Thisglossary of engineering terms is a list of definitions about the major concepts ofengineering. Please see the bottom of the page for glossaries of specific fields of engineering.

Macaulay's method

(The double integration method) is a technique used instructural analysis to determine thedeflection ofEuler-Bernoulli beams. Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading. Typically partial uniformly distributed loads (u.d.l.) and uniformly varying loads (u.v.l.) over the span and a number of concentrated loads are conveniently handled using this technique.

Mach number

The ratio of the speed of an object to the speed of sound.

Machine

A machine (or mechanical device) is amechanical structure that usespower to applyforces and controlmovement to perform an intended action. Machines can be driven byanimals andpeople, by natural forces such aswind andwater, and bychemical,thermal, orelectrical power, and include a system ofmechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also includecomputers and sensors that monitor performance and plan movement, often calledmechanical systems.

Machine code

Incomputer programming, machine code, consisting of machine languageinstructions, is alow-level programming language used to directly control a computer'scentral processing unit (CPU). Each instruction causes the CPU to perform a very specific task, such as a load, a store, ajump, or anarithmetic logic unit (ALU) operation on one or more units of data in the CPU'sregisters ormemory.

Machine element

orhardware, refers to an elementary component of amachine. These elements consist of three basic types:

1. structural components such as frame members,bearings,axles,splines,fasteners,seals, andlubricants,
2. mechanisms thatcontrol movement in various ways such asgear trains,belt orchain drives,linkages,cam andfollower systems, includingbrakes andclutches, and
3. control components such as buttons, switches, indicators, sensors, actuators and computer controllers.^[1]

While generally not considered to be a machine element, the shape, texture and color of covers are an important part of a machine that provide astyling and operational interface between the mechanical components of a machine and its users.Machine elements are basic mechanical parts and features used as the building blocks of most machines.^[2] Most arestandardized to common sizes, but customs are also common for specialized applications.^[3]

Machine learning

(ML), is the study of computeralgorithms that improve automatically through experience and by the use of data.^[4] It is seen as a part ofartificial intelligence. Machine learning algorithms build a model based on sample data, known as "training data", in order to make predictions or decisions without being explicitly programmed to do so.^[5] Machine learning algorithms are used in a wide variety of applications, such as in medicine,email filtering,speech recognition, andcomputer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.^[6]

Maclaurin series

Inmathematics, theTaylor series of afunction is aninfinite sum of terms that are expressed in terms of the function'sderivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor's series are named afterBrook Taylor, who introduced them in 1715. If zero is the point where the derivatives are considered, a Taylor series is also called a Maclaurin series, afterColin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century.

Magnetic field

A magnetic field is avector field that describes the magnetic influence on movingelectric charges,electric currents,^{[7]: ch1 [8]} and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field.^{: ch13 [9]} Apermanent magnet's magnetic field pulls onferromagnetic materials such asiron, and attracts or repels other magnets. In addition, a magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used inelectromagnets, and byelectric fields varying in time. Since both strength and direction of a magnetic field may vary with location, they are described as a map assigning a vector to each point of space or, more precisely—because of the way the magnetic field transforms under mirror reflection—as afield ofpseudovectors.Inelectromagnetics, the term "magnetic field" is used for two distinct but closely related vector fields denoted by the symbolsB andH. In theInternational System of Units,H, magnetic field strength, is measured in the SI base units ofampere per meter (A/m).^[10]B,magnetic flux density, is measured intesla (in SI base units: kilogram per second² per ampere),^[11] which is equivalent tonewton per meter per ampere.H andB differ in how they account for magnetization. Invacuum, the two fields are related through thevacuum permeability,${\displaystyle \mathbf{B}/{\mu }_0=\mathbf{H}}$; but in a magnetized material, the terms differ by the material'smagnetization at each point.

Magnetism

is a class of physical attributes that are mediated bymagnetic fields.Electric currents and themagnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. Magnetism is one aspect of the combined phenomenon ofelectromagnetism. The most familiar effects occur inferromagnetic materials, which are strongly attracted by magnetic fields and can bemagnetized to become permanentmagnets, producing magnetic fields themselves. Demagnetizing a magnet is also possible. Only a few substances are ferromagnetic; the most common ones areiron,cobalt andnickel and their alloys. The rare-earth metalsneodymium andsamarium are less common examples. The prefixferro- refers toiron, because permanent magnetism was first observed inlodestone, a form of natural iron ore calledmagnetite, Fe₃O₄.

Manufacturing engineering

is a branch of professionalengineering that shares many common concepts and ideas with other fields of engineering such as mechanical, chemical, electrical, and industrial engineering. Manufacturing engineering requires the ability to plan the practices of manufacturing; to research and to develop tools, processes, machines and equipment; and to integrate the facilities and systems for producing quality products with the optimum expenditure of capital.^[12]The manufacturing or production engineer's primary focus is to turn raw material into an updated or new product in the most effective, efficient & economic way possible.

Mass balance

A mass balance, also called amaterial balance, is an application ofconservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system,mass flows can be identified which might have been unknown, or difficult to measure without this technique. The exactconservation law used in the analysis of the system depends on the context of the problem, but all revolve around mass conservation, i.e., thatmatter cannot disappear or be created spontaneously.^{[13]: 59–62}

Mass density

Thedensity (more precisely, thevolumetric mass density; also known asspecific mass), of a substance is itsmass per unitvolume. The symbol most often used for density isρ (the lower case Greek letterrho), although the Latin letterD can also be used. Mathematically, density is defined as mass divided by volume:^[14]

${\displaystyle \rho =\frac{m}{V}}$

whereρ is the density,m is the mass, andV is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as itsweight per unitvolume,^[15] although this is scientifically inaccurate – this quantity is more specifically calledspecific weight.

Mass moment of inertia

Themoment of inertia, otherwise known as themass moment of inertia,angular mass,second moment of mass, or most accurately,rotational inertia, of arigid body is a quantity that determines thetorque needed for a desiredangular acceleration about a rotational axis, akin to howmass determines theforce needed for a desiredacceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

Mass number

The mass number (symbolA, from the German wordAtomgewicht [atomic weight]),^[16] also calledatomic mass number ornucleon number, is the total number ofprotons andneutrons (together known asnucleons) in anatomic nucleus. It is approximately equal to theatomic (also known asisotopic) mass of theatom expressed indaltons. Since protons and neutrons are bothbaryons, the mass numberA is identical with thebaryon numberB of the nucleus (and also of the whole atom orion). The mass number is different for each differentisotope of achemical element. Hence, the difference between the mass number and theatomic number Z gives thenumber of neutrons (N) in a given nucleus:N =A −Z.^[17]The mass number is written either after the element name or as asuperscript to the left of an element's symbol. For example, the most common isotope ofcarbon iscarbon-12, or¹²
C, which has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (Z) as a subscript to the left of the element symbol directly below the mass number:¹²
₆C.^[18]

Mass spectrometry

(MS), is an analytical technique that is used to measure themass-to-charge ratio ofions. The results are typically presented as amass spectrum, a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is used in many different fields and is applied to pure samples as well as complex mixtures.

Material failure theory

is an interdisciplinary field ofmaterials science andsolid mechanics which attempts topredict the conditions under which solidmaterials fail under the action ofexternal loads. The failure of a material is usually classified intobrittle failure (fracture) orductile failure (yield). Depending on the conditions (such astemperature, state ofstress, loading rate) most materials can fail in a brittle or ductile manner or both. However, for most practical situations, a material may be classified as either brittle or ductile.In mathematical terms, failure theory is expressed in the form of various failure criteria which are valid for specific materials. Failure criteria are functions instress or strain space which separate "failed" states from "unfailed" states. A precise physical definition of a "failed" state is not easily quantified and several working definitions are in use in the engineering community. Quite often, phenomenological failure criteria of the same form are used to predict brittle failure and ductile yields.

Material properties

A material's property is anintensive property of somematerial, i.e., aphysical property that does not depend on the amount of the material. These quantitative properties may be used as ametric by which the benefits of one material versus another can be compared, thereby aiding inmaterials selection.

Materials science

Theinterdisciplinary field of materials science, also commonly termedmaterials science and engineering, covers the design and discovery of new materials, particularlysolids. The intellectual origins of materials science stem from theEnlightenment, when researchers began to use analytical thinking fromchemistry,physics, andengineering to understand ancient,phenomenological observations inmetallurgy andmineralogy.^[19][20] Materials science still incorporates elements of physics, chemistry, and engineering. As such, the field was long considered by academic institutions as a sub-field of these related fields. Beginning in the 1940s, materials science began to be more widely recognized as a specific and distinct field of science and engineering, and major technical universities around the world created dedicated schools for its study.Materials scientists emphasize understanding, how the history of a material (processing) influences its structure, and thus the material's properties and performance. The understanding of processing-structure-properties relationships is called the materials paradigm. Thisparadigm is used to advance understanding in a variety of research areas, includingnanotechnology,biomaterials, andmetallurgy.Materials science is also an important part offorensic engineering andfailure analysis – investigating materials, products, structures or components, which fail or do not function as intended, causing personal injury or damage to property. Such investigations are key to understanding, for example, the causes of variousaviation accidents and incidents.

Mathematical optimization

Mathematical optimization (alternatively spelledoptimisation) ormathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives.^[21] Optimization problems of sorts arise in all quantitative disciplines fromcomputer science andengineering tooperations research andeconomics, and the development of solution methods has been of interest inmathematics for centuries.^[22]In the simplest case, anoptimization problem consists ofmaximizing or minimizing areal function by systematically choosinginput values from within an allowed set and computing thevalue of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area ofapplied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defineddomain (or input), including a variety of different types of objective functions and different types of domains.

Mathematical physics

refers to the development ofmathematical methods for application to problems inphysics. TheJournal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".^[23]

Mathematics

includes the study of such topics asquantity (number theory),^[24]structure (algebra),^[25]space (geometry),^[24] andchange (analysis).^[26][27][28] It has no generally accepteddefinition.^[29][30]Mathematicians seek and usepatterns^[31][32] to formulate newconjectures; they resolve thetruth or falsity of such bymathematical proof. Whenmathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions aboutnature. Through the use ofabstraction andlogic, mathematics developed fromcounting,calculation,measurement, and the systematic study of theshapes andmotions ofphysical objects. Practical mathematics has been a human activity from as far back aswritten records exist. Theresearch required to solve mathematical problems can take years or even centuries of sustained inquiry.

Matrix

Inmathematics, a matrix (pluralmatrices) is arectangular array or table ofnumbers,symbols, orexpressions, arranged in rows and columns, which is used to represent amathematical object or a property of such an object. For example,

is a matrix with two rows and three columns; one say often a "two by three matrix", a "2×3-matrix", or a matrix of dimension2×3.Without further specifications, matrices representlinear maps, and allow explicit computations inlinear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties andoperations of abstract linear algebra can be expressed in terms of matrices. For example,matrix multiplication representscomposition of linear maps.Not all matrices are related to linear algebra. This is in particular the case, ingraph theory, ofincidence matrices andadjacency matrices.^[33]

Matter

Inclassical physics and generalchemistry, matter is any substance that hasmass and takes up space by havingvolume.^[34] All everyday objects that can be touched are ultimately composed ofatoms, which are made up of interactingsubatomic particles, and in everyday as well as scientific usage, "matter" generally includesatoms and anything made up of them, and any particles (orcombination of particles) that act as if they have bothrest mass and volume. However it does not includemassless particles such asphotons, or other energy phenomena or waves such aslight.^{[34]: 21 [35]} Matter exists in variousstates (also known asphases). These include classical everyday phases such assolid,liquid, andgas – for examplewater exists as ice, liquid water, and gaseous steam – but other states are possible, includingplasma,Bose–Einstein condensates,fermionic condensates, andquark–gluon plasma.^[36]

Maximum-distortion energy theory

.

Maximum-normal-stress theory

.

Maximum shear stress

.

Maxwell's equations

are a set of coupledpartial differential equations that, together with theLorentz force law, form the foundation ofclassical electromagnetism, classicaloptics, andelectric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors,wireless communication, lenses, radar etc. They describe howelectric andmagnetic fields are generated bycharges,currents, and changes of the fields.^{[note 1]} The equations are named after the physicist and mathematicianJames Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon.An important consequence of Maxwell's equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in vacuum. Known aselectromagnetic radiation, these waves may occur at various wavelengths to produce aspectrum of light fromradio waves togamma rays.

