Orientador: Gerson Francisco / Coorientador: Fernando Fagundes Ferreira / Banca: Mauro Copelli / Banca: Ricardo Luiz Viana / Banca: Paulo Laerte Natti / Banca: Tiago Pereira da Silva / Resumo: Este texto é dedicado ao estudo do fenômeno de sincronização no modelo de Kuramoto. Na primeira parte o foco reside na formulação original do modelo no limite termodinâmico de infinitos osciladores e na descrição da transição para a sincronização e estabilidade das soluções em sistemas com número finito de elementos. Mostra-se também que o acoplamento crítico de sincronização 'K IND s' é determinado por um par de equações, e a solução para um caso especial com simetria na configuração de frequências naturais é obtida de forma perturbativa. A segunda parte do texto é focada na descrição do modelo de Kuramoto com acoplamento local em 1 dimensão com condições periódicas de contorno. A estrutura de árvores de sincronização média é descrita, onde ocorrem transições entre regimes caóticos e periódicos dos movimentos individuais dos osciladores. A iminência da sincronização é explorada através uma série de aproximações que mostram o comportamento crítico característico de uma bifurcação sela-nó responsável pela sincronização. A partir da definição de uma função na região sincronizada é mostrado que o acoplamento crítico de sincronização é obtido exatamente através da minimização dessa função. Através de uma sequência de exemplos de configurações com simetria é mostrado que a região sincronizada do sistema apresenta uma estrutura de múltiplas soluções estáveis, sendo a sua caracterização, análise de estabilidade e descrição das bifurcações realizada para o caso com frequências aleatórias arbitrariamente distribuídas / Abstract: This text is devoted to the study of the synchronization phenomena in the Kuramoto model. In its first part the focus lies on its original formulation of infinitely many oscillators and on the description of the synchronization transition and solutions' stability for systems with a finite number of elements. It is shown that a pair of equations characterize the critical synchronization coupling Ks, and the solution for a special case with symmetry on its natural frequencies configuration is obtained in a perturbatively way. The second part of the text is focused on the 1-dimensional Kuramoto model with periodic boundary conditions. The synchronization tree structure is described, where it is observed several transitions between chaotic and periodic regimes among the individual oscillators. The onset on synchronization is explored through a series of approximations that show the characteristic critical behavior of a saddle node bifurcation, which is responsible for the synchronization. By defining a function on the synchronized region it is shown that the critical synchronization coupling is exactly determined by the function's minimization process. Through a sequence of examples with symmetry on its configurations it is shown that the synchronized region presents a structure of multiple stable solutions. Its complete characterization, stability analysis and bifurcations' description is carried through for the case with randomly distributed natural frequencies / Doutor

Orientador: Mario Noboru Tamashiro / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-15T20:51:05Z (GMT). No. of bitstreams: 1 Constantino_MairaAlves_M.pdf: 3844438 bytes, checksum: af45f6cbe23805204e63a810f7f6de8b (MD5) Previous issue date: 2010 / Resumo: Obtivemos a energia livre eletrostática de íons próximos a uma interface dielétrica planar e esférica entre fluidos imiscíveis utilizando a teoria de dielétrico contínuo. Para a geometria planar, o íon foi modelado como uma esfera dielétrica com densidade de carga superficial uniforme e fixa. Para evitar a polarização de cargas na interface iônica, consideramos não haver contraste dielétrico entre o interior do íon e o meio dielétrico externo em que ele está presente (aproximação de dielétrico misto), permitindo uma solução exata do problema eletrostático utilizando o método de carga imagem. Mostramos que resultados publicados anteriormente na literatura para este modelo subestimam a energia livre eletrostática associada a íons não-polarizáveis por uma ordem de magnitude, especialmente quando há penetração iônica parcial na interface. Para a geometria esférica, o íon é modelado tanto como pontual quanto como uma esfera com densidade de carga superficial uniforme e fixa cujo interior é novamente modelado utilizando a aproximação de dielétrico misto. Mostramos que as energias livres eletrostáticas dos íons pontual e de raio finito para a interface esférica são numericamente idênticas na ausência de penetração na interface e são sempre inferiores à energia livre eletrostática associada com a interface planar / Abstract: We obtain the electrostatic free energy of ions near a planar and spherical dielectric interface between immiscible fluids within the framework of the classical continuum dielectric theory. For the planar geometry, the ion is modeled as a dielectric sphere with a fixed uniform surface charge density. In order to avoid the generation of additional induced charges on the ionic surface, it is assumed there is no dielectric contrast between the ion core and the external dielectric medium where it is embedded (mixed-dielectric model), which allows an exact solution of the electrostatic problem by the image-charge method. It is shown that earlier results reported in the literature, especially when there is partial ionic penetration into the interface, underestimate the electrostatic free energy associated with nonpolarizable ions by an order of magnitude. For the spherical geometry, the ion is modeled as punctual and as a dielectric sphere with a fixed uniform surface charge density whose core is again modeled as a mixed dielectric. It is shown that the electrostatic free energies of the point-like and the finite-sized ions for the spherical interface are numerically the same in the absence of penetration into the interface and that they are always lower than the electrostatic free energy associated with the planar interface / Mestrado / Física Estatistica e Termodinamica / Mestra em Física

