Estudamos um modelo de passeios aleatórios simples em grafos, conhecido como modelo dos sapos. Esse modelo pode ser descrito de maneira geral da seguinte forma: existem partículas ativas e partículas desativadas num grafo G. Cada partícula ativa desempenha um passeio aleatório simples a tempo discreto e a cada momento ela pode morrer com probabilidade 1-p. Quando uma partícula ativa entra em contato com uma partícula desativada, esta é ativada e também passa a realizar, de maneira independente, um passeio aleatório pelo grafo. Apresentamos limites superior e inferior para o parâmetro crítico de sobrevivência do modelo dos sapos na árvore, e demonstramos que este parâmetro crítico não é uma função monótona do grafo em que está definido. / We study a system of simple random walks on graphs, known as frog model. This model can be described generally speaking as follows: there are active and sleeping particles living on some graph G. Each particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1 - p. When an active particle hits a sleeping particle, the latter becomes active and starts to perform, independently, a simple random walk on the graph. We present lower and upper bounds for the surviving critical parameter on the tree, and we show that this parameter is not a monotonic function of the graph it is defined on.

Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-03-27T19:05:26Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese _ficha cartalografica.pdf: 12047542 bytes, checksum: 15c5c46a6007c1cf0e93d34e697f4e96 (MD5) / Made available in DSpace on 2017-03-27T19:05:26Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese _ficha cartalografica.pdf: 12047542 bytes, checksum: 15c5c46a6007c1cf0e93d34e697f4e96 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho estudamos o comportamento ferromagnético de uma série de multicamadas de ZnO/MT com MT = Fe, CoFe, NiFe. Este tipo de sistemas é importante por suas aplicações na spintrônica; cálculos teóricos em multicamadas de ZnO/Co fixando a espessura da camada do ZnO em 5 nm, mostram que estas estruturas podem ter até 100% de polarização de spin. As multicamadas com estrutura [ZnO(5nm)/MT(t)]x6 foram crescidas por magnetron sputtering variando a espessura do MT numa série de valores t = 0,3; 0,4; 0,6; 0,8 e 1,0 nm. A estrutura cristalográfica foi analisada com um difratômetro de raios-X (DRX), revelando um crescimento preferencial no plano (002) do ZnO e mostrando um alargamento de linha e picos satélites. A topografia foi analisada com um microscópio de força atômica (AFM), e revela uma relação entre a espessura do MT com as imperfeições da superfície. A resposta magnética estática foi analisada com um magnetômetro de amostra vibrante (VSM) obtendo curvas de magnetização em função do campo (M vs. H) e curvas de magnetização em função da temperatura (M vs. T) pelo método de medidas de zero field cooling (ZFC) e field cooling (FC). As formas das curvas de histerese revelam a mudança da serie, de um filme com interação dipolar forte a um sistema de nanopartículas não interagentes dependendo da “concentração” do MT na multicamada; as medidas de ZFC/FC confirmam que a ordem ferromagnética é favorecida quanto maior é a espessura depositada do MT. A resposta magnética dinâmica foi analisada por espectroscopia de ressonância ferromagnética (FMR), e revela o decrescimento do campo de ressonância na serie, devido á anisotropia de forma, mostrando uma mudança do eixo fácil da magnetização do plano para a perpendicular. Análise química foi feita por espectroscopia de fotoemisão de raios-X, e revela a formação de fases mistas (íons) coexistindo com o MT; e por último medidas de transmitância revelam a existência de um pico plasmon na faixa de 250 – 340 nm. Estes picos de plasmon são característicos de sistemas dielétricos com nanopartículas. O tratamento térmico de 6000C por 2 horas em vácuo da multicamada [ZnO(5nm)/Fe(t)]x6 teve a finalidade de incrementar a espessura do semicondutor magnético diluído (SMDs) na multicamada, mediante a difusão do MT na rede do ZnO; estes sistemas revelam uma mudança nas suas propriedades estruturais e magnéticas e possivelmente o aparecimento do SMDs, devido a que seu comportamento magnético não corresponde a de um filme nem a de um sistema granular. / In this work we study the ferromagnetic behavior of a series of multilayer ZnO / MT with MT = Fe, CoFe, NiFe. Such systems are important for applications in spintronics: theoretical calculations in multilayer of ZnO/Co with fixed ZnO thickness of 5 nm show that these structures can have up to 100% spin polarization. The multilayers with structure of [ZnO (5nm) / MT (t)] x6 were grown by means of magnetron sputtering varying the thickness of the MT with the values of t = 0,3; 0,4; 0,6; 0,8 and 1, 0 nm. The crystallographic structure is analyzed by X-ray diffractometer (XRD) and the results revealed a preferential growth of ZnO along (002) plane, enlargement of the width of the peaks and existence of satellite peaks. The topography is analyzed with the atomic force microscope (AFM) and it reveals a relationship between the thicknesses of the MT layers and the surface imperfections. The static magnetic response was analyzed with a vibrating sample magnetometer (VSM) and magnetization curves as a function of field (M vs. H) and as a function of temperature (Mvs. T) using the zero field cooling measurements (ZFC) and field cooling (FC) were obtained. The shapes of hysteresis curves show the changes of a film with strong dipolar interactions to a system of non-interacting nanoparticles according to the "concentration" of MT in the multilayer. Measurements of ZFC / FC M-T curves confirm that the ferromagnetic order is favored in the samples with thicker deposited MT layers. The dynamic magnetic response was analyzed by ferromagnetic resonance spectroscopy (FMR) and it shows the decrease of the resonance field in the series, which is due to the shape anisotropy, showing a change of the easy axis of magnetization from in plane to the perpendicular of the plane. The chemical analysis is done by X-ray photoemission spectroscopy (XPS) and the result shows the formation of mixed phases (ions) of the MT. Transmittance measurements reveal the existence of a peak of plasmon in the range of 250 to 340 nm. These peaks of plasmon are characteristic dielectric systems with nanoparticles. Heat treatment for the sample of [ZnO (5nm) / Fe (t)] x6 has been done at 600oC for 2 hours in vacuum in order to increase the thickness of diluted magnetic semiconductor (SMDs) layers in the multilayer system due to the diffusion process of MT atoms. These systems show changes in their structural and magnetic properties, which can be due to the appearance of SMDs since the magnetic behavior does not match to a film or to a granular system.