Mean

There are several kinds ofmean inmathematics, especially instatistics:For adata set, thearithmetic mean, also known asaverage or arithmetic average, is a central value of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbersx₁,x₂, ..., x_n is typically denoted by${\displaystyle \overline{x}}$^{[note 2]}. If the data set were based on a series of observations obtained bysampling from astatistical population, the arithmetic mean is thesample mean (denoted${\displaystyle \overline{x}}$) to distinguish it from the mean, orexpected value, of the underlying distribution, thepopulation mean (denoted${\displaystyle \mu }$ or${\displaystyle {\mu }_x}$^{[note 3]}).^[37]Inprobability andstatistics, thepopulation mean, or expected value, is a measure of thecentral tendency either of aprobability distribution or of arandom variable characterized by that distribution.^[38] In adiscrete probability distribution of a random variableX, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible valuex ofX and its probabilityp(x), and then adding all these products together, giving${\displaystyle \mu =\sum xp(x)....}$.^[39][40] An analogous formula applies to the case of acontinuous probability distribution. Not every probability distribution has a defined mean (see theCauchy distribution for an example). Moreover, the mean can be infinite for some distributions.For a finite population, thepopulation mean of a property is equal to the arithmetic mean of the given property, while considering every member of the population. For example, the population mean height is equal to the sum of the heights of every individual—divided by the total number of individuals. The sample mean may differ from the population mean, especially for small samples. Thelaw of large numbers states that the larger the size of the sample, the more likely it is that the sample mean will be close to the population mean.^[41]Outside probability and statistics, a wide range of other notions of mean are often used ingeometry andmathematical analysis.

Measure of central tendency

Instatistics, acentral tendency (ormeasure of central tendency) is a central or typical value for aprobability distribution.^[42] It may also be called acenter orlocation of the distribution. Colloquially, measures of central tendency are often calledaverages. The termcentral tendency dates from the late 1920s.^[43]The most common measures of central tendency are thearithmetic mean, themedian, and themode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as thenormal distribution. Occasionally authors use central tendency to denote "the tendency of quantitativedata to cluster around some central value."^[43][44]The central tendency of a distribution is typically contrasted with itsdispersion orvariability; dispersion and central tendency are the often characterized properties of distributions. Analysis may judge whether data has a strong or a weak central tendency based on its dispersion.

Mechanical advantage

is a measure of theforce amplification achieved by using a tool,mechanical device or machine system. The device trades off input forces against movement to obtain a desired amplification in the output force. The model for this is thelaw of thelever. Machine components designed to manage forces and movement in this way are calledmechanisms.^[45] An ideal mechanism transmits power without adding to or subtracting from it. This means the ideal mechanism does not include a power source, is frictionless, and is constructed fromrigid bodies that do not deflect or wear. The performance of a real system relative to this ideal is expressed in terms of efficiency factors that take into account departures from the ideal.

Mechanical engineering

is anengineering branch that combinesengineering physics andmathematics principles withmaterials science todesign, analyze, manufacture, and maintainmechanical systems.^[46] It is one of the oldest and broadest of theengineering branches.

Mechanical filter

is asignal processing filter usually used in place of anelectronic filter atradio frequencies. Its purpose is the same as that of a normal electronic filter: to pass a range of signal frequencies, but to block others. The filter acts on mechanical vibrations which are the analogue of the electrical signal. At the input and output of the filter,transducers convert the electrical signal into, and then back from, these mechanical vibrations.

Mechanical wave

is awave that is an oscillation ofmatter, and therefore transfers energy through amedium.^[47] While waves can move over long distances, the movement of themedium of transmission—the material—is limited. Therefore, the oscillating material does not move far from its initial equilibrium position. Mechanical waves transport energy. This energy propagates in the same direction as the wave. Any kind of wave (mechanical or electromagnetic) has a certain energy. Mechanical waves can be produced only in media which possesselasticity andinertia.

Mechanics

is the area ofphysics concerned with the motions ofphysical objects, more specifically the relationships among force, matter, and motion.^[48]Forces applied to objects result indisplacements, or changes of an object's position relative to its environment.This branch ofphysics has its origins inAncient Greece with the writings ofAristotle andArchimedes^[49][50][51] (seeHistory of classical mechanics andTimeline of classical mechanics). During theearly modern period, scientists such asGalileo,Kepler, andNewton laid the foundation for what is now known asclassical mechanics.It is a branch ofclassical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as a branch of science which deals with the motion of and forces on bodies not in the quantum realm. The field is today less widely understood in terms of quantum theory.

Mechanism

is adevice that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components which may include:

• Gears andgear trains
• Belts andchain drives
• Cams andfollowers
• Linkages
• Friction devices, such asbrakes orclutches
• Structural components such as a frame, fasteners, bearings, springs, or lubricants
• Variousmachine elements, such as splines, pins, or keys

Median

Instatistics andprobability theory, the median is the value separating the higher half from the lower half of adata sample, apopulation, or aprobability distribution. For adata set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to themean (often simply described as the "average") is that it is notskewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value.Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance inrobust statistics, as it is the mostresistant statistic, having abreakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.

Melting

Melting, orfusion, is a physical process that results in thephase transition of asubstance from asolid to aliquid. This occurs when theinternal energy of the solid increases, typically by the application ofheat orpressure, which increases the substance'stemperature to themelting point. At the melting point, the ordering ofions ormolecules in the solid breaks down to a less ordered state, and the solidmelts to become a liquid.

Melting point

The melting point (or, rarely,liquefaction point) of a substance is thetemperature at which it changesstate fromsolid toliquid. At the melting point the solid and liquid phase exist inequilibrium. The melting point of a substance depends onpressure and is usually specified at astandard pressure such as 1atmosphere or 100kPa.When considered as the temperature of the reverse change from liquid to solid, it is referred to as thefreezing point orcrystallization point. Because of the ability of substances tosupercool, the freezing point can easily appear to be below its actual value. When the "characteristic freezing point" of a substance is determined, in fact the actual methodology is almost always "the principle of observing the disappearance rather than the formation of ice, that is, themelting point."^[52]

Meson

Inparticle physics, mesons arehadronicsubatomic particles composed of an equal number ofquarks andantiquarks, usually one of each, bound together bystrong interactions. Because mesons are composed of quark subparticles, they have a meaningful physical size, a diameter of roughly onefemtometer (1×10⁻¹⁵ m),^[53] which is about 0.6 times the size of aproton orneutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Heavier mesons decay to lighter mesons and ultimately to stableelectrons,neutrinos andphotons.

Metallic bonding

is a type ofchemical bonding that arises from the electrostatic attractive force betweenconduction electrons (in the form of an electron cloud ofdelocalized electrons) and positively chargedmetalions. It may be described as the sharing offree electrons among astructure of positively charged ions (cations). Metallic bonding accounts for manyphysical properties of metals, such asstrength,ductility,thermal andelectrical resistivity and conductivity,opacity, andluster.^{[54][55][56][57]}Metallic bonding is not the only type ofchemical bonding a metal can exhibit, even as a pure substance. For example, elementalgallium consists ofcovalently-bound pairs of atoms in both liquid and solid-state—these pairs form acrystal structure with metallic bonding between them. Another example of a metal–metal covalent bond is themercurous ion (Hg²⁺
₂).

Middle-out

A combination of top-down and bottom-up design.^[58]

Mid-range

Instatistics, the mid-range ormid-extreme is a measure ofcentral tendency of asample (statistics) defined as thearithmetic mean of the maximum and minimum values of thedata set:^[59]

${\displaystyle M=\frac{maxx+minx}{2}.}$

The mid-range is closely related to therange, a measure ofstatistical dispersion defined as the difference between maximum and minimum values.The two measures are complementary in sense that if one knows the mid-range and the range, one can find the sample maximum and minimum values.The mid-range is rarely used in practical statistical analysis, as it lacksefficiency as an estimator for most distributions of interest, because it ignores all intermediate points, and lacksrobustness, as outliers change it significantly. Indeed, it is one of the least efficient and least robust statistics. However, it finds some use in special cases: it is the maximally efficient estimator for the center of a uniform distribution, trimmed mid-ranges address robustness, and as anL-estimator, it is simple to understand and compute.

Midhinge

Instatistics, the midhinge is the average of the first and thirdquartiles and is thus a measure oflocation.Equivalently, it is the 25%trimmedmid-range or 25%midsummary; it is anL-estimator.

${\displaystyle \mathrm{MH}(X)=\overline{Q_{1,3}(X)}=\frac{Q_1(X)+Q_3(X)}{2}=\frac{P_{25}(X)+P_{75}(X)}{2}=M_{25}(X)}$

The midhinge is related to theinterquartile range (IQR), the difference of the third and firstquartiles (i.e.${\displaystyle IQR=Q_3-Q_1}$), which is a measure ofstatistical dispersion. The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles.The use of the term "hinge" for the lower or upper quartiles derives fromJohn Tukey's work onexploratory data analysis in the late 1970s,^[60] and "midhinge" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than thetrimean (${\displaystyle TM}$), which originated in the same context and equals the average of themedian (${\displaystyle \tilde{X}=Q_2=P_{50}}$) and the midhinge.

${\displaystyle \mathrm{MH}(X)=2\mathrm{TM}(X)-\mathrm{med}(X)=2\frac{Q_1+2Q_2+Q3}{4}-Q_2}$

Miller indices form a notation system incrystallography for planes incrystal (Bravais) lattices.In particular, a family oflattice planes is determined by threeintegersh,k, and ℓ, theMiller indices. They are written (hkℓ), and denote the family of planes orthogonal to${\displaystyle h{\mathbf{b}}_{\mathbf{1}}+k{\mathbf{b}}_{\mathbf{2}}+\ell {\mathbf{b}}_{\mathbf{3}}}$, where${\displaystyle {\mathbf{b}}_{\mathbf{i}}}$ are thebasis of thereciprocal lattice vectors (note that the plane is not always orthogonal to the linear combination of direct lattice vectors${\displaystyle h{\mathbf{a}}_{\mathbf{1}}+k{\mathbf{a}}_{\mathbf{2}}+\ell {\mathbf{a}}_{\mathbf{3}}}$ because the lattice vectors need not be mutually orthogonal). By convention,negative integers are written with a bar, as in3 for −3. The integers are usually written in lowest terms, i.e. theirgreatest common divisor should be 1. Miller indices are also used to designate reflections inX-ray crystallography. In this case the integers are not necessarily in lowest terms, and can be thought of as corresponding to planes spaced such that the reflections from adjacent planes would have a phase difference of exactly one wavelength (2π), regardless of whether there are atoms on all these planes or not.There are also several related notations:^[61]

• the notation {hkℓ} denotes the set of all planes that are equivalent to (hkℓ) by the symmetry of the lattice.

In the context of crystaldirections (not planes), the corresponding notations are:

• [hkℓ], with square instead of round brackets, denotes a direction in the basis of thedirect lattice vectors instead of the reciprocal lattice; and
• similarly, the notation <hkℓ> denotes the set of all directions that are equivalent to [hkℓ] by symmetry.

Anelastic modulus (also known asmodulus of elasticity) is a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when astress is applied to it. The elastic modulus of an object is defined as theslope of itsstress–strain curve in the elastic deformation region:^[67] A stiffer material will have a higher elastic modulus. An elastic modulus has the form:

${\displaystyle \delta \stackrel{\text{def}}{=}\frac{\text{stress}}{\text{strain}}}$

wherestress is the force causing the deformation divided by the area to which the force is applied andstrain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter. Since strain is a dimensionless quantity, the units of${\displaystyle \delta }$ will be the same as the units of stress.^[68]

Nanoengineering

is the practice ofengineering on thenanoscale. It derives its name from thenanometre, a unit of measurement equalling one billionth of a meter. Nanoengineering is largely a synonym fornanotechnology, but emphasizes the engineering rather than the pure science aspects of the field.

Nanotechnology

The technology of systems built with moving parts on the order of a nanometre in size.

Navier–Stokes equations

Inphysics, the Navier–Stokes equations are a set ofpartial differential equations which describe the motion ofviscous fluid substances, named after French engineer and physicistClaude-Louis Navier and Anglo-Irish physicist and mathematicianGeorge Gabriel Stokes.

