Relevant bibliographies by topics / Boltzmann transport

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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 transport'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Boltzmann transport"

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Magas, V. K., L. P. Csernai, E. Molnár, A. Nyiri, and K. Tamosiunas. "Modified Boltzmann Transport Equation." Nuclear Physics A 749 (March 2005): 202–5. http://dx.doi.org/10.1016/j.nuclphysa.2004.12.035.

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Bechouche, Philippe, Frédéric Poupaud, and Juan Soler. "Quantum Transport and Boltzmann Operators." Journal of Statistical Physics 122, no. 3 (January 20, 2006): 417–36. http://dx.doi.org/10.1007/s10955-005-8082-y.

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El-Nabulsi, Rami Ahmad. "The fractional Boltzmann transport equation." Computers & Mathematics with Applications 62, no. 3 (August 2011): 1568–75. http://dx.doi.org/10.1016/j.camwa.2011.03.040.

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Mužík, Juraj. "Lattice Boltzmann Method for Two-Dimensional Unsteady Incompressible Flow." Civil and Environmental Engineering 12, no. 2 (December 1, 2016): 122–27. http://dx.doi.org/10.1515/cee-2016-0017.

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Abstract A Lattice Boltzmann method is used to analyse incompressible fluid flow in a two-dimensional cavity and flow in the channel past cylindrical obstacle. The method solves the Boltzmann’s transport equation using simple computational grid - lattice. With the proper choice of the collision operator, the Boltzmann’s equation can be converted into incompressible Navier-Stokes equation. Lid-driven cavity benchmark case for various Reynolds numbers and flow past cylinder is presented in the article. The method produces stable solutions with results comparable to those in literature and is very easy to implement.
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Kinaci, Alper, Motohisa Kado, Daniel Rosenmann, Chen Ling, Gaohua Zhu, Debasish Banerjee, and Maria K. Y. Chan. "Electronic transport in VO2—Experimentally calibrated Boltzmann transport modeling." Applied Physics Letters 107, no. 26 (December 28, 2015): 262108. http://dx.doi.org/10.1063/1.4938555.

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Warren, Patrick B. "Electroviscous Transport Problems via Lattice-Boltzmann." International Journal of Modern Physics C 08, no. 04 (August 1997): 889–98. http://dx.doi.org/10.1142/s012918319700076x.

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The application of lattice-Boltzmann methods to electroviscous transport problems is discussed, generalising the moment propagation method for convective-diffusion problems. As a simple application, electro-osmotic flow in a parallel-sided slit is analysed, and the results compared favourably with available analytic solutions for this geometry.
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Dargaville, S., A. G. Buchan, R. P. Smedley-Stevenson, P. N. Smith, and C. C. Pain. "Scalable angular adaptivity for Boltzmann transport." Journal of Computational Physics 406 (April 2020): 109124. http://dx.doi.org/10.1016/j.jcp.2019.109124.

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Guo, Yangyu, and Moran Wang. "Lattice Boltzmann modeling of phonon transport." Journal of Computational Physics 315 (June 2016): 1–15. http://dx.doi.org/10.1016/j.jcp.2016.03.041.

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Chattopadhyay, Ankur, and Arvind Pattamatta. "A Comparative Study of Submicron Phonon Transport Using the Boltzmann Transport Equation and the Lattice Boltzmann Method." Numerical Heat Transfer, Part B: Fundamentals 66, no. 4 (August 25, 2014): 360–79. http://dx.doi.org/10.1080/10407790.2014.915683.

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Majorana, Armando. "A BGK model for charge transport in graphene." Communications in Applied and Industrial Mathematics 10, no. 1 (January 1, 2019): 153–61. http://dx.doi.org/10.1515/caim-2019-0018.

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Abstract The classical Boltzmann equation describes well temporal behaviour of a rarefied perfect gas. Modified kinetic equations have been proposed for studying the dynamics of different type of gases. An important example is the transport equation, which describes the charged particles flow, in the semi-classical regime, in electronic devices. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a collision operator have been proposed to replace the standard Boltzmann integral term. These new equations are called kinetic models. The most popular and widely used kinetic model is the Bhatnagar-Gross-Krook (BGK) model. In this work we propose and analyse a BGK model for charge transport in graphene.
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Dissertations / Theses on the topic "Boltzmann transport"

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Mallinger, François. "Couplage adaptatif Boltzmann Navier-Stokes." Paris 9, 1996. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1996PA090042.

