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On the structure of generalized Poisson–Boltzmann equations
European journal of applied mathematics, 2015N. Gavish, K. Promislow
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Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy
Journal of Computational Physics, 2014Qin Li, L. Pareschi
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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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2010
Consider a monatomic gas with N molecules enclosed in a recipient of volume V. One molecule of this gas can be specified at a given time by its position x = (x1,x2,x3) and velocity c = (c1,c2,c3). Hence, a molecule can be specified as a point in a six-dimensional space spanned by its coordinates and velocity components, the so-called μ-phase space.
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Consider a monatomic gas with N molecules enclosed in a recipient of volume V. One molecule of this gas can be specified at a given time by its position x = (x1,x2,x3) and velocity c = (c1,c2,c3). Hence, a molecule can be specified as a point in a six-dimensional space spanned by its coordinates and velocity components, the so-called μ-phase space.
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Generalized Lattice-Boltzmann Equations
, 1994D. P. Weaver, B. Shizgal
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1994
We present a global existence result of weak solutions for Boltzmann equation obtained by R.J. DiPerna and the author. This result is based upon convergence properties of solutions of Boltzmann equation that we recall and discuss.
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We present a global existence result of weak solutions for Boltzmann equation obtained by R.J. DiPerna and the author. This result is based upon convergence properties of solutions of Boltzmann equation that we recall and discuss.
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Isotropic solutions of the Einstein-Boltzmann equations
, 1971R. Treciokas, G. Ellis
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