Neutrino

A neutrino (denoted by the Greek letterν) is afermion (anelementary particle withspin of⁠1/2⁠) that interacts only via theweak subatomic force andgravity.^[82][83] The neutrino is so named because it iselectrically neutral and because itsrest mass is so small (-ino) that it was long thought to be zero. Themass of the neutrino is much smaller than that of the other known elementary particles.^[84] The weak force has a very short range, the gravitational interaction is extremely weak, and neutrinos do not participate in thestrong interaction.^[85] Thus, neutrinos typically pass through normal matter unimpeded and undetected.^[86][83]

Newtonian fluid

is afluid in which theviscous stresses arising from itsflow, at every point, are linearly^[87] correlated to the localstrain rate—therate of change of itsdeformation over time.^[88][89][90] That is equivalent to saying those forces are proportional to the rates of change of the fluid'svelocity vector as one moves away from the point in question in various directions. More precisely, a fluid is Newtonian only if thetensors that describe the viscous stress and the strain rate are related by a constantviscosity tensor that does not depend on the stress state and velocity of the flow. If the fluid is alsoisotropic (that is, its mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuousshear deformation and continuouscompression or expansion, respectively.

Norton's theorem

In direct-currentcircuit theory, Norton's theorem (akaMayer–Norton theorem) is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel. Foralternating current (AC) systems the theorem can be applied toreactiveimpedances as well as resistances.

Nozzle

is a device designed to control the direction or characteristics of afluid flow (especially to increase velocity) as it exits (or enters) an enclosed chamber orpipe. A nozzle is often a pipe or tube of varying cross sectional area, and it can be used to direct or modify the flow of a fluid (liquid orgas). Nozzles are frequently used to control the rate of flow, speed, direction, mass, shape, and/or the pressure of the stream that emerges from them. In a nozzle, the velocity of fluid increases at the expense of its pressure energy.

nth root

To put a number of function to the exponential power of 1/n.

Nuclear binding energy

The difference between the total mass energy of a nucleus and the mass energy of the isolated nucleons.

Nuclear engineering

The profession that deals with nuclear power.

Nuclear fusion

is areaction in which two or moreatomic nuclei are combined to form one or more different atomic nuclei and subatomic particles (neutrons orprotons). The difference in mass between the reactants and products is manifested as either the release or the absorption ofenergy. This difference in mass arises due to the difference inatomic binding energy between the nuclei before and after the reaction. Fusion is the process that powers active ormain sequencestars and otherhigh-magnitude stars, where large amounts of energy arereleased.

Nuclear physics

The science that describes the components of atoms.

Nuclear potential energy

The energy that is given up in decay of an unstable nucleus.

Nuclear power

The use of energy derived from nuclear chain reactions for electricity production or ship propulsion.

Ohm

The SI unit of electrical resistance.

Ohm's law

A law describing the relationship between resistance, current, and voltage.

Optics

The study of light.

Organic chemistry

The study of carbon compounds.

Osmosis

The spontaneous movement of molecules or ions through a semi-permable membrane, tending to equalize concentration on both sides.

Parallel circuit

A circuit that begins and ends at the same node as another circuit.

Parity (mathematics)

Inmathematics, parity is the property of aninteger of whether it is even or odd. An integer's parity is even if it isdivisible by two with no remainders left and its parity is odd if its remainder is 1.^[91] For example, -4, 0, 82, and 178 are even because there is noremainder when dividing it by 2. By contrast, -3, 5, 7, 21 are odd numbers as they leave a remainder of 1 when divided by 2.

Parity (physics)

Inquantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign ofonespatialcoordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (apoint reflection):

${\displaystyle \mathbf{P}:\left(\begin{array}{c}x\\ y\\ z\end{array}\right)\mapsto \left(\begin{array}{c}-x\\ -y\\ -z\end{array}\right).}$

It can also be thought of as a test forchirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions ofelementary particles, with the exception of theweak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics. In interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions.A matrix representation ofP (in any number of dimensions) hasdeterminant equal to −1, and hence is distinct from arotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign isnot a parity transformation; it is the same as a 180°-rotation.Inquantum mechanics, wave functions that are unchanged by a parity transformation are described aseven functions, while those that change sign under a parity transformation are odd functions.fn=A hydrocarbon compound, solid at room temperature.

Paramagnetism

is a form ofmagnetism whereby some materials are weakly attracted by an externally appliedmagnetic 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.^[92] Paramagnetic materials include mostchemical elements and some compounds;^[93] they have a relativemagnetic permeability slightly greater than 1 (i.e., a small positivemagnetic susceptibility) and hence are attracted to magnetic fields. Themagnetic 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 aSQUIDmagnetometer.

Particle accelerator

is a machine that useselectromagnetic fields to propelchargedparticles to very high speeds and energies, and to contain them in well-definedbeams.^[94]

Particle displacement

Particle displacement or displacement amplitude is ameasurement ofdistance of the movement of asound particle from itsequilibrium position in a medium as it transmits a sound wave.^[95] TheSI unit of particle displacement is themeter (m). In most cases this is alongitudinal wave of pressure (such assound), but it can also be atransverse wave, such as thevibration of a taut string. In the case of asound wave travelling throughair, the particle displacement is evident in theoscillations of airmolecules with, and against, the direction in which the sound wave is travelling.^[96]

Particle physics

Particle physics (also known ashigh energy physics) is a branch ofphysics that studies the nature of the particles that constitutematter andradiation. Although the wordparticle can refer to various types of very small objects (e.g.protons, gas particles, or even household dust),particle physics usually investigates the irreducibly smallest detectable particles and thefundamental interactions necessary to explain their behaviour. In current understanding, theseelementary particles are excitations of thequantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called theStandard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, theHiggs boson, or even to the oldest known force field,gravity.^[97][98]

Pascal's law

Pascal's law (alsoPascal's principle^{[99][100][101]} or theprinciple of transmission of fluid-pressure) is a principle influid mechanics that states that a pressure change occurring anywhere in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.^[102] The law was established byFrenchmathematicianBlaise Pascal^[103] in 1647–48.^[104]

Pendulum

Is a weight suspended from apivot so that it can swing freely.^[105] When a pendulum is displaced sideways from its resting,equilibrium position, it is subject to arestoring force due togravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it tooscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called theperiod. The period depends on the length of the pendulum and also to a slight degree on theamplitude, the width of the pendulum's swing.

Petroleum engineering

is a field of engineering concerned with the activities related to the production ofhydrocarbons, which can be eithercrude oil ornatural gas.^[106] Exploration and production are deemed to fall within theupstream sector of the oil and gas industry.Exploration, byearth scientists, and petroleum engineering are the oil and gas industry's two main subsurface disciplines, which focus on maximizing economic recovery of hydrocarbons from subsurface reservoirs.Petroleum geology andgeophysics focus on provision of a static description of the hydrocarbon reservoir rock, while petroleum engineering focuses on estimation of the recoverable volume of this resource using a detailed understanding of the physical behavior of oil, water and gas within porous rock at very high pressure.

pH

A logarithmic measure of the concentration of hydrogen ions in an acid or base solution.

Phase (matter)

In thephysical sciences, a phase is a region of space (athermodynamic system), throughout which all physical properties of a material are essentially uniform.^{[107][108]: 86 [109]: 3} Examples of physical properties includedensity,index of refraction,magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (Seestate of matter § Glass)

Phase (waves)

Inphysics andmathematics, the phase of aperiodic function${\displaystyle F}$ of somereal variable${\displaystyle t}$ (such as time) is anangle-like quantity representing the fraction of the cycle covered up to${\displaystyle t}$. It is denoted${\displaystyle \varphi (t)}$ and expressed in such ascale that it varies by one fullturn as the variable${\displaystyle t}$ goes through eachperiod (and${\displaystyle F(t)}$ goes through each complete cycle). It may bemeasured in anyangular unit such asdegrees orradians, thus increasing by 360° or${\displaystyle 2\pi }$ as the variable${\displaystyle t}$ completes a full period.^[110]

Phase diagram

A phase diagram inphysical chemistry,engineering,mineralogy, andmaterials science is a type ofchart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinctphases (such as solid, liquid or gaseous states) occur and coexist atequilibrium.

Phase rule

Inthermodynamics, the phase rule is a general principle governing "pVT" systems (that is, systems whosestates are completely described by the variablespressure (p),volume (V) andtemperature (T)) inthermodynamic equilibrium. IfF is the number ofdegrees of freedom,C is the number ofcomponents andP is the number ofphases, then^[111][112]

${\displaystyle F=C-P+2.}$

It was derived by American physicistJosiah Willard Gibbs in his landmark paper titledOn the Equilibrium of Heterogeneous Substances, published in parts between 1875 and 1878.^[113]The rule assumes the components do notreact with each other.

Photon

is a type ofelementary particle. It is thequantum of theelectromagnetic field includingelectromagnetic radiation such aslight andradio waves, and theforce carrier for theelectromagnetic force. Photons aremassless,^[a] so they always move at thespeed of light in vacuum,299792458 m/s (or about 186,282 mi/s). The photon belongs to the class ofbosons.

Physical chemistry

is the study ofmacroscopic, and particulate phenomena inchemical systems in terms of the principles, practices, and concepts ofphysics such asmotion,energy,force,time,thermodynamics,quantum chemistry,statistical mechanics,analytical dynamics andchemical equilibrium.

Physical quantity

A physical quantity is a property of a material or system that can bequantified bymeasurement. A physical quantity can be expressed as avalue, which is the algebraic multiplication of anumerical value and aunit. For example, the physical quantitymass can be quantified asnkg, wheren is the numerical value and kg is the unit. A physical quantity possesses at least two characteristics in common. One is numerical magnitude and the other is the unit in which it is measured.

Physics

is thenatural science that studiesmatter,^[b] itsmotion and behavior throughspace and time, and the related entities ofenergy andforce.^[115] Physics is one of the most fundamentalscientific disciplines, and its main goal is to understand how theuniverse behaves.^{[c][116][117][118]}

Planck constant

The Planck constant, orPlanck's constant, is a fundamentalphysical constant denoted${\displaystyle h}$, and is of fundamental importance inquantum mechanics. Aphoton's energy is equal to its frequency multiplied by the Planck constant. Due tomass–energy equivalence, the Planck constant also relates mass to frequency.Inmetrology it is used, together with other constants, to define thekilogram, anSI unit.^[119] The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value${\displaystyle h}$ =6.62607015×10⁻³⁴ J⋅Hz⁻¹.^[120][121]

Plasma (physics)

Is one of thefour fundamental states of matter, first systematically studied byIrving Langmuir in the 1920s.^[122][123] It consists of a gas ofions – atoms or molecules which have one or more orbital electrons stripped (or, rarely, an extra electron attached), and freeelectrons.

Plasticity

Inphysics andmaterials science, plasticity, also known asplastic deformation, is the ability of asolidmaterial to undergo permanentdeformation, a non-reversible change of shape in response to applied forces.^[124][125] For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition fromelastic behavior to plastic behavior is known asyielding.

Pneumatics

The control of mechanical force and movement, generated by the application of compressed gas.

Point estimation

Instatistics, point estimation involves the use ofsampledata to calculate a single value (known as apoint estimate since it identifies apoint in someparameter space) which is to serve as a "best guess" or "best estimate" of an unknown populationparameter (for example, thepopulation mean). More formally, it is the application of a pointestimator to the data to obtain a point estimate.Point estimation can be contrasted withinterval estimation: such interval estimates are typically eitherconfidence intervals, in the case offrequentist inference, orcredible intervals, in the case ofBayesian inference. More generally, a point estimator can be contrasted with a set estimator. Examples are given byconfidence sets orcredible sets. A point estimator can also be contrasted with a distribution estimator. Examples are given byconfidence distributions,randomized estimators, andBayesian posteriors.

Polyphase system

An electrical system that uses a set of alternating currents at different phases.

Power (electric)

Electric power is the rate, per unit time, at whichelectrical energy is transferred by anelectric circuit. TheSI unit ofpower is thewatt, onejoule persecond.Electric power is usually produced byelectric generators, but can also be supplied by sources such aselectric batteries. It is usually supplied to businesses and homes (as domesticmains electricity) by theelectric power industry through anelectric power grid.Electric power can be delivered over long distances bytransmission lines and used for applications such asmotion,light orheat with highefficiency.^[126]

Power (physics)

In physics, power is the amount ofenergy transferred or converted per unit time. In theInternational System of Units, the unit of power is thewatt, equal to onejoule per second. In older works, power is sometimes calledactivity.^{[127][128][129]} Power is ascalar quantity.

Power factor

Inelectrical engineering, the power factor of anAC power system is defined as theratio of thereal power absorbed by theload to theapparent power flowing in the circuit, and is adimensionless number in theclosed interval of −1 to 1. A power factor of less than one indicates the voltage and current are not in phase, reducing the averageproduct of the two. Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product ofRMS current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power. A negative power factor occurs when the device (which is normally the load) generates power, which then flows back towards the source.

