Boltzmann equation
The derivation of the linear Boltzmann equation from a Rayleigh gas particle model
... [13]. The authors also proved that if the scatterers move with a constant random initial velocity then the convergence can be proven with significantly weaker assumptions on the force field. Closely related to the ...
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Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
... the Boltzmann equation are based on probabilistic ...the Boltzmann equation for a monatomic gas in the limit of vanishing discretization and stochastic errors ...
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A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases
... the molecular mean free path is much smaller than the characteristic flow length) macroscopic equations, such as the Navier–Stokes, Burnett, and Grad equations, can be used in some instances (Galkin & Rusakov 2005; ...
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A fast spectral method for the Boltzmann equation for monatomic gas mixtures
... the Boltzmann equation (BE) in modeling rarefied gas flows frequently encountered in high-altitude aerodynamics, vacuum technolo- gies, and microelectromechanical ...the Boltzmann collision operator ...
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Studying the Electron Energy Distribution Function (EEDF) and Electron Transport Coefficients in SF6 – He Gas Mixtures by Solving the Boltzmann Equation R. H. Jassim | Assist. Prof. M. K. Jassim
... Because of its importance for computing reaction rates, the EEDF has a fundamental role in plasma modeling [1,2]. The EEDF assumes that elastic collisions are dominating; therefore the effect of inelastic collisions ...
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Solving the Boltzmann equation deterministically by the fast spectral method : application to gas microflows
... The Boltzmann equation (BE) is a fundamental model at the microscopic level describing rarefied gas dynamics for the full range of Knudsen number (Cercignani ...the Boltzmann collision operator (BCO) ...
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VIM and FDM for solving boltzmann equation of self-gravitating gas-dust system
... While in Chapter 4, the numerical model of gas-dust Boltzmann equation is solved using Variational Iteration Method (VIM). The selected initial conditions are used in computing the solution. This chapter ...
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Nanoparticle Charge in Fluid from Atomic Force Microscopy Forces within the Nonlinear Poisson Boltzmann Equation
... Poisson-Boltzmann equation to obtain inte- raction forces between nanoparticles immersed in a fluid electrolyte and an Atomic Force Microscopy micro spherical ...
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Computable model on the collision integral of Boltzmann equation and application to rarefied aerodynamics
... the Boltzmann equation and computational costs asso- ciated with multi-dimensional problems, deterministic methods are still restricted to simple flow such as one-dimensional linear ...extended ...
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GLOBAL CLASSICAL SOLUTIONS TO THE RELATIVISTIC BOLTZMANN EQUATION WITHOUT ANGULAR CUT-OFF
... solutions [16] to the relativistic Boltzmann equation using their causality results from 1985 [18]. Here we would like to mention the work by Alexandre and Villani [4] on renormalized weak solutions with ...
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Global Classical Solutions to the Relativistic Boltzmann Equation Without Angular Cut-off
... [16] to the relativistic Boltzmann equation using their causality results from 1985 [18]. Here we would like to mention the work by Alexandre and Villani [10] on renormalized weak solutions with ...
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Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation*
... (3.7) This elliptic PDE has a non-linear term which is concave where the classical theory would require it to be convex (as in Poisson-Boltzmann equation). In particular, this prevents to use classical ...
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Assessment and development of the gas kinetic boundary condition for the Boltzmann equation
... Recently, the former problem has been tackled by the discrete velocity method (Sharipov & Bertoldo 2009b), the direct simulation Monte Carlo method (Sharipov & Strapasson 2012; Strapasson & Sharipov 2014; ...
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C0 Approximation on the Spatially Homogeneous Boltzmann Equation for Maxwellian Molecules
... 0, R (3) as 0 , is very interested for mathematical theory of Boltzmann equation as well as practical applications. We know that the energy of the solution of (1) is increasing with the time t due ...
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Benchmarking of three dimensional multicomponent lattice Boltzmann equation
... We present a challenging validation of phase field multi-component lattice Boltzmann equation (MCLBE) simulation against the Re = 0 Stokes flow regime Taylor-Einstein theory of dilute suspen- sion ...
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The Matching Conditions for the Distribution Functions of Boltzmann Equation in Nonequilibrium Transport
... the equation of motion in nonequilibrium Green function formalism, the matching conditions for the distribu- tion functions of Boltzmann equation at interfaces of metallic multilayers are ...
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A fast iterative scheme for the linearized Boltzmann equation
... In the present paper we develop a SIS to solve the linearized Boltzmann equation (LBE) for Poiseuille and thermal tran- spiration flows. Although for the single-species LBE these canonical flows have been ...
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Benchmarking of three dimensional multicomponent lattice Boltzmann equation
... (Received 17 August 2017; revised manuscript received 25 October 2017; published 15 November 2017) We present a challenging validation of phase field multicomponent lattice Boltzmann equation (MCLBE) ...
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Probabilistic Interpretation for the Nonlinear Poisson-Boltzmann Equation in Molecular Dynamics
... (PB) equation describes the electrostatic potential of a biomolec- ular system composed by a molecule in a ...PB equation is very ...PB equation with Backward Stochastic Differential Equations ...
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