrophilic polymers. Contact angle measurements and Laplace force calculations support the characterization of PDMS's hydrophobic nature, which expectedly corresponds with its experimentally verified independence to relative humidity. PDMS' adhesive forces are also independent of rest time, capable of versatilely performing under varying relative humidity conditions, and possesses a lower coefficient of friction than that of Silicon. PDMS coatings facilitate mitigation of high-velocity problems, such as preventing sliding. Thus, friction at contact surfaces remains low even at considerably high velocities. In fact, on the microscale, friction reduces with increasing velocity. The hydrophobicity and low friction coefficient of PDMS have given rise to its potential in being further incorporated within NEMS experiments that are conducted at varying relative humidities and high relative sliding velocities.

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==== PDMS-coated piezoresistive nanoelectromechanical systems diaphragm ====
PDMS is frequently used within NEMS technology. For instance, PDMS coating on a diaphragm can be used for chloroform vapor detection.
Researchers from the National University of Singapore invented a polydimethylsiloxane (PDMS)-coated nanoelectromechanical system diaphragm embedded with silicon nanowires (SiNWs) to detect chloroform vapor at room temperature. In the presence of chloroform vapor, the PDMS film on the micro-diaphragm absorbs vapor molecules and consequently enlarges, leading to deformation of the micro-diaphragm. The SiNWs implanted within the micro-diaphragm are linked in a Wheatstone bridge, which translates the deformation into a quantitative output voltage. In addition, the micro-diaphragm sensor also demonstrates low-cost processing at low power consumption. It possesses great potential for scalability, ultra-compact footprint, and CMOS-IC process compatibility. By switching the vapor-absorption polymer layer, similar methods can be applied that should theoretically be able to detect other organic vapors.
In addition to its inherent properties discussed in the Materials section, PDMS can be used to absorb chloroform, whose effects are commonly associated with swelling and deformation of the micro-diaphragm; various organic vapors were also gauged in this study. With good aging stability and appropriate packaging, the degradation rate of PDMS in response to heat, light, and radiation can be slowed.
=== Biohybrid NEMS ===
The emerging field of bio-hybrid systems combines biological and synthetic structural elements for biomedical or robotic applications. The constituting elements of bio-nanoelectromechanical systems (BioNEMS) are of nanoscale size, for example DNA, proteins or nanostructured mechanical parts. Examples include the facile top-down nanostructuring of thiol-ene polymers to create cross-linked and mechanically robust nanostructures that are subsequently functionalized with proteins.
== Simulations ==
Computer simulations have long been important counterparts to experimental studies of NEMS devices. Through continuum mechanics and molecular dynamics (MD), important behaviors of NEMS devices can be predicted via computational modeling before engaging in experiments. Additionally, combining continuum and MD techniques enables engineers to efficiently analyze the stability of NEMS devices without resorting to ultra-fine meshes and time-intensive simulations. Simulations have other advantages as well: they do not require the time and expertise associated with fabricating NEMS devices; they can effectively predict the interrelated roles of various electromechanical effects; and parametric studies can be conducted fairly readily as compared with experimental approaches. For example, computational studies have predicted the charge distributions and "pull-in" electromechanical responses of NEMS devices. Using simulations to predict mechanical and electrical behavior of these devices can help optimize NEMS device design parameters.
== Reliability and Life Cycle of NEMS ==
=== Reliability and Challenges ===
Reliability provides a quantitative measure of the component's integrity and performance without failure for a specified product lifetime. Failure of NEMS devices can be attributed to a variety of sources, such as mechanical, electrical, chemical, and thermal factors. Identifying failure mechanisms, improving yield, scarcity of information, and reproducibility issues have been identified as major challenges to achieving higher levels of reliability for NEMS devices. Such challenges arise during both manufacturing stages (i.e. wafer processing, packaging, final assembly) and post-manufacturing stages (i.e. transportation, logistics, usage).
==== Packaging ====
Packaging challenges often account for 75–95% of the overall costs of MEMS and NEMS. Factors of wafer dicing, device thickness, sequence of final release, thermal expansion, mechanical stress isolation, power and heat dissipation, creep minimization, media isolation, and protective coatings are considered by packaging design to align with the design of the MEMS or NEMS component. Delamination analysis, motion analysis, and life-time testing have been used to assess wafer-level encapsulation techniques, such as cap to wafer, wafer to wafer, and thin film encapsulation. Wafer-level encapsulation techniques can lead to improved reliability and increased yield for both micro and nanodevices.
==== Manufacturing ====
Assessing the reliability of NEMS in early stages of the manufacturing process is essential for yield improvement. Forms of surface forces, such as adhesion and electrostatic forces, are largely dependent on surface topography and contact geometry. Selective manufacturing of nano-textured surfaces reduces contact area, improving both adhesion and friction performance for NEMS. Furthermore, the implementation of nanopost to engineered surfaces increase hydrophobicity, leading to a reduction in both adhesion and friction.
Adhesion and friction can also be manipulated by nanopatterning to adjust surface roughness for the appropriate applications of the NEMS device. Researchers from Ohio State University used atomic/friction force microscopy (AFM/FFM) to examine the effects of nanopatterning on hydrophobicity, adhesion, and friction for hydrophilic polymers with two types of patterned asperities (low aspect ratio and high aspect ratio). Roughness on hydrophilic surfaces versus hydrophobic surfaces are found to have inversely correlated and directly correlated relationships respectively.
Due to its large surface area to volume ratio and sensitivity, adhesion and friction can impede performance and reliability of NEMS devices. These tribological issues arise from natural down-scaling of these tools; however, the system can be optimized through the manipulation of the structural material, surface films, and lubricant. In comparison to undoped Si or polysilicon films, SiC films possess the lowest frictional output, resulting in increased scratch resistance and enhanced functionality at high temperatures. Hard diamond-like carbon (DLC) coatings exhibit low friction, high hardness and wear resistance, in addition to chemical and electrical resistances. Roughness, a factor that reduces wetting and increases hydrophobicity, can be optimized by increasing the contact angle to reduce wetting and allow for low adhesion and interaction of the device to its environment.
Material properties are size-dependent. Therefore, analyzing the unique characteristics on NEMS and nano-scale material becomes increasingly important to retaining reliability and long-term stability of NEMS devices. Some mechanical properties, such as hardness, elastic modulus, and bend tests, for nano-materials are determined by using a nano indenter on a material that has undergone fabrication processes. These measurements, however, do not consider how the device will operate in industry under prolonged or cyclic stresses and strains. The theta structure is a NEMS model that exhibits unique mechanical properties. Composed of Si, the structure has high strength and is able to concentrate stresses at the nanoscale to measure certain mechanical properties of materials.

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==== Residual stresses ====
To increase reliability of structural integrity, characterization of both material structure and intrinsic stresses at appropriate length scales becomes increasingly pertinent. Effects of residual stresses include but are not limited to fracture, deformation, delamination, and nanosized structural changes, which can result in failure of operation and physical deterioration of the device.
Residual stresses can influence electrical and optical properties. For instance, in various photovoltaic and light emitting diodes (LED) applications, the band gap energy of semiconductors can be tuned accordingly by the effects of residual stress.
Atomic force microscopy (AFM) and Raman spectroscopy can be used to characterize the distribution of residual stresses on thin films in terms of force volume imaging, topography, and force curves. Furthermore, residual stress can be used to measure nanostructures' melting temperature by using differential scanning calorimetry (DSC) and temperature dependent X-ray Diffraction (XRD).
== Future ==
Key hurdles currently preventing the commercial application of many NEMS devices include low-yields and high device quality variability. Before NEMS devices can actually be implemented, reasonable integrations of carbon based products must be created. A recent step in that direction has been demonstrated for diamond, achieving a processing level comparable to that of silicon. The focus is currently shifting from experimental work towards practical applications and device structures that will implement and profit from such novel devices. The next challenge to overcome involves understanding all of the properties of these carbon-based tools, and using the properties to make efficient and durable NEMS with low failure rates.
Carbon-based materials have served as prime materials for NEMS use, because of their exceptional mechanical and electrical properties.
Recently, nanowires of chalcogenide glasses have shown to be a key platform to design tunable NEMS owing to the availability of active modulation of Young's modulus.
The global market of NEMS is projected to reach $108.88 million by 2022.
== Applications ==
Nanoelectromechanical relay
Nanoelectromechanical systems mass spectrometer
=== Nanoelectromechanical-based cantilevers ===
Researchers from the California Institute of Technology developed a NEM-based cantilever with mechanical resonances up to very high frequencies (VHF). It is incorporation of electronic displacement transducers based on piezoresistive thin metal film facilitates unambiguous and efficient nanodevice readout. The functionalization of the device's surface using a thin polymer coating with high partition coefficient for the targeted species enables NEMS-based cantilevers to provide chemisorption measurements at room temperature with mass resolution at less than one attogram. Further capabilities of NEMS-based cantilevers have been exploited for the applications of sensors, scanning probes, and devices operating at very high frequency (100 MHz).
== References ==

