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Burgers' equation is a fundamental partial differential equation from fluid mechanics . It occurs in various areas of applied mathematics , such as modelling of gas dynamics and traffic flow . It is named for Johannes Martinus Burgers (1895-1981). For a given velocity u and viscosity coefficient , the general form of Burgers' equation is: . When , Burgers' equation becomes the...
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The Price equation (also known as Price's equation ) is a covariance equation which is a mathematical description of evolution and natural selection . The Price equation was derived by George R. Price , working in London to rederive W.D. Hamilton 's work on kin selection . Suppose we have a population whose elements are labeled i . Element i has fitness w i and z i is some...
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The advection equation is the partial differential equation that governs the motion of a conserved scalar as it is advected by a known velocity field . It is derived using the scalar's conservation law , together with Gauss's theorem , and taking the infinitesimal limit. Perhaps the best image to have in mind is the transport of dissolved salt in water. The advection...
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Burgers' equation is a fundamental partial differential equation from fluid mechanics . It occurs in various areas of applied mathematics , such as modelling of gas dynamics and traffic flow . It is named for Johannes Martinus Burgers (1895-1981). For a given velocity u and viscosity coefficient , the general form of Burgers' equation is: . When , Burgers' equation becomes the...
http://www.all-about-all.info/article/Burgers' equation
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The Boltzmann equation , devised by Ludwig Boltzmann , describes the statistical distribution of particles in a fluid . It is one of the most important equations of non-equilibrium statistical mechanics, the area of statistical mechanics that deals with systems far from thermodynamic equilibrium ; for instance, when there is an applied temperature gradient or electric field . The Boltzmann...
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In mathematics or its applications, a functional equation is an equation in terms of independent variables , and also unknown functions , which are to be solved for. Many properties of functions can be determined by studying the types of functional equations they satisfy. Usually the term functional equation is reserved for equations that are not in some simple sense reducible to algebraic...
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In mathematics , a quartic equation is the result of setting a quartic function equal to zero. An example of a quartic equation is the equation the general form is where . Contents showTocToggle("show","hide") 1 Solving the quartic equation 1.1 Special cases 1.1.1 Quartics in name only 1.1.2 Biquadratic equations 1.2 The general case,...
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The Henderson-Hasselbalch equation in chemistry describes the derivation of pH as a measure of acidity (using pK a , the acid dissociation constant ) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions . Two equivalent forms of the equation are: or ...
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The Roothaan equations are a representation of the Hartree-Fock equation in a non orthonormal basis set which can be of Gaussian-type or Slater-type . The method was developed independently by Clemens Roothaan and George G. Hall in the early 1950s, and are thus sometimes called the Roothaan-Hall equations . The Roothaan equations can be written in the form of generalized...
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The Saha ionization equation was developed by the Indian astrophysicist Meghnad Saha in 1920 . For a gas at a high enough temperature, the thermal collisions of the atoms will ionize some of the atoms. One or more of the electrons that are normally bound to the atom in orbits around the atomic nucleus will be ejected from the atom and will form an electron gas that co-exists with the gas of atomic...
http://www.all-about-all.info/article/Saha ionization equation
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