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The Poisson-Boltzmann Equation An Introduction
This brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced...
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Relativistic Boltzmann Equation
The special and general relativistic generalizations of the Boltzmann equation are considered as well as the methods to solve this equation—the...
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The Poisson-Boltzmann Equation
The first Chapter of the book discusses the formulation and the solutions of the Poisson-Boltzmann equation for simple salts (like sodium chloride,...
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Extending Cercignani’s Conjecture Results from Boltzmann to Boltzmann–Fermi–Dirac Equation
We establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the...
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Boltzmann Equation and the H-Theorem
Although the formula engraved on Boltzmann’s tombstone is Eq. ( 8.1 ), connecting the entropy of a...
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Learning Invariance Preserving Moment Closure Model for Boltzmann–BGK Equation
As one of the main governing equations in kinetic theory, the Boltzmann equation is widely utilized in aerospace, microscopic flow, etc. Its...
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A Non-local Quasi-Equilibrium State in the Bhatnagar–Gross–Krook Boltzmann Equation for Thermo-hydrodynamics: Conservation Laws, The Boltzmann H-Theorem, and the Fluctuation-Dissipation Theorem
The Bhatnagar–Gross–Krook (BGK) Boltzmann equation with the Maxwellian–Boltzmann-type equilibrium state leads to the set of thermo-hydrodynamic...
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Boundary Layer Solution of the Boltzmann Equation for Specular Boundary Condition
In the paper, we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in L
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On Solutions of the Modified Boltzmann Equation
We study the self-similar solutions and related questions for the modified Boltzmann equation. This equation formally coincides with the classical...
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Solution of the Boltzmann Equation in the Continuum Flow Regime
AbstractA method for solving the Boltzmann equation is presented that makes it possible to calculate gas flows in the continuum flow regime described...
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The Boltzmann equation and equilibrium thermodynamics in Lorentz-violating theories
In this work, we adapt the foundations of relativistic kinetic theory and the Boltzmann equation to particles with Lorentz-violating dispersion...
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Accelerating the Solution of the Boltzmann Equation by Controlling Contributions to the Collision Integral
AbstractA method of reducing the number of arithmetic operations needed to evaluate the Boltzmann collision integral by the conservative projection...
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Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation
AbstractThis paper overviews the state of the art in the study of nonequilibrium gas flows with nonclassical transport, in which the Stokes and...
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The Compressible Euler and Acoustic Limits from Quantum Boltzmann Equation with Fermi–Dirac Statistics
This paper justifies the compressible Euler and acoustic limits from quantum Boltzmann equation with Fermi–Dirac statistics rigorously. By employing...
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Numerical Solution of Boltzmann Equation Based on Adaptive Physics-Informed Neural Networks (aPINN)
Boltzmann equation is a partial differential equation (PDE) describing the statistical behavior of non-equilibrium thermodynamics systems which is...
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Heat Transfer Problem for the Boltzmann Equation in a Channel with Diffusive Boundary Condition
In this paper, the authors study the 1D steady Boltzmann flow in a channel. The walls of the channel are assumed to have vanishing velocity and given...
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Boltzmann Equation in Aggregation Kinetics
We consider the application of the Boltzmann equation to aggregation kinetics, where the transport mechanism is the ballistic motion of particles....
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Viscous and thermal velocity slip coefficients via the linearized Boltzmann equation with ab initio potential
The viscous and thermal velocity slip coefficients of various monatomic gases are computed via the linearized classical Boltzmann equation, with ab...
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Study and Optimization of N-Particle Numerical Statistical Algorithm for Solving the Boltzmann Equation
AbstractThe main goal of this work is to check the hypothesis that the well-known N -particle statistical algorithm yields a solution estimate for...
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Efficient Method for Solving the Boltzmann Equation on a Uniform Mesh
AbstractA new numerical method for solving the Boltzmann equation on a uniform mesh in velocity space is proposed. The asymptotic complexity of the...