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Performance science is the multidisciplinary study of human performance. It draws together methodologies across numerous scientific disciplines, including those of biomechanics, economics, physiology, psychology, and sociology, to understand the fundamental skills, mechanisms, and outcomes of performance activities and experiences. It carries implications for various domains of skilled human activity, often performed under extreme stress and/or under the scrutiny of audiences or evaluators. These include performances across the arts, sport, education, and business, particularly those occupations involving the delivery of highly trained skills such as in surgery and management.
== Centers of research and teaching ==
USC Performance Science Institute, University of Southern California
711th Human Performance Wing, Wright-Patterson Air Force Base
Centre for Human Performance Sciences, Stellenbosch University
Centre for Performance Science, a partnership of the Royal College of Music and Imperial College London
Human Performance Science Research Group, University of Edinburgh
Performance and Science Working Group, Theatre and Performance Research Association
Performance Science Unit, Sports Institute for Northern Ireland
== See also ==
Environmental psychology
Industrial and organizational psychology
Military psychology
Music psychology
Sport psychology
== References ==
== External links ==
International Symposium on Performance Science
Frontiers in Psychology: Performance Science (journal)

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Regulatory science is the scientific and technical foundations upon which regulations are based in various industries – particularly those involving health or safety. Regulatory bodies employing such principles in the United States include, for example, the FDA for food and medical products, the EPA for the environment, and the OSHA for work safety.
"Regulatory science" is contrasted with regulatory affairs and regulatory law, which refer to the administrative or legal aspects of regulation, in that the former is focused on the regulations' scientific underpinnings and concerns – rather than the regulations' promulgation, implementation, compliance, or enforcement.
== History ==
Probably the first investigator who recognized the nature of regulatory science was Alvin Weinberg, who described the scientific process used to evaluate effects of ionizing radiation as trans science. The origin of the term regulatory science is unknown. It was probably coined sometimes in the late 1970s in an undated memorandum prepared by A. Alan Moghissi, who was describing scientific issues that the newly formed US Environmental Protection Agency (EPA) was facing . During that period the EPA was forced to meet legally mandated deadlines to make decisions that would require reliance upon science that was not meeting conventional scientific requirements. At that time the prevailing view was that there was no need to establish a new scientific discipline because "science is science" regardless of its application. In the spring of 1985, Moghissi established the Institute for Regulatory Science in the commonwealth of Virginia as a nonprofit organization with the objective to perform scientific studies "at the interface between science and the regulatory system". Moghissi et al. have provided an extensive description of history of regulatory science including various perception of regulatory science leading to the acceptance of regulatory science by the FDA.
== Definition ==
Two federal regulatory agencies have provided definitions for regulatory science. According to Food and Drug Administration: “Regulatory Science is the science of developing new tools, standards, and approaches to assess the safety, efficacy, quality, and performance of all FDA-regulated products”. According to Environmental Protection Agency (EPA): “Regulatory science means scientific information including assessments, models, criteria documents, and regulatory impact analyses that provide the basis for significant regulatory decisions”.
Moghissi et al. have described the history of regulatory science and define it as:
“Regulatory science consists of an applied version of various scientific disciplines used in the regulatory process”. Based on their definition the generalized FDA definition is: Regulatory science is the science of developing new tools, standards, and approaches derived from various scientific disciplines to assess the safety, efficacy, quality, and performance of all FDA-regulated products. Similarly, the generalized EPA definition is:
Regulatory science means scientific information including assessments, models, criteria documents, and regulatory impact analyses derived from various scientific disciplines that provide the basis for EPA final significant regulatory decisions.
There have been several attempts to define regulatory science. In many cases there are claims that there is a difference between regulatory science and “normal science”, “academic science”, “research science”. or compliance with regulations. The primary problem is the lack of appreciation that many branches of science are evolving and much of the evolving science includes inherent uncertainties.
== Application of regulatory science ==
Regulatory science is included in every regulation that includes science. The regulatory science community consists of three groups of regulatory scientists:
Those who are involved in development of regulations. Typically this group is employed by regulatory agencies
Those who must comply with regulations. Typically this group consists of employees or contractors of regulated community.
Those segments of the scientific community who perform research and development in areas relevant to the relevant regulated community.
The third group is of particular significance as they consist of organizations and individuals who support the first two groups. Included in this group are members of numerous advisory panels, organizations that provide peer reviews, and members of peer review panels. An example of this group is the National Academies consisting of the National Academy of Science, National Academy of Engineering, Institute of Medicine, and National Research Council.
The application of regulatory science occurs in three phases. During the first phase the regulators must meet a legislative or court- mandated deadline and promulgate regulations using their best judgment. The second phase provides opportunity to develop regulatory science tools. These include human health and ecological risk assessment procedures and post marketing evaluation method d processes for drugs ad medical devices. The third Standard Operating phase, used tools developed during the second phase to improve the initial decision. (Moghissi et al.)
== Regulatory engineering ==
Engineering is the development of new products and processes, hence regulatory engineering encompasses principally the development of products and processes to facilitate or better examine regulations or their scientific foundations. Another related segment of regulatory science deal with the application of engineering design or analysis to operations such as the safety of nuclear and other power plants, chemical production facilities, mining operations, and air transportation.
Sometimes the term "regulatory engineer(ing)" is misused to refer to essentially administrative or regulatory roles dealing with organizing or coordinating regulatory matters for an organization; however, "engineering" refers only to functional design of products and processes, and in many jurisdictions this definition is legally enforced (see Regulation and licensure in engineering).
== Areas of focus ==

