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Books on the topic 'Boltzmann's equation'

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Published: 4 June 2021

Last updated: 18 February 2022

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1

Hydrodynamic limits of the Boltzmann equation. Springer, 2009.

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2

Rezakhanlou, Fraydoun, and Cédric Villani. Entropy Methods for the Boltzmann Equation. Edited by François Golse and Stefano Olla. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-73705-6.

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3

Cercignani, Carlo. The Boltzmann Equation and Its Applications. Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1039-9.

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4

Saint-Raymond, Laure. Hydrodynamic Limits of the Boltzmann Equation. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-92847-8.

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5

Cercignani, Carlo. The Boltzmann equation and its applications. Springer-Verlag, 1988.

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6

Wolfgang, Wagner, ed. Stochastic numerics for the Boltzmann equation. Springer, 2005.

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7

Discrete nonlinear models of the Boltzmann equation. General Editorial Board for Foreign Language Publications, Nauka Publishers, 1987.

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8

Hong, Sung-Min. Deterministic solvers for the Boltzmann transport equation. Springer, 2011.

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9

Cercignani, Carlo, and Gilberto Medeiros Kremer. The Relativistic Boltzmann Equation: Theory and Applications. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8165-4.

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10

Hong, Sung-Min, Anh-Tuan Pham, and Christoph Jungemann. Deterministic Solvers for the Boltzmann Transport Equation. Springer Vienna, 2011. http://dx.doi.org/10.1007/978-3-7091-0778-2.

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11

Cercignani, Carlo. The Relativistic Boltzmann Equation: Theory and Applications. Birkhäuser Basel, 2002.

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12

Vedenyapin, Victor. Kinetic Boltzmann, Vlasov and related equations. Elsevier Science, 2011.

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13

Luigi, Preziosi, ed. Fluid dynamic applications of the discrete Boltzmann equation. World Scientific, 1991.

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14

name, No. Lecture notes on the discretization of the Boltzmann equation. World Scientific, 2003.

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15

Harris, Stewart. An introduction to the theory of the Boltzmann equation. Dover Publications, 2004.

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16

Li, Jun. Multiscale and Multiphysics Flow Simulations of Using the Boltzmann Equation. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-26466-6.

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17

Kun, Xu. Connection between the lattice Boltzmann equation and the beam scheme. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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18

An introduction to the Boltzmann equation and transport processes in gases. Springer, 2010.

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19

Kremer, Gilberto Medeiros. An Introduction to the Boltzmann Equation and Transport Processes in Gases. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11696-4.

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20

Weiss, Jan-Philipp. Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval. Univ.-Verl. Karlsruhe, 2006.

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21

Direct methods for solving the Boltzmann equation and study of nonequilibrium flows. Kluwer Academic Publishers, c, 2001.

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22

Aristov, V. V. Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0866-2.

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23

V, Aristov V. Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Springer Netherlands, 2001.

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24

author, Saint-Raymond Laure, Texier Benjamin author, and European Mathematical Society, eds. From Newton to Boltzmann: Hard spheres and short-range potentials. European Mathematical Society, 2013.

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25

Kirk, Steven Robert. 3-D finite element solution of the even-party Boltzmann neutron transport equation. University ofSalford, 1992.

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26

Hwang, Danny P. Numerical solution of a three-dimensional cubic cavity flow by using the Boltzmann equation. National Aeronautics and Space Administration, 1992.

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27

Computation of semiconductor properties using moments of the Inverse Scattering Operator of the Boltzmann Equation. Hartung-Gorre, 2006.

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28

1973-, Villani Cédric, and Centre Émile Borel, eds. Entropy methods for the Boltzmann equation: Lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001. Springer, 2008.

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29

Luo, Li-Shi. Applications of the Lattice Boltzmann method to complex and turbulent flows. ICASE, NASA Langley Research Center, 2002.