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Nous étudions les écoulements externes en régime semi raréfié à grands nombre de mach. Pour ce faire, nous proposons une stratégie de décomposition de domaine couplant les modèles Boltzmann et Navier-Stokes. Le couplage est réalisé par le biais de conditions aux limites. Les domaines de calcul Boltzmann et Navier-Stokes sont déterminés de manière automatique par un critère analysant la validité de la solution Navier-Stokes. Nous proposons donc un algorithme de couplage adaptatif qui prend en compte d'une part la détermination automatique des domaines, et d'autre part un algorithme de marche en temps pour le couplage des modèles. Le couplage adaptatif résulte d'une interprétation cinétique des équations de Navier-Stokes. Pour le généraliser, nous étudions la transition entre régimes microscopiques (Boltzmann) and macroscopiques (Navier-Stokes) pour des gaz diatomiques, en étendant la démarche initiale de grad. Enfin nous donnons une justification mathématique du couplage Boltzmann Navier-Stokes
We study external flows for semirarefied régimes at high mach number. We propose a domain décomposition strategy coupling Boltzmann and Navier-Stokes models. The coupling is done by boundary conditions. The Boltzmann and Navier-Stokes computational domains are defined automatically thanks to a critérium analysing the validity of the numerical Navier-Stokes solution. We propose therefore an adaptative coupling algorithm taking into account both the automatic définition of the computation domains and a time marching algorithm to couple the models. The whole strategy results from the transition between the microscopie model (Boltzmann) and the macroscopie model (Navier-Stokes). In order to generalize this adaptative coupling, we study this connection for diatomic gases. Finally, we justify the coupled problem from a mathematical view point
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Capuani, Fabrizio. "Lattice-Boltzmann simulations of driven transport in colloidal systems." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2004. http://dare.uva.nl/document/74690.

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McCulloch, Richard. "Advances in radiation transport modeling using Lattice Boltzmann Methods." Thesis, Kansas State University, 2015. http://hdl.handle.net/2097/20516.

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Master of Science
Mechanical and Nuclear Engineering
Hitesh Bindra
This thesis extends the application of Lattice Boltzmann Methods (LBM) to radiation transport problems in thermal sciences and nuclear engineering. LBM is used to solve the linear Boltzmann transport equation through discretization into Lattice Boltzmann Equations (LBE). The application of weighted summations for the scattering integral as set forth by Bindra and Patil are used in this work. Simplicity and localized discretization are the main advantages of using LBM with fixed lattice configurations for radiation transport problems. Coupled solutions to radiation transport and material energy transport are obtained using a single framework LBM. The resulting radiation field of a one dimensional participating and conducting media are in very good agreement with benchmark results using spherical harmonics, the P₁ method. Grid convergence studies were performed for this coupled conduction-radiation problem and results are found to be first-order accurate in space. In two dimensions, angular discretization for LBM is extended to higher resolution schemes such as D₂Q₈ and a generic formulation is adopted to derive the weights for Radiation Transport Equations (RTEs). Radiation transport in a two dimensional media is solved with LBM and the results are compared to those obtained from the commercial software COMSOL, which uses the Discrete Ordinates Method (DOM) with different angular resolution schemes. Results obtained from different lattice Boltzmann configurations such as D₂Q₄ and D₂Q₈ are compared with DOM and are found to be in good agreement. The verified LBM based radiation transport models are extended for their application into coupled multi-physics problems. A porous radiative burner is modeled as a homogeneous media with an analytical velocity field. Coupling is performed between the convection-diffusion energy transport equation with the analytical velocity field. Results show that radiative transport heats the participating media prior to its entering into the combustion chamber. The limitations of homogeneous models led to the development of a fully coupled LBM multi-physics model for a heterogeneous porous media. This multi-physics code solves three physics: fluid flow, conduction-convection and radiation transport in a single framework. The LBE models in one dimension are applied to solve one-group and two-group eigenvalue problems in bare and reflected slab geometries. The results are compared with existing criticality benchmark reports for different problems. It is found that results agree with benchmark reports for thick slabs (>4 mfp) but they tend to disagree when the critical slab dimensions are less than 3 mfp. The reason for this disagreement can be attributed to having only two angular directions in the one dimensional problems.
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MUSTIELES, MORENO. "L'equation de boltzmann des semiconducteurs etude mathematique et simulation numerique." Palaiseau, École polytechnique, 1990. http://www.theses.fr/1990EPXX0002.