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=== Regulatory pharmaceutical medicine ===
Consistent with its mission, the Food and Drug Administration (FDA) suggests, “Regulatory science is the science of developing new tools, standards and approaches to assess the safety, efficacy, quality and performance of FDA-regulated products.”
Based on several decades of experience regulatory science is logically defined as a distinct scientific discipline constituting the scientific foundation of regulatory, legislative, and judicial decisions. Much like many scientific disciplines that have evolved within the last several decades, regulatory science is both interdisciplinary and multidisciplinary and relies upon a large number of basic and applied scientific disciplines.
Regulatory science is an emerging area of interest within pharmaceutical medicine as the shaping and implementation of legislation and guidelines. One definition of “regulatory science” is the science of developing new tools, standards and approaches to evaluate the efficacy, safety, quality and performance of medical products in order to assess benefit-risk and facilitate a sound and transparent regulatory decision-making. It has been recognized as having a significant impact on the industry’s ability to bring new medicines and medical devices to patients in need. Regulatory science challenges current concepts of benefit/risk assessment, submission and approval strategies, patient’s involvement and ethical aspects. It creates the platform for launching new ideas – not only by the pharmaceutical industry and regulatory authorities, but also by, for example, academia, who wants to contribute to better use of their research activities within medical aspects. Regulatory science has the potential as an enabler for directing companies towards more efficient global development of medical products as well as more robust quality decision-making processes.
=== Human health ===
By far the predominant foci of regulatory science pertain to human health and well-being. This realm covers a broad range of scientific areas – including pollution and toxicology, work safety, food, drugs, and numerous others.
=== Ecology ===
Regulatory ecology covers the protection of various species, protection of wetlands, and numerous other regulated areas, including ecotoxicology.
For example, the US Clean Water Act is based upon an interest in protecting water quality for its own sake, in contrast with the Clean Air Act which is premised upon protecting air quality only for the sake of human health; however, these are ideological policy premises rather than scientific matters themselves.
The US Department of Agriculture regulates animal care, and the FDA regulates humaneness for animal studies.
The US Department of Interior, Fish and Wildlife Service (USFWS), and National Oceanographic and Atmospheric Administration, National Marine Fisheries Service, implement the development and enforcement of policies required by the Federal Endangered Species Act (FESA), Migratory Bird Treaty Act, and other biological resources laws. The FESA requires that the decisions to list a species as endangered or threatened are based on the best available scientific data. To that end, the USFWS and other government agencies fund research to determine the conservation status of proposed species. Regulatory scientists within the Services review, evaluate, and incorporate data from these studies of proposed species in their published regulations. Survey protocols for listed species are also developed from scientific studies of their target species. The purpose of the protocols is to reliably and accurately determine the residency of the target species in a given study area.
== Regulatory economics ==
There are numerous economic decisions in the regulatory process, including the economics part of cost-benefit analysis.
== Science in legislation and in courts ==
Although often less than fully recognized, the scientific foundation of legislative decisions is included in regulatory science and should be based on reliable science. Similarly, courts have recognized the need to rely upon information that meets scientific requirements.
== References ==
== Further reading ==
Honda, Hiroshi (2016). "Overview of Issues and Discussions in Regulatory Science and Engineering over the Past Four Years in Global Arena" (PDF). American Journal of Environmental Engineering and Science. 3 (1): 1–20. ISSN 2381-1153.

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Although the subject of sexual dimorphism is not in itself controversial, the measures by which it is assessed differ widely. Most of the measures are used on the assumption that a random variable is considered so that probability distributions should be taken into account. In this review, a series of sexual dimorphism measures are discussed concerning both their definition and the probability law on which they are based. Most of them are sample functions, or statistics, which account for only partial characteristics, for example the mean or expected value, of the distribution involved. Further, the most widely used measure fails to incorporate an inferential support.
== Introduction ==
It is widely known that sexual dimorphism is an important component of the morphological variation in biological populations (see, e.g., Klein and Cruz-Uribe, 1984; Oxnard, 1987; Kelley, 1993). In higher Primates, sexual dimorphism is also related to some aspects of the social organization and behavior (Alexander et al., 1979; Clutton-Brock, 1985). Thus, it has been observed that the most dimorphic species tend to polygyny and a social organization based on male dominance, whereas in the less dimorphic species, monogamy and family groups are more common. Fleagle et al. (1980) and Kay (1982), on the other hand, have suggested that the behavior of extinct species can be inferred on the basis of sexual dimorphism and, e.g. Plavcan and van Schaick (1992) think that sex differences in size among primate species reflect processes of an ecological and social nature. Some references on sexual dimorphism regarding human populations can be seen in Lovejoy (1981), Borgognini Tarli and Repetto (1986) and Kappelman (1996).
These biological facts do not appear to be controversial. However, they are based on a series of different sexual dimorphism measures, or indices. Sexual dimorphism, in most works, is measured on the assumption that a random variable is being taken into account. This means that there is a law which accounts for the behavior of the whole set of values that compose the domain of the random variable, a law which is called distribution function. Because both studies of sexual dimorphism aim at establishing differences, in some random variable, between sexes and the behavior of the random variable is accounted for by its distribution function, it follows that a sexual dimorphism study should be equivalent to a study whose main purpose is to determine to what extent the two distribution functions - one per sex - overlap (see shaded area in Fig. 1, where two normal distributions are represented).
== Measures based on sample means ==
In Borgognini Tarli and Repetto (1986) an account of indices based on sample means can be seen. Perhaps, the most widely used is the quotient,
X
¯
m
X
¯
f
,
{\displaystyle {\frac {{\bar {X}}_{m}}{{\bar {X}}_{f}}},}
where
X
¯
m
{\displaystyle {\bar {X}}_{m}}
is the sample mean of one sex (e.g., male) and
X
¯
f
{\displaystyle {\bar {X}}_{f}}
the corresponding mean of the other. Nonetheless, for instance,
log
⁡
X
¯
m
X
¯
f
,
{\displaystyle \operatorname {log} {\frac {{\bar {X}}_{m}}{{\bar {X}}_{f}}},}
100
X
¯
m
−
X
¯
f
X
¯
f
,
{\displaystyle 100{\frac {{\bar {X}}_{m}-{\bar {X}}_{f}}{{\bar {X}}_{f}}},}
100
X
¯
m
−
X
¯
f
X
¯
f
+
X
¯
f
,
{\displaystyle 100{\frac {{\bar {X}}_{m}-{\bar {X}}_{f}}{{\bar {X}}_{f}+{\bar {X}}_{f}}},}
have also been proposed.
Going over the works where these indices are used, the reader misses any reference to their parametric counterpart (see reference above). In other words, if we suppose that the quotient of two sample means is considered, no work can be found where, in order to make inferences, the way in which the quotient is used as a point estimate of
μ
m
μ
f
,
{\displaystyle {\frac {\mu _{m}}{\mu _{f}}},}
is discussed.
By assuming that differences between populations are the objective to analyze, when quotients of sample means are used it is important to point out that the only feature of these populations that seems to be interesting is the mean parameter. However, a population has also variance, as well as a shape which is defined by its distribution function (notice that, in general, this function depends on parameters such as means or variances).
== Measures based on something more than sample means ==
Marini et al. (1999) have illustrated that it is a good idea to consider something other than sample means when sexual dimorphism is analyzed. Possibly, the main reason is that the intrasexual variability influences both the manifestation of dimorphism and its interpretation.
=== Normal populations ===
==== Sample functions ====
It is likely that, within this type of indices, the one used the most is the well-known statistic with Student's t distribution see, for instance, Green, 1989. Marini et al. (1999) have observed that variability among females seems to be lower than among males, so that it appears advisable to use the form of the Student's t statistic with degrees of freedom given by the Welch-Satterthwaite approximation,
T
=
X
¯
1
−
X
¯
2
−
(
μ
1
−
μ
2
)
S
1
2
n
1
+
S
2
2
n
2
:
t
ν
,
{\displaystyle T={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}-(\mu _{1}-\mu _{2})}{\sqrt {{\frac {S_{1}^{2}}{n_{1}}}+{\frac {S_{2}^{2}}{n_{2}}}}}}:t_{\nu },}
ν
=
(
S
1
2
n
1
+
S
2
2
n
2
)
2
S
1
2
n
1
(
n
1
−
1
)
+
S
2
2
n
2
(
n
2
−
1
)
,
{\displaystyle \nu ={\frac {({\frac {S_{1}^{2}}{n_{1}}}+{\frac {S_{2}^{2}}{n_{2}}})^{2}}{{\frac {S_{1}^{2}}{n_{1}(n_{1}-1)}}+{\frac {S_{2}^{2}}{n_{2}(n_{2}-1)}}}},}
where
S
i
2
,
n
i
,
i
=
1
,
2
{\displaystyle S_{i}^{2},n_{i},i=1,2}
are sample variances and sample sizes, respectively.
It is important to point out the following:

