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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-StokesWe 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 ScienceMechanical 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 proposéesHeterogeneous 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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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 are then proved to satisfy either the linearized Euler or the Stokes system of equations (depending on the chosen scaling), by passing to the limit in the conservation relations derived from the Boltzmann equation. A theorem injecting continuously the intersection of certain weak spaces into a normed one is proved. Together with properties of the Euler semigroup, this allows to show strong convergence of the first three moments of the distribution function toward the macroscopic quantities density, bulk velocity and temperature, solutions of the linearized Euler system. The Stokes case is treated somewhat differently, through the introduction of a result, proved by using the adjoint formulation for linear kinetic equations, that extends the averaging theory of Golse-Lions-Perthame-Sentis. The desired convergence for the divergence-free component of the second moment toward the macroscopic velocity is then shown.
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Yamazaki, Mitsuru. "Sur les modeles discrets de l'equation de boltzmann avec termes lineaires et quadratiques." Palaiseau, Ecole polytechnique, 1993. http://www.theses.fr/1993EPXX0005.
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On etudie les modeles discrets de l'equation de boltzmann qui decrivent l'etat d'un gaz rarefie dont les vitesses des molecules appartiennent a un ensemble fini i de vecteurs. Il s'agit d'un systeme semi-lineaire d'ordre un, qui represente le mouvement des molecules dans un tube mince infini sous l'influence des interactions binaires et de la reflexion contre la paroi du tube. On suppose toujours que des conditions physiques sont verifiees. A notre connaissance, personne n'a etudie jusqu'a present ce systeme comportant des termes lineaires et quadratiques. Pour les vitesses distinctes, on demontre l'existence globale de solutions pour des donnees d'entropie localement finie sous la condition microreversibilite, ce qui est, jusqu'a present, le resultat exigeant le moins de regularite sur les conditions initiales pour obtenir l'existence globale, meme s'il n'y a pas de termes lineaires. Ensuite on demontre l'existence globale de solutions pour des donnees localement bornees, en supposant la conservation de la quantite de mouvement au cours de collisions. Ensuite, on montre que la solution reste bornee pour des donnees sommables et bornees, en supposant les conservations de la quantite de mouvement au cours de collisions et au cours de la reflexion. En plus, pour ces memes conditions, on demontre le comportement asymptotique des solutions: pour des donnees sommables et bornees, les solutions convergent vers une fonction presque partout. Et puis, pour les vitesses distinctes, on demontre la convergence uniforme de solutions. Dans le chapitre sept, on traite le cas de donnees petites, en supposant que suffisamment de coefficients de reflexion sont non nuls, ce qui est incompatible avec la conservation de la quantite de mouvement au cours de la reflexion. On demontre alors, selon l'argument du a shizuta et kawashima, la decroissance des solutions
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Hamzeh, Hani. "Résolution de l'équation de transport de Boltzmann pour les phonons et applications." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00778705.
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Cette thèse est consacrée à l'étude de la dynamique et du transport des phonons via la résolution de l'équation de transport de Boltzmann (ETB) pour les Phonons. Un 'solveur' Monte Carlo dédié à la résolution de l'ETB des phonons dans l'espace réciproque, prenant en compte tous les processus d'interactions Normaux et Umklapp à trois-phonons, est proposé. Une prise en compte rigoureuse des lois de conservation de l'énergie et de la quantité de mouvement est entreprise. Des relations de dispersion réalistes, intégrant tous les modes de polarisations, sont considérées. Le calcul des taux d'interactions à trois-phonons de tous les processus Normaux et Umklapp est effectué en utilisant l'approche théorique due à Ridley qui ne nécessite qu'un unique paramètre semi-ajustable pour chaque mode de polarisation, nommément : le coefficient de couplage anharmonique représenté par les constantes de Grüneisen. Les taux d'interactions ainsi calculés ne servent pas uniquement à la résolution de l'ETB des phonons, mais ont permis aussi une analyse complète des canaux de relaxation des phonons longitudinaux optiques de centre de zone. Cette analyse a montré que le canal de Vallée-Bogani est négligeable dans le GaAs, et que vraisemblablement les temps de vie des phonons LO de centre de zone dans l'InAs et le GaSb rapportés dans la littérature sont fortement sous-estimés. Pour la première fois à notre connaissance, un couplage de deux solveurs Monte Carlo indépendants l'un dédié aux porteurs de charges (Thèse E. Tea) et l'autre dédié aux phonons, est effectué. Cela permet d'étudier l'effet des phonons chauds sur le transport des porteurs de charges. Cette étude a montré que l'approximation de temps de relaxation surestime souvent l'effet bottleneck des phonons. Le 'solveur' Monte Carlo est étendu pour résoudre l'ETB des phonons dans l'espace réel (en plus de l'espace réciproque), cela a permet d'étudier le transport des phonons et ainsi de la chaleur. La théorie généralisée de Ridley est toujours utilisée avec des particules de simulations qui interagissent les unes avec les autres directement. Les règles de conservation de l'énergie et de la quantité de mouvement sont rigoureusement respectées. L'effet des processus Umklapp sur la quantité de mouvement totale des phonons est fidèlement traduit; tout comme l'effet des interactions sur les directions des phonons, grâce à une procédure prenant en compte les directions vectorielles respectives lors d'une interaction, au lieu, de la distribution aléatoire usuellement utilisée. Les résultats préliminaires montrent la limite de l'équation analytique de conduction de la chaleur.
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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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Hamzeh, Hani. "Résolution de l’équation de transport de Boltzmann pour les phonons et applications." Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112371/document.
