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Dissertations / Theses on the topic 'Boltzmann's equation'

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Published: 4 June 2021

Last updated: 18 February 2022

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1

Godinho, Pereira David. "Contribution à l'étude des équations de Boltzmann, Kac et Keller-Segel à l'aide d'équations différentielles stochastiques non linéaires." Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00975091.

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L'objet de cette thèse est l'étude de l'asymptotique des collisions rasantes pour les équations de Kac et de Boltzmann ainsi que l'étude de la propagation du chaos pour l'équation de Keller-Segel dans un cadre sous-critique à l'aide d'équations différentielles stochastiques non linéaires. Le premier chapitre est consacré 'a l'équation de Kac avec un potentiel Maxwellien. Nous commençons par donner une vitesse de convergence explicite (que l'on pense être optimale) dans le cadre de l'asymptotique des collisions rasantes. Puis nous approchons la solution de l'équation de Kac dans le cadre généra

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2

Rassy, Tilman. "On the rigorous derivation of a kinetic equation for a chemical reaction taking place in a simple mechanical model system, following Boltzmann's ideas using the "Stosszahlansatz"." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972887261.

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3

Vong, Seak Weng. "Two problems on the Navier-Stokes equations and the Boltzmann equation /." access full-text access abstract and table of contents, 2005. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b19885805a.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2005.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy" Includes bibliographical references (leaves 72-77)

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4

Garlapati, Revanth Reddy. "Reduced basis method for Boltzmann equation." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39218.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.<br>Includes bibliographical references (p. 103-106).<br>The main aim of the project is to solve the BGK model of the Knudsen parameterized Boltzmann equation which is 1-d with respect to both space and velocity. In order to solve the Boltzmann equation, we first transform the original differential equation by replacing the dependent variable with another variable, weighted with function t(y); next we obtain a Petrov Galerkin weak form of this new transformed equation. To obtain a stable

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5

Houllier, Trescases Ariane. "Modélisation et Analyse Mathématique d'Equations aux Dérivées Partielles Issues de la Physique et de la Biologie." Thesis, Cachan, Ecole normale supérieure, 2015. http://www.theses.fr/2015DENS0037/document.

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Ce manuscrit présente des résultats d’analyse mathématique autour de deux exemples de problèmes singuliers d’équations aux dérivées partielles issus de la modélisation. I. Diffusion croisée en dynamique des populations. En dynamique des populations, les systèmes de réaction –diffusion croisée modélisent l’évolution de populations d’espèces en compétition avec un effet répulsif entre les individus. Pour ces systèmes fortement couplés, souvent non linéaires, une question aussi fondamentale que l’existence de solutions se révèle extrêmement complexe. Dans ce manuscrit, on introduit une approche b

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6

Wood, Andrew Maclean. "Lattice Boltzmann magnetohydrodynamics." Thesis, University of Glasgow, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312788.

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7

Zhou, Yulong. "Stochastic control and approximation for Boltzmann equation." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/392.

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In this thesis we study two problems concerning probability. The first is stochastic control problem, which essentially amounts to find an optimal probability in order to optimize some reward function of probability. The second is to approximate the solution of the Boltzmann equation. Thanks to conservation of mass, the solution can be regarded as a family of probability indexed by time. In the first part, we prove a dynamic programming principle for stochastic optimal control problem with expectation constraint by measurable selection approach. Since state constraint, drawdown constraint, tar

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8

Jrad, Ibrahim. "Analyse spectrale et calcul numérique pour l'équation de Boltzmann." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMR020/document.

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Dans cette thèse, nous étudions les solutions de l'équation de Boltzmann. Nous nous intéressons au cadre homogène en espace où la solution f(t; x; v) dépend uniquement du temps t et de la vitesse v. Nous considérons des sections efficaces singulières (cas dit non cutoff) dans le cas Maxwellien. Pour l'étude du problème de Cauchy, nous considérons une fluctuation de la solution autour de la distribution Maxwellienne puis une décomposition de cette fluctuation dans la base spectrale associée à l'oscillateur harmonique quantique. Dans un premier temps, nous résolvons numériquement les solutions e

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9

Liu, Jing. "Time-implicit solution of the Lattice Boltzmann equation." Laramie, Wyo. : University of Wyoming, 2008. http://proquest.umi.com/pqdweb?did=1594487041&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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10

Homolle, Thomas (Thomas Michel Marie). "Efficient particle methods for solving the Boltzmann equation." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/38649.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.<br>Includes bibliographical references (leaves 85-86).<br>A new particle simulation method for solving the Boltzmann equation is presented and tested. This method holds a significant computational efficiency advantage for low-signal flows compared to traditional particle methods such as the Direct Simulation Monte Carlo (DSMC). More specifically, the proposed algorithm can efficiently simulate arbitrarily small deviations from equilibrium (e.g. low speed flows) at a computational cost that does n

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11

Briant, Marc. "On the Boltzmann equation, quantitative studies and hydrodynamical limits." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/246471.