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Pour bien decrire le fonctionnement des nouveaux dispositifs electroniques ultra-rapides, il devient necessaire de recourir au modele cinetique des semiconducteurs. Dans ce modele, les porteurs de charge sont modelises par une fonction de distribution dont levolution est decrite par l'equation de boltzmann des semiconducteurs. Dans la premiere partie de la these, nous abordons la resolution numerique de cette equation par une methode particulaire deterministe (methode particulaire ponderee), pour differentes problemes physiques: semiconductor massif, transport bidimensionnel d'electrons parallelement a l'interface d'une heterojonction, interactions binaires entre particules. La deuxieme partie de la these est consacree a l'etude mathematique de l'equation de boltzmann des semiconducteurs dans deux directions: existence et unicite de solutions classiques par techniques d'interpolation, et existence de solutions faibles en utilisant des resultats de compacite en moyenne pour les equations de transport. Dans la derniere partie de la these, nous presentons une methode particulaire nouvelle pour l'approximation des equations de convection-diffusion
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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 nous concentrerons sur quelques modèles mathématiques qui peuvent être utilisés pour la description de matériaux aléatoires. Une attention particulière sera accordée aux tessellations stochastiques, où un domaine est partitionné en polyèdres convexes en échantillonnant des hyperplans aléatoires selon une probabilité donnée. Les inclusions stochastiques de sphères dans une matrice seront également brièvement introduites. Un code informatique sera développé afin de construire explicitement de telles géométries par des méthodes de Monte Carlo. Dans la deuxième partie, nous évaluerons ensuite les caractéristiques générales du transport de particules dans des milieux aléatoires. Pour ce faire, nous allons considérer quelques benchmarks assez simples pour permettre une compréhension approfondie des effets des géométries aléatoires sur les trajectoires de particules tout en conservant les propriétés clés du transport linéaire. Les calculs de transport seront réalisés en utilisant le code de transport de particules Monte Carlo Tripoli4, développé au SERMA. Les cas de modèles de désordre quenched et annealed seront considérés séparément. Dans le premier, un ensemble de géométries sera généré en utilisant notre code, et le problème de transport sera résolu pour chaque configuration: des moyennes d'ensemble seront alors prises pour les observables d'intérêt. Dans le second cas, un modèle de transport efficace capable de reproduire les effets du désordre dans une seule réalisation sera étudié. Les approximations des modèles annealed seront élucidées, et des améliorations significatives seront proposées
Heterogeneous and disordered media emerges in several applications in nuclear science and engineering, especially in relation to neutron and photon propagation. Examples are widespread and concern for instance the double-heterogeneity of the fuel elements in pebble-bed reactors, or the assessment of re-criticality probability due to the random arrangement of fuel resulting from severe accidents. In this Thesis, we will investigate linear particle transport in random media. In the first part, we will focus on some mathematical models that can be used for the description of random media. Special emphasis will be given to stochastic tessellations, where a domain is partitioned into convex polyhedra by sampling random hyperplanes according to a given probability. Stochastic inclusions of spheres into a matrix will be also briefly introduced. A computer code will be developed in order to explicitly construct such geometries by Monte Carlo methods. In the second part, we will then assess the general features of particle transport within random media. For this purpose, we will consider some benchmark problems that are simple enough so as to allow for a thorough understanding of the effects of the random geometries on particle trajectories and yet retain the key properties of linear transport. Transport calculations will be realized by using the Monte Carlo particle transport code Tripoli4, developed at SERMA. The cases of quenched and annealed disorder models will be separately considered. In the former, an ensemble of geometries will be generated by using our computer code, and the transport problem will be solved for each configuration: ensemble averages will then be taken for the observables of interest. In the latter, effective transport model capable of reproducing the effects of disorder in a single realization will be investigated. The approximations of the annealed disorder models will be elucidated, and significant ameliorations will be proposed
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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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Magnin, Yann. "Tranport de spin dans des matériaux magnétiques en couches minces par simulations Monte Carlo." Thesis, Cergy-Pontoise, 2011. http://www.theses.fr/2011CERG0527/document.