Please read the abstract in the section 00front of this document / Dissertation (MSc (Physics))--University of Pretoria, 2007. / Physics / unrestricted

No description available.

No description available.

No description available.

Statistical physics has been the foundation for much of our understanding about plasma physics. Often, plasma physics phenomena are explained using statistical physics principles and theories. Here, I reverse this paradigm to instead use plasma experiments to test statistical physics principles. In this thesis, I test statistical physics principles with an experimental dusty plasma, which is a four-component mixture of micron-sized ``dust'' particles, electrons, ions, and neutral gas molecules. When immersed in the plasma, the dust particles acquire large negative charges, since they accumulate more electrons than ions. Due to their large electric charges, the dust particles have interparticle potential energies that greatly exceed their kinetic energies, so that the collection of dust particles is considered to be a strongly coupled plasma. Like other strongly coupled plasma, the collection of dust particles can exhibit solid-like or liquid-like behavior. A key advantage offered by dusty plasma experiments is the ability to track the motion of individual dust particles. Dust particles are sufficiently large to allow for direct imaging using a video camera, so that time series data can be obtained for particle positions and velocities. These particle-level data provide a richer description of the dynamics and structure than can be obtained for most other strongly coupled plasmas, simple liquids, or solid materials. In particular, the particle-level data of positions and velocities are often required inputs for testing statistical physics theories or principles. The dusty plasma data I analyze are from the experiment of Haralson~\textit{et al.} [1,2], where dust particles were electrically levitated in a single horizontal layer within a vacuum chamber. The collection of dust particles initially settled into a crystalline lattice with solid-like behavior. To reach a liquid-like state, or to drive a shear flow, dust particles were manipulated using the radiation pressure force of lasers. In this thesis, I test three different statistical physics principles using an experimental dusty plasma. First, I test the fluctuation theorem, which was first was presented in 1993 by Evans, Cohen, and Morriss [3]. The fluctuation theorem, which is one of the most important recent developments in statistical physics, quantifies the probability that the entropy production rate will temporarily fluctuate to negative values in ``violations'' of the second law of thermodynamics. The original formulation of the fluctuation theorem described the entropy production due to viscous heating in a shear flow; this version of the fluctuation theorem had never been experimentally demonstrated in a liquid of any kind. In Chapter 2, I provide the first such demonstration by showing that the entropy production rate in a liquid-like dusty plasma shear flow satisfies the fluctuation theorem. This result also serves as the first demonstration that a strongly coupled plasma obeys the fluctuation theorem. Second, I measure the Einstein frequency $\Omega_E$, which describes the stochastic process of collisions in a strongly coupled plasma, and I compare my measurement to predictions made in the literature that used simulation data. Often, for weakly coupled plasma, a collision frequency is obtained to provide a measure of the strength of particle-particle interactions. However, for strongly coupled plasma (and likewise for liquids and solids), a collision frequency is not well defined since collisions are multibody and occur continuously. Another quantity is needed to describe the strength of particle-particle interactions. I propose that the Einstein frequency $\Omega_E$, a concept more commonly used in solid physics, is better suited for describing particle-particle interactions in a strongly coupled plasma. In Chapter 3, I present and use a new method to obtain the Einstein frequency of a 2D dusty plasma in both a liquid-like state and a crystalline state. My measurement of the Einstein frequency, which serves as a proxy for a collision frequency, is consistent with simulation predictions in the literature. Third, I present particle-coordination survival functions, which provide a richer description of microscopic dynamics in a liquid than the commonly used relaxation time. Relaxation times have been used, for example the Maxwell relaxation time, to describe the characteristic time scale for the crossover between elastic and viscous behavior in viscoelastic liquids. However, relaxation times are single-value measures that cannot fully describe the complexity of a liquid. In Chapter 4, using a survival function that retains temporal information about the local structural in a liquid, I discover that the microscopic arrangements in a liquid-like 2D dusty plasma have multiple time scales. Unexpectedly, non-defects have two time scales, while defects have one. My survival functions are time-series graphs of the probability that a particle's number of nearest neighbors, i.e., its coordination, remains the same. The two time scales for non-defects are revealed by an elbow in their survival-function curve. As a spinoff with a considerable amount of importance, I performed the simplest fluctuation theorem experiment to date, using an aerosol. An aerosol is simply a particle that is immersed in air. In Chapter 5, I show that the fluctuation theorem is applicable for an aerosol particle undergoing free-fall in air due to gravity. While the particle typically fell downwards, it is observed to occasionally fall upwards, against the force of gravity. For such upward displacements, the work done on the particle is negative, which is a temporary violation of the second law. I find that the probability of these temporarily violations obeys the work fluctuation theorem. This result also allowed an application: a novel diagnostic method to measure the mass of aerosol particles.