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Cette thèse est consacrée à l’étude de la dynamique et du transport des phonons via la résolution de l’équation de transport de Boltzmann (ETB) pour les Phonons. Un ‘solveur’ Monte Carlo dédié à la résolution de l’ETB des phonons dans l’espace réciproque, prenant en compte tous les processus d’interactions Normaux et Umklapp à trois-phonons, est proposé. Une prise en compte rigoureuse des lois de conservation de l’énergie et de la quantité de mouvement est entreprise. Des relations de dispersion réalistes, intégrant tous les modes de polarisations, sont considérées. Le calcul des taux d’interactions à trois-phonons de tous les processus Normaux et Umklapp est effectué en utilisant l’approche théorique due à Ridley qui ne nécessite qu’un unique paramètre semi-ajustable pour chaque mode de polarisation, nommément : le coefficient de couplage anharmonique représenté par les constantes de Grüneisen. Les taux d’interactions ainsi calculés ne servent pas uniquement à la résolution de l’ETB des phonons, mais ont permis aussi une analyse complète des canaux de relaxation des phonons longitudinaux optiques de centre de zone. Cette analyse a montré que le canal de Vallée-Bogani est négligeable dans le GaAs, et que vraisemblablement les temps de vie des phonons LO de centre de zone dans l’InAs et le GaSb rapportés dans la littérature sont fortement sous-estimés. Pour la première fois à notre connaissance, un couplage de deux solveurs Monte Carlo indépendants l’un dédié aux porteurs de charges (Thèse E. Tea) et l’autre dédié aux phonons, est effectué. Cela permet d’étudier l’effet des phonons chauds sur le transport des porteurs de charges. Cette étude a montré que l’approximation de temps de relaxation surestime souvent l’effet bottleneck des phonons. Le ‘solveur’ Monte Carlo est étendu pour résoudre l’ETB des phonons dans l’espace réel (en plus de l’espace réciproque), cela a permet d’étudier le transport des phonons et ainsi de la chaleur. La théorie généralisée de Ridley est toujours utilisée avec des particules de simulations qui interagissent les unes avec les autres directement. Les règles de conservation de l’énergie et de la quantité de mouvement sont rigoureusement respectées. L’effet des processus Umklapp sur la quantité de mouvement totale des phonons est fidèlement traduit; tout comme l’effet des interactions sur les directions des phonons, grâce à une procédure prenant en compte les directions vectorielles respectives lors d’une interaction, au lieu, de la distribution aléatoire usuellement utilisée. Les résultats préliminaires montrent la limite de l’équation analytique de conduction de la chaleurThis work is dedicated to the study of phonon transport and dynamics via the solution of Boltzmann Transport Equation (BTE) for phonons. The Monte Carlo stochastic method is used to solve the phonon BTE. A solution scheme taking into account all the different individual types of Normal and Umklapp processes which respect energy and momentum conservation rules is presented. The use of the common relaxation time approximation is thus avoided. A generalized Ridley theoretical scheme is used instead to calculate three-phonon scattering rates, with the Grüneisen constant as the only adjustable parameter. A method for deriving adequate adjustable anharmonic coupling coefficients is presented. Polarization branches with real nonlinear dispersion relations for transverse or longitudinal optical and acoustic phonons are considered. Zone-center longitudinal optical (LO) phonon lifetimes are extracted from the MC simulations for GaAs, InP, InAs, and GaSb. Decay channels contributions to zone-center LO phonon lifetimes are investigated using the calculated scattering rates. Vallée-Bogani’s channel is found to have a negligible contribution in all studied materials, notably GaAs. A comparison of phonons behavior between the different materials indicates that the previously reported LO phonon lifetimes in InAs and GaSb were quite underestimated in the literature. For the first time, to our knowledge, a coupling of two independent Monte Carlo solvers, one for charge carriers [PhD manuscript, E. TEA], and one for phonons, is undertaken. Hot phonon effect on charge carrier dynamics is studied. It is shown that the relaxation time approximation overestimates the phonon bottleneck effect. The phonon MC solver is extended to solve the phonon’s BTE in real space simultaneously with the reciprocal space, to study phonon and heat transport. Ridley’s generalized theoretical scheme is utilized again with simulation particles interacting directly together. Energy and momentum conservation laws are rigorously implemented. Umklapp processes effect on the total phonon momentum is thoroughly reproduced, as for the anharmonic interactions effect on resulting phonon directions. This is thanks to a procedure taking in consideration the respective vector directions during an interaction, instead of the randomization procedure usually used in literature. Our preliminary results show the limit of the analytic macroscopic heat conduction equation
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Anwar, Shadab. "Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers." FIU Digital Commons, 2008. http://digitalcommons.fiu.edu/etd/22.
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A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.
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Niclot, Bernard. "Etude numerique de l'equation de boltzmann des semiconducteurs par methode particulaire." Palaiseau, École polytechnique, 1988. http://www.theses.fr/1988EPXXX002.
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Resolution de cette equation dans une geometrie simplifiee et demonstration de la validite de cette methode tant pour les modeles de collision lineaires (anteraction optique ou intervallee) que non-lineaires (prise en compte du principe de pauli, ou interaction interelectroniques). Une echelle numerique detaillee et une etude theorique de convergence et de stabilite viennent completer ces resultats
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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."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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Roussel, Olivier. "Génération aléatoire de structures ordonnées par le modèle de Boltzmann." Paris 6, 2012. http://www.theses.fr/2012PA066282.
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Dans le domaine de la combinatoire, la génération aléatoire d’objets est un problème central relié à de nombreux aspects de la science combinatoire, que ce soit à l’énumération exacte ou asymptotique, ou à la vérification de conjectures. De nombreuses méthodes ont été proposées afin de résoudre efficacement ce problème, dont le modèle de Boltzmann. Ce modèle, au prix d’un contrôle moindre sur la taille des objets générés, assure les propriétés de complexité linéaire dans beaucoup de cas réels, et de facilité d’automatisation pour de larges classes d’objets. Cette thèse vise à étendre encore les classes d’objets combinatoires sur lesquelles ce modèle de Boltzmann peut s’appliquer, tout en conservant les propriétés d’efficacité et d’automatisation. La première partie est une étude des algorithmes de générations de Boltzmann existants, ainsi que de leur propriétés et leurs fondations mathématiques sous-jacentes. Dans une seconde partie, nous présentons notre idée de biaiser ces algorithmes pour étendre leur domaine de validité. Nous proposons une extension très générale, avant de l’appliquer à plusieurs opérateurs combinatoires tels que la dérivation, le produit de shuffle et l’opération de dépointage. Enfin, nous présentons un algorithme de génération uniforme pour le produit de Hadamard. Nous appuyons nos algorithmes et résultats par des exemples et données expérimentales illustrant le bien fondé de nos méthodesUniform random generation is a central issue in combinatorics. Indeed, random sampling is virtually connected to all parts of combinatorics, whether to exact or asymptotic enumeration, or to the experimental verification of conjectures. Various methods have been developed in order to efficiently solve that issue. Boltzmann model is among them. This method, relaxing some constraints about the size of the object being currently generated, ensures a linear complexity in many actual cases, and can easily be automatized for various combinatorial classes. This thesis aims at enlarging the set of such admissible classes, while keeping the nice properties of linear complexity and ease of automation. The first part is devoted to the presentation of the Boltzmann model and existing Boltzmann samplers, and the study of their properties and mathematical foundations. In the second part, we introduce our idea of biasing those samplers in order to enlarge their range of validity. Firstly, we present a general extension, and then specialize it to several combinatorial operations such as the derivation, the shuffle product or the unpointing operation. Finally, we present a uniform random sampler for the Hadamard product. We highlight our algorithms through this thesis with examples and experimental results, illustrating the efficiency of our methods
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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.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.
Includes bibliographical references (leaves 193-195).
by Yannick L. Le Coz.
Ph.D.
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Yoshino, Masato. "Numerical Analysis of Transport Phenomena in Porous Structure by the Lattice Boltzmann Method." Kyoto University, 2000. http://hdl.handle.net/2433/157089.