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Depuis le début du XX siècle, la thématique de transport a concentré l’attentionde nombreux chercheurs. L’objectif étant alors d’identifier et de comprendre lesdifférentes sources de diffusions prenant part à la résistivité de la matière. Les deuxpremières sources diffusives mises en évidence ont été les phonons dépendant de latempérature, et les défauts du réseau cristallin. Dans les années 1950, l’étude des semiconducteursa fait émerger une troisième source de diffusion, la diffusion magnétique.Dès la mise en évidence du rôle joué par le magnétisme sur la résistivité de certainsmatériaux, il a rapidement été établi que la résistivité magnétique R est tributaire dela stabilité de l’ordre magnétique du réseau. A basse température T, la diffusion desélectrons s’ opère par l e biais des ondes de spins. A haute température, R est proportionnelleaux corrélations spin-spin. Cependant, les mécanismes de diffusion ayant lieuau voisinage de la température de transition ordre/désordre magnétique restent encoremal comprise. L’objectif de cette thèse a consisté à étudier ce problème à l’aide d’uneapproche nouvelle basée sur la simulation Monte Carlo. En effet, les théories existantessont toutes construites avec des hypothèses sur les mécanismes à l’origine du comportementde résistance tels que : fonction corrélation spin-spin, longueur de localisation.Elles utilisent beaucoup d’approximations au cours du calcul telles que théorie du champmoyen, approximation du temps de relaxation, la portée des fonctions de corrélation. Lesprincipaux handicaps de ces théories sont de n’être valables que pour certaines gammesde températures, et d’être tributaires du type de magnétisme porté par les réseaux cristallins.Notre approche offre quant à elle une procédure unifiée concernant l’étude desrésistivités magnétiques fonction de la température. Cette méthode peut s’appliquer `atout type de matériaux, tout ordre magnétique (ferromagnétique, antiferromagnétique,ferrimagnétique, verre de spin, ...), tout type de modèle de spins (Ising, Heisenberg, XY,...), enfin tout type de réseau cristallin. Seule la connaissance du Hamiltonien permet defaire la simulation, et de reproduire des mesures expérimentales avec la possibilité d’unecomparaison quantitative.Dans un premier temps, nous traitons de structures ferromagnétiques et interprétons les différents mécanismes de diffusion en fonction de la température. Nousétendons ensuite l´étude aux systèmes antiferromagnétiques, frustrés et non-frustrés. Cessystèmes n’ont fait l’objet que de peu d’études. Dans le cas des systèmes antiferromagnétiques non-frustrés, nous sommes en mesure de contredire une prédiction théoriquefaite par Haas en 1968, concernant la forme de la résistance magnétique à la transition dephase . Dès lors, nous nous consacrerons à l’étude des mécanismes de transport dansdes systèmes antiferromagnétiques frustrés. Ces travaux ont permis de mettre en évidencedes comportements nouveaux des transitions de phases des résistances magnétiques : nousmontrons que ces résistances subissent une transition du premier ordre , mais qu’ilest également possible par le contrôle d’un paramètre du modèle, de choisir le sens de latransition : des hautes résistances vers les basses résistances ou inversement .Pour finir, nous confrontons nos résultats de simulations avec des mesures expérimentalesen réalisant une étude de transport sur un matériau semiconducteur antiferromagnétique :MnTe. Il résulte de cette étude un bon accord entre nos résultats de simulations et lesmesures expérimentales
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Chiloyan, Vazrik. "Variational approach to solving the phonon Boltzmann transport equation for analyzing nanoscale thermal transport experiments." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/115727.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 133-140).
Over time, technology has shrunk to smaller length scales, and as a result the heat transport in these systems has entered the nanoscale regime. With increasing computational speed and power consumption, there is a need to efficiently dissipate the heat generated for proper thermal management of computer chips. The ability to understand the physics of thermal transport in this regime is critical in order to model, engineer, and improve the performance of materials and devices. In the nanoscale regime, thermal transport is no longer diffusive, and the Fourier heat conduction equation, which we commonly utilize at the macroscale, fails to accurately predict heat flow at the nanoscale. We model the heat flow due to phonons (crystal lattice vibrations), the dominant heat carriers in semiconductors and dielectrics, by solving the Boltzmann transport equation (BTE) to develop an understanding of nondiffusive thermal transport and its dependence on the system geometry and material properties, such as the phonon mean free path. A variety of experimental heat transfer configurations have been established in order to achieve short time scales and small length scales in order to access the nondiffusive heat conduction regime. In this thesis, we develop a variational approach to solving the BTE, appropriate for different experimental configurations, such as transient thermal grating (TTG) and time-domain thermoreflectance (TDTR). We provide an efficient and general methodology to solving the BTE and gaining insight into the reduction of the effective thermal conductivity in the nondiffusive regime, known as classical size effects. We also extend the reconstruction procedure, which aims to utilize both modeling efforts as well as experimental measurements to back out the material properties such as phonon mean free path distributions, to provide further insight into the material properties relevant to transport. Furthermore, with the developed methodology, we aim to provide an analysis of experimental geometries with the inclusion of a thermal interface, to provide insight into the role the interface transmissivity plays in thermal transport in the nondiffusive regime. Lastly, we explore a variety of phonon source distributions that are achieved by heating a system, and show the important link between the system geometry and the distribution of phonons initiated by the heating. We show the exciting possibility that under certain nonthermal phonon distributions, it is possible to achieve enhanced thermal transport at the nanoscale, contrary to the current understanding of size effects only leading to reduced thermal conductivities at the nanoscale for thermal phonon distributions.
by Vazrik Chiloyan.
Ph. D.
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Erasmus, Bernard. "The Lattice Boltzmann Method applied to linear particle transport / Bernard Erasmus." Thesis, North-West University, 2012. http://hdl.handle.net/10394/8691.

