Results 211 to 220 of about 18,741 (266)
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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
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The approximation of the Boltzmann equation by stochastic equations
USSR Computational Mathematics and Mathematical Physics, 1988See the review Zbl 0648.65082.
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2012
For about two decades, the lattice Boltzmann method (LBM) has made a major breakthrough in the numerical solution of fluid flow problems and has become a real and efficient alternative with respect to the traditional route of CFD tools and software. Seen from afar, the method looks like a toy algorithm that is easily written as a one page program to ...
Michel O. Deville, Thomas B. Gatski
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For about two decades, the lattice Boltzmann method (LBM) has made a major breakthrough in the numerical solution of fluid flow problems and has become a real and efficient alternative with respect to the traditional route of CFD tools and software. Seen from afar, the method looks like a toy algorithm that is easily written as a one page program to ...
Michel O. Deville, Thomas B. Gatski
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1991
The degree of complexity of today’s devices makes numerical methods for evaluating their electrical behavior mandatory. The special demands of modeling therefore require a simple formulation of carrier transport containing the essential physics in a way expressible in numerical code. It is often impossible to derive special physical features from first
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The degree of complexity of today’s devices makes numerical methods for evaluating their electrical behavior mandatory. The special demands of modeling therefore require a simple formulation of carrier transport containing the essential physics in a way expressible in numerical code. It is often impossible to derive special physical features from first
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2020
Abstract Thermodynamics describes the relationship between heat, work, energy and motion. The key concepts are the conservation of energy and the maximisation of entropy (or disorder) as given by the first and second laws of thermodynamics.
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Abstract Thermodynamics describes the relationship between heat, work, energy and motion. The key concepts are the conservation of energy and the maximisation of entropy (or disorder) as given by the first and second laws of thermodynamics.
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2004
Abstract The evolution of the velocity of the distribution function is governed by the Boltzmann equation. This chapter derives the Boltzmann equation for the homogeneous cooling granular gas and discusses the properties of the collision in general.
Nikolai V. Brilliantov +1 more
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Abstract The evolution of the velocity of the distribution function is governed by the Boltzmann equation. This chapter derives the Boltzmann equation for the homogeneous cooling granular gas and discusses the properties of the collision in general.
Nikolai V. Brilliantov +1 more
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2016
The phase coordinate of a particle is its position and momentum: \((\vec{r},\vec{p}\:)\). It is a six-dimensional variable, \(\left (x,y,z,p_{x},p_{y},p_{z}\right )\), a point in a six-dimensional phase space. In this book, instead of momentum \(\vec{p}\) we will mostly use two variables: particle energy E and a unit vector: \(\vec{\Omega } =\vec{ p ...
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The phase coordinate of a particle is its position and momentum: \((\vec{r},\vec{p}\:)\). It is a six-dimensional variable, \(\left (x,y,z,p_{x},p_{y},p_{z}\right )\), a point in a six-dimensional phase space. In this book, instead of momentum \(\vec{p}\) we will mostly use two variables: particle energy E and a unit vector: \(\vec{\Omega } =\vec{ p ...
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2015
The Einstein equations are insufficient to describe the Universe unless we complement them with a model of its content. In this chapter we shall introduce the Boltzmann formalism, a statistical treatment of the Universe matter content that naturally coexists with general relativity. Each matter component (photons, baryons, cold dark matter, dark energy
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The Einstein equations are insufficient to describe the Universe unless we complement them with a model of its content. In this chapter we shall introduce the Boltzmann formalism, a statistical treatment of the Universe matter content that naturally coexists with general relativity. Each matter component (photons, baryons, cold dark matter, dark energy
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