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本文データは平成22年度国立国会図書館の学位論文(博士)のデジタル化実施により作成された画像ファイルを基にpdf変換したものであるKyoto University (京都大学)
0048
新制・課程博士
博士(工学)
甲第8403号
工博第1968号
新制||工||1178(附属図書館)
UT51-2000-F307
京都大学大学院工学研究科化学工学専攻
(主査)教授 荻野 文丸, 教授 小森 悟, 教授 田門 肇
学位規則第4条第1項該当
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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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Teichert, Steffen. "Elektrischer Transport und allgemeine Charakterisierung der halbleitenden Silicide Beta-FeSi 2 und MnSi 1,73." [S.l. : s.n.], 1996. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10324503.
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Protik, Nakib Haider. "Phonon and Carrier Transport in Semiconductors from First Principles:." Thesis, Boston College, 2019. http://hdl.handle.net/2345/bc-ir:108608.
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Thesis advisor: David BroidoWe present fundamental studies of phonon and electron transport in semiconductors. First principles density functional theory (DFT) is combined with exact numerical solutions of the Boltzmann transport equation (BTE) for phonons and electrons to calculate various transport coefficients. The approach is used to determine the lattice thermal conductivity of three hexagonal polytypes of silicon carbide. The calculated results show excellent agreement with recent experiments. Next, using the infinite orders T-matrix approach, we calculate the effect of various neutral and charged substitution defects on the thermal conductivity of boron arsenide. Finally, we present a general coupled electron-phonon BTEs scheme designed to capture the mutual drag of the two interacting systems. By combining first principles calculations of anharmonic phonon interactions with phenomenological models of electron-phonon interactions, we apply our implementation of the coupled BTEs to calculate the thermal conductivity, mobility, Seebeck and Peltier coefficients of n-doped gallium arsenide. The measured low temperature enhancement in the Seebeck coefficient is captured using the solution of the fully coupled electron-phonon BTEs, while the uncoupled electron BTE fails to do so. This work gives insights into the fundamental nature of charge and heat transport in semiconductors and advances predictive ab initio computational approaches. We discuss possible extensions of our work
Thesis (PhD) — Boston College, 2019
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Physics
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Batany, Stéphane. "Influence d’un macropore sur l’écoulement et le transport de solutés en milieu poreux : expérimentations sur sol modèle macroporé et simulations numériques." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1085/document.
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La modélisation des écoulements et du transport dans les milieux poreux est un domaine actif pour, notamment, progresser dans la compréhension du transfert des polluants dans les sols. Les sols présentent fréquemment des hétérogénéités comme des macropores (provoqués par la faune, la flore ou des fissures) et un certain nombre de modèles numériques utilisent les concepts de double ou de multi-perméabilité pour tenir compte de tous les types d’écoulements susceptibles de coexister dans de tels systèmes. Cependant, les modèles classiques semblent sous-estimer l’effet de la macroporosité sur l’écoulement et le transfert préférentiels et restreindre la zone d’écoulement préférentiel au seul volume occupé par la macroporosité. Diverses études expérimentales antérieures à cette thèse ont questionné cette hypothèse. Cette étude se propose de comprendre l’établissement de l’écoulement et du transport préférentiel et en particulier les mécanismes d’échange d’eau et de masse entre un macropore et une matrice poreuse environnante en condition saturée. Pour cela, des traçages de l’eau sont réalisés pour un milieu poreux modèle constitué de billes de verre, traversé par un macropore synthétique et mis en place en colonnes de laboratoire. Elution et transfert dans les colonnes sont caractérisés par suivi de la concentration en sortie et par imagerie par résonance magnétique. Un modèle numérique développé sur la base de la méthode de Boltzmann sur réseau est utilisé pour simuler numériquement des écoulements dans un système macroporé et identifier les mécanismes d’écoulements préférentiels à l’échelle de pores. Les données expérimentales montrent que le transfert du traceur est fortement dépendant du débit d’injection ainsi que du coefficient de diffusion dans l’eau. À fort débit, le transfert semble s’effectuer exclusivement dans le macropore, avec très peu d’échange avec la matrice. Pour des débits plus faibles, la percée présente une inflexion suivie d’un pic. Les images IRM montrent alors un échange significatif de traceur entre le macropore et la matrice poreuse environnante. Les simulations numériques sont utilisées pour calculer le champ de vitesse de l’écoulement dans le système en fonction du débit. Les modélisations numériques montrent que l’écoulement préférentiel est étendu dans la matrice poreuse sur une zone de même dimension que le diamètre moyen des grains indépendamment de la taille du macropore et du débit, dans la gamme de débits simulés. Ces résultats expérimentaux et numériques montrent que l’influence du macropore sur les transferts doit être étendue dans la matrice poreuse sur une zone de la taille des grains pour l’écoulement et sur une zone dépendant du coefficient de diffusion du traceur ainsi que du temps de séjour moyen de celui-ci pour le transfert des solutésFlow and transport modeling through porous media is of primary concern nowadays, especially in order to progress in the understanding of pollutant transfers through soils. Soils present frequently heterogeneities such as macropores (caused by fauna, flora or cracks) and several numerical models use double or multi permeability concepts in order to take into account all flow types that may exist in such porous systems. Nevertheless, classical models seem underestimate the macropore effect on preferential flow and transport by restricting the preferential flow zone only to the volume occupied by the macroporosity. Various experimental studies prior to this thesis have questioned this hypothesis. This study proposes to understand the establishment of preferential flow and transport and in particular the mechanism of flow and solute exchanges between a synthetic macropore and a surrounding porous matrix in saturated condition. For this purpose, water tracing are realized for a model porous media constituted by glass beads, crossed by a synthetic macropore and implemented in laboratory columns. Breakthrough and transport in columns are characterized by monitoring the concentration at the end of the column by magnetic nuclear resonance. A numerical model developed on the basis of lattice-Boltzmann method is used to simul ate flow in macroporous system and identify preferential flow mechanisms at pore scale. Experimental data show that tracer transport is strongly dependent on injection flow rate and the diffusion coefficient in water. At high flow rate, the transport seems to occur exclusively in the macropore, with very little masse exchange with the porous matrix. At lower flow rates, the breakthrough exhibits an inflexion followed by a peak. The MRI images show a significant mass exchange of tracer between the macropore and the surrounding porous matrix. The numerical simulations are used to calculate the flow field in a porous system as a function of flow rate. They show that preferential flow is extended in porous matrix into a zone of same dimension the mean diameter of beads regardless of macropore size or injected flow rate, in the range of simulated flow rates. These experimental and numerical results show that macropore influence on transport should be extended through the surrounding porous matrix into a zone of the same size of grains diameter for flow and into a zone depending on diffusion coefficient as well as mean residence time of the studied tracer for solute transport
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Baré, Jonathan <1981>. "Spectrum reconstruction from a scattering measurement using the adjoint Boltzmann transport equation for photons." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amsdottorato.unibo.it/4892/.