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In this study, the applicability of the Lattice Boltzmann Method to neutron transport is investigated. The transport model used, is derived from the Boltzmann equation for neutral particles by inverting the streaming operator and casting the integral transport equation into an operator form. From the operator equation, an iterative solution to the transport problem is presented, with the first collision source as the starting point for the iteration scheme. One of the main features of the method is the simultaneous discretization of the phase space of the problem, whereby particles are restricted to move on a lattice. A full description of the discretization scheme is given along with the iterative procedure and quadrature set used for the angular discretization. To mitigate lattice ray effects, an angular refinement scheme is introduced to increase the angular coverage of the problem phase space. The method is then applied to a model problem to investigate its applicability to neutron transport. Three cases are considered where constant, linear and exponential interpolants are used to account for the accumulation of flux due to the streaming of particles between nodes. The results obtained are compared to a reference solution, that was calculated by using the MCNP code and to the values calculated using a nodal SN method. Finally, areas of improvement are identified and possible extensions to the algorithm are provided.
Thesis (MIng (Engineering Sciences in Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013
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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, target constraint, quantile hedging and floor constraint can all be reformulated into expectation constraint, we apply our results to prove the corresponding dynamic programming principles for these five classes of stochastic control problems in a continuous but non-Markovian setting. In order to solve the Boltzmann equation numerically, in the second part, we propose a new model equation to approximate the Boltzmann equation without angular cutoff. Here the approximate equation incorporates Boltzmann collision operator with angular cutoff and the Landau collision operator. As a first step, we prove the well-posedness theory for our approximate equation. Then in the next step, we show the error estimate between the solutions to the approximate equation and the original equation. Compared to the standard angular cutoff approximation method, our method results in higher order of accuracy.
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Books on the topic "Boltzmann transport"

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

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

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

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

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

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

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

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

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

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Book chapters on the topic "Boltzmann transport"

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Hess, Karl. "Boltzmann Transport Equation." In The Physics of Submicron Semiconductor Devices, 33–43. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-2382-0_2.

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Jacoboni, Carlo. "Boltzmann Equation." In Theory of Electron Transport in Semiconductors, 163–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10586-9_10.

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Kersch, Alfred, and William J. Morokoff. "The Boltzmann Equation." In Transport Simulation in Microelectronics, 11–48. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9080-9_1.

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Dosch, Alexander, and Gary P. Zank. "The Boltzmann Transport Equation." In Transport Processes in Space Physics and Astrophysics, 77–135. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24880-6_2.

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Zank, Gary P. "The Boltzmann Transport Equation." In Transport Processes in Space Physics and Astrophysics, 71–119. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8480-6_3.

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Cercignani, Carlo. "Linear Transport." In The Boltzmann Equation and Its Applications, 158–231. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-1039-9_4.