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The present thesis deals with the mathematical treatment of kinetic theory and focuses more precisely on the Boltzmann equation. We investigate several properties of the solutions to the latter equation: their positivity and their hydrodynamical limits for instance. We also study the local Cauchy problem for a quantic version of the Boltzmann equation.

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12

Yu, Huidan. "Lattice Boltzmann equation simulations of turbulence, mixing, and combustion." Texas A&M University, 2004. http://hdl.handle.net/1969.1/3081.

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We explore the capability of lattice Boltzmann equation (LBE) method for complex fluid flows involving turbulence, mixing, and reaction. In the first study, LBE schemes for binary scalar mixing and multi-component reacting flow with reactions are developed. Simulations of initially non-premixed mixtures yield scalar probability distribution functions that are in good agreement with numerical data obtained from Navier-Stokes (NS) equation based computation. One-dimensional chemically-reacting flow simulation of a premixed mixture yields a flame speed that is consistent with experimentally deter

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13

Campini, Marco. "The fluid dynamical limits of the linearized Boltzmann equation." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185664.

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The old question concerning the mathematical formulation of the fluid dynamic limits of kinetic theory is examined by studying the solution of the Cauchy problem for two differently scaled linearized Boltzmann equations on periodic domain as the mean free path of the particles becomes small. Under minimal assumptions on the initial data, by using an a priori estimate, it is possible, in a Hilbert space functional frame, to prove the weak convergence of solutions toward a function that has the form of an infinitesimal maxwellian in the velocity variable. The velocity moments of this function ar

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14

Morris, Aaron Benjamin. "Investigation of a discrete velocity Monte Carlo Boltzmann equation." Thesis, [Austin, Tex. : University of Texas, 2009. http://hdl.handle.net/2152/ETD-UT-2009-05-127.

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15

Egginton, Matthew. "Long range particle dynamics and the linear Boltzmann equation." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/100738/.

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This thesis aims to give full and complete details of the first proof that the particle density for a tagged particle interacting with a background of particles via a long range potential φ converges weak-* to a weak solution of the linear Boltzmann equation for φ . This convergence is shown to hold for potentials where there is a τ > 0, and such that for sufficiently large [x] we have ∇∅(x)≤Ce-|x|3/2÷τ The main difficulty in this context are the many grazing collisions in the particle dynamics which prevents a Markovian structure of the dynamics. We remove grazing collisions via the use of a

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16

Lui, Ho Man. "Runge-Kutta Discontinuous Galerkin method for the Boltzmann equation." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39215.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.<br>Includes bibliographical references (p. 85-87).<br>In this thesis we investigate the ability of the Runge-Kutta Discontinuous Galerkin (RKDG) method to provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic flow length scales become of the order of, or smaller than, the molecular mean free path, the Navier-Stokes description fails. The prevale

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17

Kim, Hyeon-Deuk. "Local nonequilibrium effects in kinetic theory : The Boltzmann equation." Kyoto University, 2004. http://hdl.handle.net/2433/64954.

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Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(人間・環境学)<br>甲第10956号<br>人博第243号<br>15||198(吉田南総合図書館)<br>新制||人||60(附属図書館)<br>UT51-2004-G803<br>京都大学大学院人間・環境学研究科人間・環境学専攻<br>(主査)教授冨田博之, 助教授早川尚男, 助教授阪上雅昭<br>学位規則第4条第1項該当

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18

Viljoen, Brandon. "Boltzmann equation studies of the off-equilibrium QCD phenomena." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/20971.

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Much of the evolution of the quark-gluon plasma (QGP) produced in heavy-ion collisions can be modeled by relativistic (viscous) hydrodynamics, which assumes that the partons are sufficiently close to equilibrium. We would like to explore the dynamics of QGP, even before this (quasi) equilibrium stage is reached. To that end, a useful tool from the stage where we can assume the partons to be on-shell is the relativistic Boltzmann equation. We develop parallel code to solve the relativistic Boltzmann equation in the relaxation time approximation in 3 + 1 dimensions (without simplifying assumptio

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19

Sakamoto, Shota. "Mathematical analysis of global solutions to the Boltzmann equation." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225680.

