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Dissertação (mestrado)—Universidade de Brasília, Instituto de Física, 2006. / Submitted by leandro spinola (l.spinolafla@gmail.com) on 2009-11-17T17:17:46Z No. of bitstreams: 1 FábioMacêdoMendes.doc: 754688 bytes, checksum: a319a1b3ed09a4a5ade0e96b65b15db5 (MD5) / Approved for entry into archive by Carolina Campos(carolinacamposmaia@gmail.com) on 2009-11-17T18:18:18Z (GMT) No. of bitstreams: 1 FábioMacêdoMendes.doc: 754688 bytes, checksum: a319a1b3ed09a4a5ade0e96b65b15db5 (MD5) / Made available in DSpace on 2009-11-17T18:18:18Z (GMT). No. of bitstreams: 1 FábioMacêdoMendes.doc: 754688 bytes, checksum: a319a1b3ed09a4a5ade0e96b65b15db5 (MD5) Previous issue date: 2006-04 / Estudo sobre os fundamentos estatísticos da termodinâmica com ênfase na fórmula da entropia de Boltzmann e os métodos de contagem também introduzidos por ele. Ao adotar umponto de vistamoderno sobre o significado das probabilidades, a termodinâmica segue, com pouquíssimas adições e de maneira bastante geral, apenas da identificação S(X) = ln P(X). Ao enfatizar o modelo estatístico em oposição a leis da física, nossa apresentação não fica restrita ao equilíbrio e nem a fórmulas predeterminadas para a entropia. Seguindo este quadro conceitual unificado, esboçamos um formalismo de não-equilíbrio bastante incipiente e introduzimos o conceito de entropia generalizada de maneira bastante natural, onde vemos que a forma usual decorre de uma hipótese com algum apelo físico, mas estritamente desnecessária. ________________________________________________________________________________________ ABSTRACT / An study on the statistical foundations of thermodynamicswhich emphasizes Boltzmann’s counting procedures and entropy formula. Once one adopt a modern point of view regarding themeaning of probabilities, thermodynamics follows, with very fewadditions and in a very general fashion, just from the identification S(X) = k ln P(X). By choosing to focus on the statistical model instead of physical law, our description isn’t stuck to equilibrium situations and neither to predefined entropy formulas. A seminal non-equilibriumformalismis presented and the concept of generalized entropies follows on a very natural fashion where the usual formula is implied by an hypothesis with some physical appeal, but strictly unnecessary.

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Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The differential-operator approximation to the linear Boltzmann operator (the Master equation operator) has been studied by several authors. In 1960 Siegel proposed a systematic approach called the CD expansion. He represents the approximating series in terms of creation and destruction operators for Hermite functions. In this thesis we study the physical meaning of a small parameter which usually exists in the CD expansion and which ensures the convergence of the series. We also establish the CD-expansion formalism for N-dimensional processes and initiate the study of the CD-expansion of the linear Boltzmann collision operator in the kinetic theory of gases. In the case of one-dimensional processes; the models we study are the density fluctuations with a particle reservoir of finite volume, Alkemade's diode model, and Rayleigh disk. We find that the expansion parameter is the ratio of the average microscopic agitation interval to the macroscopic relaxation time. We further prove that this ratio is equal to the ratio of the average variance of the discontinuity of the random process determined by the linear. Boltzmann operator to the variance of the macroscopic observable at equilibrium. Since the CD expansion is an expansion with respect to the parameter of discontinuity, the expansion series reduces to the Fokker-Planck operator in the limiting case where the parameter becomes zero. In the N-dimensional formalism, we use tensor Hermite polynomials and find a formalism valid for processes of any finite dimensionality. In extending the study to the kinetic theory of gases, we establish a method of obtaining derivate moments directly from the collision operator, and obtain a formula for the Hermite coefficients of derivate moments for an arbitrary force field. We propose the CD hypothesis: The terms of the CD expansion are homogeneous and of successively increasing order in the parameter of discontinuity of the process. This hypothesis I holds for all the models we study in the one-dimension case. In three-dimensional collision processes it holds for an intermolecular force field obeying an inverse power law and for rigid spheres. Beyond these cases, the necessary and sufficient conditions for the hypothesis are rather complicated. A sufficient condition is, however, that the scattering cylinder (scattering cross section multiplied by the magnitude of the relative velocity) be a homogeneous function of the magnitude of the relative velocity. In addition to the general results mentioned in the above, we obtain a number of particular results. Special cases of our density fluctuation model are the density fluctuations studied by van Kampen (1961), and Ehrenfest's urn model. We also introduce an isotropic Maxwellian particle which corresponds to s-wave scattering in wave mechanics, and which yields the CD expansion in a diagonal form. / 2999-01-01

