Este trabalho constitui-se numa monografia para ser apresentada como requisito para o título de Doutor em Ciências dentro do Programa de Pós-Graduação em Física da Universidade Federal do Rio Grande do Sul. Faz parte da pesquisa teórica desenvolvida pelo Grupo de Física de Plasmas do IF-UFRGS, e tem por objetivo participar do esforço de tornar comercialmente viável a tecnologia de fusão termonuclear como fonte geradora de energia elátrica. Conhecimento científico e tecnológico que é imprescindível para um país em desenvolvimento como o Brasil. Dentro deste contexto, o trabalho desenvolvido segue a linha de pesquisa do estudo de processos de geraçãao de correntes em tokamaks por meio de interações onda-partícula. Assim, estudamos os efeitos devido a ocorrência de transporte radial de partículas em um tokamak na eficiência de geração de corrente devido a ondas de radio freqüência (RF), na presença de barreiras internas de transporte (ITB - Internal Transport Barriers). Para isso, considerou-se dois casos: no primeiro, a geração de corrente ocorre devido somente a ondas do tipo híbrida inferior (LH - Lower Hybrid), e no segundo, a geração com ação combinada das ondas LH e do tipo eletrônica de cíclotron (EC - Electron Cyclotron). Os resultados foram obtidos por solução numérica da equação de Fokker-Planck que rege a evolução da função distribuição de elétrons. Nós consideramos que o transporte radial de partículas pode ser devido a utuações magnéticas ou eletrostáticas. Considerando ambos os tipos de utuações, a eficiência da geração de corrente mostrou um crescimento com o crescimento das utuações que originam o transporte. A dependência da eficiência da geração de corrente na profundidade e posição da barreira também foi investigada. / This work constitutes a monograph to be presented as requirement to the title of PhD at the Physics Graduate Program at Federal University of Rio Grande do Sul. It is part of a theoretical research developed by the Plasma Physics Group of the IF-UFRGS, and it have the purpose to participe on the e ort to make feasible the thermonuclear fusion technology as a source of electric energy. Scienti c and technological knowledge that are indispensable to a developing country as the Brazil. In that context, the work under development follows the research line of the study of the process of current drive in tokamaks by means of wave-particle interaction. Therefore, we studied the e ects due to the occurrence of radial transport of particles in a tokamak on the e ciency of current drive due the radio frequency waves (RF), in the presence of an Internal Transport Barrier (ITB). For this, we consider two cases: at rst, the current drive occur due to Lower Hybrid waves (LH) only, and at second case, the current drive with combined action of LH and Electron Cyclotron (EC) waves. The present results are obtained by numerical solution of the Fokker-Planck equation which rules the evolution of the electron distribution function. We assume that the radial transport of particles can be due to magnetic or to eletrostatic utuations. It considering both the utuations types, the e ciency of current drive is shown to increase with the increase of the utuations which originate the transport. The dependence of the current drive e ciency on the depth and position of the barrier is also investigated.

