Relevant bibliographies by topics / Boltzmann's equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Boltzmann's equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Boltzmann's equation"

1

Woods, L. C. "Limitations of Boltzmann's kinetic equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2095 (2008): 1923–40. http://dx.doi.org/10.1098/rspa.2008.0074.

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It is often assumed that Boltzmann's kinetic equation (BKE) for the evolution of the velocity distribution function f ( r , w , t ) in a gas is valid regardless of the magnitude of the Knudsen number defined by ϵ ≡ τ d ln ϕ /d t , where ϕ is a macroscopic variable like the fluid velocity v or temperature T , and τ is the collision interval. Almost all accounts of transport theory based on BKE are limited to terms in O ( ϵ )≪1, although there are treatments in which terms in O ( ϵ 2 ) are obtained, classic examples being due to Burnett and Grad. The mathematical limitations that arise are discu
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Mendoza, M., S. Succi, and H. J. Herrmann. "High-order kinetic relaxation schemes as high-accuracy Poisson solvers." International Journal of Modern Physics C 26, no. 05 (2015): 1550055. http://dx.doi.org/10.1142/s0129183115500552.

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We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and investigate the influence of higher-order terms on the resulting macroscopic equations. By performing an appropriate expansion of the equilibrium distribution, we provide a method to remove the unnecessary terms up to a desired order and show that it is possible to find, with high level of accuracy, the steady-state solution of the diffusion equation for sizeable Knu
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Di, Yana, Yuwei Fan, Ruo Li, and Lingchao Zheng. "Linear Stability of Hyperbolic Moment Models for Boltzmann Equation." Numerical Mathematics: Theory, Methods and Applications 10, no. 2 (2017): 255–77. http://dx.doi.org/10.4208/nmtma.2017.s04.

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AbstractGrad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems and thus the regularized models attain local well-posedness for Cauchy data. The hyperbolic regularization is only related to the convection term in Boltzmann equation. We in this paper studied the regularized models with the presentation of collision terms. It is proved that the regularized models are linearly stable at the local equilibrium and satisfy Yong's first stability condition with commonly used approximate collision terms, and particularly with Boltzmann's binary collision mo
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Lions, P. L. "Conditions at infinity for boltzmann's equation." Communications in Partial Differential Equations 19, no. 1-2 (1994): 335–67. http://dx.doi.org/10.1080/03605309408821019.

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Maass, W. "Stability properties of a class kinetic equations including Boltzmann's equation." Physica A: Statistical Mechanics and its Applications 133, no. 3 (1985): 539–50. http://dx.doi.org/10.1016/0378-4371(85)90148-7.

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Jagannathan, Kannan. "Anxiety and the Equation: Understanding Boltzmann's Entropy." American Journal of Physics 87, no. 9 (2019): 765. http://dx.doi.org/10.1119/1.5116583.

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Busoni, Giorgio, F. Glose, and B. Perthame. "Stationary Boltzmann's Equation With a Source Term." Communications in Partial Differential Equations 15, no. 12 (1990): 471–81. http://dx.doi.org/10.1080/03605309908820747.

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Banggu, Z. "Isolated collisionless uniform spherical solution of Boltzmann's equation." Journal of Physics A: Mathematical and General 20, no. 15 (1987): L959—L963. http://dx.doi.org/10.1088/0305-4470/20/15/005.

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Rousseau, M., and J. C. De Jaeger. "2D-Hydrodynamic Energy Model Including Avalanche Breakdown Phenomenon for Power Field Effect Transistors." VLSI Design 13, no. 1-4 (2001): 323–28. http://dx.doi.org/10.1155/2001/69472.

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A 2D-Hydrodynamic model is carried out to predict the breakdown voltage of microwave field effect transistors. The model is based on the conservation equations inferred from Boltzmann's transport equation, coupled with Poisson’s equation. In order to take into account the channel avalanche breakdown, the charge conservation equations for electrons and holes are considered and a generation term is introduced. The set of equations is solved using finite difference and different computational methods have been tested to save computing time. The model allows us to obtain accurate predictions for p
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Snyder, Randy W., C. Wade Sheen, and Paul C. Painter. "The Effect of Temperature on the Infrared Spectra of a Polyimide." Applied Spectroscopy 42, no. 3 (1988): 503–8. http://dx.doi.org/10.1366/0003702884427870.

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The effect of high temperature on the infrared spectra of fully cured PMDA/ODA polyimide is discussed. Changes in some bands can be explained by Boltzmann effects on the distribution of excited states. Other bands, in particular the 1780-cm−1 band that is often used for cure measurements, change in ways that cannot be related to Boltzmann's equation. These band position and intensity changes are explained as configurational changes occurring during heating. Determination of correction factors for integrated peak areas from spectra taken at elevated temperature are discussed.
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Dissertations / Theses on the topic "Boltzmann's equation"

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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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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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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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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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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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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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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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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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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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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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Books on the topic "Boltzmann's equation"

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Hydrodynamic limits of the Boltzmann equation. Springer, 2009.

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

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

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

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

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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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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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Book chapters on the topic "Boltzmann's equation"

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Robson, Robert E., Ronald D. White, and Malte Hildebrandt. "Numerical Techniques for Solution of Boltzmann's Equation." In Fundamentals of Charged Particle Transport in Gases and Condensed Matter. CRC Press, 2017. http://dx.doi.org/10.4324/9781315120935-12.

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Hänsch, Wilfried. "Boltzmann’s Equation." In Computational Microelectronics. Springer Vienna, 1991. http://dx.doi.org/10.1007/978-3-7091-9095-1_1.