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This investigation is concerned with the evaluation and interpretation of the propagator, or conditional probability distribution function P(y,t| y0), of the Linear Boltzmann or Master equation from the "central limit viewpoint". We have obtained what is to our knowledge the first evaluation in series of the propagator for the typical kinetic-theoretical processes studied here, which are those underlying the problems usually studied in the approximation of the Fokker-Planck equation. We have been able to put the successive terms of this series in closed form; and have shown that the series can be interpreted as a generalized solution of the central limit problem of mathematical probability theory, the generalization consisting in the extension to a process in continuous time with non-independent increments. [TRUNCATED] / 2999-01-01

O presente trabalho pretende discutir o papel da noção de modelo dentro da Bildtheorie, ou concepção-Bild, de Boltzmann por meio de uma reconstrução parcial das visões sobre a Natureza e sobre a Ciência deste cientista-filósofo austríaco, em termos de imagem científica de natureza e imagem filosófica de ciência. Queremos destacar as contribuições epistemológicas de Boltzmann para a Física e para a Filosofia da Ciência a partir de sua concepção de mundo (Weltanschauung), baseadas em uma visão mecânico-estatística de natureza e em suas posturas filosóficas pautadas pelo pluralismo, pelo representacionalismo e pelo naturalismo (bem como sua defesa ao atomismo, ao método hipotético-dedutivo, a bem da criatividade científica). Consideramos estes os elementos fundamentais para a compreensão do papel da noção de modelo dentro da ecologia cognitiva global boltzmanniana, papel que se nos parece fundamental para a manutenção da coerência desta estrutura global. / The present work intends to discuss the role of the notion of the model within Boltzmann\'s Bildtheorie, or conception-Bild, by means of a partial reconstruction of the visions on the Nature and on the Science of this Austrian scientist-philosopher, in terms of scientific image of nature and philosophical image of science. We want to emphasize Boltzmann\'s epistemological contributions to Physics and to the Philosophy of Science from his world\'s conception (Weltanschauung), based on a mechanical-statistical view of nature and its philosophical positions guided by pluralism, representationalism and naturalism (as well as his defense of atomism, the hypothetical-deductive method, for the sake of scientific creativity). We consider these the fundamental elements for the understanding the role of the notion of the model within Boltzmann\'s global cognitive ecology, role that seems fundamental to the maintenance of the coherence of his global structure.