Cette thèse a pour objectif d'étudier la dynamique spatio-temporelle des atomes refroidis par laser dans un piège magnéto-optique (PMO). Il a été montré qu'un nuage d'atomes froids dans le régime de diffusion multiple peut présenter un comportement instable sans modulation externe du système. Cependant, ces instabilités n'ont pas encore été modélisées de façon satisfaisante. Une nouvelle configuration du PMO a été mise en oeuvre pour tenter d'étudier des instabilités dans une seule direction. Ce PMO, qualifié d'anisotrope, n'utilise pas des lasers de mêmes fréquences dans chaque direction de l'espace. Il met en évidence les forts couplages existants entre les directions du piège, si bien qu'il n'est pas possible de l'utiliser pour réduire le nombre de dimensions dans lesquelles les instabilités s'établissent. Toutefois, cette étude constitue un premier pas vers une meilleure description tridimensionnelle du piège. Elle nous a notamment permis de mesurer la probabilité pour qu'un photon diffusé soit réabsorbé à l'intérieur du nuage. Cette quantité est caractéristique du PMO mais elle n'avait jusqu'à là jamais été mesurée. Nous avons également établi un modèle spatio-temporel unidimensionnel du PMO. Il est constitué d'un système d'équations non-linéaires couplées reliant la densité atomique et les intensités des faisceaux lasers. Ce système contient notamment une équation de Vlasov-Fokker-Planck, rencontrée dans de nombreux domaines de la physique. Des simulations numériques ont été effectuées dans un cas simple. D'un point de vue expérimental, l'utilisation d'une caméra rapide nous a permis de mettre en évidence la structure spatiale d'instabilités de type stochastique. / The aim of this thesis is to study the spatio-temporal dynamics of laser cooled atoms in a magneto-optical trap (MOT). Recent works have shown that in the multiple scattering regime, an atomic cloud can have an unstable behavior without external modulation of the system. Nevertheless, these instabilities have not yet been modeled in a satisfactory way. A new configuration of the MOT has been built up as a possible way to study instabilities in only one direction. This trap, called anisotropic MOT, is not made of laser beams with the same laser frequencies along each direction of space. It exhibits the strong couplings between the directions of the trap, with the result that it cannot be used to reduce the number of directions in which instabilities grow up. However, this study can be considered as a new step to a better 3D description of the MOT physics. In particular, it gives us a way to measure the probability that a scattered photon is reabsorbed inside the atomic cloud. This quantity is a characteristic of the MOT but it has never been measured so far. We also develop a 1D spatio-temporal model of the MOT. It consists in a set of coupled nonlinear equations linking the atomic density and the laser intensities. This set contains a Vlasov-Fokker-Planck equation which is used to model a lot of systems in various fields and not only in physics. Numerical simulations have been done in a simple case. In the experiment, the use of a fast video camera allows us to observe the spatial structure of one type of instabilities, the so-called stochastic instabilities.

In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).

No description available.

We extend sociodynamic modeling of the financial business cycle to the Euro Area and Japan. Using an opinion-formation model and machine learning techniques we find stable model estimation of the financial business cycle using central bank lending surveys and a few selected macroeconomic variables. We find that banks have asymmetric response to good and bad economic information, and that banks adapt to their peers' opinions when changing lending policies.

Collision strength, the measure of strength for a binary collision, hasn't been defined clearly. In practice, many physical arguments have been employed for the purpose and taken for granted. A scattering angle has been widely and intensively used as a measure of collision strength in plasma physics for years. The result of this is complication and unnecessary approximation in deriving some of the basic kinetic equations and in calculating some of the basic physical terms. The Boltzmann equation has a five-fold integral collision term that is complicated. Chandrasekhar and Spitzer's approaches to the linear Fokker-Planck coefficients have several approximations. An effective variable-change technique has been developed in this dissertation as an alternative to scattering angle as the measure of collision strength. By introducing the square of the reduced impulse or its equivalencies as a collision strength variable, many plasma calculations have been simplified. The five-fold linear Boltzmann collision integral and linearized Boltzmann collision integral are simplified to three-fold integrals. The arbitrary order linear Fokker-Planck coefficients are calculated and expressed in a uniform expression. The new theory provides a simple and exact method for describing the equilibrium plasma collision rate, and a precise calculation of the equilibrium relaxation time. It generalizes bimolecular collision reaction rate theory to a reaction rate theory for plasmas. A simple formula of high precision with wide temperature range has been developed for electron impact ionization rates for carbon atoms and ions. The universality of the concept of collision strength is emphasized. This dissertation will show how Arrhenius' chemical reaction rate theory and Thomson's ionization theory can be unified as one single theory under the concept of collision strength, and how many important physical terms in different disciplines, such as activation energy in chemical reaction theory, ionization energy in Thomson's ionization theory, and the Coulomb logarithm in plasma physics, can be unified into a single one -- the threshold value of collision strength. The collision strength, which is a measure of a transfer of momentum in units of energy, can be used to reconcile the differences between Descartes' opinion and Leibnitz's opinion about the "true'' measure of a force. Like Newton's second law, which provides an instantaneous measure of a force, collision strength, as a cumulative measure of a force, can be regarded as part of a law of force in general.