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when this statistic is taken into account in sexual dimorphism studies, two normal populations are involved. From these populations two random samples are extracted, each one corresponding to a sex, and such samples are independent.
when inferences are considered, what we are testing by using this statistic is that the difference between two mathematical expectations is a hypothesized value, say
μ
0
=
μ
1
−
μ
2
.
{\displaystyle \mu _{0}=\mu _{1}-\mu _{2}.}
However, in sexual dimorphism analyses, it does not appear reasonably (see Ipiña and Durand, 2000) to assume that two independent random samples have been selected. Rather on the contrary, when we sample we select some random observations - making up one sample - that sometimes correspond to one sex and sometimes to the other.
==== Taking parameters into account ====
Chakraborty and Majumder (1982) have proposed an index of sexual dimorphism that is the overlapping area - to be precise, its complement - of two normal density functions (see Fig. 1). Therefore, it is a function of four parameters
μ
i
,
σ
i
2
,
i
=
1
,
2
{\displaystyle \mu _{i},\sigma _{i}^{2},i=1,2}
(expected values and variances, respectively), and takes the shape of the two normals into account. Inman and Bradley (1989) have discussed this overlapping area as a measure to assess the distance between two normal densities.
Regarding inferences, Chakraborty and Majumder proposed a sample function constructed by considering the Laplace-DeMoivre's theorem (an application to binomial laws of the central limit theorem). According to these authors, the variance of such a statistic is,
var
⁡
(
D
^
)
=
p
^
m
(
1
−
p
^
m
)
n
m
+
p
^
f
(
1
−
p
^
f
)
n
f
,
{\displaystyle \operatorname {var} ({\widehat {D}})={\frac {{\widehat {p}}_{m}(1-{\widehat {p}}_{m})}{n_{m}}}+{\frac {{\widehat {p}}_{f}(1-{\widehat {p}}_{f})}{n_{f}}},}
where
D
^
{\displaystyle {\widehat {D}}}
is the statistic, and
p
^
i
,
n
i
,
i
=
m
,
f
{\displaystyle {\widehat {p}}_{i},n_{i},i=m,f}
(male, female) stand for the estimate of the probability of observing the measurement of an individual of the
i
{\displaystyle i}
sex in some interval of the real line, and the sample size of the i sex, respectively. Notice that this implies that two independent random variables with binomial distributions have to be regarded. One of such variables is number of individuals of the f sex in a sample of size
n
f
{\displaystyle n_{f}}
composed of individuals of the f sex, which seems nonsensical.
=== Mixture models ===
Authors such as Josephson et al. (1996) believe that the two sexes to be analyzed form a single population with a probabilistic behavior denominated a mixture of two normal populations. Thus, if
X
{\displaystyle X}
is a random variable which is normally distributed among the females of a population and likewise this variable is normally distributed among the males of the population, then,
f
(
x
)
=
∑
i
=
1
n
π
i
f
i
(
x
)
,
−
∞
<
x
<
∞
,
{\displaystyle f(x)=\sum _{i=1}^{n}\pi _{i}f_{i}(x),-\infty <x<\infty ,}
is the density of the mixture with two normal components, where
f
i
,
π
i
,
i
=
1
,
2
{\displaystyle f_{i},\pi _{i},i=1,2}
are the normal densities and the mixing proportions of both sexes, respectively. See an example in Fig. 2 where the thicker curve represents the mixture whereas the thinner curves are the
π
i
f
i
{\displaystyle \pi _{i}f_{i}}
functions.
It is from a population modelled like this that a random sample with individuals of both sexes can be selected. Note that on this sample tests which are based on the normal assumption cannot be applied since, in a mixture of two normal components,
π
i
f
i
{\displaystyle \pi _{i}f_{i}}
is not a normal density.
Josephson et al. limited themselves to considering two normal mixtures with the same component variances and mixing proportions. As a consequence, their proposal to measure sexual dimorphism is the difference between the mean parameters of the two normals involved. In estimating these central parameters, the procedure used by Josephson et al. is the one of Pearson's moments. Nowadays, the EM expectation maximization algorithm (see McLachlan and Basford, 1988) and the MCMC Markov chain Monte Carlo Bayesian procedure (see Gilks et al., 1996) are the two competitors for estimating mixture parameters.
Possibly the main difference between considering two independent normal populations and a mixture model of two normal components is in the mixing proportions, which is the same as saying that in the two independent normal population model the interaction between sexes is ignored. This, in turn implies that probabilistic properties change (see Ipiña and Durand, 2000).
==== The MI measure ====
Ipiña and Durand (2000, 2004) have proposed a measure of sexual dimorphism called
M
I
{\displaystyle MI}
. This proposal computes the overlapping area between the
π
1
f
1
{\displaystyle \pi _{1}f_{1}}
and
π
2
f
2
{\displaystyle \pi _{2}f_{2}}
functions, which represent the contribution of each sex to the two normal components mixture (see shaded area in Fig. 2). Thus,
M
I
{\displaystyle MI}
can be written,
M
I
=
∫
R
min
⁡
[
π
1
f
1
(
x
)
,
(
1
−
π
1
)
f
2
(
x
)
]
d
x
,
{\displaystyle MI=\int _{R}\operatorname {min} [\pi _{1}f_{1}(x),(1-\pi _{1})f_{2}(x)]\,dx,}

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R
{\displaystyle R}
being the real line.
The smaller the overlapping area the greater the gap between the two functions
π
1
f
1
{\displaystyle \pi _{1}f_{1}}
and
π
2
f
2
{\displaystyle \pi _{2}f_{2}}
, in which case the sexual dimorphism is greater. Obviously, this index is a function of the five parameters that characterize a mixture of two normal components
(
μ
i
,
σ
i
2
,
π
1
,
i
=
1
,
2
)
{\displaystyle (\mu _{i},\sigma _{i}^{2},\pi _{1},i=1,2)}
. Its range is in the interval
(
0
,
0.5
]
{\displaystyle (0,0.5]}
, and the interested reader can see, in the work of the authors who proposed the index, the way in which an interval estimate is constructed.
=== Measures based on non-parametric methods ===
Marini et al. (1999) have suggested the Kolmogorov-Smirnov distance as a measure of sexual dimorphism. The authors use the following form of the statistic,
max
x
⁡
|
F
1
(
x
)
−
F
2
(
x
)
|
,
{\displaystyle \operatorname {max} _{x}|F_{1}(x)-F_{2}(x)|,}
with
F
i
,
i
=
1
,
2
{\displaystyle F_{i},i=1,2}
being sample cumulative distributions corresponding to two independent random samples.
Such a distance has the advantage of being applicable whatever the form of the random variable distributions concerned, yet they should be continuous. The use of this distance assumes that two populations are involved. Further, the Kolmogorov-Smirnov distance is a sample function whose aim is to test that the two samples under analysis have been selected from a single distribution. If one accepts the null hypothesis, then there is not sexual dimorphism; otherwise, there is.
== See also ==
Bateman's principle
Digit ratio
Gender differences
Sexual dimorphism
== References ==