Pressure

Pressure (symbol:p orP) is theforce applied perpendicular to the surface of an object per unitarea over which that force is distributed.^{: 445 [130]}Gauge pressure (also spelledgage pressure)^[d] is the pressure relative to the ambient pressure.Variousunits are used to express pressure. Some of these derive from a unit of force divided by a unit of area; theSI unit of pressure, thepascal (Pa), for example, is onenewton persquare metre (N/m²); similarly, thepound-force persquare inch (psi) is the traditional unit of pressure in theimperial andU.S. customary systems. Pressure may also be expressed in terms ofstandard atmospheric pressure; theatmosphere (atm) is equal to this pressure, and thetorr is defined as1⁄760 of this. Manometric units such as thecentimetre of water,millimetre of mercury, andinch of mercury are used to express pressures in terms of the height ofcolumn of a particular fluid in a manometer.

Probability

is the branch ofmathematics concerning numerical descriptions of how likely anevent is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.^{[note 4][131][132]} The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

Probability distribution

Inprobability theory andstatistics, a probability distribution is the mathematicalfunction that gives the probabilities of occurrence of different possibleoutcomes for anexperiment.^[133][134] It is a mathematical description of arandom phenomenon in terms of itssample space and theprobabilities ofevents (subsets of the sample space).^[51]For instance, ifX is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution ofX would take the value 0.5 (1 in 2 or 1/2) forX = heads, and 0.5 forX = tails (assuming that the coin is fair). Examples of random phenomena include the weather condition in a future date, the height of a randomly selected person, the fraction of male students in a school, the results of asurvey to be conducted, etc.^[135]

Probability theory

is the branch ofmathematics concerned withprobability. Although there are several differentprobability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ofaxioms. Typically these axioms formalise probability in terms of aprobability space, which assigns ameasure taking values between 0 and 1, termed theprobability measure, to a set of outcomes called thesample space. Any specified subset of these outcomes is called anevent.Central subjects in probability theory include discrete and continuousrandom variables,probability distributions, andstochastic processes, which provide mathematical abstractions ofnon-deterministic or uncertain processes or measuredquantities that may either be single occurrences or evolve over time in a random fashion.Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are thelaw of large numbers and thecentral limit theorem.As a mathematical foundation forstatistics, probability theory is essential to many human activities that involve quantitative analysis of data.^[136] Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as instatistical mechanics orsequential estimation. A great discovery of twentieth-centuryphysics was the probabilistic nature of physical phenomena at atomic scales, described inquantum mechanics.^{[137][unreliable source?]}

Process

Pulley

is awheel on anaxle orshaft that is designed to support movement and change of direction of a taut cable or belt, or transfer of power between the shaft and cable or belt. In the case of a pulley supported by a frame or shell that does not transfer power to a shaft, but is used to guide the cable or exert a force, the supporting shell is called a block, and the pulley may be called a sheave.A pulley may have agroove or grooves betweenflanges around itscircumference to locate the cable or belt. The drive element of a pulley system can be arope,cable,belt, orchain.

Pump

is a device that moves fluids (liquids orgases), or sometimesslurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they use to move the fluid:direct lift,displacement, andgravity pumps.^[138]Pumps operate by some mechanism (typicallyreciprocating orrotary), and consumeenergy to performmechanical work moving the fluid. Pumps operate via many energy sources, including manual operation,electricity,engines, orwind power, and come in many sizes, from microscopic for use in medical applications, to large industrial pumps.

Quantum electrodynamics

In particle physics, quantum electrodynamics (QED) is therelativisticquantum field theory ofelectrodynamics. In essence, it describes howlight andmatter interact and is the first theory where full agreement betweenquantum mechanics andspecial relativity is achieved. QED mathematically describes allphenomena involvingelectrically charged particles interacting by means of exchange ofphotons and represents thequantum counterpart ofclassical electromagnetism giving a complete account of matter and light interaction.

Quantum field theory

Intheoretical physics, quantum field theory (QFT) is a theoretical framework that combinesclassical field theory,special relativity andquantum mechanics,^[139]: xi butnotgeneral relativity's description ofgravity. QFT is used inparticle physics to constructphysical models ofsubatomic particles and incondensed matter physics to construct models ofquasiparticles.

Quantum mechanics

is a fundamental theory inphysics that provides a description of the physical properties ofnature at the scale ofatoms andsubatomic particles.^[140]: 1.1 It is the foundation of all quantum physics includingquantum chemistry,quantum field theory,quantum technology, andquantum information science.

Regelation

The phenomena of melting under pressure, then freezing when the pressure is reduced.

Relative density

Relative density, or specific gravity,^[141][142] is theratio of thedensity (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect towater at its densest (at 4 °C or 39.2 °F); for gases, the reference is air atroom temperature (20 °C or 68 °F). The term "relative density" is often preferred in scientific usage.

Relative velocity

Therelative velocity${\displaystyle {\overrightarrow{v}}_{B\mid A}}$ (also${\displaystyle {\overrightarrow{v}}_{BA}}$ or${\displaystyle {\overrightarrow{v}}_{B\mathrm{rel}A}}$) is the velocity of an object or observerB in the rest frame of another object or observerA.

Reliability engineering

is a sub-discipline ofsystems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time.^[143] Reliability is closely related toavailability, which is typically described as the ability of a component or system to function at a specified moment or interval of time.

Resistivity

Electrical resistivity (also called specific electrical resistance or volume resistivity) and its inverse, electrical conductivity, is a fundamental property of a material that quantifies how strongly it resists or conductselectric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by theGreek letterρ (rho). TheSI unit of electrical resistivity is theohm-meter (Ω⋅m).^{[144][145][146]} For example, if a1 m × 1 m × 1 m solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.

Resistor

is apassivetwo-terminalelectrical component that implementselectrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, todivide voltages,bias active elements, and terminatetransmission lines, among other uses. High-power resistors that can dissipate manywatts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads forgenerators.Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity.

Reynolds number

The Reynolds number (Re) helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to beturbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances ofcavitation. Reynolds numbers are an importantdimensionless quantity influid mechanics.

Rheology

is the study of the flow of matter, primarily in a liquid or gas state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids.^[147]

Rigid body

Inphysics, a rigid body (also known as arigid object^[148]) is a solidbody in whichdeformation is zero or so small it can be neglected. Thedistance between any two givenpoints on a rigid body remains constant in time regardless of externalforces ormoments exerted on it. A rigid body is usually considered as acontinuous distribution ofmass. In the study ofspecial relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near thespeed of light. Inquantum mechanics, a rigid body is usually thought of as a collection ofpoint masses. For instance,molecules (consisting of the point masses: electrons and nuclei) are often seen as rigid bodies (seeclassification of molecules as rigid rotors).

Robonaut

A development project conducted by NASA to create humanoid robots capable of using space tools and working in similar environments to suited astronauts.

Robot-assisted surgery

Robotic surgeries are types ofsurgical procedures that are done usingrobotic systems. Robotically-assisted surgery was developed to try to overcome the limitations of pre-existingminimally-invasive surgical procedures and to enhance the capabilities of surgeons performing open surgery.In the case of robotically-assisted minimally-invasive surgery, instead of directly moving the instruments, the surgeon uses one of two methods to administer the instruments. These include using a directtelemanipulator or through computer control. A telemanipulator is a remote manipulator that allows the surgeon to perform the normal movements associated with the surgery. Therobotic arms carry out those movements usingend-effectors andmanipulators to perform the actual surgery. In computer-controlled systems, the surgeon uses a computer to control the robotic arms and its end-effectors, though these systems can also still use telemanipulators for their input. One advantage of using the computerized method is that the surgeon does not have to be present, leading to the possibility forremote surgery.

Robotics

Is aninterdisciplinary field that integratescomputer science andengineering.^[149] Robotics involves design, construction, operation, and use ofrobots. The goal of robotics is to design machines that can help and assist humans. Robotics integrates fields ofmechanical engineering,electrical engineering,information engineering,mechatronics,electronics,bioengineering,computer engineering,control engineering,software engineering, among others.

Root mean square

Inmathematics and its applications, the root mean square (RMS or rms) is defined as thesquare root of themean square (thearithmetic mean of thesquares of aset of numbers).^[150]The RMS is also known as thequadratic mean^[151][152] and is a particular case of thegeneralized mean with exponent 2. RMS can also be defined for a continuously varyingfunction in terms of anintegral of the squares of the instantaneous values during a cycle. Foralternating electric current, RMS is equal to the value of the constantdirect current that would produce the same power dissipation in aresistive load.^[150] Inestimation theory, theroot-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data.

Root-mean-square speed

In thephysics ofgas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas iscalculated using the following equation:

${\displaystyle v_{\text{RMS}}=\sqrt{\frac{3RT}{M}}}$

whereR represents thegas constant, 8.314 J/(mol·K),T is the temperature of the gas inkelvins, andM is themolar mass of the gas in kilograms per mole. In physics, speed is defined as the scalar magnitude of velocity. For a stationary gas, the average speed of its molecules can be in the order of thousands of km/h, even though the average velocity of its molecules is zero.

Rotational energy

Rotational energy orangular kinetic energy iskinetic energy due to therotation of an object and is part of itstotal kinetic energy. Looking at rotational energy separately around an object'saxis of rotation, the following dependence on the object'smoment of inertia is observed:

${\displaystyle E_{\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}}=\frac{1}{2}I{\omega }^2}$

where

${\displaystyle \omega }$ is theangular velocity

${\displaystyle I}$ is themoment of inertia around the axis of rotation

${\displaystyle E}$ is thekinetic energy

Rotational speed (orspeed of revolution) of an object rotating around an axis is the number ofturns of the object divided by time, specified asrevolutions per minute (rpm),cycles per second (cps), radians per second (rad/s), etc.^[153]The symbol for rotational speed is${\displaystyle {\omega }_{\text{cyc}}}$^{[citation needed]}(theGreek lowercase letter "omega").Tangential speedv, rotational speed${\displaystyle {\omega }_{\text{cyc}}}$, andradial distancer, are related by the following equation:^[154]

${\displaystyle v=2\pi r{\omega }_{\text{cyc}}}$

${\displaystyle v=r{\omega }_{\text{rad}}}$

An algebraic rearrangement of this equation allows us to solve for rotational speed:

${\displaystyle {\omega }_{\text{cyc}}=v/2\pi r}$

${\displaystyle {\omega }_{\text{rad}}=v/r}$

Thus, the tangential speed will be directly proportional tor when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand. The direct proportionality ofv tor is not valid for theplanets, because the planets have different rotational speeds (ω).Rotational speed can measure, for example, how fast a motor is running. Rotational speed andangular speed are sometimes used as synonyms, but typically they are measured with a different unit. Angular speed, however, tells the change inangle per time unit, which is measured inradians per second in the SI system. Since there are 2π radians per cycle, or 360 degrees per cycle, we can convert angular speed to rotational speed by

${\displaystyle {\omega }_{\text{cyc}}={\omega }_{\text{rad}}/2\pi }$

and

${\displaystyle {\omega }_{\text{cyc}}={\omega }_{\text{deg}}/360}$

where

• ${\displaystyle {\omega }_{\text{cyc}}}$ is rotational speed in cycles per second
• ${\displaystyle {\omega }_{\text{rad}}}$ is angular speed in radians per second
• ${\displaystyle {\omega }_{\text{deg}}}$ is angular speed in degrees per second

For example, astepper motor might turn exactly one complete revolution each second.Its angular speed is 360degrees per second (360°/s), or 2πradians per second (2π rad/s), while the rotational speed is 60 rpm.Rotational speed is not to be confused withtangential speed, despite some relation between the two concepts. Imagine a rotating merry-go-round. No matter how close or far one stands from the axis of rotation, the rotational speed will remain constant. However, tangential speed does not remain constant. If one stands two meters from the axis of rotation, the tangential speed will be double the amount if one were standing only one meter from the axis of rotation.

Safe failure fraction (SFF)

A term used infunctional safety for the proportion of failures that are either non-hazardous or detected automatically. The opposite of SFF is the proportion of undetected, hazardous failures.^[155][156]

Safety data sheet

A safety data sheet (SDS),^[157] material safety data sheet (MSDS), or product safety data sheet (PSDS) are documents that list information relating tooccupational safety and health for the use of various substances and products. SDSs are a widely used system for cataloguing information onchemicals,chemical compounds, and chemicalmixtures. SDS information may include instructions for the safe use and potentialhazards associated with a particular material or product, along with spill-handling procedures. The older MSDS formats could vary from source to source within a country depending on national requirements; however, the newer SDS format is internationally standardized.

Sanitary engineering

Sanitary engineering, also known as public health engineering or wastewater engineering, is the application of engineering methods to improvesanitation of human communities, primarily by providing the removal and disposal of human waste, and in addition to the supply of safepotable water.

