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Exact Lattice Boltzmann Equation
Physical Review Letters, 2013The lattice Boltzmann equation is derived from the Bhatnagar-Gross-Krook kinetic equation using the Euler-Maclaurin integration formula. Unlike previous attempts to connect the lattice Boltzmann method with the kinetic theory, the result is free of any relaxation-type approximation.
Bösch F, Karlin IV
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Quasiparticle Boltzmann equation in semiconductors
Physical Review B, 1994The quasiparticle approximation and corrections beyond it are derived from expansion in the spirit of the virial corrections. This way, the Boltzmann equation for electrons in semiconductors is recovered from the nonequilibrium Green's functions without unjustified neglect of the former theory.
, Spicka, , Lipavsk
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THE BOLTZMANN EQUATION IS A RENORMALIZATION GROUP EQUATION
International Journal of Modern Physics B, 2000It is known that renormalization group (RG) approaches to partial differential equations give reduced equations, e.g., amplitude equations, as renormalization group equations. Therefore, equations governing slow or global behaviors ought to be derived RG-theoretically.
Pashko, O., Oono, Yoshitsugu
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ON THE RELATIVISTIC BOLTZMANN EQUATION
Acta Mathematica Scientia, 1998Summary: The author shows the invalidity of M. Dudyński's and M. L. Ekiel-Jeżewska's existence proof (1992) for the relativistic Boltzmann equation. He proves global existence of mild solutions of its initial value problem with initial data only satisfying the natural bound, i.e., finite mass, ``inertia'', energy and entropy.
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1988
In the previous chapter we saw that the problem of describing the state of thermal equilibrium of a monatomic perfect gas can be nicely solved; in particular, we found a very simple formula for the one-particle distribution P (1) in the form of a Maxwellian. This result has a large variety of applications in the statistical description of matter in the
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In the previous chapter we saw that the problem of describing the state of thermal equilibrium of a monatomic perfect gas can be nicely solved; in particular, we found a very simple formula for the one-particle distribution P (1) in the form of a Maxwellian. This result has a large variety of applications in the statistical description of matter in the
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1995
Systems consisting of a large number of particles are often most easily described by a probability density function / ( # , p , t), which gives the probability of finding a particle (molecule, photon, electron, etc.) at a position x and with momentum p.
Alfred Kersch, William J. Morokoff
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Systems consisting of a large number of particles are often most easily described by a probability density function / ( # , p , t), which gives the probability of finding a particle (molecule, photon, electron, etc.) at a position x and with momentum p.
Alfred Kersch, William J. Morokoff
openaire +1 more source