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Spacecraft electric propulsion encompasses propulsion systems that use electric energy to accelerate and expel propellant, generating thrust through electric or magnetic fields. Their principal advantage over chemical rockets is much higher specific impulse, meaning greater propellant efficiency, but the limited electrical power available aboard spacecraft yields much lower thrust, making electric propulsion unsuitable for launch from Earth's surface and better suited to long-duration in-space maneuvers.
The main families of spacecraft electric propulsion include electrostatic devices such as gridded ion engines, Hall-effect thrusters, and colloid thrusters; electromagnetic devices such as pulsed plasma thrusters, magnetoplasmadynamic thrusters, and pulsed inductive thrusters; and electrothermal devices such as resistojets and arcjets. Radio-frequency and electron cyclotron resonance ion engines form a further subclass that avoids physical electrode contact with the propellant plasma.
Electric propulsion concepts date to Konstantin Tsiolkovsky's 1911 writings and Robert H. Goddard's 1917 electrostatic accelerator patent, with the first laboratory thruster built by Valentin Glushko at the Gas Dynamics Laboratory in 1933. The first electric engine operated in space aboard SERT-1 in 1964, and Hall-effect thrusters entered operational service on Soviet Meteor spacecraft in the 1970s. After the Cold War, Western researchers gained direct access to Soviet Hall thruster technology, and by the late 1990s electric propulsion had entered routine commercial geostationary satellite service and deep-space primary propulsion with Deep Space 1. Later milestones include Dawn's ion-propelled orbits of Vesta and Ceres, BepiColombo's high-performance gridded ion thruster system, and Psyche's first use of Hall Effect thrusters in interplanetary space.
== Background and history ==
Traditional rocketry has dominated aerospace propulsion in the 20th and early 21st centuries. Conventional rockets achieve motion by expelling mass, most commonly the combustion output from chemical propellants to generate thrust via Newton's third law, which is the familiar rocket launch with explosive flame and smoke beneath it. Electric propulsion developed as a parallel track for spacecraft propulsion, focusing on electrical and electrostatic methods of accelerating propellant rather than relying solely on chemical combustion.
=== 1900s to the 1950s ===
Early antecedents of electric propulsion emerged by the early 20th century. Konstantin Tsiolkovsky writing in 1911 included an early published statement of the basic electric-propulsion idea: using electricity to increase the velocity of ejected particles. Tsiolkovsky wrote:
It is possible that in time we may use electricity to produce a large velocity for the particles ejected from a rocket device.
Early work on electrostatic acceleration dates to Robert H. Goddard, whose 1917 patent application (granted 1920) Edgar Choueiri has described in Journal of Propulsion and Power as the first documented electrostatic ion accelerator intended for propulsion. In his 1918-1919 manuscript "To whomsoever will read in order to build", Yuri Kondratyuk discussed electric propulsion in the context of cathode rays and described thrust from electrically discharging and repelling material particles, alongside a schematic that Choueiri noted may be the "first conceptualization of a colloid thruster". Hermann Oberth's 1929 book Wege zur Raumschiffahrt defined, in Edgar Choueiri's assessment, 'for the first time publicly and unambiguously' that related propulsion concepts were 'a serious and worthy pursuit in astronautics'.
During the interwar period, early electric-propulsion work began moving from theory toward experiment. Valentin Glushko joined the Gas Dynamics Laboratory in Leningrad in 1929, and by 1933 with staff developed an early electric thruster prototype, an electrothermal approach intended for spacecraft propulsion. The device was likely the first electric thruster to ever be studied on a thruster stand, and was the first electrothermal thruster ever built.
According to Choueiri, early thinking and experimentation in related propulsion research focused mainly on electrostatic concepts, but the first laboratory electric thruster was electrothermal and the first electric thruster to fly in space was a mostly electromagnetic pulsed plasma device. After the 1930s, related electric-propulsion research reached a lull in public published activity for over a decade through and after World War II.
The postwar period saw growing institutional interest in electric propulsion within both military and civilian research programs. The first clear postwar reappearance of these propulsion concepts in open scientific literature was in December 1945, in the Journal of the American Rocket Society, where the term "ion rocket" was first coined by Herbert Radd. In 1947 at Fort Bliss, Wernher von Braun encouraged Ernst Stuhlinger to investigate his spacecraft propulsion ideas, telling Stuhlinger, "I wouldn't be a bit surprised if one day we flew to Mars electrically!"
=== 1960s-1970s ===
During the 1960s through the 1970s, electric and electromagnetic propulsion matured experimentally, with some systems flying in limited operational roles. Electric propulsion research during this period expanded across multiple countries and institutional settings.

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In West Germany, electric-propulsion development also proceeded from 1960 at German Aerospace Center (DLR) institutes in Stuttgart and Braunschweig and at the University of Giessen. At Gießen, Horst Löb's group began development of radio-frequency ion thrusters of the RIT type, which use radio frequency fields rather than physical electrodes to ionize propellant, starting with the conception, laboratory model, and first tests of the RIT-10; the prototype was further improved through the 1960s and transferred to industry for qualification in 1970. A June 1960 decree of the Central Committee and Council of Ministers (No. 715-296), declassified after the Soviet period, directed the development of "space electric rocket engines". This included ion and electroplasma thrusters with target specific impulse of 5,000-10,000 seconds, a measure of propellant efficiency, assigning work to OKB-1, the Kurchatov Institute, and other named bureaus as part of a broader 1960-1967 Soviet Union space development plan. In 1964, Ernst Stuhlinger published Ion Propulsion for Space Flight, characterized by Choueiri as the first comprehensive book on electric rocket technology, marking the field's transition into a serious engineering discipline.
On 20 July 1964, two electrostatic ion engines were tested in space in the Space Electric Rocket Test (SERT I), and the mercury electron-bombardment engine produced thrust in flight. SERT I was the first spacecraft to incorporate electric propulsion; its mercury electron bombardment ion engine, which ionizes mercury vapor by bombarding it with electrons and then accelerates the resulting ions electrically, ran for 31 minutes, becoming the first electric engine to operate in space. A 1966 NASA Lewis Research Center overview stated that electric-propulsion spacecraft then under study could not be expected to take off from Earth and therefore would need to be launched to Earth orbit by chemical rockets before beginning low-thrust operation. The 30 November 1964 Zond 2 mission to Mars from the Soviet Union marked the first planetary use of electric propulsion. Following the Zond 2 demonstration, pulsed plasma thruster development was transferred from the Kurchatov Institute to OKB Fakel, whose "Globus" pulsed propulsion unit flew in 1968. The follow-on Space Electric Rocket Test II (SERT II), launched on 3 February 1970, was the first long-duration operation of ion thrusters in space; its two mercury electron-bombardment engines accumulated over 5 months and 3.5 months of continuous operation respectively, and after intermittent restarts, one thruster logged over 11 years of total operation through 1981.
Alongside ion engine development, a distinct line of electromagnetic thruster research was advancing in the Soviet Union. In the 1960s, A. I. Morozov proposed the stationary plasma thruster (SPT), a Hall-effect device that accelerates ionized propellant using perpendicular electric and magnetic fields. Within decades, hundreds would fly in space.
The first SPT was tested in orbit aboard a Meteor spacecraft in 1972, with corrective propulsion units operating on further Meteor missions through 1980.
=== 1980s ===
Commercial electrothermal propulsion entered operational satellite service during this period. Hydrazine resistojets, electric thrusters that heat propellant before expelling it, began commercial geostationary north-south orbital station-keeping, used to maintain orbital position, with Intelsat V in 1980.
=== 1990s ===
The end of the Cold War opened access to previously restricted Soviet electric propulsion technology. U.S. electric propulsion specialists traveled to Russia in 1991 to evaluate the Russian SPT-100 at the Scientific-Research Institute of Thermal Processes in Moscow and at Fakel in Kaliningrad using U.S. instrumentation. Brophy's subsequent JPL report said the measured performance appeared close to the advertised values, and noted claims that more than fifty lower-power SPT units had already flown on Russian spacecraft. The report laid out a second program phase in which thrusters would be brought to the United States for testing toward possible Western use. That work fed into the later Ballistic Missile Defense Organization Russian Hall Electric Thruster Technology (RHETT) effort to move Hall thruster technology toward Western operational use.
Electric-propulsion work matured across the decade. Hydrazine-based arcjet rockets were deployed in 1993 on Telstar 401, extending electrothermal electric propulsion into higher-performance commercial geostationary use.
Alongside these experimental programs, electric propulsion was also entering routine commercial service. Commercial electric propulsion also entered Western geostationary satellite operations in the 1990s, as Hughes Boeing 601HP communications satellites began using gridded xenon ion thrusters (XIPS) for station-keeping in 1997. After initial Russian usage from the 1970s, beginning in the 1990s qualified SPT units entered service on American and European spacecraft as well. European electric propulsion programs reached similar milestones in the years that followed. The Gießen RIT line later reached flight application on the European Space Agency's Artemis satellite, launched in 2001, which carried two German RIT-10 thrusters for station-keeping. By the late 1990s, ESA was already positioning solar electric primary propulsion as a key technology for future deep-space missions through SMART-1, whose PPS-1350-G Hall thruster was later developed in the CNES Stentor satellite program and adapted from a geostationary station-keeping design.
By the late 1990s, electric propulsion had moved from experimental and military programs into routine commercial satellite operations, particularly for geostationary station-keeping, orbit raising, and related orbit-control maneuvers. Deep Space 1 became the first U.S. space mission to use an ion thruster as its primary means of propulsion through 1998, validating NASA's NSTAR solar electric propulsion system in long-duration flight.
=== 21st century ===