Context: Fluid-particle systems are seldom used in games, the apparent performance costs of simulating a fluid-particle system discourages the developer to implement a system of such. The processing power delivered by a modern GPU enables the developer to implement complex particle systems such as fluid-particle systems. Writing efficient fluid-particle systems is the key when striving for real-time fluid-particle simulations with good scalability. Objectives: This thesis ultimately tries to provide the reader with a well-performing and scalable fluid-particle system simulated in real-time using a great number of particles. The fluid-particle system implements two different fluid physics models for diversity and comparison purposes. The fluid-particle system will then be measured for each fluid physics model and provide results to educate the reader on how well the performance of a fluid-particle system might scale with the increase of active particles in the simulation. Finally, a performance comparison of the particle scalability is made by completely excluding the fluid physics calculations and simulate the particles using only gravity as an affecting force to be able to demonstrate how taxing the fluid physics calculations are on the GPU. Methods: The fluid-particle system has been run using different simulation scenarios, where each scenario is defined by the amount of particles being active and the dimensions of our fluid-particle simulation space. The performance results from each scenario has then been saved and put into a collection of results for a given simulation space. Results: The results presented demonstrate how well the fluid-particle system actually scales being run on a modern GPU. The system reached over a million particles while still running at an acceptable frame rate, for both of the fluid physics models. The results also shows that the performance is greatly reduced by simulating the particle system as a fluid-particle one, instead of only running it with gravity applied. Conclusions: With the results presented, we are able to conclude that fluid-particle systems scale well with the number of particles being active, while being run on a modern GPU. There are many optimizations to be done to be able to achieve a well-performing fluid-particle system, when developing fluid-particle system you should be wary of the many performance pitfalls that comes with it. / Vätskebaserade partikelsystem används sällan inom realtidsspel. Dessa system är väldigt prestandakrävande, till den grad att de avskräcker utvecklare från att implementera dem i sina realtidsspel. GPGPU ger utvecklare möjligheten att implementera komplexa partikelsystem, såsom vätskepartikelsystem, och simulera dessa system i realtid. Den här uppsatsen utforskar två olika fysikmodeller som kan användas för vätskesimulering, och sedan utförs det prestandamätningar under varierande omständigheter. Baserat på dessa prestandamätningar så kan slutsatser dras om hur skalbart ett vätskepartikelsystem är, alltså hur prestandan sjunker i förhållande till antalet partiklar i systemet. Slutsatser som dras efter att samtliga mätningar har utförts är att dessa system har en god skalbarhet, men att det finns många prestandafallgropar man måste se upp för när man utvecklar ett vätskepartikelsystem.