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Quality control of medical radiological systems is of fundamental importance, and requires efficient methods for accurately determine the X-ray source spectrum. Straightforward measurements of X-ray spectra in standard operating require the limitation of the high photon flux, and therefore the measure has to be performed in a laboratory. However, the optimal quality control requires frequent in situ measurements which can be only performed using a portable system.
To reduce the photon flux by 3 magnitude orders an indirect technique based on the scattering of the X-ray source beam by a solid target is used. The measured spectrum presents a lack of information because of transport and detection effects. The solution is then unfolded by solving the matrix equation that represents formally the scattering problem. However, the algebraic system is ill-conditioned and, therefore, it is not possible to obtain a satisfactory solution. Special strategies are necessary to circumvent the ill-conditioning. Numerous attempts have been done to solve this problem by using purely mathematical methods. In this thesis, a more physical point of view is adopted. The proposed method uses both the forward and the adjoint solutions of the Boltzmann transport equation to generate a better conditioned linear algebraic system.
The procedure has been tested first on numerical experiments, giving excellent results. Then, the method has been verified with experimental measurements performed at the Operational Unit of Health Physics of the University of Bologna. The reconstructed spectra have been compared with the ones obtained with straightforward measurements, showing very good agreement.
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Zelmanse, Alain. "Formulation cinétique et schémas de Boltzmann pour le calcul numérique en mécanique des fluides." Paris 13, 1995. http://www.theses.fr/1995PA132008.
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On s'intéresse à l'application des schémas de type Boltzmann au cas des écoulements de gaz réels. De manière plus précise, on étudie la classe des schémas cinétiques dont la fonction de distribution a un support borné. Le principe d'un gamma équivalent est utilisé, c'est a dire que l'on se ramène localement en temps et en espace au cas du gaz parfait (schémas de perthame) ou au cas du gaz parfait isentropique (schémas de perthame et de kaniel). Le comportement de ces schémas en limite d'incompressibilité est plus particulièrement étudié. Par ailleurs, la formulation cinétique donne l'occasion d'introduire le terme source au niveau cinétique, ce qui permet de le décentrer de manière naturelle. Les résultats numériques dans le cas du gaz réel mettent en évidence la nécessité d'une grande limitation du pas de temps, tant pour compenser les problèmes dus à la vitesse de propagation numérique qui peut être inferieure à la vitesse du son, que pour éviter les oscillations provoquées par les discontinuités des dérivées de la loi d'état. Ces différents schémas ont été testés sur un problème réputé difficile. Les résultats obtenus montrent la nécessité d'utiliser un grand nombre de mailles du fait de l'importance de la viscosité numérique et incitent à la plus grande prudence quant a l'utilisation de schémas de Boltzmann en limite d'incompressibilité.
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Li, Li. "The asymptotic behavior for the Vlasov-Poisson-Boltzmann system & heliostat with spinning-elevation tracking mode /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b30082419f.pdf.
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Thesis (Ph.D.)--City University of Hong Kong, 2009."Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [84]-87)
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Meded, Velimir. "Electronic Transport in Materials." Doctoral thesis, Uppsala University, Department of Physics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4768.
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Transport properties within the Boltzmann transport equation for metallic multi-layer structures as well as bulk materials, were the prime topic of this work. Ab initio total energy calculations for Hydrogen loaded metallic multi-layers were performed in order to shed some light onto problem of H depleted layers at the interfaces that have been experimentally observed. It was explained in connection with structural relaxation of the interface layers.
Further on conductivity behavior of Fe/V vs. Mo/V during Hydrogen load was discussed. The difference in, on first sight, rather similar multi-layer structures was explained by the magnitude of Hydrogen induced Vanadium expansion. Problem of variation of conductivity with changed c/a ratio of metals and semiconductors in general was addressed as well. The variations due to change of the Fermi surface of the corresponding materials were observed as well as some intriguing general patterns. The phenomenon could be regarded as piezoresistivity on electronic structure level. For the 3d transition metals variation of conductivity/resistivity through the period was studied.
A possible explanation for anomalous behavior of Manganese resistivity due to its much greater lattice constant in comparison to its neighbors in the period is presented. Field of disordered alloys and low dimensional magnetism was touched by discussing Mo/Ru formation energy as well as magnetic nano-wires grown on surfaces.
All total energy calculations as well as band structure calculations were performed by using Density Functional Theory based numerical computations. A short but comprehensive review of most common linear-response electron transport techniques is given.
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YIN, CHUKAI. "A NEW FLUX-LIMITED DIFFUSION METHOD FOR NEUTRAL PARTICLE TRANSPORT CALCULATIONS." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1129768153.
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Vanson, Jean-Mathieu. "Interdépendence entre géométrie, adsorption et transport dans les matériaux à porosité hiérachique." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE040/document.
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Cette thèse, par une étude combinant modélisation et expériences, s'attache à comprendre l'interdépendance entre porosité, transport et adsorption dans les matériaux poreux hiérarchiques. Le transport et l'adsorption sont simulés dans les matériaux poreux à l'aide d'un modèle de Lattice Boltzmann étendu pour prendre en compte l'adsorption. Ce modèle mésoscopique permet de simuler le comportement d’un fluide présent au sein des pores du matériau ainsi que d'espèces en solution. La synthèse des matériaux poreux hiérarchiques par ice-templating et la caractérisation de la géométrie des échantillons par tomographie aux rayons X a permis de réaliser des simulations sur des géométries réelles. La comparaison des résultats de simulation et des résultats expérimentaux a prouvé la capacité du modèle à reproduire le comportement du fluide et des espèces dans le matériau. Grâce au modèle employé, l'interdépendance entre transport et adsorption a pu être mise en évidence, montrant notamment que le flux de fluide pouvait avoir une influence sur la densité adsorbée. Une étude sur l'influence de la géométrie et de la rugosité sur le couplage entre transport et adsorption a été menée sur des géométries bien caractérisées. Enfin, la modification du modèle de Lattice-Boltzmann pour rendre compte de l'effet d'un pic de traceurs a été développé. Cette modification permet notamment d'observer la cinétique hors régime stationnaire des traceurs dans le matériau et de rendre compte de l'effet du flux sur l'accessibilité des sites d'adsorptionThe aim of this work concerns the interplay between porosity, transport and adsorption in hierarchical porous materials. This work combine a simulation and an experimental approach. Transport and adsorption are simulated with a Lattice-Boltzmann model recently extended to take adsorption into account. This mesoscopic model allows to compute fluid and solute behavior in porous materials. The synthesis of hierarchical porous materials using ice-templating and the characterization of materials geometry with X-ray tomography allowed to compute simulations on real materials. The comparison between experimental and simualtion results have proved the efficency of the model to model fluid and species behavior in the materials. Using this model, the interplay between transport and adsorption have been studied highlighting an effect of the fluid flow on adsorbed density. The effect of roughness and material geometry have also been studied. Finally the modification of the modelallows now to simulate the kinematic of a pulse of species. This modification gives a tool to perform simulation in non-steady state flow and evaluate the adsorption site accessibility regarding to the flow field
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Nolting, Westly. "Electronic Transport in Thermoelectric Bismuth Telluride." ScholarWorks@UNO, 2012. http://scholarworks.uno.edu/td/1539.
