Results 211 to 220 of about 37,594 (263)
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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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2009
Abstract The statistical evolution of a classical system of N particles with pair interactions can in principle be studied by means of the BBGKY hierarchy for the reduced distribution functions. If no approximation is made, the evolution equation of the one-particle distribution function involves the two-particle distribution function ...
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Abstract The statistical evolution of a classical system of N particles with pair interactions can in principle be studied by means of the BBGKY hierarchy for the reduced distribution functions. If no approximation is made, the evolution equation of the one-particle distribution function involves the two-particle distribution function ...
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2011
Ludwig Eduard Boltzmann (1844–1906), the Austrian physicist whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms and molecules (microscopic properties) determine the phenomenological (macroscopic) properties of matter such as the viscosity, thermal conductivity, and ...
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Ludwig Eduard Boltzmann (1844–1906), the Austrian physicist whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms and molecules (microscopic properties) determine the phenomenological (macroscopic) properties of matter such as the viscosity, thermal conductivity, and ...
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2016
Boltzmann equation is the fundamental equation on the distribution function and is reduced to (8.12) in Sect. 8.2. When the collisional term is negligible, (8.12) becomes Vlavov equation. Collisional term under the assumption of Markoff process is reduced to Fokker–Planck collision term (8.22) in Sect. 8.3.
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Boltzmann equation is the fundamental equation on the distribution function and is reduced to (8.12) in Sect. 8.2. When the collisional term is negligible, (8.12) becomes Vlavov equation. Collisional term under the assumption of Markoff process is reduced to Fokker–Planck collision term (8.22) in Sect. 8.3.
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