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20

FIGUEIREDO, MARCIO B. "Espectroscopia de plasma gerado por laser em regime temporal de nanosegundos e femtosegundos em padrões de aço inoxidável ferrítico." reponame:Repositório Institucional do IPEN, 2007. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11566.

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Made available in DSpace on 2014-10-09T12:53:20Z (GMT). No. of bitstreams: 0<br>Made available in DSpace on 2014-10-09T14:09:35Z (GMT). No. of bitstreams: 0<br>Dissertacao (Mestrado)<br>IPEN/D<br>Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

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21

Andallah, Laek Sazzad. "A hexagonal collision model for the numerical solution of the Boltzmann equation." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=974861626.

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22

Hantsch, Andreas. "A lattice Boltzmann equation model for thermal liquid film flow." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2013. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-130098.

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Liquid film flow is an important flow type in many applications of process engineering. For supporting experiments, theoretical and numerical investigations are required. The present state of the art is to model the liquid film flow with Navier--Stokes-based methods, whereas the lattice Boltzmann method is employed here. The final model has been developed within this treatise by means of a two-phase flow and a heat transfer model, and boundary and initial conditions. All these sub-models have been applied to simple test cases. It could be found that the two-phase model is capable of solving fl

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23

Ghomeshi, Shahin. "Existence and uniqueness of solutions to the steady Boltzmann equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0004/MQ36613.pdf.

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24

Zhang, Mei. "Some problems on conservation laws and Vlasov-Poisson-Boltzmann equation /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749465f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [90]-94)

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25

Grunow, Ernst William. "Full 3+1 dimensional simulation of the relativistic Boltzmann equation." Master's thesis, Faculty of Science, 2021. http://hdl.handle.net/11427/33705.

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Relativistic hydrodynamics has been the tool of choice to simulate the dynamics of the quark-gluon plasma produced in heavy-ion collisions. Despite the success of hydrodynamics, it has several shortcomings stemming from the fact that it assumes a system close to equilibrium. An alternative to hydrodynamics is solving the Boltzmann equation, which describes the evolution of the full distribution function of the system without the close to equilibrium requirement. Large scale simulations using the Boltzmann equation, however, has hitherto proved computationally intractable due to their computati

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26

Larmier, Coline. "Stochastic particle transport in disordered media : beyond the Boltzmann equation." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS388/document.

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Des milieux hétérogènes et désordonnés émergent dans plusieurs applications de la science et de l'ingénierie nucléaires, en particulier en ce qui concerne la propagation des neutrons et des photons. Les exemples sont très répandus et concernent par exemple la double hétérogénéité des éléments combustibles dans les réacteurs à lit de boulets ou l'évaluation de la probabilité de re-criticité suite aux arrangements aléatoires du combusitble résultant d'accidents graves. Dans cette thèse, nous étudierons le transport linéaire de particules dans des milieux aléatoires. Dans la première partie, nous

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27

Kollu, Gautham. "Large-Scale Parallel Computation of the Phonon Boltzmann Transport Equation." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406291205.

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28

Wolvaardt, F. P. "Exact non-equilibrium solutions of the Einstein-Boltzmann equations." Doctoral thesis, University of Cape Town, 1994. http://hdl.handle.net/11427/17445.

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Includes bibliographical references.<br>In this thesis we use the exact solution of the Boltzmann equation, with a relaxation-time model of collisions, to find solutions of the Einstein-Boltzmann system of equations. A covariant harmonic decomposition of the distribution function is used to obtain exact results. The conditions imposed by the conservation of particle number and energy-momentum, and by the H-theorem are determined. The properties of exact truncated Boltzmann solutions with first and second order anisotropies are investigated. Exact entropy results are obtained for the solution w

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29

Leiler, Gregor. "On a derivation of the Boltzmann equation in Quantum Field Theory." Thesis, Cardiff University, 2010. http://orca.cf.ac.uk/55024/.

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The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equa

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30

Khurana, Saheba. "Numerical method for solving the Boltzmann equation using cubic B-splines." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/46532.

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A numerical method for solving a one-dimensional linear Boltzmann equation is developed using cubic B-splines. Collision kernels are derived for smooth and rough hard spheres. A complete velocity kernel for spherical particles is shown that is reduced to the smooth, rigid sphere case. Similarly, a collision kernel for the rough hard sphere is derived that depends upon velocity and angular velocity. The exact expression for the rough sphere collision kernel is reduced to an approximate expression that averages over the rotational degrees of freedom in the system. The rough sphere collision kern

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31

Kurotaki, Takuji. "Asymptotic solution of the Boltzmann-Krook equation for the Rayleigh flow." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/42479.