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An experimental investigation of the electronic transport properties of bismuth telluride nanocomposite materials is presented. The primary transport measurements are electrical conductivity, Seebeck coefficient and Hall effect. An experimental apparatus for measuring Hall effect and electrical conductivity was designed, constructed and tested. Seebeck coefficient measurements were performed on a commercial instrument. The Hall effect and Seebeck coefficient measurements are two of the most important tools for characterizing thermoelectric materials and are widely used in the semiconductor industry for determining carrier types, carrier concentration and mobility. Further, these transport parameters are used to determine the thermal to electrical conversion efficiency of a thermoelectric material. The Boltzmann transport equation was used to analyze the Seebeck coefficient, carrier mobility and electrical conductivity as a function of carrier concentration for eleven samples. The relationship between the electronic transport and material/composite composition is discussed.
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Brosten, Tyler Ryan. "Flow and transport studies of porous systems by magnetic resonance microscopy and Lattice Boltzmann simulations." Diss., Montana State University, 2010. http://etd.lib.montana.edu/etd/2010/brosten/BrostenT0510.pdf.
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Nuclear magnetic resonance experiments and Lattice-Boltzmann simulations are powerful techniques for studying pore scale dynamics in porous media. Several applications of these methods to the study of pore scale hydrodynamics and transport are discussed. Of special interest are concepts relating to pore structure characterization. In the first application it is shown that nuclear magnetic resonance measurements of pre-asymptotic transport dynamics in random open cell foams provide a characteristic structure length scale. These measurements and Lattice-Boltzmann simulations for a model foam structure demonstrate dynamical behavior similar to lower porosity consolidated granular porous media; suggesting a generalized approach to pore structure characterization. Normalizing the data by the characteristic length collapses data for different foam samples and mono-disperse packed beds. The non-equilibrium statistical mechanics theory of pre-asymptotic dispersion is used to model the hydrodynamic dispersive dynamics. In the second application transport of hard sphere colloidal particles under flow through an open cell foam is studied using nuclear magnetic resonance. The temporal dynamics of the colloidal particles and suspending fluid phase are obtained through spectral chemical resolution. The data is interpreted in the broader context of classic hydrodynamic dispersion theory and mechanisms of transport for each phase. In the third application pore scale hydrodynamics of flow over a model porous surface are investigated using three dimensional Lattice-Boltzmann simulations and nuclear magnetic resonance. The Lattice-Boltzmann and nuclear magnetic resonance data are used to interpret classic interfacial hydrodynamic boundary conditions. Finally, in the fourth application a study of magnetic resonance microscopy to novel tape cast porous ceramics is conducted.
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Charpentier, Nicolas. "Théorie de Boltzmann chirale pour le transport dans les multicouches, électrons et photons, balistique et diffusif." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00675443.
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Cette thèse aborde le problème du transport diffusif dans les matériaux multicouches lorsque l'épaisseur des couches est comparable voire plus petit que le libre parcours moyen. Nous présentons un formalisme qui à la fois effectue une synthèse et permet d'aller au delà des divers modèles existants, dérive-diffusion, le modèle Valet-Fert, la méthode des flux ou encore le modèle de Fuchs-Sondheimer. Ce formalisme est applicable à deux types de structures: (i) la géométrie dite CPP (Current Perpendicular to Plane) où le courant moyen est perpendiculaire aux interfaces séparant les couches, et (ii) la géométrie dite CIP (Current In Plane) où le courant moyen est parallèle aux interfaces. Ce nouveau modèle de transport est bâti à partir d'une équation de Boltzmann où les collisions dans les couches et aux interfaces sont représentées par des intégrales de collision linéaires pouvant décrire aussi bien des réflexions spéculaires que des collisions aléatoires non nécessairement isotropes. La résolution de cette équation de Boltzmann pour déterminer les quantités macroscopiques locales d'intérêt se fait en trois étapes : pour chacune des couches, (1) la distribution locale des particules est séparée en deux " chiralités " caractérisés par le signe de la projection du vecteur vitesse de chaque particule le long de l'axe perpendiculaire aux interfaces ; (2) la description locale complète de la distribution angulaire des vitesses pour chaque chiralité est obtenue en développant sur une nouvelle base polynômes orthogonaux adaptée à l'existence de deux chiralités ; (3) pour effectuer la moyenne chirale sur la distribution angulaire des vitesses on définit une troncature minimale de ce développement adaptée aux quantités macroscopiques locales d'intérêt.L'étape (1) est nécessaire afin de pouvoir décrire correctement les collisions d'interfaces, l'étape (3) est usuelle mais l'ingrédient clef de ce formalisme est le point (2) qui seul permet de rendre cohérent les étapes (1) et (3) en présence d'interfaces. Pour la géométrie CPP, ce formalisme " Boltzmann chiral " permet d'unir les systèmes balistique et diffusif sous une même approche macroscopique. En présence de polarisation en spin, ce nouveau formalisme permet d'obtenir entre autre les résistances d'interfaces du modèle Valet-Fert en fonction des coefficients de transmission généralisés associés aux collisions d'interface. Pour les structures CIP, ce modèle permet d'obtenir des expressions analytiques pour les conductivités locales par couche (avec ou sans polarisation en spin) et de plus il rend le lien avec le transport CPP plus transparent. Ce formalisme n'étant pas propre au transport électrique, nous montrons sa versatilité sur une application au transport lumineux en revisitant le problème de Milne pour lequel nous retrouvons un résultat exact de façon beaucoup plus simple. Nous présentons pour terminer une méthode variationnelle fournissant une interprétation intéressante du modèle de Fuchs-Sondheimer.
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Ayodele, Segun Gideon [Verfasser]. "Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations in Non-equilibrium Transport Processes / Segun Gideon Ayodele." Aachen : Shaker, 2013. http://d-nb.info/1050344170/34.
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Mittal, Arpit. "Prediction of Non-Equilibrium Heat Conduction in Crystalline Materials Using the Boltzmann Transport Equation for Phonons." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1316471562.
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Gurrum, Siva P. "Thermal Modeling and Characterization of Nanoscale Metallic Interconnects." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10435.