Saturated compound

Inchemistry, a saturated compound is achemical compound (or ion) that resists the addition reactions, such ashydrogenation,oxidative addition, and binding of aLewis base. The term is used in many contexts and for many classes of chemical compounds. Overall, saturated compounds are less reactive than unsaturated compounds. Saturation is derived from the Latin wordsaturare, meaning 'to fill')^[158]

Scalar (mathematics)

.

Scalar (physics)

.

Scalar multiplication

Inmathematics, scalar multiplication is one of the basic operations defining avector space inlinear algebra^{[159][160][161]} (or more generally, amodule inabstract algebra^[162][163]). In common geometrical contexts, scalar multiplication of arealEuclidean vector by a positive real number multiplies the magnitude of the vector—without changing its direction. The term "scalar" itself derives from this usage: a scalar is that whichscales vectors. Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished frominner product of two vectors (where the product is a scalar).

Screw

A screw is a mechanism that convertsrotational motion tolinear motion, and atorque (rotational force) to a linearforce.^[164] It is one of the six classicalsimple machines. The most common form consists of a cylindrical shaft withhelical grooves or ridges calledthreads around the outside.^[165][166] The screw passes through a hole in another object or medium, with threads on the inside of the hole that mesh with the screw's threads. When the shaft of the screw is rotated relative to the stationary threads, the screw moves along its axis relative to the medium surrounding it; for example rotating awood screw forces it into wood. In screw mechanisms, either the screw shaft can rotate through a threaded hole in a stationary object, or a threaded collar such as anut can rotate around a stationary screw shaft.^[167][168] Geometrically, a screw can be viewed as a narrowinclined plane wrapped around acylinder.^[164]

Series circuit

An electrical circuit in which the same current passes through each component, with only one path.

Servo

A motor that moves to and maintains a set position under command, rather than continuously moving.

Servomechanism

An automatic device that uses error-sensing negative feedback to correct the performance of a mechanism.

Shadow matter

Inphysics, mirror matter, also called shadow matter or Alice matter, is a hypothetical counterpart to ordinary matter.^[169]

Shear flow

The term shear flow is used insolid mechanics as well as influid dynamics. The expressionshear flow is used to indicate:

• ashear stress over a distance in a thin-walled structure (in solid mechanics);^[170]
• the flowinduced by a force (in a fluid).

Shear strength

is the strength of a material or component against the type ofyield orstructural failure when the material or component fails inshear. A shear load is aforce that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. When a paper is cut with scissors, the paper fails in shear.Instructural andmechanical engineering, the shear strength of a component is important for designing the dimensions and materials to be used for the manufacture or construction of the component (e.g.beams,plates, orbolts). In areinforced concrete beam, the main purpose ofreinforcing bar (rebar) stirrups is to increase the shear strength.

Shear stress

Shear stress, often denoted byτ (Greek:tau), is the component ofstress coplanar with a material cross section. It arises from theshear force, the component offorce vectorparallel to thematerial cross section.Normal stress, on the other hand, arises from the force vector componentperpendicular to the material cross section on which it acts.

Shortwave radiation

Shortwave radiation (SW) isradiant energy with wavelengths in thevisible (VIS), near-ultraviolet (UV), andnear-infrared (NIR) spectra.There is no standard cut-off for the near-infrared range; therefore, the shortwave radiation range is also variously defined. It may be broadly defined to include all radiation with a wavelength of 0.1μm and 5.0μm or narrowly defined so as to include only radiation between 0.2μm and 3.0μm.There is little radiation flux (in terms ofW/m²) to the Earth's surface below 0.2μm or above 3.0μm, although photon flux remains significant as far as 6.0μm, compared to shorter wavelength fluxes.UV-C radiation spans from 0.1μm to .28μm,UV-B from 0.28μm to 0.315μm,UV-A from 0.315μm to 0.4μm, the visible spectrum from 0.4μm to 0.7μm, andNIR arguably from 0.7μm to 5.0μm, beyond which the infrared is thermal.^[171]Shortwave radiation is distinguished fromlongwave radiation. Downward shortwave radiation is sensitive tosolar zenith angle,cloud cover.^[172]

SI units

TheInternational System of Units (SI, abbreviated from theFrenchSystème international (d'unités)) is the modern form of themetric system. It is the onlysystem of measurement with an official status in nearly every country in the world. It comprises acoherent system ofunits of measurement starting with sevenbase units, which are thesecond (the unit oftime with the symbol s),metre (length, m),kilogram (mass, kg),ampere (electric current, A),kelvin (thermodynamic temperature, K),mole (amount of substance, mol), andcandela (luminous intensity, cd). The system allows for an unlimited number of additional units, calledderived units, which can always be represented as products of powers of the base units.^[e] Twenty-two derived units have been provided with special names and symbols.^[f] The seven base units and the 22 derived units with special names and symbols may be used in combination to express other derived units,^[g] which are adopted to facilitate measurement of diverse quantities. The SI also provides twentyprefixes to the unit names and unit symbols that may be used when specifying power-of-ten (i.e. decimal) multiples and sub-multiples of SI units. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology ofmeasurement progresses and the precision of measurements improves.

Signal processing

Is anelectrical engineering subfield that focuses on analysing, modifying, and synthesizingsignals such assound,images, and scientific measurements.^[173] Signal processing techniques can be used to improve transmission, storage efficiency and subjective quality and to also emphasize or detect components of interest in a measured signal.^[174]

Simple machine

is a mechanical device that changes the direction or magnitude of aforce.^[175] In general, they can be defined as the simplest mechanisms that usemechanical advantage (also calledleverage) to multiply force.^[176] Usually the term refers to the six classical simple machines that were defined byRenaissance scientists:^{[177][178][179]}

• Lever
• Wheel and axle
• Pulley
• Inclined plane
• Wedge
• Screw

Siphon

A closed tube that conveys liquids between two levels without pumping.

Solid mechanics

also known asmechanics of solids, is the branch ofcontinuum mechanics that studies the behavior ofsolid materials, especially their motion anddeformation under the action offorces,temperature changes,phase changes, and other external or internal agents.

Solid-state physics

is the study of rigidmatter, orsolids, through methods such asquantum mechanics,crystallography,electromagnetism, andmetallurgy. It is the largest branch ofcondensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from theiratomic-scale properties. Thus, solid-state physics forms a theoretical basis ofmaterials science. It also has direct applications, for example in the technology oftransistors andsemiconductors.

Solid solution strengthening

is a type ofalloying that can be used to improve thestrength of a pure metal. The technique works by adding atoms of one element (the alloying element) to the crystalline lattice of another element (the base metal), forming asolid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impedingdislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms (e.g. theprecipitation ofintermetallic compounds).

Solubility

is the property of asolid,liquid orgaseouschemical substance calledsolute to dissolve in a solid, liquid or gaseoussolvent. The solubility of a substance fundamentally depends on thephysical andchemical properties of the solute and solvent as well as on temperature, pressure and presence of other chemicals (including changes to thepH) of the solution. The extent of the solubility of a substance in a specific solvent is measured as the saturationconcentration, where adding more solute does not increase the concentration of the solution and begins to precipitate the excess amount of solute.

Solubility equilibrium

is a type ofdynamic equilibrium that exists when achemical compound in the solid state is inchemical equilibrium with asolution of that compound. The solid may dissolve unchanged, with dissociation or with chemical reaction with another constituent of the solution, such as acid or alkali. Each solubility equilibrium is characterized by a temperature-dependentsolubility product which functions like anequilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.

Sound

Inphysics, sound is avibration that propagates as anacoustic wave, through atransmission medium such as a gas, liquid or solid.

Special relativity

Inphysics, thespecial theory of relativity, orspecial relativity for short, is a scientific theory regarding the relationship betweenspace and time. InAlbert Einstein's original treatment, the theory is based on twopostulates:^{[180][181][182]}

1. Thelaws of physics areinvariant (that is, identical) in allinertial frames of reference (that is, frames of reference with noacceleration).
2. Thespeed of light invacuum is the same for all observers, regardless of the motion of the light source or observer.

Specific heat

The amount of energy required to change the temperature of a unit mass of substance by one degree.

Specific gravity

The ratio between the mass density of a substance to that of water.

Specific volume

The volume of a unit mass of a substance.

Specific weight

The weight of a substance per unit volume.

Spontaneous combustion

Spontaneous combustion orspontaneous ignition is a type ofcombustion which occurs by self-heating (increase in temperature due toexothermic internal reactions), followed bythermal runaway (self heating which rapidly accelerates to high temperatures) and finally,autoignition.^[183]

Stagnation pressure

Influid dynamics, stagnation pressure (orpitot pressure) is thestatic pressure at astagnation point in a fluid flow.^[184] At a stagnation point the fluid velocity is zero. In an incompressible flow, stagnation pressure is equal to the sum of the free-streamstatic pressure and the free-streamdynamic pressure.^[185]

Standard electrode potential

.

State of matter

Inphysics, a state of matter is one of the distinct forms in whichmatter can exist. Four states of matter are observable in everyday life:solid,liquid,gas, andplasma. Many intermediate states are known to exist, such asliquid crystal, and some states only exist under extreme conditions, such asBose–Einstein condensates,neutron-degenerate matter, andquark–gluon plasma, which only occur, respectively, in situations of extreme cold, extreme density, and extremely high energy. For a complete list of all exotic states of matter, see thelist of states of matter.

Statics

The study of forces in a non-moving, rigid body.

Statistics

is the discipline that concerns the collection, organization, analysis, interpretation, and presentation ofdata.^{[186][187][188]} In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with astatistical population or astatistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design ofsurveys andexperiments.^[189]

Steam table

Thermodynamic data table containing steam or water properties .^[190]

Stefan–Boltzmann law

The Stefan–Boltzmann law describes the power radiated from ablack body in terms of itstemperature. Specifically, the Stefan–Boltzmann law states that the totalenergy radiated per unitsurface area of ablack body acrossall wavelengths per unittime${\displaystyle j^{\star }}$ (also known as the black-bodyradiant emittance) is directlyproportional to the fourth power of the black body'sthermodynamic temperatureT:

${\displaystyle j^{\star }=\sigma T^4.}$

Theconstant of proportionalityσ, called theStefan–Boltzmann constant, is derived from other knownphysical constants.Since 2019, the value of the constant is

${\displaystyle \sigma =\frac{2{\pi }^5{k}^4}{15c^2{h}^3}=5.670374\dots \times {10}^{-8}\mathrm{W}{\mathrm{m}}^{-2}{\mathrm{K}}^{-4},}$

wherek is theBoltzmann constant,h is thePlanck constant, andc isthe speed of light in vacuum. Theradiance from a specified angle of view (watts per square metre persteradian) is given by

${\displaystyle L=\frac{j^{\star }}{\pi }=\frac{\sigma }{\pi }{T}^4.}$

A body that does not absorb all incident radiation (sometimes known as a grey body) emits less total energy than a black body and is characterized by anemissivity,:

${\displaystyle j^{\star }=\epsilon \sigma T^4.}$

The radiant emittance${\displaystyle j^{\star }}$ hasdimensions ofenergy flux (energy per unit time per unit area), and theSI units of measure arejoules per second per square metre, or equivalently,watts per square metre. The SI unit for absolute temperatureT is thekelvin.${\displaystyle \epsilon }$ is theemissivity of the grey body; if it is a perfect blackbody,${\displaystyle \epsilon =1}$. In the still more general (and realistic) case, the emissivity depends on the wavelength,${\displaystyle \epsilon =\epsilon (\lambda )}$.To find the totalpower radiated from an object, multiply by its surface area,${\displaystyle A}$:

${\displaystyle P=A{j}^{\star }=A\epsilon \sigma T^4.}$

Wavelength- and subwavelength-scale particles,^[191]metamaterials,^[192] and other nanostructures are not subject to ray-optical limits and may be designed to exceed the Stefan–Boltzmann law.

Stewart platform

is a type ofparallel manipulator that has sixprismatic actuators, commonlyhydraulic jacks or electriclinear actuators, attached in pairs to three positions on the platform's baseplate, crossing over to three mounting points on a top plate. All 12 connections are made viauniversal joints. Devices placed on the top plate can be moved in thesix degrees of freedom in which it is possible for a freely-suspended body to move: three linear movements x, y, z (lateral, longitudinal, and vertical), and the three rotations (pitch, roll, and yaw).