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Vassiliev, Oleg N. "The Boltzmann Equation." In Monte Carlo Methods for Radiation Transport, 49–104. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44141-2_3.

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Masmoudi, Nader. "Hydrodynamic Limits of the Boltzmann Equation." In Transport in Transition Regimes, 217–30. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4613-0017-5_13.

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Torres-Rincon, Juan M. "Boltzmann-Uehling-Uhlenbeck Equation." In Hadronic Transport Coefficients from Effective Field Theories, 33–45. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00425-9_2.

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Kremer, Gilberto Medeiros. "The Boltzmann Equation." In An Introduction to the Boltzmann Equation and Transport Processes in Gases, 37–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11696-4_2.

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Conference papers on the topic "Boltzmann transport"

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Amon, Cristina H., Jayathi Y. Murthy, and Sreekant V. J. Narumanchi. "Modeling Nanoscale Thermal Transport via the Boltzmann Transport Equation." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-62508.

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In modern microelectronics, where extreme miniaturization has led to feature sizes in the sub-micron and nanoscale range, Fourier diffusion has been found to be inadequate for the prediction of heat conduction. Over the past decade, the phonon Boltzmann transport equation (BTE) in the relaxation time approximation has been employed to make thermal predictions in dielectrics and semiconductors at micron and nanoscales. This paper presents a review of the BTE-based solution methods widely employed in the literature. Particular attention is given to the problem of self-heating (hotspot) in sub-micron transistors. First, the solution approaches based on the gray formulation of the BTE are presented. In this class of solution methods, phonons are characterized by one single group velocity and relaxation time. Phonon dispersion is not accounted for in any detail. This is the most widely employed approach in the literature. The semi-gray BTE approach, moments of the Boltzmann equation, the lattice Boltzmann approach, and the ballistic-diffusive approximation are presented. Models which incorporate greater details of phonon dispersion are also discussed. This includes a full phonon dispersion model developed recently by the authors. This full phonon dispersion model satisfies energy conservation, incorporates the different phonon modes, and well as the interactions between the different modes, and accounts for the frequency dependence for both the phonon group velocity and relaxation times. Results which illustrate the differences between some of these models reveal the importance of developing models that incorporate substantial details of phonon physics.
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Tian, Fuzhi, Baoming Li, and Daniel Y. Kwok. "Simulation of Electroosmotic Flows in Micro- and Nanochannels Using a Lattice Boltzmann Model." In ASME 2004 2nd International Conference on Microchannels and Minichannels. ASMEDC, 2004. http://dx.doi.org/10.1115/icmm2004-2435.

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A Lattice Boltzman Model (LBM) with the Poisson-Boltzmann equation for charge distribution is presented for the simulation of electroosmotic transport in straight rectangular micro and nanochannels. Our results from the LBM are in excellent agreement with the corresponding analytical solution. We have shown that the Lattice Boltzmann Model in the presence of an external force may be used an effective computational tool to simulate the electroosmotic transport phenomena in micro- and nanochannels.
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Bo Wu and Ting-wei Tang. "Quantum corrected Boltzmann transport model for tunneling effects." In IEEE International Conference on Simulation of Semiconductor Processes and Devices. IEEE, 2003. http://dx.doi.org/10.1109/sispad.2003.1233691.

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Chunjian Ni and Jayathi Murthy. "Parallel computation of the phonon Boltzmann transport equation." In 2008 11th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (I-THERM). IEEE, 2008. http://dx.doi.org/10.1109/itherm.2008.4544384.

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Vallabhaneni, Ajit K., Man Prakash Gupta, and Satish Kumar. "Thermal transport in high electron mobility transistors: A Boltzmann transport equation study." In 2017 16th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm). IEEE, 2017. http://dx.doi.org/10.1109/itherm.2017.7992462.

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Sellan, Daniel P., Joseph E. Turney, Eric S. Landry, Alan J. H. McGaughey, and Cristina H. Amon. "Phonon Transport in Thin Films: A Lattice Dynamics/Boltzmann Transport Equation Study." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22623.