En raison de la tendance positives pour le développement durable, les systèmes solaires(capteurs solaires, concentrateur solaire, etc.) Intègrent (et demandent d'intégrer encore plus)intensivement les résidences et les industries. Dans ce contexte, les systèmes diphasiques comme le caloduc semblent être très efficaces en raison de leurs capacités élevées de transport de chaleur et de leur fonctionnement passif appliqués aux capteurs. Compte-tenu de la complexité des caloducs à structure poreuse dans ce type d'application, la plupart des systèmes existants sur le marché utilisent des thermosiphons. Ainsi, le besoin croissant de solutions de contrôle thermique fiables et plus efficaces croit rapidement pour de tels systèmes.Ce travail de thèse porte sur la caractérisation des performances des caloducs à structure poreuse utilisés dans les applications solaires. Une étude numérique a été réalisée pour modéliser et simuler le comportement d'un caloduc typique à l'aide de la méthode Lattice Boltzmann. Une étude expérimentale a également été réalisée pour caractériser les performances de trois prototypes testes dans différentes conditions (température du condenseur, puissance introduite et angle d'inclinaison). Les effets induits par plusieurs paramètres incluant le taux de remplissage, le fluide de travail et la symétrie de la puissance appliquée sur les performances de ces dispositifs ont également été étudiés. En particulier, l'asymétrie du chauffage induit un assèchement plus précoce, toutes choses étant égales par ailleurs. L'inclinaison optimale est également déterminée là où est équilibrée la chaleur solaire maximale disponible et reçue par le caloduc et l'écoulement de liquide assisté par gravité à l'intérieur de ce dispositif. / Owing to the trend to development sustainability, solar systems (solar collector, solar concentrator, etc.) Are integrating (and asked to integrate even more) intensively residences and industries. In this context, two-phase systems like heat pipe seem highly effective because of their high heat transport capabilities and their passive operation in collectors’ technology. In view of the complexity of the heat pipes with a porous structure in this kind of application,most of the existing systems on the market use thermosyphons. Thus, the growing need of reliable and more efficient thermal control solutions is increasing for such systems. This thesis work focuses on the performance characterization of heat pipes with porous structure used in solar applications. A numerical study has been performed to model and simulate the behavior of a typical heat pipe using the Lattice Boltzmann method. An experimental study has also been done to characterize the performance of three prototypes tested under different conditions (condenser temperature, heat input and inclination angle). The effects induced by several parameters including the filling rate, working fluid and symmetry of the applied heat on the performance of these devices has also been investigated. In particular, heating asymmetry is found to induce dry-out earlier, all other things being equal. Optimal inclination is also determined where is balanced the maximum solar heat available and received by the heat pipe and the gravity-assisted liquid flow inside that device.

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

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 . / ....

Aurorae often break down into elongated filaments parallel to the geomagnetic field lines (B) with cylindrically symmetric structures. The object of this thesis is to study the ion distribution function and transport properties in response to the sudden introduction of a radial electric field (E) in such a cylindrical geometry. Both collision-free and collisional situations are considered.<p> The thesis starts by solving a collision-free problem where the electric field is constant in time but increases linearly with radius, while the initial ion density is uniform in space. The attendant Boltzmann equation is solved by tracking the ions back in time, thereby using the temporal link between the initial position and velocity of an ion and its position and velocity at an arbitrary time and place. Complete analytical solutions show that the ion distribution function is a pulsating Maxwellian in time, and all transport parameters (e.g., bulk speed, temperature, etc.) oscillate in time but independent of radius. If the ion-neutral collisions are taken into account by employing a simple relaxation model, analytical solutions are also obtained. In this case, the ion distribution function can be driven to horseshoe shapes which are symmetric with respect to the ExB direction. The bulk parameters evolve in a transition period of the order of one collision time as they go from oscillating to the non-oscillating steady state.<p> In more realistic electric field structures which are spatially inhomogeneous but still constant in time, a generalized semi-numerical code is developed under collision-free conditions. This code uses a backmapping approach to calculate the ion velocity distribution and bulk parameters. With arbitrarily selected electric field rofiles, calculations reveal various shapes of ion velocity distribution functions (e.g., tear-drop, core-halo, ear-donut, etc). The associated transport properties are also obtained and discussed.<p> Under both collision-free and collisional conditions, the effect of the density inhomogeneities at the initial time is studied in an electric field which is proportional to radius and constant in time. With two profiles of the initial ion density for the collision-free case, and one profile for the collisional case, complete analytical solutions are obtained. The results reveal that the distribution function and the bulk properties are now strongly dependent on radial position.<p> If the radial electric field is unable to stay constant with time but modulated by in-coming charged particles, a fluid formalism is used to study the excitation of several plasma waves under different kinds of initial conditions. These identified waves include the ion cyclotron oscillation, the ion and electron upper-hybrid oscillations, and the lower-hybrid oscillation.<p> The results of this thesis are expected to be applicable to high-resolution observations. Future work should also include the mirror effect and the formation of conics in velocity space. Finally, the velocity distributions obtained in this thesis could trigger various plasma instabilities, and this topic should also be looked at in the future.