Stiffness

is the extent to which an object resistsdeformation in response to an appliedforce.^[193]The complementary concept isflexibility or pliability: the more flexible an object is, the less stiff it is.^[194]

Stoichiometry

refers to the relationship between the quantities ofreactants andproducts before, during, and followingchemical reactions.Stoichiometry is founded on thelaw of conservation of mass where the total mass of the reactants equals the total mass of the products, leading to the insight that the relations among quantities of reactants and products typically form a ratio of positive integers. This means that if the amounts of the separate reactants are known, then the amount of the product can be calculated. Conversely, if one reactant has a known quantity and the quantity of the products can be empirically determined, then the amount of the other reactants can also be calculated.

Strain

.

Strain hardening

Work hardening, also known as strain hardening, is thestrengthening of a metal or polymer byplastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.This strengthening occurs because ofdislocation movements and dislocation generation within thecrystal structure of the material.^[195] Many non-brittle metals with a reasonably highmelting point as well as several polymers can be strengthened in this fashion.^[196] Alloys not amenable toheat treatment, including low-carbon steel, are often work-hardened. Some materials cannot be work-hardened at low temperatures, such asindium,^[197] however others can be strengthened only via work hardening, such as pure copper and aluminum.^[198]

Strength of materials

The field of strength of materials, also calledmechanics of materials, typically refers to various methods of calculating thestresses andstrains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as itsyield strength,ultimate strength,Young's modulus, andPoisson's ratio. In addition, the mechanical element's macroscopic properties (geometric properties) such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.

Stress

Incontinuum mechanics, stress is aphysical quantity that expresses the internalforces that neighbouringparticles of a continuous material exert on each other, whilestrain is the measure of the deformation of the material. For example, when asolid vertical bar is supporting an overheadweight, each particle in the bar pushes on the particles immediately below it. When aliquid is in a closed container underpressure, each particle gets pushed against by all the surrounding particles. The container walls and thepressure-inducing surface (such as a piston) push against them in (Newtonian)reaction. These macroscopic forces are actually the net result of a very large number ofintermolecular forces andcollisions between the particles in thosemolecules. Stress is frequently represented by a lowercase Greek letter sigma (σ).

Stress–strain analysis

Stress–strain analysis (orstress analysis) is anengineering discipline that uses many methods to determine thestresses andstrains in materials and structures subjected toforces. Incontinuum mechanics, stress is aphysical quantity that expresses the internalforces that neighboringparticles of acontinuous material exert on each other, while strain is the measure of the deformation of the material.In simple terms we can define stress as the force of resistance per unit per unit area, offered by a body against deformation. Stress is the ratio of force over area (S =R/A, where S is the stress, R is the internal resisting force and A is the cross-sectional area). Strain is the ratio of change in length to the original length, when a given body is subjected to some external force (Strain= change in length÷the original length).

Stress–strain curve

In engineering andmaterials science, a stress–strain curve for a material gives the relationship betweenstress andstrain. It is obtained by gradually applyingload to a test coupon and measuring thedeformation, from which the stress and strain can be determined (seetensile testing). These curves reveal many of theproperties of a material, such as theYoung's modulus, theyield strength and theultimate tensile strength.

Structural analysis

is the determination of the effects ofloads on physicalstructures and theircomponents.Structures subject to this type ofanalysis include all that must withstand loads, such as buildings, bridges, aircraft and ships. Structural analysis employs the fields ofapplied mechanics,materials science andapplied mathematics to compute a structure'sdeformations, internalforces,stresses, support reactions, accelerations, andstability. The results of the analysis are used to verify a structure's fitness for use, often precludingphysical tests. Structural analysis is thus a key part of theengineering design of structures.^[199]

Structural load

A structural load orstructural action is aforce,deformation, oracceleration applied tostructural elements.^[200][201] A load causesstress,deformation, anddisplacement in astructure.Structural analysis, a discipline inengineering, analyzes the effects loads on structures and structural elements. Excess load may causestructural failure, so this should be considered and controlled during the design of a structure. Particular mechanical structures—such asaircraft,satellites,rockets,space stations,ships, andsubmarines—are subject to their own particular structural loads and actions.^[202] Engineers often evaluate structural loads based upon publishedregulations,contracts, orspecifications. Acceptedtechnical standards are used foracceptance testing andinspection.

Sublimation

is the transition of a substance directly from thesolid to thegas state,^[203] without passing through the liquid state.^[204] Sublimation is anendothermic process that occurs at temperatures and pressures below a substance'striple point in itsphase diagram, which corresponds to the lowest pressure at which the substance can exist as a liquid. The reverse process of sublimation isdeposition or desublimation, in which a substance passes directly from a gas to a solid phase.^[205] Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition (deposition).^[206] Whilevaporization from liquid to gas occurs asevaporation from the surface if it occurs below the boiling point of the liquid, and asboiling with formation of bubbles in the interior of the liquid if it occurs at the boiling point, there is no such distinction for the solid-to-gas transition which always occurs as sublimation from the surface.

Subsumption architecture

is a reactiverobotic architecture heavily associated withbehavior-based robotics which was very popular in the 1980s and 90s. The term was introduced byRodney Brooks and colleagues in 1986.^{[207][208][209]} Subsumption has been widely influential inautonomous robotics and elsewhere inreal-timeAI.

Surface tension

is the tendency ofliquid surfaces at rest to shrink into the minimumsurface area possible. Surface tension is what allows objects with a higher density than water to float on a water surface without becoming even partly submerged.

Superconductivity

is a set of physical properties observed in certain materials whereelectrical resistance vanishes andmagnetic flux fields are expelled from the material. Any material exhibiting these properties is asuperconductor. Unlike an ordinary metallicconductor, whose resistance decreases gradually as its temperature is lowered even down to nearabsolute zero, a superconductor has a characteristiccritical temperature below which the resistance drops abruptly to zero. Anelectric current through a loop ofsuperconducting wire can persist indefinitely with no power source.^{[210][211][212][213]}

Superhard material

is a material with a hardness value exceeding 40 gigapascals (GPa) when measured by theVickers hardness test.^{[214][215][216][217]} They are virtually incompressible solids with high electron density and highbond covalency. As a result of their unique properties, these materials are of great interest in many industrial areas including, but not limited to,abrasives, polishing andcutting tools,disc brakes, andwear-resistant and protective coatings.

Supersaturation

Supersaturation occurs with achemical solution when the concentration of asolute exceeds the concentration specified by the value equilibriumsolubility. Most commonly the term is applied to a solution of a solid in a liquid. A supersaturated solution is in ametastable state; it may be brought to equilibrium by forcing the excess of solute to separate from the solution. The term can also be applied to a mixture of gases.

Tangential acceleration

The velocity of a particle moving on a curved path as afunction of time can be written as:

${\displaystyle \mathbf{v}(t)=v(t)\frac{\mathbf{v}(t)}{v(t)}=v(t){\mathbf{u}}_{\mathrm{t}}(t),}$

withv(t) equal to the speed of travel along the path, and

${\displaystyle {\mathbf{u}}_{\mathrm{t}}=\frac{\mathbf{v}(t)}{v(t)},}$

aunit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speedv(t) and the changing direction ofu_t, the acceleration of a particle moving on a curved path can be written using thechain rule of differentiation^[218] for the product of two functions of time as:

whereu_n is the unit (inward)normal vector to the particle's trajectory (also calledthe principal normal), andr is its instantaneousradius of curvature based upon theosculating circle at timet. These components are called the tangential acceleration and the normal or radial acceleration (or centripetal acceleration in circular motion, see alsocircular motion andcentripetal force).Geometrical analysis of three-dimensional space curves, which explains tangent, (principal) normal and binormal, is described by theFrenet–Serret formulas.^[219][220]

Technical standard

A technical standard is an establishednorm orrequirement for a repeatable technical task. It is usually a formal document that establishes uniform engineering or technical criteria, methods, processes, and practices. In contrast, a custom,convention, company product, corporate standard, and so forth that becomes generally accepted and dominant is often called ade facto standard.

Temperature

is a physical quantity that expresses hot and cold. It is the manifestation ofthermal energy, present in all matter, which is the source of the occurrence ofheat, a flow of energy, when a body is in contact with another that is colder. Temperature ismeasured with athermometer. Thermometers are calibrated in varioustemperature scales that historically have used various reference points and thermometric substances for definition. The most common scales are theCelsius scale (formerly calledcentigrade, denoted °C), theFahrenheit scale (denoted °F), and theKelvin scale (denoted K), the last of which is predominantly used for scientific purposes by conventions of theInternational System of Units (SI).

Tempering (metallurgy)

Heat treatment to alter the crystal structure of a metal such as steel.

Tensile force

Pulling force, tending to lengthen an object.

Tensile modulus

Young's modulus${\displaystyle E}$, theYoung modulus, or themodulus of elasticity in tension, is a mechanical property that measures the tensilestiffness of asolid material. It quantifies the relationship between tensilestress${\displaystyle \sigma }$ (force per unit area) and axialstrain${\displaystyle \epsilon }$ (proportional deformation) in thelinear elastic region of a material and is determined using the formula:^[221]$${\displaystyle E=\frac{\sigma }{\epsilon }}$$Young's moduli are typically so large that they are expressed not inpascals but in gigapascals (GPa).

Tensile strength

Ultimate tensile strength (UTS), often shortened to tensile strength (TS), ultimate strength, or${\displaystyle F_{\text{tu}}}$ within equations,^{[222][223][224]} is the maximumstress that a material can withstand while being stretched or pulled before breaking. Inbrittle materials the ultimate tensile strength is close to theyield point, whereas inductile materials the ultimate tensile strength can be higher.

Tensile testing

Tensile testing, also known as tension testing,^[225] is a fundamentalmaterials science andengineering test in which a sample is subjected to a controlledtension until failure. Properties that are directly measured via a tensile test areultimate tensile strength,breaking strength, maximumelongation and reduction in area.^[226] From these measurements the following properties can also be determined:Young's modulus,Poisson's ratio,yield strength, andstrain-hardening characteristics.^[227]Uniaxial tensile testing is the most commonly used for obtaining the mechanical characteristics ofisotropic materials. Some materials usebiaxial tensile testing. The main difference between these testing machines being how load is applied on the materials.

Tension member

Tension members are structural elements that are subjected to axialtensile forces. Examples of tension members are bracing for buildings andbridges,truss members, andcables in suspendedroof systems.

Thermal conduction

is the transfer ofinternal energy by microscopic collisions of particles and movement of electrons within a body. The colliding particles, which include molecules, atoms and electrons, transfer disorganized microscopic kinetic and potential energy, jointly known as internal energy. Conduction takes place in allphases: solid, liquid, and gas.

Thermal equilibrium

Twophysical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys thezeroth law of thermodynamics. A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially uniform and temporally constant.Systems inthermodynamic equilibrium are always in thermal equilibrium, but the converse is not always true. If the connection between the systems allows transfer of energy as 'change ininternal energy' but does not allow transfer of matter or transfer of energy aswork, the two systems may reach thermal equilibrium without reaching thermodynamic equilibrium.

Thermal radiation

iselectromagnetic radiation generated by thethermal motion of particles inmatter. All matter with atemperature greater thanabsolute zero emits thermal radiation. Particle motion results incharge-acceleration ordipole oscillation which produces electromagnetic radiation.

Thermodynamics

is a branch ofphysics that deals withheat,work, andtemperature, and their relation toenergy,radiation, and physical properties ofmatter. The behavior of these quantities is governed by the fourlaws of thermodynamics which convey a quantitative description using measurable macroscopicphysical quantities, but may be explained in terms ofmicroscopic constituents bystatistical mechanics. Thermodynamics applies to a wide variety of topics inscience andengineering, especiallyphysical chemistry,biochemistry,chemical engineering andmechanical engineering, but also in other complex fields such asmeteorology.

Theory of relativity

usually encompasses two interrelated theories byAlbert Einstein:special relativity andgeneral relativity, proposed and published in 1905 and 1915, respectively.^[228] Special relativity applies to all physical phenomena in the absence ofgravity. General relativity explains the law of gravitation and its relation to other forces of nature.^[229] It applies to thecosmological and astrophysical realm, including astronomy.^[230]

Thévenin's theorem

As originally stated in terms of direct-currentresistive circuits only, Thévenin's theorem states that "For anylinearelectrical network containing onlyvoltage sources,current sources andresistances can be replaced at terminals A–B by an equivalent combination of a voltage source V_th in aseries connection with a resistance R_th."

• The equivalent voltageV_th is the voltage obtained at terminals A–B of the network with terminals A–Bopen circuited.
• The equivalent resistanceR_th is the resistance that the circuit between terminals A and B would have if all ideal voltage sources in the circuit were replaced by a short circuit and all ideal current sources were replaced by an open circuit.
• If terminals A and B are connected to one another, the current flowing from A to B will beV_th/R_th. This means thatR_th could alternatively be calculated asV_th divided by the short-circuit current between A and B when they are connected together.