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Temperature rise due to Joule heating of on-chip interconnects can severely affect performance and reliability of next generation microprocessors. Thermal predictions become difficult due to large number of features, and the impact of electron size effects on electrical and thermal transport. It is thus necessary to develop efficient numerical approaches, and accurate metal and dielectric thermal characterization techniques. In this research, analytical, numerical, and experimental techniques were developed to enable accurate and efficient predictions of interconnect temperature rise.
A finite element based compact thermal model was developed to obtain temperature rise with fewer elements and acceptable accuracy. Temperature drop across the interconnect cross-section was ignored. The compact model performed better than standard finite element model in two and three-dimensional case studies, and the predictions for a real world structure agreed closely with experimentally measured temperature rise.
A numerical solution was developed for electron transport based on the Boltzmann Transport Equation (BTE). This deterministic technique, based on the path integral solution of BTE within the relaxation time approximation, free electron model, and linear response, was applied to a constriction in a finite size thin metallic film. A correlation for effective conductance was obtained for different constriction sizes.
The Atomic Force Microscope (AFM) based Scanning Joule Expansion Microscopy (SJEM) was used to develop a new technique to measure thermal conductivity of thin metallic films in the size effect regime. This technique does not require suspended metal structures, and thus preserves the original electron interface scattering characteristics. The thermal conductivities of 43 nm and 131 nm gold films were extracted to be 82 W/mK and 162 W/mK respectively. These measurements were close to Wiedemann-Franz Law predictions and are significantly smaller than the bulk value of 318 W/mK due to electron size effects. The technique can potentially be applied to interconnects in the sub-100 nm regime.
A semi-analytical solution for the 3-omega method was derived to account for thermal conduction within the metallic heater. It is shown that significant errors can result when the previous solution is applied for anisotropic thermal conductivity measurements.
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Lindsay, Lucas R. "Theory of Phonon Thermal Transport in Single-walled Carbon Nanotubes and Graphene." Thesis, Boston College, 2010. http://hdl.handle.net/2345/1167.
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Thesis advisor: David A. BroidoA theory is presented for describing the lattice thermal conductivities of graphene and single-walled carbon nanotubes. A phonon Boltzmann transport equation approach is employed to describe anharmonic phonon-phonon, crystal boundary, and isotopic impurity scattering. Full quantum mechanical phonon scattering is employed and an exact solution for the linearized Boltzmann transport equation is determined for each system without use of common relaxation time and long-wavelength approximations. The failures of these approximations in describing the thermal transport properties of nanotubes is discussed. An efficient symmetry based dynamical scheme is developed for carbon nanotubes and selection rules for phonon-phonon scattering in both graphene and nanotubes are introduced. The selection rule for scattering in single-walled carbon nanotubes allows for calculations of the thermal conductivities of large-diameter and chiral nanotubes that could not be previously studied due to computational limitations. Also due to this selection rule, no acoustic-only umklapp scattering can occur, thus, acoustic-optic scattering must be included in order to have thermal resistance from three-phonon processes. The graphene selection rule severely restricts phonon-phonon scattering of out-of-plane modes. This restriction leads to large contributions to the total thermal conductivity of graphene from the acoustic, out-of-plane modes which have been previously neglected. Empirical potentials used to model interactions in carbon-based materials are optimized to better describe the lattice dynamics of graphene-derived systems. These potentials are then used to generate the interatomic force constants needed to make calculations of the thermal conductivities of graphene and carbon nanotubes. Calculations of the thermal conductivities of single-walled carbon nanotubes and graphene for different temperatures and lengths are presented. The thermal conductivities of SWCNTs saturate in the diffusive regime when the effects of higher-order scattering processes are estimated and correctly reproduce the ballistic limit for short-length nanotubes at low temperatures. The effects of isotopic impurity scattering on the thermal conductivities of graphene and SWCNTs are explored. Isotopic impurities have little effect in the low (high) temperature regime where boundary (umklapp) scattering dominates the behavior of the thermal conductivities. In the intermediate temperature regime, modest reductions in the thermal conductivities, 15-20%, occur due to impurities. The thermal conductivities of a wide-range of SWCNTs are explored. The thermal conductivities of successively larger-diameter, one-dimensional nanotubes approach the thermal conductivity of two-dimensional graphene
Thesis (PhD) — Boston College, 2010
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Physics
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Dugast, Florian. "Optimisation topologique en convection thermique avec la méthode de Lattice Boltzmann." Thesis, Nantes, 2018. http://www.theses.fr/2018NANT4056/document.
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L’optimisation des transferts de chaleur est un enjeu de recherche important pour améliorer les performances des systèmes énergétiques, notamment des échangeurs de chaleur. Cette optimisation peut s’appuyer sur différents leviers, comme le choix du régime d’écoulement, ou la modification de la géométrie de l’échangeur. C’est sur ce deuxième angle que nous avons travaillé au cours de cette thèse, en proposant une méthode d’optimisation topologique. Le nombre de paramètres impliqués dans cette méthode est important (plusieurs milliers). Une méthode à gradient est donc employée. Le calcul du gradient de la fonction de coût en fonction des paramètres de design est facilité par l’emploi d’une méthode adjointe. Le problème direct est résolu à l’aide de la méthode de Lattice Boltzmann (LBM). L’implémentation aisée des conditions aux limites dans l’algorithme LBM est un bénéfice pour l’optimisation topologique. De plus, la formulation de la LBM est explicite et hautement parallélisable, notamment sur les cartes graphiques (GPU), utilisées au cours de cette thèse. Ensuite le domaine d’optimisation est composé de fluide et de solide. Leur distribution est définie par une fonction Level- Set (LSF). Cette fonction est continue et le contour zéro définit précisément l’interface fluide/solide. La méthode d’optimisation développée a été testée et validée pour différents objectifs (minimisation de la température moyenne, maximisation de l’échange de chaleur) et contraintes (limitation des pertes de charges, porosité fixée)Heat transfer enhancement is an important research area to improve the efficiency of energy systems, especially for heat exchangers. There are different ways of optimizing such systems as the choice of flow regime or the modification on the fluid channels geometry. This thesis is focused on the latter option with the development of a topology optimization method. The number of design parameters involved in this technique is important (several thousands) so a gradient-based method is employed. The calculation of the cost function gradient with respect to the design variables is done with an adjoint-state method. The forward problem is solved with the Lattice Boltzmann Method (LBM). The simple implementation of the LBM boundary conditions is an interesting feature for topology optimization. The LBM algorithm is also highly parallelizable and GPU cards have been used in this thesis to obtain fast computational times. The efficiency of the LBM is important because the forward problem must be solved at each optimization step. Then, the optimization domain is composed of either solid of fluid elements. This material distribution is defined by a Level-Set Function (LSF). This is a continuous function in which the zero contour defines the fluid/solid interface, allowing an accurate description of both domains. The proposed optimization method has been tested for different objectives (minimization of the mean temperature, maximization of heat transfer rate) and constraints (pressure drops limitation, fixed porosity)
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Fiorentino, Eve-Agnès. "Phénomènes électrocinétiques et transport multiphasique en milieux poreux." Thesis, Strasbourg, 2016. http://www.theses.fr/2016STRAH008/document.