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30

Lallemand, Pierre. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. National Aeronautics and Space Administration, Langley Research Center, 2000.

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31

Eric, Johnson. Anxiety and the Equation: Understanding Boltzmann's Entropy. MIT Press, 2018.

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32

ANXIETY AND THE EQUATION: UNDERSTANDING BOLTZMANN'S ENTROPY. MIT PRESS, 2018.

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33

Eric, Johnson. Anxiety and the Equation: Understanding Boltzmann's Entropy. MIT Press, 2018.

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34

Eric, Johnson. Anxiety and the Equation: Understanding Boltzmann's Entropy. MIT Press, 2018.

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35

Darrigol, Olivier. The Boltzmann Equation and the H Theorem (1872–1875). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816171.003.0004.

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This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments,

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36

Succi, Sauro. Model Boltzmann Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0008.

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This chapter deals with simplified models of the Boltzmann equation, aimed at reducing its mathematical complexity, while still retaining the most salient physical features. As observed many times in this book, the Boltzmann equation is all but an easy equation to solve. The situation surely improves by moving to its linearized version, but even then, a lot of painstaking labor is usually involved in deriving special solutions for the problem at hand. In order to ease this state of affairs, in the mid-fifties, stylized models of the Boltzmann equations were formulated, with the main intent of

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37

Succi, Sauro. Boltzmann’s Kinetic Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0002.

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Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic int

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38

Theory of the lattice Boltzmann method: Lattice Boltzmann models for non-ideal gases. ICASE, NASA Langley Research Center, 2001.

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39

Succi, Sauro. Stochastic Particle Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0009.

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Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical devel

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40

Succi, Sauro. The Lattice Boltzmann Equation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.001.0001.

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Over the past near three decades, the Lattice Boltzmann method has gained a prominent role as an efficient computational method for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales, from fully developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic subnuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this book presents a survey of the major developments w

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41

Succi, Sauro. Lattice Boltzmann Models for Microflows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0029.

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The Lattice Boltzmann method was originally devised as a computational alternative for the simulation of macroscopic flows, as described by the Navier–Stokes equations of continuum mechanics. In many respects, this still is the main place where it belongs today. Yet, in the past decade, LB has made proof of a largely unanticipated versatility across a broad spectrum of scales, from fully developed turbulence, to microfluidics, all the way down to nanoscale flows. Even though no systematic analogue of the Chapman–Enskog asymptotics is available in this beyond-hydro region (no guarantee), the fa

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42

Succi, Sauro. Approach to Equilibrium, the H-Theorem and Irreversibility. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0003.

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Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underl

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43

Deruelle, Nathalie, and Jean-Philippe Uzan. Kinetic theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0010.

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This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equ

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44

Bobylev, Alexander V. Kinetic Equations : Volume 1: Boltzmann Equation, Maxwell Models, and Hydrodynamics Beyond Navier-Stokes. de Gruyter GmbH, Walter, 2020.

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45

Bobylev, Alexander V. Kinetic Equations : Volume 1: Boltzmann Equation, Maxwell Models, and Hydrodynamics Beyond Navier-Stokes. de Gruyter GmbH, Walter, 2020.

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46

Bobylev, Alexander V. Kinetic Equations : Volume 1: Boltzmann Equation, Maxwell Models, and Hydrodynamics Beyond Navier-Stokes. de Gruyter GmbH, Walter, 2020.

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47

Cercignani, Carlo. The Boltzmann Equation and Its Applications. Springer, 2012.

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48

Sergej, Rjasanow Wolfgang Wagner. Stochastic Numerics for the Boltzmann Equation. Springer, 2008.

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49

Wagner, Wolfgang, and Sergej Rjasanow. Stochastic Numerics for the Boltzmann Equation. Springer, 2010.

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50

Stochastic Numerics for the Boltzmann Equation. Springer-Verlag, 2005. http://dx.doi.org/10.1007/3-540-27689-0.

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