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The cross-plane and in-plane phonon thermal conductivities of Stillinger-Weber (SW) silicon thin films are predicted using the Boltzmann transport equation under the relaxation time approximation. We model the thin films using bulk phonon properties obtained from harmonic and anharmonic lattice dynamics calculations. The cross-plane and in-plane thermal conductivities are reduced from the corresponding bulk value. This reduction is more severe for the cross-plane direction than for the in-plane direction. For the in-plane direction, we find that the predicted reduction in thermal conductivity gives a good lower bound to available experimental results. Including the effects of boundary scattering using the Matthiessen rule, which assumes that scattering mechanisms are independent, yields thermal conductivity predictions that are at most 12% lower than our more accurate results. Neglecting optical phonon modes, while valid for bulk systems, introduces 22.5% error when modeling thin films. Using phonon properties along the [001] direction (i.e., the isotropic approximation) yields bulk predictions that are 15% lower than that when all of the phonon modes are considered. For thin films, this deviation increases to 25%. Our results show that a single bulk phonon mean free path is an inadequate metric for predicting the thermal conductivity reduction in thin films.
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Ni, Chunjian, and Jayathi Y. Murthy. "Improved Phonon Transport Modeling Using Boltzmann Transport Equation With Anisotropic Relaxation Times." In ASME 2009 InterPACK Conference collocated with the ASME 2009 Summer Heat Transfer Conference and the ASME 2009 3rd International Conference on Energy Sustainability. ASMEDC, 2009. http://dx.doi.org/10.1115/interpack2009-89181.

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A sub-micron thermal transport model based on the phonon Boltzmann transport equation (BTE) is developed using anisotropic relaxation times. A previously-published model, the full-scattering model, developed by Wang, directly computes three-phonon scattering interactions by enforcing energy and momentum conservation. However, it is computationally very expensive because it requires the evaluation of millions of scattering interactions during the iterative numerical solution procedure. The anisotropic relaxation time phonon BTE model employs a single-mode relaxation time idea, but the relaxation time is a function of wave-vector. The resulting model is significantly less expensive than the full-scattering model, but incorporates directional and dispersion behavior as well as relaxation times satisfying conservation rules. A critical issue in the model development is the accounting for the role of three-phonon N scattering processes. Direct inclusion of N processes into the anisotropic relaxation time model is not possible because such an inclusion would engender thermal resistance. Following Callaway, the overall relaxation rate is modified to include the shift in the phonon distribution function due to N processes. The relaxation times so obtained are compared with the data extracted from equilibrium molecular dynamics simulation by Henry and Chen. The anisotropic relaxation time phonon BTE model is validated by comparing the predicted bulk thermal conductivities of silicon and silicon thin-film thermal conductivities with experimental measurements.
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Chunjian Ni and Jayathi Murthy. "Sub-micron thermal transport modeling by phonon Boltzmann Transport with anisotropic relaxation times." In 2008 11th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (I-THERM). IEEE, 2008. http://dx.doi.org/10.1109/itherm.2008.4544383.

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Aksamija, Zlatan, Mohamed Y. Mohamed, and Umberto Ravaioli. "Parallel Implementation of Boltzmann Transport Simulation of Carbon Nanotubes." In 2009 13th International Workshop on Computational Electronics (IWCE 2009). IEEE, 2009. http://dx.doi.org/10.1109/iwce.2009.5091137.

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Narumanchi, Sreekant V. J., Jayathi Y. Murthy, and Cristina H. Amon. "Boltzmann Transport Equation-based Thermal Modeling Approaches for Microelectronics." In Thermal Sciences 2004. Proceedings of the ASME - ZSIS International Thermal Science Seminar II. Connecticut: Begellhouse, 2004. http://dx.doi.org/10.1615/ichmt.2004.intthermscisemin.940.

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Reports on the topic "Boltzmann transport"

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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), June 2013. http://dx.doi.org/10.2172/1087140.

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Prinja, Anil K. A Generalized Boltzmann Fokker-Planck Method for Coupled Charged Particle Transport. Office of Scientific and Technical Information (OSTI), January 2012. http://dx.doi.org/10.2172/1033565.

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Prinja, A. K. Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport. Office of Scientific and Technical Information (OSTI), August 1995. http://dx.doi.org/10.2172/106676.

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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), June 2001. http://dx.doi.org/10.2172/792485.

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Wilcox, Jr., T. P. COG: A particle transport code designed to solve the Boltzmann equation for deep-penetration (shielding) problems: Volume 1: User's Manual. Office of Scientific and Technical Information (OSTI), February 1989. http://dx.doi.org/10.2172/6029480.

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