Orientador: Elso Drigo Filho / Banca: João Ruggiero Neto / Banca: Mario José de Oliveira / Banca: Nelson Augusto Alves / Banca: Waldemar Donizete Bastos / Resumo: Este trabalho versa sobre o emprego da equação de Fokker-Planck (EFP) na descrição da difusão através de canais iônicos presentes na estrutura celular. Os canais possuem grande importância para o funcionamento celular por promoverem o equilíbrio químico entre o meio interno e externo da célula. Este controle do equilíbrio químico é diretamente relacionado à sua capacidade de abertura e fechamento (gating) e seletividade. Inicialmente fazemos uma breve apresentação da equação de Fokker- Planck mostrando sua relação com a equação de Langevin e os métodos de solução para diferentes modelos. Dentre os modelos mencionados focamos a adoção de diferentes dependências temporais no termo referente ao drift e no coeficiente de difusão. Para estes casos as soluções foram obtidas por meio de um ansatz. Em seguida, buscamos associar estes modelos matemáticos de EFP com a difusão através de canais iônicos, mas desconsiderando o gating. Esta associação é feita através da descrição da mudança de potencial na membrana plasmática quando íons fluem entre o meio interno e externo da célula. Outro aspecto abordado em um dos modelos foi descrever a difusão quando há o fechamento do canal com o tempo. O resultado obtido para este exemplo foi comparado a dados da literatura. Por fim, apresentamos uma breve discussão sobre a equação de Fokker-Planck em um sistema de coordenadas cilíndricas / Abstract: This work focus on the use of the Fokker-Planck equation (FPE) to describe the diffusion through ionic channels located in the cell membrane. The channels are responsible by the control of the ionic chemical equilibrium between the internal and external cell environment. The regulation of the chemical equilibrium is related to its capacity of opening and closing (gating) and its selectivity. Initially, we brief by present of the Fokker-Planck equation, where we show its relation with the Langevin equation and the methods of solution to different models. Among the models mentioned, we focus on adoption of different temporal dependence in the drift term and diffusion coefficient. The solutions for these cases are obtained by an ansatz that satisfies the boundary conditions of the models. We associate these mathematic models of FPE with diffusion through ionic channels without consider the gating process. This association is done describing the change of the membrane potential when there is diffusion of ions between the inside and outside of the cell. Another aspect described by one of the models is the diffusion when there is the closing of the channel with the time. The result obtained for this case is compared with results from the literature. Finally, we present a brief discussion of the Fokker-Planck equation in a cylindrical coordinate system / Doutor

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21585号 / 理博第4492号 / 新制||理||1645(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 谷村 吉隆, 教授 林 重彦, 教授 寺嶋 正秀 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23000号 / 理博第4677号 / 新制||理||1671(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川合 光, 教授 田中 貴浩, 准教授 吉岡 興一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Sedimenting suspensions exist in a varity of natural phenomena and industrial applications. It is already observed in experiments that the dilute fibre suspensions experience a hydrodynamics instability under gravity at low Reynolds numbers. Initially well-mixed suspensions become inhomogeneous and anisotropic due to this instability.The main goal of this work is to understand the instability in a dilute fibre suspension by means of an Eulerian approach which is based on the Navier-Stokes equations coupled to Fokker-Planck equation for the PDF of fibres.Using a linear stability analysis, we show that inertia and hydrodynamic translational diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. For small, but finite Reynolds number of the fluid bulk motion, the most unstable wavenumber is a finite value which increases with Reynolds number, and where the diffusion narrows the range of unstable wavenumbers. With periodic boundary conditions, numerical simulations of the full non-linear evolution in time of a normal mode perturbation show that the induced flow may either die or saturate on a finite amplitude. The character of this long time behaviour is dictated by the wavenumber and the presence or absence of the translational and rotational diffusivities.In a simulation domain confined by vertical walls, a series of alternating structures of risers and streamers emerge continuously from the walls until they meet in the middle of the domain. For moderate times, this agrees qualitatively with experimental and theoretical results. Moreover, our simulation in a vessel of infinite height obtained an increasing wavelength evolution due to the congregation of the streamers or risers. In the end, there is constantly only one streamer left, and it drifts randomly to one side of the container until the evolution reaches a steady state. It is also found that the perturbations added to the initial conditions can induce more high density regions whose sizes and velocities are strongly linked to the initial perturbations of the number density or the flow field. In addition, the maximum number of streamers increases with Reynolds number, volume fraction and channel width. / QC 20120625