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1991.<br>Title as it appears in the Feb. 1991 M.I.T. Graduate List: Asymptotic solution of the Boltzman-Krock equation for the Rayleigh flow.<br>Includes bibliographical references (leaves 88-90).<br>by Takuji Kurotaki.<br>M.S.

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32

Lian, Zhengyi. "Discontinuous Galerkin solution of the Boltzmann equation in multiple spatial dimensions." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/41560.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Includes bibliographical references (leaves 77-79).<br>This thesis focuses on the numerical solution of a kinetic description of small scale dilute gas flows when the Navier-Stokes description breaks down. In particular, it investigates alternative solution techniques for the Boltzmann equation typically used when the Knudsen number (ra

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33

Behrend, Oliver Patrick. "Numerical simulations of colloidal suspensions via the lattice Boltzmann equation method." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/13762.

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A numerical method to simulate concentrated colloidal suspensions has been developed. It is based on a combination of the fluctuating lattice Boltzmann equation method for the flow of the fluid with molecular dynamics for the suspended particles; its main advantage is that it scales linearly with the number of particles. In extensive tests, the method has been shown to reproduce fully the time-dependent many-body hydrodynamic interactions. Brownian motion of the particles can be simulated via random fluctuations in the fluid stress tensor, thus corresponding to the physical origin of the motio

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34

D'ALMEIDA, AMAH SENA. "Etude des solutions des equations de boltzmann discretes et applications." Paris 6, 1995. http://www.theses.fr/1995PA066007.

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L'etude de certains ecoulements de gaz rarefies necessite la resolution effective de l'equation de boltzmann. La theorie cinetique discrete permet de remplacer cette equation par un systeme d'equations aux derivees partielles plus simples. A l'oppose de la theorie cinetique continue, les modeles discrets peuvent ne pas avoir toutes les variables macroscopiques physiques independantes ou au contraire avoir en plus des variables macroscopiques non physiques. Ces problemes sont resolus par un choix convenable de modeles. De plus, les definitions usuelles de la temperature et de la pression ne son

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35

Poupaud, Frédéric. "Etude mathematique et simulations numeriques de quelques equations de boltzmann." Paris 6, 1988. http://www.theses.fr/1988PA066489.

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On presente une methode particulaire determinante, alternative aux methodes monte carlo, pour la resolution des equations cinetiques. La vitesse de convergence et des tests numeriques sont donnes dans le cas de l'equation de transport des neutrons. L'equation de boltzmann est simule numeriquement dans un cas d'interet physique. On etudie ensuite les limites fluides des equations cinetiques. Dans ce but on explicite les comportements des solutions stationnaires du probleme de milne de la dynamique des gaz. Une etude complete: existence, probleme de milne, approximation par la diffusion, est fai

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36

Buchan, Andrew George. "Adaptive spherical wavelets for the angular discretisation of the Boltzmann transport equation." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.441955.

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Baker, Lowell L. (Lowell Lane) 1980. "Efficient numerical methods for solving the Boltzmann equation for small scale flows." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/39744.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.<br>Includes bibliographical references (p. 104-107).<br>The Navier-Stokes equations of continuum fluid mechanics fail to accurately describe dilute gas flows when the characteristic lengthscale of the system is on the order of (or smaller than) the molecular mean free path. At these lengthscales, gaseous hydrodynamics may be described by a kinetic description, namely the Boltzmann equation. Currently, the prevalent method for solving the Boltzmann equation is a particle simulation method known as dir

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Baker, Lowell L. (Lowell Lane) 1980. "Efficient numerical methods for solving the Boltzmann equation for low-speed flows." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/17922.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.<br>Includes bibliographical references (leaves 66-67).<br>When the Knudsen number, typically defined as the ratio of the molecular mean free path to the characteristic length scale of a dilute gas flow, is larger than approximately 0.1, the Navier-Stokes equations are no longer valid. In this case, which is frequently encountered in small-scale flows, one must solve the more general Boltzmann equation. The objective of this work is to develop a method which requires a lower computational cost than exis

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39

Al-Mohssen, Husain Ali 1977. "An excursion with the Boltzmann equation at low speeds : variance-reduced DSMC." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/61591.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 133-139).<br>The goal of the present thesis is to develop a practical method for simulating low-signal kinetic (small-scale) gaseous flows. These flows have recently received renewed attention in connection with the design and optimization of MEMS/NEMS devices operating in gaseous environments; they are typically described using the Boltzmann equation which is most efficiently solved using a stochastic particle simula

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40

Evans, Benjamin James. "Finite element solution of the Boltzmann equation for rarefied macroscopic gas flows." Thesis, Swansea University, 2008. https://cronfa.swan.ac.uk/Record/cronfa42618.