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SMART-1, launched in 2003, demonstrated solar electric primary propulsion in flight for ESA and carried the Hall thruster system that had been developed from late-1990s European work on commercial electric-propulsion applications and deep-space mission preparation.
While electric-propulsion research and deployment continued, new systems were also launched into space. Hayabusa was launched by the Japan Aerospace Exploration Agency in 2003, propelled by electrodeless plasma thruster technology. By 2012, more than 270 Hall-effect SPT units had operated on over 60 Russian spacecraft. NASA's Dawn became the first spacecraft to orbit an object in the main asteroid belt at Vesta in 2011, and the first to orbit a dwarf planet at Ceres in 2015. Its ion propulsion system made Dawn the only spacecraft ever to orbit two extraterrestrial destinations. ESA's GOCE in 2009 and JAXA's Super Low Altitude Test Satellite "TSUBAME" (2017-2019) marked later electric-propulsion milestones by demonstrating continuous drag compensation and ion-engine-supported super-low-altitude operations in very low Earth orbit.
ESA and JAXA's BepiColombo, launched in 2018, marked a later major milestone in solar electric propulsion when its Solar Electric Propulsion System began in-flight commissioning in November 2018, in what ESA described as the first in-flight operation of the most powerful and highest-performance electric propulsion system flown on any space mission to date.
In November 2023, Psyche became the first spacecraft to use Hall effect thrusters in interplanetary space, beyond the Earth-Moon system. The spacecraft uses its electric thrusters for both primary propulsion and momentum control and carries no chemical propulsion system. It is scheduled to enter orbit around the asteroid (16) Psyche in 2029.
== Definitions ==
Spacecraft electric propulsion is generally classified by how electrical energy is used to accelerate propellant: electrothermal systems heat propellant before expansion, electrostatic systems accelerate ions through electric fields, and electromagnetic systems accelerate plasma through the interaction of electric currents and magnetic fields. Over time, the boundaries between these classes have sometimes been drawn differently in surveys and program literature, especially for devices that combine more than one acceleration mechanism.
Within electric and electromagnetic propulsion, thrust is generated by accelerating and expelling propellant using electric or magnetic fields rather than by coupling to an external environment. Examples include electrostatic ion engines, Hall-effect thrusters, pulsed plasma thrusters, magnetoplasmadynamic thrusters, pulsed inductive thrusters, electrothermal thrusters, and radio-frequency or electron-cyclotron-resonance ion engines.
Conservation of momentum remains a fundamental requirement because these systems close momentum through exhaust rather than through external fields or media.
== Types ==
A wide range of electric propulsion methods have been proposed or demonstrated. Spacecraft electric propulsion is commonly grouped into electrothermal, electrostatic, and electromagnetic systems according to how electrical energy is used to heat, ionize, and accelerate propellant. Electric propulsion is most useful in missions where propellant efficiency matters more than rapid acceleration. In practice it has been used for geostationary station-keeping, orbit raising, deep-space probes, precision attitude and position control, and drag compensation in Earth orbit. These advantages come with operational tradeoffs: low-thrust transfers can require longer maneuver times and, in some cases, higher total delta-v than impulsive chemical maneuvers, so combined chemical-electric mission profiles remain common when transfer time is constrained.
=== Demonstrated ===
Various electric and electromagnetic propulsion approaches and systems have achieved experimental validation, flight heritage, or sustained engineering development.
==== Electric and electromagnetic with carried propellant ====

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Three families of electromagnetic thruster, pulsed plasma thrusters (PPTs), magnetoplasmadynamic thrusters (MPD), and pulsed inductive thrusters (PIT), rely on strong fields. The three differ in lifetime, efficiency, and power scaling, but share advantages common to electromagnetic acceleration: high specific impulse, precision suitable for satellite positioning, robustness, high power processing capability, and relatively simple system-level scaling with available spacecraft power.
PPTs are the only electromagnetic thrusters used on operational satellites. Solid-propellant PPTs first flew in the Soviet Union in 1964 and in the United States in 1968; they initiate an arc discharge across a solid fluorinated polymer bar, ablating a small amount of propellant and accelerating it by the Lorentz body force. Their compact, low-power, pulsed configurations make them suited to satellite positioning and drag compensation, unlike later concepts that rely on inductive or steady-state operation.
MPDs generate thrust through the Lorentz force produced by the interaction of discharge currents with self-induced or externally applied magnetic fields, and have been investigated for both quasi-steady and steady-state spaceflight applications. MPD thrusters have also flown in space in experimental regimes.
The PIT concept originated in the late 1960s and evolved through successive experimental designs focused on performance scaling, circuit optimization, and propellant compatibility. PITs were developed to overcome the erosion and lifetime limitations of electrode-based systems by inducing plasma currents through time-varying magnetic fields, accelerating neutral propellants without physical contact between conductors and plasma. No PIT system has flown in space, but the thruster class remains of interest for high-efficiency, long-duration propulsion with minimal material degradation, particularly in missions requiring flexible propellant selection and reduced contamination risk.
Electron cyclotron resonance thrusters (ECR) use electron cyclotron resonance, in which microwaves transfer energy to electrons spiraling in a magnetic field, to ionize and accelerate a gaseous propellant (commonly xenon), particularly in ionospheric or high-altitude environments. ECRs using electron cyclotron resonance with microwave discharge have flown in space, most notably as the μ10 ion engine system on JAXA's Hayabusa and Hayabusa2 asteroid missions.
Stationary plasma thrusters (SPT), also called Hall-effect thrusters, accelerate ionized propellant (typically xenon) using perpendicular electric and magnetic fields and a circulating electron current. The concept was proposed by A. I. Morozov in the early 1960s, and a 1968 paper on near-wall conductivity in strongly magnetized plasma provided key theoretical grounding for the discharge channel physics. The first SPT was tested in space aboard a Meteor spacecraft launched in December 1971, with orbital firings conducted between February and June 1972; subsequent corrective propulsion units operated on further Meteor missions through 1980. By 2012, more than 270 SPD-70 and SPD-100 thrusters had operated on over 60 Russian spacecraft, and beginning in the 1990s qualified SPT units entered service on American and European spacecraft as well.
The Gießen RIT line used a radio-frequency, electrode-less xenon discharge, a design Löb described as avoiding electrode-related wear while offering high efficiency and high exhaust velocity.
=== Development and testing ===
These are concepts under active engineering development or testing that adapt electric or electromagnetic propulsion principles for new operational regimes.
==== Environment-fed electric propulsion ====
Atmosphere-breathing electric propulsion is a concept in which a spacecraft collects residual atmospheric particles in very low Earth orbit, ionizes them, and accelerates them electromagnetically instead of carrying all propellant onboard. A 2018 European Space Agency technology demonstration was described as the first firing of an air-breathing electric thruster using collected atmospheric molecules as propellant, but no such system has yet flown in space.
Related operational milestones in very low Earth orbit preceded true atmosphere-breathing concepts. ESA's Gravity Field and Steady-State Ocean Circulation Explorer (GOCE), launched on 17 March 2009, became the first-ever mission to fly drag free in low Earth orbit using an electric propulsion system that continually compensated atmospheric drag. JAXA's Super Low Altitude Test Satellite (SLATS) "TSUBAME", launched on 23 December 2017, transitioned to ion-engine orbit-keeping operations in April 2019 and later demonstrated maintenance of six orbital altitudes between 271.1 and 181.1 km, validating super-low-altitude Earth observation operations.
== Selected milestones ==
The following table summarizes selected systems and mission milestones in spacecraft electric propulsion, including both flight-proven applications and developmental concepts discussed in this article.
== See also ==
Bussard ramjet – Proposed spacecraft propulsion method
Emerging technologies – Technology still to be fully developed
Field propulsion – Propulsion concepts and technologies
History of aviation
History of rockets
History of spaceflight
New Millennium Program – NASA projects to test new space technologies
Non-rocket spacelaunch – Concepts for launch into space
Timeline of aviation
Timeline of rocket and missile technology
Timeline of spaceflight
== References ==
This article incorporates public domain material from websites or documents of the United States government.