Plus de 50% de la population mondiale vit dans des zones urbaines et cette proportion devrait augmenter dans les prochaines décennies. Comprendre ce qui régit l'évolution des systèmes urbains est donc devenu d'une importance fondamentale. Ce renouveau d'intérêt combiné avec la disponibilité de données à grande échelle, permet d'entrevoir l'avènement d'une nouvelle science des villes, interdisciplinaire et basée sur les données.Des études récentes ont montré l'existence de régularités statistiques et de lois d'échelle pour plusieurs indicateurs socio-économiques, tels que la consommation d'essence, la distance moyenne parcourue quotidiennement, le cout des infrastructures, etc. Malgré plusieurs tentatives récentes, la compréhension théorique de ces résultats observés empiriquement demeure très partielle.Le but de cette thèse est d'obtenir une modélisation simplifiée, hors-équilibre de la croissance urbaine, en s'appuyant sur un petit nombre de mécanismesimportants et qui fournit des prédictions quantitatives en accord avec lesdonnées empiriques. Pour cela, nous nous inspirerons des études en géographiequantitative et en économie spatiale et nous revisiterons certains de ces anciens modèles avec une nouvelle approche intégrant les outils et concepts de la physique. / More than 50 % of the world population lives in urban areas and this proportion is expected to increase in the coming decades. Understanding what governs the evolution of urban systems has thus become of paramount importance.This renewed interest combined with the availability of large-scale data, allows a glimpse into the dawn of a new science of cities, interdisciplinary and based on data.Recent studies have shown the existence of statistical regularities and scaling laws for several socio-economic indicators such as fuel consumption, average commuting distance, cost of infrastructure, etc., and despite several recent attempts, the theoretical understanding of these results empirically observed remains very partial. The purpose of this thesis is to obtain a simplified, out of equilibrium model of urban growth, based on a small number of important mechanisms and which provides quantitative predictions in agreement with empirical data. For this, we will draw on studies in quantitative geography and spatial economy and we will revisit some of these old models with a new approach that integrates the tools and concepts of physics.

Polymer gels undergo the volume phase transition in response to an infinitesimal environmental change. This remarkable phenomenon results in many potential applications of polymer gels. This dissertation systematically investigates the chemical and physical properties of polymer gels. It is found that infrared radiation laser not only induces a volume phase transition in N-isopropylacrylamide (NIPA) gel, but also causes the gel to bend toward the laser beam. The transmission of visible laser light through a NIPA gel can also be controlled by adjusting the infrared laser power. A new class of environmentally responsive materials based on spatial modulation of the chemical nature of gels has been proposed and demonstrated. Three simple applications based on the modulated gels are presented: a bi-gel strip, a shape memory gel, and a gel hand. The bending of bi-gels has been studied as a function of temperature, acetone aqueous solution, and salt solution. As the polymer network concentration increases, the behavior of shear modulus of acrylamide (PAAM) gels deviates significantlyfromthe classical theory. The ionic NIPA gels undergo two sequential volume phase transitions: one occurs in dilute NaCl solution, the other occurs in concentrated NaCl solution. An interpenetrating polymer network (IPN) of PAAM--NIPA has also been synthesized using free radical polymerization. It is found that the IPN gels preserve the essential properties of individual components. The volume phase transition of the IPN gels can be triggered by multiple external stimuli including temperature, acetone concentration, and salt concentration.

No description available.