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Le coefficient d'électrofiltration est simulé par méthode Lattice Boltzmann dans un chenal 2-D sur une grande gamme de salinité. L'influence de la permittivité et de la viscosité est discutée. La validité de l'équation d'Helmholtz Smoluchowski à de forts potentiels zeta est évaluée. Un modèle de conductivité intrinsèque est développé en prenant en compte les variations locales de conductivité, qui ont un impact significatif en la présence d'espèces polyvalentes. Étendu aux conditions non saturées, l'algorithme montre que la densité de charge électrique associée à l'interface eau-air est une composante clé. Le coefficient présente une attitude non monotone, avec une augmentation par rapport à l'état saturé. L'amplitude de cette augmentation dépend de l'état dynamique des bulles, mobiles ou piégées. L'aspect transport multiphasique est complété par une étude numérique de l'impact de la forme des échantillons sur la mesure des lois reliant saturation et pression capillaire en hydrologieThe electrokinetic coefficient is simulated in a large range of salinities using the Lattice Boltzmann method in a 2-D channel. The effect of permittivity and viscosity is discussed. The validity of the Helmholtz Smoluchowski equation using strong zeta potentials is assessed. A model of bulk fluid conductivity is derived, taking into account the local variations of conductivity which have a significant impact in the presence of polyvalent counterions. Extended to unsaturated conditions, the model shows that the electrical charge density associated to the air-water interface is a key component. The coefficient shows a non monotonous behaviour, with an enhancement compared to the saturated state. The magnitude of this enhancement depends on the dynamic state of the bubbles, moving or entrapped. The multiphase transport aspect is associated to a numerical study of the influence of the sample geometry on the measurement of the capillary pressure / saturation relationships used in hydrology
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Rashid, Mohammad Zunaidur. "ATOMISTIC MODELING OF COUPLED ELECTRON-PHONON TRANSPORT IN NANOSTRUCTURES." OpenSIUC, 2021. https://opensiuc.lib.siu.edu/dissertations/1939.
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Electronics industry has been developing at a tremendous rate for last five decades and currently is one of the biggest industries in the world. The key to the rapid growth of electronics industry is innovation that made possible the constant scaling of transistors with reduced cost and improved performance. Scaling transistors were simpler at the beginning, but currently as the gate length of transistors has reached few nanometers, different short channel effects have emerged and power density of transistors has also increased drastically, which made further scaling much more challenging. To study electro-thermal transport in these reduced dimensionality devices, continuum models are no longer sufficient. In this work, the electrical and thermal transport properties have been modeled by solving Boltzmann Transport Equation (BTE) for electrons and phonons, respectively, using the Monte Carlo (MC) technique. To solve BTE for the phonons, a coupled Molecular Mechanics-Monte Carlo approach is employed where phonon band-structure is obtained using the atomistic modified Valence Force Field (VFF) model and is coupled with a Monte Carlo Phonon Transport kernel which solves the BTE for phonons. The phonon-phonon scattering is modeled in relaxation time approximation (RTA) using Holland’s formalism. Diffusive boundary scattering for phonons has been modeled using the Beckmann-Kirchhoff (B-K) surface roughness scattering model taking into account the effects of phonon wavelength, incident angles and degree of surface roughness. The effect of rough surface on longitudinal acoustic (LA) and transverse acoustic (TA) phonon branches has been studied with the help of the B-K model and it has been found that, at elevated temperatures, there is less backscattering to the LA branch due to rough surface. Effort has been made then to couple the developed phonon Monte Carlo transport simulator with an electron Monte Carlo transport simulator to study the origin and effects of self-heating in a nanoscale field-effect transistor (FET). In contrast to the widely used continuum model, where Fourier heat diffusion equation is usually solved to describe the thermal transport, the simulator developed in this dissertation treats both the electrons and the phonons at the particle level. Acoustic and intervalley g and f type electron-phonon scattering mechanisms are considered and the resulting local temperature modification has been used to bridge the electron and phonon transport paths. Phonon transport at the oxide-silicon interface has been modeled using the Diffuse Mismatch (DM) model, whereas, the phonons in the oxide have been described using the Debye model and temperature and frequency dependent relaxation time. The simulator is then benchmarked and used to study the electron-phonon transport processes in a FinFET device with a gate length of 18 nm, channel width of 4 nm, and a fin height of 8 nm. Preliminary results show that there can be a current degradation of as high as ~9.56% due to self-heating effect. Also, temperature in the entire channel region could rise due to self-heating. The maximum temperature rise in the channel region is found to be ~30K.
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Dziekan, Thomas. "Electronic Transport in Strained Materials." Doctoral thesis, Uppsala University, Department of Physics and Materials Science, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8471.
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In this thesis the conductivity of strained materials has been investigated using density functional theory and a semiclassical transport theory based on the Boltzmann equation.
In transition metals trends are reproduced without adjustable parameters. The introduction of one temperature dependent cross section allowed the reproduction of resistivity trends between 10 and 1000K.
The effect of strain on transition metals in bcc and fcc structure was studied deforming the unit cell along the tetragonal deformation path. The anisotropy of the conductivity varied on wide range of the c/a-ratio. The orbitals at the Fermi level determined the principal behavior. Pairs of elements with permutated number of electrons and holes in the 4d band showed similar behavior. The concept of the tetragonal deformation was also applied on semiconductors.
The deformation of Vanadium in X/V superlattices (X=Cr,~Fe,~Mo) due to Hydrogen loading depends on the properties of X. It was found that counteracting effects due to the presence of Hydrogen influence the conductivity.
It is shown that a small magnetic moment of the V host reduces the hydrogen solubility. Depending on the magnitude of the tetragonal distortion of V, the hydrogen dissolution becomes favored for larger moments.
Finally, extra charge filling of the bandstructure of Cr and Mo decreases the Fermi velocity and increases the density of states at the Fermi energy.
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Sanja, Ožvat. "One-dimensional mathematical modeling of flow and sediment transport in open channels using the lattice Boltzmann method." Phd thesis, Univerzitet u Novom Sadu, Fakultet tehničkih nauka u Novom Sadu, 2019. https://www.cris.uns.ac.rs/record.jsf?recordId=108606&source=NDLTD&language=en.