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Sports science is a discipline that studies how the healthy human body adapts during acute and long-term exercise, and how sports and physical activity promote health and performance from cellular to whole body perspectives. The study of sports science traditionally incorporates areas of physiology (exercise physiology), psychology (sport psychology), anatomy, biomechanics (sports biomechanics), biochemistry, and kinesiology.
== Origins of exercise physiology ==
Sports science can trace its origins back to Ancient Greece. The noted ancient Greek physician Galen (131–201) wrote 87 detailed essays about improving health (proper nutrition), aerobic fitness, and strengthening muscles.
New ideas upon the working and functioning of the human body emerged during the Renaissance as anatomists and physicians challenged the previously known theories. These spread with the implementation of the printed word, the result of Gutenberg's printing press in the 15th century. Allied with this was a large increase in academia in general, universities were forming all around the world. Importantly, these new scholars went beyond the simplistic notions of the early Greek physicians, and shed light upon the complexities of the circulatory, and digestive systems. Furthermore, by the middle of the 19th century, early medical schools (such as the Harvard Medical School, formed 1782) began appearing in the United States, whose graduates went on to assume positions of importance in academia and allied medical research.
Medical journal publications increased significantly in number during this period. In 1898, three articles on physical activity appeared in the first volume of the American Journal of Physiology. Other articles and reviews subsequently appeared in prestigious journals. The German applied physiology publication, Internationale Zeitschrift fur Physiologie einschliesslich Arbeitphysiologie (1929–1940; now known as the European Journal of Applied Physiology and Occupational Physiology), became a significant journal in the field of research.
A number of key figures have made significant contributions to the study of sports science:
Austin Flint, Jr., (1836–1915) One of the first American pioneer physicians, studied physiological responses to exercise in his influential medical textbooks.
Edward Hitchcock, Jr., (1828–1911) Amherst College Professor of Hygiene and Physical Education, devoted his academic career to the scientific study of physical exercise, training, and the body. Coauthored 1860 text on exercise physiology.
George Wells Fitz, M.D. (1860–1934) Created the first departmental major in Anatomy, Physiology, and Physical Training at Harvard University in 1891.
August Krogh (1874–1949) Won the 1920 Nobel Prize in physiology for discovering the mechanism that controlled capillary blood flow in resting or active muscle.
Per-Olof Åstrand (1922–2015) Professor at the Department of Physiology, Karolinska Institute, Stockholm. Wrote a seminal paper which evaluated the physical working capacity of men and women aged 4–33 years.
== Study of sports science ==
A notable amount of research in the field of sports science is completed at universities or dedicated research centers. Higher-education degrees in Sports Science or Human Physiology are also becoming increasingly popular, with many universities now offering both undergraduate, postgraduate and distance learning degrees in the discipline. Opportunities for graduates in these fields include employment as a Physical Education teacher, Dietician or Nutritionist, Performance Analyst, Sports coach, Sports therapist, Fitness center manager, Sports administrator, Strength and Conditioning specialist, or retail manager of a sports store. Graduates may also be well-positioned to undertake further training to become an accredited Physiotherapist, Exercise Physiologist, Research Scientist and Sports Medical Doctor.
Sports science may also be useful for providing information on the aging body. Older adults are aware of the benefits of exercise, but many are not performing the exercise needed to maintain these benefits. Sports science provides a means of allowing older people to regain more physical competence without focusing on doing so for the purposes of anti-aging. Sports science can also provide a means of helping older people avoid falls and have the ability to perform daily tasks more independently.
In Australia, the majority of sports science research from 1983 to 2003 was done in laboratories and nearly half of the research was done with sub-elite or elite athletes. Over two-thirds of the research was done regarding four sports: rowing, cycling, athletics, and swimming. In America, sports play a big part of the American identity, however, sports science has slowly been replaced with exercise science. Sports science can allow athletes to train and compete more effectively at home and abroad.
José Mourinho, a football manager who won UEFA Champions League twice, reflected his studies of sport science as "sometimes it is difficult to understand if it is sport or if it is science".
== Academic journals in sports science ==
Journal of Applied Biomechanics
International Journal of Computer Science in Sport
Journal of Strength & Conditioning Research
Science and Medicine in Football
Medicine & Science in Sports & Exercise
Journal of Science and Medicine in Sport
== Reproducibility ==
A 2018 study criticized the field of exercise and sports science for insufficient replication studies, limited reporting of both null and trivial results, and insufficient research transparency. Statisticians have criticized sports science for common use of magnitude-based inference, a controversial statistical method which has allowed sports scientists to extract apparently significant results from noisy data where ordinary hypothesis testing would have found none. In response to these concerns, metaresearch (research on research) is emerging as a sub-field within sport science. Metaresearch aims to systematically evaluate and improve research practices by examining study design, statistical methods, reporting standards, and ethical considerations. This approach encourages early intervention to prevent poor practices from becoming entrenched, promotes interdisciplinary collaboration, and supports the development of dedicated centres to enhance scientific quality and reproducibility in sport science.
== See also ==
Computer science in sport
Heuristics and sports
Kinanthropometry
Kinesiology
Sports biomechanics
Sports medicine
== References ==
== External links ==
Sport Science International Register
British Association of Sport and Exercise Sciences. Archived 25 May 2017 at the Wayback Machine.
American College of Sports Medicine
European College of Sport Science (archived)
Exercise & Sports Science Australia
National Strength & Conditioning Association