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This thesis presents research carried out at The Civil and Computational Engineering Centre at Swansea University between September 2004 and December 2007. The focus of the research was the application of modern finite element solution techniques to the governing equations of molecular gas dynamics in order to solve macroscopic gas flow problems. The journey of research began by considering and comparing various finite difference and finite element formulations in the solution of a simple scalar convection equation. This formed the basis for developing a solver for a variety of forms of the Bo

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41

Qiao, Zhonghua. "Numerical solution for nonlinear Poisson-Boltzmann equations and numerical simulations for spike dynamics." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/727.

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Dai, Longxiang. "Lattice Boltzmann equation models for migration of ions in brain and their applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq25039.pdf.

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43

Le, Coz Yannick L. "Semiconductor device simulation : a spectral method for solution of the Boltzmann transport equation." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14482.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1988.<br>Title as it appeared in M.I.T. Graduate List, February 1988: Simulation of semiconductor devices : a spectral method for solution of the Boltzmann transport equation.<br>Includes bibliographical references (leaves 193-195).<br>by Yannick L. Le Coz.<br>Ph.D.

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44

Håkman, Olof. "Boltzmann Equation and Discrete Velocity Models : A discrete velocity model for polyatomic molecules." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-76143.

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In the study of kinetic theory and especially in the study of rarefied gas dynamics one often turns to the Boltzmann equation. The mathematical theory developed by Ludwig Boltzmann was at first sight applicable in aerospace engineering and fluid mechanics. As of today, the methods in kinetic theory are extended to other fields, for instance, molecular biology and socioeconomics, which makes the need of finding efficient solution methods still important. In this thesis, we study the underlying theory of the continuous and discrete Boltzmann equation for monatomic gases. We extend the theory whe

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45

Allu, Pareekshith. "A Hybrid Ballistic-Diffusive Method to Solve the Frequency Dependent Boltzmann Transport Equation." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1451998769.

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46

Luo, Li-Shi. "Lattice-gas automata and lattice Boltzmann equations for two-dimensional hydrodynamics." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/30259.

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47

Vecil, Francesco. "A contribution to the simulation of Vlasov-based models." Doctoral thesis, Universitat Autònoma de Barcelona, 2007. http://hdl.handle.net/10803/3100.

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Esta tesis está dedicada al desarrollo, aplicación y test de métodos para la simulación numérica de problemas procedentes de la física y de la ingeniería electrónica. La principal herramienta aplicada a lo largo de todo el trabajo es la ecuación de Vlasov (transporte) en la forma de la Boltzmann Transport Equation (BTE) para la descripción del transporte de partículas cargadas en plasmas y dispositivos electrónicos: las cargas se mueven bajo el efecto de un campo de fuerza y sufren scattering debido a otras cargas o fonones (pseudo-partículas que describen de manera efectiva las vibraciones de

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48

Weiß, Jan-Philipp. "Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval." Karlsruhe : Univ.-Verl. Karlsruhe, 2006. http://www.uvka.de/univerlag/volltexte/2006/179/.

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49

Wu, Jingshu. "Direct simulation of flexible particle suspensions using lattice-boltzmann equation with external boundary force." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33858.

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Determination of the relation between the bulk or rheological properties of a particle suspension and its microscopic structure is an old and important problem in physical science. In general, the rheology of particle suspension is quite complex, and the problem becomes even more complicated if the suspending particle is deformable. Despite these difficulties, a large number of theoretical and experimental investigations have been devoted to the analysis and prediction of the rheological behavior of particle suspensions. However, among these studies there are very few investigations that focus

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50

Petersson, Mikael. "Comparison of modes of convergence in a particle system related to the Boltzmann equation." Thesis, Linköpings universitet, Matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-61303.

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The distribution of particles in a rarefied gas in a vessel can be described by the Boltzmann equation. As an approximation of the solution to this equation, Caprino, Pulvirenti and Wagner [3] constructed a random N-particle system. In the equilibrium case, they prove in [3] that the L1-distance between the density function of k particles in the N-particle process and the k-fold product of the solution to the stationary Boltzmann equation is of order 1/N. They do this in order to show that the N-particle system converges to the system described by the stationary Boltzmann equation as the numbe

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