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A one-dimensional unsteady open-channel flow with sediment transport lattice Boltzmann model is developed. The unsteady water flow model is based on the discharge-water level definition of the Saint-Venant equations. For the sediment active-layer concept is used. Geometrical transformations are applied to the governing equations, in order to transform non-uniform physical spatial grid, characteristic for natural geometry, into an uniform computational grid. New form of equilibrium distribution functions is derived. Bifurcation boudary conditions suitable with the lattice Bolcmann method are derived. Verification of the proposed model is obtained by testing unsteady flow model on three cases: steday flow in a prismatic channel, usteady flow in an unprismatic channel and unsteady flow in a natural watercourse – Danube River case study. Sediment transport model is tested on two cases:
advection-diffusion in a prismatic channel and unsteady flow with sediment transport in a natural watercouse – Danube River case study.
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Ali, Syed Ashraf. "Phonon Boltzmann Transport Equation (BTE) Based Modeling of Heat Conduction in Semiconductor Materials at Sub-Micron Scales." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1482776207590992.
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Scheben, Fynn. "Iterative methods for criticality computations in neutron transport theory." Thesis, University of Bath, 2011. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545319.
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This thesis studies the so-called “criticality problem”, an important generalised eigenvalue problem arising in neutron transport theory. The smallest positive real eigenvalue of the problem contains valuable information about the status of the fission chain reaction in the nuclear reactor (i.e. the criticality of the reactor), and thus plays an important role in the design and safety of nuclear power stations. Because of the practical importance, efficient numerical methods to solve the criticality problem are needed, and these are the focus of this thesis. In the theory we consider the time-independent neutron transport equation in the monoenergetic homogeneous case with isotropic scattering and vacuum boundary conditions. This is an unsymmetric integro-differential equation in 5 independent variables, modelling transport, scattering, and fission, where the dependent variable is the neutron angular flux. We show that, before discretisation, the nonsymmetric eigenproblem for the angular flux is equivalent to a related eigenproblem for the scalar flux, involving a symmetric positive definite weakly singular integral operator(in space only). Furthermore, we prove the existence of a simple smallest positive real eigenvalue with a corresponding eigenfunction that is strictly positive in the interior of the reactor. We discuss approaches to discretise the problem and present discretisations that preserve the underlying symmetry in the finite dimensional form. The thesis then describes methods for computing the criticality in nuclear reactors, i.e. the smallest positive real eigenvalue, which are applicable for quite general geometries and physics. In engineering practice the criticality problem is often solved iteratively, using some variant of the inverse power method. Because of the high dimension, matrix representations for the operators are often not available and the inner solves needed for the eigenvalue iteration are implemented by matrix-free inneriterations. This leads to inexact iterative methods for criticality computations, for which there appears to be no rigorous convergence theory. The fact that, under appropriate assumptions, the integro-differential eigenvalue problem possesses an underlying symmetry (in a space of reduced dimension) allows us to perform a systematic convergence analysis for inexact inverse iteration and related methods. In particular, this theory provides rather precise criteria on how accurate the inner solves need to be in order for the whole iterative method to converge. The theory is illustrated with numerical examples on several test problems of physical relevance, using GMRES as the inner solver. We also illustrate the use of Monte Carlo methods for the solution of neutron transport source problems as well as for the criticality problem. Links between the steps in the Monte Carlo process and the underlying mathematics are emphasised and numerical examples are given. Finally, we introduce an iterative scheme (the so-called “method of perturbation”) that is based on computing the difference between the solution of the problem of interest and the known solution of a base problem. This situation is very common in the design stages for nuclear reactors when different materials are tested, or the material properties change due to the burn-up of fissile material. We explore the relation ofthe method of perturbation to some variants of inverse iteration, which allows us to give convergence results for the method of perturbation. The theory shows that the method is guaranteed to converge if the perturbations are not too large and the inner problems are solved with sufficiently small tolerances. This helps to explain the divergence of the method of perturbation in some situations which we give numerical examples of. We also identify situations, and present examples, in which the method of perturbation achieves the same convergence rate as standard shifted inverse iteration. Throughout the thesis further numerical results are provided to support the theory.
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Christensen, Adam Paul. "Multiscale modeling of thermal transport in gallium nitride microelectronics." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31681.
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Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2010.Committee Chair: Samuel Graham; Committee Member: Donald Dorsey; Committee Member: Douglas Yoder; Committee Member: Michael Leamy; Committee Member: Sankar Nair; Committee Member: Zhuomin Zhang. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Nghiem, Thi Thu Trang. "Numerical study of electro-thermal effects in silicon devices." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00827633.
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The ultra-short gate (LG < 20 nm) CMOS components (Complementary Metal-Oxide-Semiconductor) face thermal limitations due to significant local heating induced by phonon emission by hot carriers in active regions of reduced size. This phenomenon, called self-heating effect, is identified as one of the most critical for the continuous increase in the integration density of circuits. This is especially crucial in SOI technology (silicon on insulator), where the presence of the buried insulator hinders the dissipation of heat.At the nanoscale, the theoretical study of these heating phenomena, which cannot be led using the macroscopic models (heat diffusion coefficient), requires a detailed microscopic description of heat transfers that are locally non-equilibrium. It is therefore appropriate to model, not only the electron transport and the phonon generation, but also the phonon transport and the phonon-phonon and electron-phonon interactions. The formalism of the Boltzmann transport equation (BTE) is very suitable to study this problem. In fact, it is widely used for years to study the transport of charged particles in semiconductor components. This formalism is much less standard to study the transport of phonons. One of the problems of this work concerns the coupling of the phonon BTE with the electron transport.In this context, wse have developed an algorithm to calculate the transport of phonons by the direct solution of the phonon BTE. This algorithm of phonon transport was coupled with the electron transport simulated by the simulator "MONACO" based on a statistical (Monte Carlo) solution of the BTE. Finally, this new electro-thermal simulator was used to study the self-heating effects in nano-transistors. The main interest of this work is to provide an analysis of electro-thermal transport beyond a macroscopic approach (Fourier formalism for thermal transport and the drift-diffusion approach for electric current, respectively). Indeed, it provides access to the distributions of phonons in the device for each phonon mode. In particular, the simulator provides a better understanding of the hot electron effects at the hot spots and of the electron relaxation in the access.
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Rosén, Tomas. "Determination of water saturation dependent gas transport properties of PEFC gas diffusion layers via the Lattice Boltzmann method." Thesis, KTH, Mekanik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-41814.
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Lantermann, Udo. "Simulation der Transport- und Depositionsvorgänge von Nanopartikeln in der Gasphase mittels Partikel-Monte-Carlo- und Lattice-Boltzmann-Methoden." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98136439X.
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Jörres, Christian Verfasser], Michael [Akademischer Betreuer] [Herty, Martin [Akademischer Betreuer] Frank, and Lorenzo [Akademischer Betreuer] Pareschi. "Numerical methods for Boltzmann transport equations in radiotherapy treatment planning / Christian Jörres ; Michael Herty, Martin Frank, Lorenzo Pareschi." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://d-nb.info/1129787443/34.
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