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Strategic Urban Planning (SUP) is a methodical approach aimed at shaping the future of urban areas. It involves setting clear objectives, coordinating public and private efforts, and adapting to new circumstances to enhance the living conditions of the affected citizens. SUP is not a new concept; it has been applied to various aspects of human activity, with notable figures such as Sun Tzu, Arthur Thomson, and Henry Mintzberg contributing to its development.
Fifteen years of practice proved to be enough time for the technique to spread and for the first “Meeting of American and European cities for the Exchange of Experiences in Strategic Planning” to be organized. Institutions sponsoring the meeting, held in Barcelona in 1993, included the Inter-American Development Bank, the European Community Commission and the Iberoamerican Cooperation Institute. The cities of Amsterdam, Lisbon, Lille, Barcelona, Toronto and Santiago de Chile participated, among others.
At that meeting it was demonstrated, along with other relevant aspects, that if cooperative processes are used in large cities in order to carry out strategic planning processes, and if a reasonable degree of comprehension is reached between the administration, businesses and an ample representation of social agents, organizational synergies will develop that will eventually improve resource management and citizens’ quality of life.
== History ==
Strategic Urban Planning processes (SUP), also known as Urban Renewal Projects, began to appear at the end of the 20th century. The city of San Francisco (U.S.A.) carried out its process between 1982 and 1984. The main motivation behind starting strategic urban planning processes was the attempt to adequately react to problematic situations (mainly economic crisis or standstill). At the beginning of the 21st century, this kind of organization is not reactive but proactive. In the case of Spain, crisis situations are not the main causes of these processes, rather they are motivated by the search for an improved level of public-private cooperation, the wish to coordinate activity, continued improvements, the wish to launch revitalization processes and even to follow others . The initial determination needed to launch this type of processes varies by region; in Spain, most processes are fronted by public entities, approximately 50%, while a significant percentage has mixed public-private leadership.
== Description of SUP processes ==
An SUP process, according to Borja and Castells is:
The definition of a city project that unifies diagnoses, specifies public and private actions and establishes a coherent mobilization framework for the cooperation of urban social actors. A participative process is a priority when defining contents, as this process will be the basis for the viability of the objectives and actions proposed. The result of the Strategic plan should not necessarily be the creation of regulations or a government program (although its adoption by the State and Local Government should mean the instigation of regulations, investment, administrative measures, policy initiatives, etc) but rather a policy contract between public institutions and civil society. For this reason, the process following the approval of the plan and the monitoring and implementation of measures or actions is just as or more important than the process of elaboration and consensual approval.
SUP is now considered a type of Governance.
== Basic Stages of an SUP process ==
Using the work of the Technical Secretary as a starting point, work groups debate and approve a diagnosis of the city that includes its localisation. The document must be approved by the executive committee, by the General Council or a full meeting of the corporation as the case may be.
Based on the diagnosis, and keeping in mind its antecedents and conclusions, strengths and weaknesses, the next step is the creation of scenarios and, based on the use of imagination and rigour, the development of prospective tasks related to the creation of future alternatives so that the executive committee can select a model or vision for the city. Their choice will be the basis for the generation of related key topics and/or directions for general actions to be taken.
Once the work teams have been reorganized, mainly made up of key decision-makers and implementers, each key topic and line of action will be dealt with separately, designing a detailed list of necessary and/or advisable projects. Once the results have been consolidated, a prioritised list of projects will be made available from which a selection will be made. The next step is the elaboration of an action plan that includes the agents involved, timing and resources. The people involved in the structure of the process, at least theoretically, are capable of carrying it out; for an example, please consult the document from the General Council of SUP of Valencia [1].
Once all of the previously mentioned documents have been approved, the next step is implementation - carrying out the project itself. This stage is decisive; at this point plans are usually given a structure in which the organization is even more explicitly clarified.
== Implementation of SUP processes ==
The social and economic importance of these processes is quite relevant as they affect millions of people [2] . In Spain, [3] there are nearly one hundred localities that use this methodology, affecting a total population of nearly 15 million people.
== Critical Comments on SUP processes ==
Sectors in the area of civic participation, as well as planning professionals and political activists have all expressed criticism of SUP processes.
However, SUP processes include aspects that favour selective participation, territorial organization and coordination/cooperation between public and private sectors. On the other hand, Strategic Urban Planning processes seem to be independent of political ideologies (for example, the SUP processes in Barcelona [4], Bilbao [5] and Valencia [6] are carried out with mixed Government teams including the following Spanish political formations: PSC-PSOE [7], PNV [8] and PP [9] respectively) and can produce a notable degree of stability in the majority behind the project.
== Theoretical Development ==
Knowledge relating to strategic urban planning processes is evolving in two complementary directions that can be denominated, borrowing concepts from programming, as Bottom-Up and Top-down.

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=== Bottom-Up ===
There are clear differences between what could be called the traditional approach to Strategic planning and the emerging approach (Fernández Güell. Strategic planning of cities).
Before Product predominance, now Process predominance
Before Sector specific, now Integrated
Before Normative, now Strategic
Before Goal-oriented, now Cost-benefit oriented
Before Urban-offer oriented, now Urban-demand oriented
Before Subject to administrative limitations, now Supersedes administrative limitations and enters in Metropolitan areas
Before Open participation, now Focused Participation
Of course, in 2006 there was a clear evolution that attempted to adapt to changes, political sensitivities and even trends. In any case, this is a line of thought and action that takes full advantage of the experience of projects that have already been implemented.
=== Top-Down ===
Given that:
The influence of each agent in the global process under consideration for implementation is yet to be determined;
There are no generally accepted criteria when creating instruments for measuring progress or regression on the path toward achieving main goals;
Cooperation processes among different agents within the city to carry out strategic planning are usually undertaken using a “framework” organisational structure which highlights differences;
Both politics and outside events affect a large city;
this line of research seeks to further the design of a model that will determine the factors related to the success of strategic planning processes in large cities and metropolitan areas [10] es:Aglomeraciones urbanas en la Unión Europea es:Area Metropolitana es:Área metropolitana de Valencia.
Within this branch of research, which seeks a more general theory, two recent Doctoral Theses mentioned in the bibliography can be consulted for further information.
It should be pointed out that a theory explaining Strategic Urban Planning in Metropolitan Areas and/or Regions would involve furthering the consolidation of Social Design es:Diseño Social as a scientific study.
== Bibliography ==
Borja y Castells. “Local y Global”. 1998.
Fernández Güell, J. Miguel. Planificación estratégica de ciudades. 1997.
Ganau Casas, Mallarach Isern. “Planificació estratégica territorial a Catalunya”. 2003.
Pascual Esteve, Josep Mª. “La gestión estratégica de las ciudades”. 2002.
Quintás Alonso, José. “Análisis de los factores y políticas comunitarias que favorecen el diseño y ejecución de la planificación estratégica de Grandes Ciudades y Áreas Metropolitanas, basándose en las experiencias de Barcelona, Bilbao y Valencia”, tesis doctoral leída en febrero de 2006.
Sanguino Galván, Ramón. “Gestión del conocimiento y competitividad: análisis en las ciudades españolas”, tesis doctoral leída en enero de 2005.
Seisdedos, Gildo. Cómo gestionar las ciudades del siglo XXI. Introducción de A. Ruiz Gallardón. Madrid: Prentice Hall (Financial Times), 2007. 204 p. ISBN 978-8483223567
Seisdedos, Gildo. El futuro de la planificación estratégica urbana: del PEU a la EDU. Análisis Local, Vol.78, marzo 2008, (3): 17 - 23. ISSN 1575-5266 http://www.eeg.afi.es/EEGPublicaciones/publicaciones/992429/746522/analisis-local-78-numero-78-iii-2008.html
== See also ==
Planning
Strategic Planning
Urban Planning

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Superslow processes are processes in which values change so little that their capture is very difficult because of their smallness in comparison with the measurement error.
== Applications ==
Most of the time, the superslow processes lie beyond the scope of investigation due to the reason of their superslowness. Multiple gaps can be easily detected in biology, astronomy, physics, mechanics, economics, linguistics, ecology, gerontology, etc.
Biology: Traditional scientific research in this area was focused on the describing some brain reactions.
Mathematics: In mathematics, when the fluid flows through thin and long tubes it forms stagnation zones where the flow becomes almost immobile. If the ratio of tube length to its diameter is large, then the potential function and stream function are almost invariable on very extended areas. The situation seems uninteresting, but if we remember that these minor changes occur in the extra-long intervals, we see here a series of first-class tasks that require the development of special mathematical methods.
Mathematics: Apriori information regarding the stagnation zones contributes to optimization of the computational process by replacing the unknown functions with the corresponding constants in such zones. Sometimes this makes it possible to significantly reduce the amount of computation, for example in approximate calculation of conformal mappings of strongly elongated rectangles.
Economic Geography: The obtained results are particularly useful for applications in economic geography. In a case where the function describes the intensity of commodity trade, a theorem about its stagnation zones gives us (under appropriate restrictions on the selected model) geometric dimensions estimates of the stagnation zone of the world-economy (for more information about a stagnation zone of the world-economy, see Fernand Braudel, Les Jeux de L'echange).
For example, if the subarc of a domain boundary has zero transparency, and the flow of the gradient vector field of the function through the rest of the boundary is small enough, then the domain for such function is its stagnation zone.
Stagnation zones theorems are closely related to pre-Liouville's theorems about evaluation of solutions fluctuation, which direct consequences are the different versions of the classic Liouville theorem about conversion of the entire doubly periodic function into the identical constant.
Identification of what parameters impact the sizes of stagnation zones opens up opportunities for practical recommendations on targeted changes in configuration (reduction or increase) of such zones.
== References ==