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Economou, Eleftherios N. "Boltzmann’s Equation." In The Physics of Solids. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-02069-8_30.

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Miyamoto, Kenro. "Boltzmann’s Equation." In Plasma Physics for Controlled Fusion. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-49781-4_8.

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Li, Jun. "Boltzmann Equation." In Multiscale and Multiphysics Flow Simulations of Using the Boltzmann Equation. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26466-6_2.

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Jacoboni, Carlo. "Boltzmann Equation." In Theory of Electron Transport in Semiconductors. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10586-9_10.

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Sone, Yoshio. "Boltzmann Equation." In Kinetic Theory and Fluid Dynamics. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0061-1_2.

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Eu, Byung Chan. "Boltzmann Equation." In Nonequilibrium Statistical Mechanics. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-2438-8_3.

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Mohamad, A. A. "The Boltzmann Equation." In Lattice Boltzmann Method. Springer London, 2019. http://dx.doi.org/10.1007/978-1-4471-7423-3_2.

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Mohamad, A. A. "The Diffusion Equation." In Lattice Boltzmann Method. Springer London, 2019. http://dx.doi.org/10.1007/978-1-4471-7423-3_5.

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Conference papers on the topic "Boltzmann's equation"

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Novitsky, A., S. V. Zhukovsky, D. Novitsky, and A. V. Lavrinenko. "Metamaterial characterization using Boltzmann's kinetic equation for electrons." In 2013 7th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS 2013). IEEE, 2013. http://dx.doi.org/10.1109/metamaterials.2013.6809066.

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Bernhoff, Niclas. "Discrete quantum Boltzmann equation." In 31ST INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD31. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5119631.

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Pulvirenti, M. "On the Quantum Boltzmann Equation." In RAREFIED GAS DYNAMICS: 24th International Symposium on Rarefied Gas Dynamics. AIP, 2005. http://dx.doi.org/10.1063/1.1941511.

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Alder, Berni J. "Reflections on the Boltzmann equation." In RAREFIED GAS DYNAMICS: 22nd International Symposium. AIP, 2001. http://dx.doi.org/10.1063/1.1407535.

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Saveliev, V. L. "On invariant discretizations of Boltzmann equation." In PROCEEDINGS OF THE 29TH INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902580.

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Bobylev, A. V. "Eternal Solutions of the Boltzmann Equation." In RAREFIED GAS DYNAMICS: 23rd International Symposium. AIP, 2003. http://dx.doi.org/10.1063/1.1581520.

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Ichinose, Shoichi. "Velocity–Field Theory, Boltzmann’s Transport Equation and Geometry." In Proceedings of the 12th Asia Pacific Physics Conference (APPC12). Journal of the Physical Society of Japan, 2014. http://dx.doi.org/10.7566/jpscp.1.012132.

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JAKOVÁC, A. "QUANTUM CORRECTIONS TO BOLTZMANN EQUATIONS." In Proceedings of the SEWM2002 Meeting. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704498_0054.

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Mavriplis, Dimitri. "Multigrid Solution of the Lattice-Boltzmann Equation." In 17th AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2005. http://dx.doi.org/10.2514/6.2005-5104.

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Kweyu, Cleophas, Martin Hess, Lihong Feng, Matthias Stein, and Peter Benner. "REDUCED BASIS METHOD FOR POISSON-BOLTZMANN EQUATION." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2103.5891.

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Reports on the topic "Boltzmann's equation"

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Szoke, Abraham, and Eugene D. Brooks, III. The Boltzmann equation in the difference formulation. Office of Scientific and Technical Information (OSTI), 2015. http://dx.doi.org/10.2172/1184176.

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Domokos, G., S. Kovesi-Domokos, and C. K. Zoltani. Boltzmann Equation Approach to Two-Phase Flow Turbulence. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada196153.

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Drallos, P. J., and M. E. Riley. Boltzmann-equation simulations of radio-frequency-driven, low-temperature plasmas. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/83882.

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Shen, Jie, and Weinan E. Solving Boltzmann and Fokker-Planck Equations Using Sparse Representation. Defense Technical Information Center, 2011. http://dx.doi.org/10.21236/ada564031.

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Lee, B. Improved Multiple-Coarsening Methods for Sn Discretizations of the Boltzmann Equation. Office of Scientific and Technical Information (OSTI), 2008. http://dx.doi.org/10.2172/945566.

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Szczekutowicz, Anna Agnieszka, Jeffrey Robert Haack, and Irene M. Gamba. Velocity dependent Coulomb logarithm in the Landau limit of the Boltzmann equation. Office of Scientific and Technical Information (OSTI), 2018. http://dx.doi.org/10.2172/1468558.

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Larsen, Edward. A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation. Office of Scientific and Technical Information (OSTI), 2013. http://dx.doi.org/10.2172/1087140.

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Bhuiyan, L. B., and C. W. Outhwaite. Modified Poisson-Boltzmann Equation in the Electric Double Layer Theory for an Electrolyte with Size Asymmetric Ions. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada201410.

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Fasso, A. Heavy Ion Interactions From Coulomb Barrier to Few GeV/n: Boltzmann Master Equation Theory and FLUKA Code Performances. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/839786.

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Williams, Mark L. Pointwise Energy Solution of the Boltzmann Transport Equation for Thermal Neutrons - Final Report - 07/01/1999 - 06/30/2001. Office of Scientific and Technical Information (OSTI), 2001. http://dx.doi.org/10.2172/792485.

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