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Books on the topic 'Boltzmann transport'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

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

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2

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

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3

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

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4

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

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5

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

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6

Harris, Stewart. An introduction to the theory of the Boltzmann equation. Mineola, N.Y: Dover Publications, 2004.

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7

Alexeev, Boris V. Generalized Boltzmann physical kinetics. Amsterdam: Elsevier, 2004.

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8

Stochastic dynamics and Boltzmann hierarchy. Berlin: Walter de Gruyter, 2009.

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9

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

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10

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

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11

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

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12

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

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13

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

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14

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

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15

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

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16

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

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17

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. Berlin: Springer, 2008.

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18

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

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19

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

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20

Jungemann, Christoph, Sung-Min Hong, and Anh-Tuan Pham. Deterministic Solvers for the Boltzmann Transport Equation. Springer, 2013.

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21

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

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22

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

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23

The Boltzmann Equation and Its Applications. Springer, 2011.

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24

N, Bellomo, and Arlotti L, eds. Lecture notes on the mathematical theory of the Boltzmann equation. Singapore: World Scientific, 1995.

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25

Vedenyapin, Victor, Alexander Sinitsyn, and Eugene Dulov. Kinetic Boltzmann, Vlasov and Related Equations. Elsevier, 2011.

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26

Succi, Sauro. Relativistic Lattice Boltzmann (RLB). Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0034.

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Relativistic hydrodynamics and kinetic theory play an increasing role in many areas of modern physics. Besides their traditional arenas, astrophysics and cosmology, relativistic fluids have recently attracted much attention also within the realm of high-energy and condensed matter physics, mostly in connection with quark-gluon plasmas experiments in heavy-ion colliders and electronic transport in graphene. This chapter describes the extension of the Lattice Boltzmann formalism to the case of relativistic fluids.
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27

Succi, Sauro. Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press, 2013.

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28

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, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.
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29

Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer, 2005.

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30

Succi, Sauro. The Lattice Boltzmann Equation: For Complex States of Flowing Matter. Oxford University Press, 2018.

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31

N, Bellomo, and Gatignol Renée, eds. Lecture notes on the discretization of the Boltzmann equation. River Edge, NJ: World Scientific, 2003.

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32

Kremer, Gilberto M. An Introduction to the Boltzmann Equation and Transport Processes in Gases. Springer, 2010.

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33

Alexeev, Boris. Unified Non-Local Theory of Transport Processes: Generalized Boltzmann Physical Kinetics. Elsevier Science & Technology Books, 2015.

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34

Aristov, V. V. Methods of direct solving the Boltzmann equation and study of nonequilibrium flows (Fluid Mechanics and Its Applications). Springer, 2001.

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35

Aristov, V. V. Methods of direct solving the Boltzmann equation and study of nonequilibrium flows (Fluid Mechanics and Its Applications). Springer, 2001.

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36

Farhat, Hassan, Joon Sang Lee, and Sasidhar Kondaraju. Accelerated Lattice Boltzmann Model for Colloidal Suspensions: Rheology and Interface Morphology. Springer, 2014.

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37

Yeh, Chou, and Institute for Computer Applications in Science and Engineering., eds. Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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38

Ye, Zhou, and Institute for Computer Applications in Science and Engineering., eds. Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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39

Yeh, Chou, and Institute for Computer Applications in Science and Engineering., eds. Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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40

Ye, Zhou, and Institute for Computer Applications in Science and Engineering., eds. Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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41

The Relativistic Boltzmann Equation: Theory and Applications (Progress in Mathematical Physics). Birkhäuser Basel, 2002.

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42

Yamamoto, Takahiro, Kazuyuki Watanabe, and Satoshi Watanabe. Thermal transport of small systems. Edited by A. V. Narlikar and Y. Y. Fu. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199533046.013.6.

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This article focuses on the phonon transport or thermal transport of small systems, including quasi-one-dimensional systems such as carbon nanotubes. The Fourier law well describes the thermal transport phenomena in normal bulk materials. However, it is no longer valid when the sample dimension reduces down to below the mean-free path of phonons. In such a small system, the phonons propagate coherently without interference with other phonons. The article first considers the Boltzmann–Peierls formula of diffusive phonon transport before discussing coherent phonon transport, with emphasis on the Landauer formulation of phonon transport, ballistic phonon transport and quantized thermal conductance, numerical calculation of the phonon-transmission function, and length dependence of the thermal conductance.
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43

The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Numerical Mathematics and Scientific Computation). Oxford University Press, USA, 2001.

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44

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 introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.
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45

Numerical investigations of low-density nozzle flow by solving the Boltzmann equation. Washington, DC: National Aeronautics and Space Administration, 1995.

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46

(Editor), N. Bellomo, and Renee Gatignol (Editor), eds. Lecture Notes on the Discretization of the Boltzmann Equation (Series on Advances in Mathematics for Applied Sciences). World Scientific Publishing Company, 2003.

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47

Lapeyre, Bernard, Etienne Pardoux, and Rémi Sentis. Méthodes de Monte-Carlo pour les équations de transport et de diffusion (Mathématiques et Applications). Springer, 1997.

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48

1940-, Wilson John W., Badavi F. F, and Langley Research Center, eds. Extension of the BRYNTRN code to monoenergetic light ion beams. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1994.

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49

Morawetz, Klaus. Relaxation-Time Approximation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0018.

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A conserving relaxation time approximation is presented resulting into a Mermin-type of polarisation functions. The transport properties are calculated for the relaxation time approximation and an arbitrary band structure. The results for metals and gases are discussed and the shortcoming of relaxation time approximation to describe experimental values is outlined. As improvement, the exact solution of the linearised quantum Boltzmann equation is presented leading to momentum-depended relaxation times specific for each observable. Explicit expressions are given for the electric and thermal conductivity as well as the shear viscosity.
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50

Succi, Sauro. Generalized Hydrodynamics Beyond Navier–Stokes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0006.

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The work of Chapman and Enskog opened a long period, lasting about three decades, in which most of the activity in kinetic theory was directed to the computation of the transport coefficients for different types of intermolecular potentials. Seeking the solution of the full Boltzmann equation itself was not much in focus, mostly on account of its daunting complexity. This situation took a sharp turn in 1949, with the publication of Harold Grad’s thesis. This Chapter presents the derivation of generalized hydrodynamics beyond the realm of the Navier-Stokes description, with special reference to Grad’s thirteen-moment formulation.
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