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The mathematical theory of dilute gases
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TLDR
In this article, the authors present rigorous mathematical results in the kinetic theory of a gas of hard spheres, including the Boltzmann equations, global existence theory, and the fluid-dynamical limits.Abstract:
This book is devoted to the presentation of rigorous mathematical results in the kinetic theory of a gas of hard spheres. Recent developments as well as classical results are presented in a unified way, such that the book should become the standard reference on the subject. There is no such book available at present. The reader will find a systematic treatment of the main mathematical results, a discussion of open problems, and a guide to the existing literature. There is a rigorous and comprehensive presentation of strict validation of the Boltzmann equations, global existence theory, and the fluid-dynamical limits. The authors also review and discuss classical derivation and properties of the Boltzmann equation, particle simulation methods, and boundary conditions.read more
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Data on Internal Rarefied Gas Flows
Felix Sharipov,V. D. Seleznev +1 more
TL;DR: In this article, the authors present a review of the main parameters, determining rarefied gas flows through a capillary, and a critical analysis of corresponding numerical data and analytical results available in the literature.
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On convex sobolev inequalities and the rate of convergence to equilibrium for fokker-planck type equations
TL;DR: In this paper, an elementary derivation of Bakry-Emery type conditions, results concerning perturbations of invariant measures with general admissible entropies, sharpness of convex Sobolev inequalities, applications to non-symmetric linear and certain non-linear Fokker-Planck type equations (Desai-Zwanzig model, drift-diffusion-Poisson model).
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Heterophilious Dynamics Enhances Consensus
TL;DR: In this paper, a general class of models for self-organized dynamics based on alignment is reviewed, and a natural question which arises in this context is to ask when and how clusters emerge through the self-alignment of agents and what types of "rules of engagement" influence the formation of such clusters.
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On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations
TL;DR: In this article, the spatially homogeneous Boltzmannian equation without cut-off, the Fokker-Planck Landau equation, and the asymptotics of grazing collisions for a broad class of potentials were derived.