Incircuit theory terms, the theorem allows anyone-port network to be reduced to a singlevoltage source and a single impedance.The theorem also applies to frequency domain AC circuits consisting ofreactive andresistiveimpedances. It means the theorem applies for AC in an exactly same way to DC except that resistances are generalized to impedances.

Three-phase electric power

is a common method ofalternating currentelectric powergeneration,transmission, anddistribution.^[231] It is a type ofpolyphase system and is the most common method used byelectrical grids worldwide to transfer power. It is also used to power largemotors and other heavy loads.

Torque

Inphysics andmechanics, torque is the rotational equivalent of linearforce.^[232] It is also referred to as themoment,moment of force,rotational force orturning effect, depending on the field of study. The concept originated with the studies byArchimedes of the usage oflevers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of theline of action of a force from theaxis of rotation. The symbol for torque is typically${\displaystyle \mathit{\tau }}$ orτ, the lowercaseGreek lettertau. When being referred to asmoment of force, it is commonly denoted byM.

Torsional vibration

is angularvibration of an object—commonly a shaft along its axis of rotation. Torsional vibration is often a concern inpower transmission systems using rotating shafts or couplings where it can cause failures if not controlled. A second effect of torsional vibrations applies to passenger cars. Torsional vibrations can lead to seat vibrations or noise at certain speeds. Both reduce the comfort.

Toughness

Inmaterials science andmetallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing.^[233] One definition of material toughness is the amount of energy per unit volume that a material can absorb beforerupturing. This measure of toughness is different from that used forfracture toughness, which describes load bearing capabilities of materials with flaws.^[234] It is also defined as a material's resistance to fracture whenstressed.Toughness requires a balance ofstrength andductility.^[233]

Trajectory

A trajectory orflight path is the path that anobject withmass inmotion follows throughspace as a function of time. Inclassical mechanics, a trajectory is defined byHamiltonian mechanics viacanonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.The mass might be aprojectile or asatellite.^[235] For example, it can be anorbit — the path of aplanet,asteroid, orcomet as it travels around acentral mass.Incontrol theory, a trajectory is a time-ordered set ofstates of adynamical system (see e.g.Poincaré map). Indiscrete mathematics, a trajectory is a sequence${\displaystyle (f^k(x){)}_{k\in \mathbb{N}}}$ of values calculated by the iterated application of a mapping${\displaystyle f}$ to an element${\displaystyle x}$ of its source.

Transducer

is a device thatconverts energy from one form to another. Usually a transducer converts asignal in one form of energy to a signal in another.^[236]Transducers are often employed at the boundaries ofautomation,measurement, andcontrol systems, where electrical signals are converted to and from other physical quantities (energy, force, torque, light, motion, position, etc.). The process of converting oneform of energy to another is known as transduction.^[237]

Transformer

is apassive component that transfers electrical energy from one electrical circuit to another circuit, or multiplecircuits. A varying current in any one coil of the transformer produces a varyingmagnetic flux in the transformer's core, which induces a varyingelectromotive force across any other coils wound around the same core. Electrical energy can be transferred between separate coils without a metallic (conductive) connection between the two circuits.Faraday's law of induction, discovered in 1831, describes the induced voltage effect in any coil due to a changing magnetic flux encircled by the coil.

Trigonometric functions

Inmathematics, the trigonometric functions (also calledcircular functions,angle functions orgoniometric functions^[238][239]) arereal functions which relate an angle of aright-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related togeometry, such asnavigation,solid mechanics,celestial mechanics,geodesy, and many others. They are among the simplestperiodic functions, and as such are also widely used for studying periodic phenomena throughFourier analysis.The trigonometric functions most widely used in modern mathematics are thesine, thecosine, and thetangent. Theirreciprocals are respectively thecosecant, thesecant, and thecotangent, which are less used. Each of these six trigonometric functions has a correspondinginverse function, and an analog among thehyperbolic functions.

Trigonometry

Is a branch ofmathematics that studies relationships between side lengths andangles oftriangles. The field emerged in theHellenistic world during the 3rd century BC from applications ofgeometry toastronomical studies.^[240] The Greeks focused on thecalculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also calledtrigonometric functions) such assine.^[241]

Trimean

The trimean is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles

Triple point

Inthermodynamics, the triple point of a substance is thetemperature andpressure at which the threephases (gas,liquid, andsolid) of that substance coexist inthermodynamic equilibrium.^[242] It is that temperature and pressure at which thesublimation curve,fusion curve and thevaporisation curve meet. For example, the triple point ofmercury occurs at a temperature of −38.83440 °C (−37.90192 °F) and a pressure of 0.165mPa. In addition to the triple point for solid, liquid, and gas phases, a triple point may involve more than one solid phase, for substances with multiplepolymorphs.Helium-4 is a special case that presents a triple point involving two different fluid phases (lambda point).^[242]

Trouton's rule

Trouton's rule states that theentropy of vaporization is almost the same value, about 85–88 J/(K·mol), for various kinds ofliquids at theirboiling points.^[243] The entropy of vaporization is defined as the ratio between theenthalpy of vaporization and the boiling temperature. It is named afterFrederick Thomas Trouton.It can be expressed as a function of thegas constantR:

${\displaystyle \mathrm{\Delta }{\overline{S}}_{\text{vap}}\approx 10.5R.}$

A similar way of stating this (Trouton's ratio) is that thelatent heat is connected toboiling point roughly as

${\displaystyle \frac{L_{\text{vap}}}{T_{\text{boiling}}}\approx 85-88\frac{\text{J}}{\text{K}\cdot \text{mol}}.}$

Ultimate tensile strength

Ultimate tensile strength (UTS), often shortened totensile strength (TS),ultimate strength, orFtu within equations,^{[222][223][224]} is the capacity of a material or structure to withstand loads tending to elongate, as opposed tocompressive strength, which withstands loads tending to reduce size. In other words, tensile strength resiststension (being pulled apart), whereas compressive strength resistscompression (being pushed together). Ultimate tensile strength is measured by the maximumstress that a material can withstand while being stretched or pulled before breaking. In the study ofstrength of materials, tensile strength, compressive strength, andshear strength can be analyzed independently.

Uncertainty principle

Inquantum mechanics, theuncertainty principle (also known asHeisenberg's uncertainty principle) is any of a variety ofmathematical inequalities^[250] asserting a fundamental limit to the precision with which certain pairs of physical properties of aparticle, known ascomplementary variables, such aspositionx andmomentump, can be known.

Unicode

A standard for the consistent encoding of textual characters.

Unit vector

Inmathematics, aunit vector in anormed vector space is avector (often aspatial vector) oflength 1. A unit vector is often denoted by a lowercase letter with acircumflex, or "hat":${\displaystyle \hat{ı}}$ (pronounced "i-hat"). The termdirection vector is used to describe a unit vector being used to represent spatial direction, and such quantities are commonly denoted asd. .

Unsaturated compound

.

Upthrust

Buoyancy, or upthrust, is an upwardforce exerted by afluid that opposes theweight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and (as explained byArchimedes' principle) is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. thedisplaced fluid.

Utility frequency

The utility frequency, (power) line frequency (American English) or mains frequency (British English) is the nominalfrequency of the oscillations ofalternating current (AC) in awide area synchronous grid transmitted from apower station to theend-user. In large parts of the world this is 50 Hz, although in the Americas and parts of Asia it is typically 60 Hz. Current usage by country or region is given in the list ofmains electricity by country.

Vacuole

is amembrane-boundorganelle which is present inplant andfungalcells and someprotist,animal^[251] andbacterial cells.^[252] Vacuoles are essentially enclosed compartments which are filled with water containing inorganic and organic molecules includingenzymes insolution, though in certain cases they may contain solids which have been engulfed. Vacuoles are formed by the fusion of multiple membranevesicles and are effectively just larger forms of these.^[253] The organelle has no basic shape or size; its structure varies according to the requirements of the cell.

Vacuum

An absence of mass in a volume.

Valence

Inchemistry, thevalence orvalency of anelement is a measure of its combining power with other atoms when it formschemical compounds ormolecules. The concept of valence developed in the second half of the 19th century and helped successfully explain the molecular structure of inorganic and organic compounds.^[254] The quest for the underlying causes of valence led to the modern theories of chemical bonding, including thecubical atom (1902),Lewis structures (1916),valence bond theory (1927),molecular orbitals (1928),valence shell electron pair repulsion theory (1958), and all of the advanced methods ofquantum chemistry.

Valence band

Insolid-state physics, the valence band and conduction band are thebands closest to theFermi level and thus determine theelectrical conductivity of the solid. In non-metals, the valence band is the highest range ofelectronenergies in which electrons are normally present atabsolute zero temperature, while the conduction band is the lowest range of vacantelectronic states. On a graph of theelectronic band structure of a material, the valence band is located below the Fermi level, while the conduction band is located above it. The distinction between the valence and conduction bands is meaningless in metals, because conduction occurs in one or more partially filled bands that take on the properties of both the valence and conduction bands.

Valence bond theory

Inchemistry, valence bond (VB) theory is one of the two basic theories, along withmolecular orbital (MO) theory, that were developed to use the methods ofquantum mechanics to explainchemical bonding. It focuses on how theatomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.^[255]

Valence electron

Inchemistry andphysics, a valence electron is an outer shellelectron that is associated with anatom, and that can participate in the formation of achemical bond if the outer shell is not closed; in a singlecovalent bond, both atoms in the bond contribute one valence electron in order to form ashared pair.

Valence shell

The valence shell is the set oforbitals which are energetically accessible for accepting electrons to formchemical bonds. For main group elements, the valence shell consists of the ns and np orbitals in the outermostelectron shell. In the case oftransition metals (the (n-1)d orbitals), andlanthanides andactinides (the (n-2)f and (n-1)d orbitals), the orbitals involved can also be in an inner electron shell. Thus, theshell terminology is amisnomer as there is no correspondence between the valence shell and any particular electron shell in a given element. A scientifically correct term would bevalence orbital to refer to the energetically accessible orbitals of an element.

Valve

is a device ornatural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, orslurries) by opening, closing, or partially obstructing various passageways. Valves are technicallyfittings, but are usually discussed as a separate category. In an open valve, fluid flows in a direction from higher pressure to lower pressure. The word is derived from the Latinvalva, the moving part of a door, in turn fromvolvere, to turn, roll.

van der Waals equation

Inchemistry andthermodynamics, the Van der Waals equation (orVan der Waals equation of state; named after Dutch physicistJohannes Diderik van der Waals) is anequation of state that generalizes theideal gas law based on plausible reasons thatreal gases do not actideally. The ideal gas law treats gasmolecules aspoint particles that interact with their containers but not each other, meaning they neither take up space nor changekinetic energy duringcollisions (i.e. all collisions areperfectly elastic).^[256] The ideal gas law states thatvolume (V) occupied bynmoles of any gas has apressure (P) attemperature (T) inkelvins given by the following relationship, whereR is thegas constant:

${\displaystyle PV=nRT}$

To account forthe volume that a real gas molecule takes up, the Van der Waals equation replacesV in the ideal gas law with${\displaystyle (V_m-b)}$, whereV_m is themolar volume of the gas andb is the volume that is occupied by one mole of the molecules. This leads to:^[256]

${\displaystyle P(V_m-b)=RT}$

The second modification made to the ideal gas law accounts for the fact that gas molecules do in fact interact with each other (they usually experience attraction at low pressures and repulsion at high pressures) and that real gases therefore show different compressibility than ideal gases. Van der Waals provided forintermolecular interaction by adding to the observed pressureP in the equation of state a term${\displaystyle a/V_m^2}$, wherea is a constant whose value depends on the gas. TheVan der Waals equation is therefore written as:^[256]

${\displaystyle \left(P+a\frac{1}{V_m^2}\right)(V_m-b)=RT}$

and, forn moles of gas, can also be written as the equation below:

${\displaystyle \left(P+a\frac{n^2}{V^2}\right)(V-nb)=nRT}$

whereV_m is the molar volume of the gas,R is the universal gas constant,T is temperature,P is pressure, andV is volume. When the molar volumeV_m is large,b becomes negligible in comparison withV_m,a/V_m² becomes negligible with respect toP, and the Van der Waals equation reduces to the ideal gas law,PV_m=RT.^[256]It is available via its traditional derivation (a mechanical equation of state), or via a derivation based instatistical thermodynamics, the latter of which provides thepartition function of the system and allows thermodynamic functions to be specified. It successfully approximates the behavior of realfluids above theircritical temperatures and is qualitatively reasonable for theirliquid and low-pressuregaseous states at low temperatures. However, near thephase transitions between gas and liquid, in the range ofp,V, andT where the liquid phase and the gas phase are inequilibrium, the Van der Waals equation fails to accurately model observed experimental behaviour, in particular thatp is a constant function ofV at given temperatures. As such, the Van der Waals model is not useful only for calculations intended to predict real behavior in regions near thecritical point. Corrections to address these predictive deficiencies have since been made, such as theequal area rule or theprinciple of corresponding states.

van der Waals force

Inmolecular physics, the Van der Waals force, named after Dutch physicistJohannes Diderik van der Waals, is a distance-dependent interaction between atoms or molecules. Unlikeionic orcovalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The Van der Waals force quickly vanishes at longer distances between interacting molecules.

van 't Hoff equation

relates the change in theequilibrium constant,K_eq, of a chemical reaction to the change intemperature,T, given thestandard enthalpy change,Δ_rH^⊖, for the process. It was proposed by Dutch chemistJacobus Henricus van 't Hoff in 1884 in his bookÉtudes de dynamique chimique (Studies in Dynamic Chemistry).^[257]The Van 't Hoff equation has been widely utilized to explore the changes instate functions in athermodynamic system. TheVan 't Hoff plot, which is derived from this equation, is especially effective in estimating the change inenthalpy andentropy of achemical reaction.

van 't Hoff factor

is a measure of the effect of a solute oncolligative properties such asosmotic pressure, relative lowering invapor pressure,boiling-point elevation andfreezing-point depression. The Van 't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and theconcentration of a substance as calculated from its mass. For most non-electrolytes dissolved in water, the Van 't Hoff factor is essentially 1. For mostionic compounds dissolved in water, the Van 't Hoff factor is equal to the number of discrete ions in aformula unit of the substance. This is true forideal solutions only, as occasionallyion pairing occurs in solution. At a given instant a small percentage of the ions are paired and count as a single particle. Ion pairing occurs to some extent in all electrolyte solutions. This causes the measured Van 't Hoff factor to be less than that predicted in an ideal solution. The deviation for the Van 't Hoff factor tends to be greatest where the ions have multiple charges.

Variable capacitor

is acapacitor whose capacitance may be intentionally and repeatedly changed mechanically or electronically. Variable capacitors are often used inL/C circuits to set the resonance frequency, e.g. to tune a radio (therefore it is sometimes called atuning capacitor ortuning condenser), or as a variablereactance, e.g. forimpedance matching inantenna tuners.

Variable resistor

.

Vector space

A vector space (also called alinear space) is aset of objects calledvectors, which may beadded together andmultiplied ("scaled") by numbers, calledscalars. Scalars are often taken to bereal numbers, but there are also vector spaces with scalar multiplication bycomplex numbers,rational numbers, or generally anyfield. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vectoraxioms . To specify that the scalars are real or complex numbers, the termsreal vector space andcomplex vector space are often used.

Venturi effect

is the reduction influid pressure that results when a fluid flows through a constricted section (or choke) of a pipe. The Venturi effect is named after its discoverer, the 18th century Italianphysicist,Giovanni Battista Venturi.

Vibration

is a mechanical phenomenon wherebyoscillations occur about anequilibrium point. The word comes from Latinvibrationem ("shaking, brandishing"). The oscillations may beperiodic, such as the motion of a pendulum—orrandom, such as the movement of a tire on a gravel road.Vibration can be desirable: for example, the motion of atuning fork, thereed in awoodwind instrument orharmonica, amobile phone, or the cone of aloudspeaker.In many cases, however, vibration is undesirable, wastingenergy and creating unwantedsound. For example, the vibrational motions ofengines,electric motors, or anymechanical device in operation are typically unwanted. Such vibrations could be caused byimbalances in the rotating parts, unevenfriction, or the meshing ofgear teeth. Careful designs usually minimize unwanted vibrations.

Virtual leak

Traces of gas trapped in cavities within a vacuum chamber, slowly dissipating out in the main chamber, thus appearing like a leak from the outside.

Viscoelasticity

Inmaterials science andcontinuum mechanics, viscoelasticity is the property ofmaterials that exhibit bothviscous andelastic characteristics when undergoingdeformation. Viscous materials, like water, resistshear flow andstrain linearly with time when astress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain. Whereas elasticity is usually the result ofbond stretching alongcrystallographic planes in an ordered solid, viscosity is the result of the diffusion of atoms or molecules inside anamorphous material.^[258]

Viscosity

Theviscosity of afluid is the measure of itsresistance to gradual deformation byshear stress ortensile stress.^[259] For liquids, it corresponds to the informal concept of "thickness": for example,honey has a higher viscosity thanwater.^[260]

Volt-ampere

(VA), is the unit used for theapparent power in anelectrical circuit. The apparent power equals the product ofroot-mean-square (RMS)voltage and RMScurrent.^[261] Indirect current (DC) circuits, this product is equal to thereal power (active power)^[262] inwatts. Volt-amperes are useful only in the context ofalternating current (AC) circuits. The volt-ampere is dimensionally equivalent to thewatt (inSI units, 1 VA = 1 N m A⁻¹ s⁻¹ A = 1 N m s⁻¹ = 1 J s⁻¹ = 1 W). VA rating is most useful in rating wires and switches (and other power handling equipment) for inductive loads.

Volt-ampere reactive

In electric powertransmission anddistribution, volt-ampere reactive (var) is a unit of measurement ofreactive power. Reactive power exists in an AC circuit when the current and voltage are not in phase. The termvar was proposed by the Romanianelectrical engineerConstantin Budeanu and introduced in 1930 by theIEC inStockholm, which has adopted it as the unit forreactive power.Special instruments calledvarmeters are available to measure the reactive power in a circuit.^[263]The unit "var" is allowed by theInternational System of Units (SI) even though the unit var is representative of a form of power.^[264] SI allows one to specify units to indicatecommon sense physical considerations. Per EUdirective 80/181/EEC (the "metric directive"), the correct symbol is lower-case "var",^[265] although the spellings "Var" and "VAr" are commonly seen, and "VAR" is widely used throughout the power industry.

Volta potential

TheVolta potential (also calledVolta potential difference,contact potential difference,outer potential difference, Δψ, or "delta psi") inelectrochemistry, is theelectrostatic potential difference between two metals (or one metal and oneelectrolyte) that are in contact and are in thermodynamic equilibrium. Specifically, it is the potential difference between a point close to the surface of the first metal, and a point close to the surface of the second metal (orelectrolyte).^[266]

Voltage

Voltage,electric potential difference,electric pressure orelectric tension is the difference inelectric potential between two points. The difference in electric potential between two points (i.e., voltage) is defined as thework needed perunit of charge against a staticelectric field to move atest charge between the two points. In theInternational System of Units, thederived unit for voltage is namedvolt.^[267] In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1joule (of work) per 1coulomb (of charge). The official SI definition forvolt uses power and current, where 1 volt = 1watt (of power) per 1ampere (of current).^[267]

Volumetric flow rate

also known asvolume flow rate,rate of fluid flow orvolume velocity, is the volume of fluid which passes per unit time; usually represented by the symbolQ (sometimesV̇). TheSI unit is m³/s (cubic metres per second).

von Mises yield criterion

Thevon Mises yield criterion (also known as the maximum distortion energy criterion^[268]) suggests thatyielding of a ductile material begins when thesecond deviatoric stress invariant${\displaystyle J_2}$ reaches a critical value.^[269] It is part of plasticity theory that applies best toductile materials, such as some metals. Prior to yield, material response can be assumed to be of a nonlinear elastic, viscoelastic, or linear elastic behavior.Inmaterials science andengineering the von Mises yield criterion can also be formulated in terms of thevon Mises stress orequivalent tensile stress,${\displaystyle {\sigma }_v}$. This is a scalar value of stress that can be computed from theCauchy stress tensor. In this case, a material is said to start yielding when the von Mises stress reaches a value known asyield strength,${\displaystyle {\sigma }_y}$. The von Mises stress is used to predict yielding of materials under complex loading from the results of uniaxial tensile tests. The von Mises stress satisfies the property where two stress states with equal distortion energy have an equal von Mises stress.

Watt

The SI unit of power, rate of doing work.

Wave

is a disturbance that transfersenergy throughmatter or space, with little or no associatedmass transport. Waves consist ofoscillations orvibrations of a physicalmedium or afield, around relatively fixed locations. From the perspective of mathematics, waves, as functions of time and space, are a class ofsignals.^[270]

Wavelength

is thespatial period of a periodic wave—the distance over which the wave's shape repeats.^[271][272] It is thus theinverse of thespatial frequency. Wavelength is usually determined by considering the distance between consecutive corresponding points of the samephase, such as crests, troughs, orzero crossings and is a characteristic of both traveling waves andstanding waves, as well as other spatial wave patterns.^[273][274] Wavelength is commonly designated by theGreek letterlambda (λ). The termwavelength is also sometimes applied tomodulated waves, and to the sinusoidalenvelopes of modulated waves or waves formed byinterference of several sinusoids.^[275]' .

Wedge

is atriangular shaped tool, and is a portableinclined plane, and one of the six classicalsimple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting aforce applied to its blunt end into forces perpendicular (normal) to its inclined surfaces. Themechanical advantage of a wedge is given by the ratio of the length of its slope to its width.^[276][277] Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle.

Weighted arithmetic mean

Theweighted arithmetic mean is similar to an ordinaryarithmetic mean (the most common type ofaverage), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role indescriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as thearithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance inSimpson's paradox.

Wet-bulb temperature

The temperature of a wetted thermometer with an air current across it. Used in psychrometry.

Wheel and axle

are one of sixsimple machines identified by Renaissance scientists drawing from Greek texts on technology.^[278] The wheel and axle consists of awheel attached to a smalleraxle so that these two parts rotate together in which a force is transferred from one to the other. Ahinge orbearing supports the axle, allowing rotation. It can amplify force; a small force applied to the periphery of the large wheel can move a larger load attached to the axle.

Winsorized mean

is awinsorizedstatisticalmeasure of central tendency, much like themean andmedian, and even more similar to thetruncated mean. It involves the calculation of the mean after replacing given parts of aprobability distribution orsample at the high and low end with the most extreme remaining values,^[279] typically doing so for an equal amount of both extremes; often 10 to 25 percent of the ends are replaced. The winsorized mean can equivalently be expressed as aweighted average of the truncated mean and the quantiles at which it is limited, which corresponds to replacing parts with the corresponding quantiles.

Work hardening

also known asstrain hardening, is thestrengthening of a metal or polymer byplastic deformation. This strengthening occurs because ofdislocation movements and dislocation generation within thecrystal structure of the material.^[195]

X-axis

in algebraic geometry, the axis on agraph that is usually drawn left to right and usually shows the range of values of anindependent variable.^[280]

Y-axis

in algebraic geometry, the axis on agraph that is usually drawn from bottom to top and usually shows the range of values ofvariable dependent on one other variable, or the second of twoindependent variables.^[281]

Yield

The point of maximum elastic deformation of a material; above yield the material is permanently deformed.

Young's modulus

A measure of the stiffness of a material; the amount of force per unit area require to produce a unit strain.

Z-axis

In algebraic geometry, the axis on agraph of at least threedimensions that is usually drawn vertically and usually shows the range of values of avariable dependent on two other variables or the third independent variable.^[282]

Zero defects

A quality assurance philosophy that aims to reduce the need for inspection of components by improving their quality.

Zero force member

In the field ofengineering mechanics, azero force member is a member (a single truss segment) in atruss which, given a specificload, is at rest: neither intension, nor incompression. In a truss a zero force member is often found at pins (any connections within the truss) where no external load is applied and three or fewer truss members meet. Recognizing basic zero force members can be accomplished by analyzing theforces acting on an individual pin in a physicalsystem.Note: If the pin has an external force ormoment applied to it, then all of the members attached to that pin are not zero force membersunless the external force acts in a manner that fulfills one of the rules below:

• If two non-collinear members meet in an unloadedjoint, both are zero-force members.
• If three members meet in an unloaded joint of which two are collinear, then the third member is a zero-force member.

Reasons for zero-force members in a truss system

• These members contribute to the stability of the structure, by providing buckling prevention for long slender members under compressive forces
• These members can carry loads in the event that variations are introduced in the normal external loading configuration.

Zeroth law of thermodynamics

The equivalence principle applied to temperature; two systems in thermal equilibrium with a third are also in thermal equilibrium with each other.