It is a great challenge to develop a computer game. Today many games are developed in large game studios where lots of skilled people are working together. Everyone has to know what the final game should look like. Game designers are responsible for how the game should feel and look like. This also means that they decide if a programmer has to develop new techniques or not. Sometimes the game designers require lots of new techniques to be developed. Such a new technique may be rendering particle systems with a lot of particles in it. This is where this report will focus. To render particle systems it is necessary to know about the limitations there are in both hardware and software. Until today particle systems have been updated and calculated using the Central Processing Unit of the computer. With Microsoft Direct3D 10 there are new ways to render particles using Geometry Shaders. Geometry Shaders runs on the graphics card. This thesis focuses on testing rendering performance between using Geometry Shaders and not using Geometry Shaders. A questionnaire was sent to Swedish game developers to get more information about relevant topics for investigation. A general answer was that Geometry Shaders always increase particle rendering performance. This thesis investigates if and when the statement is true or not. The hypothesis was obtained from the answers to the questionnaire. Two test applications were used to investigate if the hypothesis was true or false. One test application has particle calculations on the CPU of the computer. The other test application has particle calculations on the GPU of the graphics card. Six different tests were done and the Geometry Shader approach went out to be the fastest in five of the tests. Since not all tests were faster than the CPU approach the hypothesis is not always true.

Cette thèse comporte trois parties essentiellement indépendantes, dont chacune est consacrée à l'étude d'un système de particules, suivant une dynamique déterministe ou aléatoire, et à l'intérieur duquel les interactions se font uniquement aux collisions entre les particules.La Partie I propose une étude numérique et théorique des états stationnaires hors de l'équilibre du Modèle d'Échange Complet, introduit en physique pour comprendre le transport de la chaleur dans certains matériaux poreux.La Partie II est consacrée à un système de particules browniennes évoluant sur la droite réelle et interagissant à travers leur rang. Le comportement limite de ce système, en temps long et à grand nombre de particules, est décrit, puis les résultats sont appliqués à l'étude d'un modèle de marché financier dit modèle d'Atlas en champ moyen.La Partie III introduit une version multitype du système de particules étudié dans la partie précédente, qui permet d'approcher des systèmes paraboliques d'équations aux dérivées partielles non-linéaires. La limite petit bruit de ce système est appelée dynamique des particules collantes multitype et approche cette fois des systèmes hyperboliques. Une étude détaillée de cette dynamique donne des estimations de stabilité en distance de Wasserstein sur les solutions de ces systèmes. / This thesis contains three independent parts, each one of which is dedicated to the study of a particle system, following either a deterministic or a stochastic dynamics, and in which interactions only occur at collisions. Part I contains a numerical and theoretical study of nonequilibrium steady states of the Complete Exchange Model, which was introduced by physicists in order to understand heat transfer in some porous materials. Part II is dedicated to a system of Brownian particles evolving on the real line and interacting through their ranks. The long time and mean-field behaviour of this system is described, then the results are applied to the study of a model of equity market called the mean-field Atlas model. Part III introduces a multitype version of the particle system studied in the previous part, which allows to approximate parabolic systems of nonlinear partial differential equations. The small noise limit of of this system is called multitype sticky particle dynamics and now approximates hyperbolic systems. A detailed study of this dynamics provides stability estimates in Wasserstein distance for the solutions of these systems.

Modelling and rendering natural phenomena, such as rain, is an important aspect of creating a realistic driving simulator. Rain is a crucial issue when driving in the real world as it for instance obstructs the driver’s vision. The difficulty is to implement it in a visually appealing way while simultaneously making it look realistic and keeping the computational cost low. In this report, a GPGPU (general-purpose computing on graphical processing units) based approach is presented where the final product is a rain simulation rendered onto a 2D texture, which can then be applied to a surface. The simulated raindrops interact with gravity, wind, a windshield wiper as well as with each other, and are then used to distort the background behind them in a convincing manner. The simulation takes into account multiple physical properties of raindrops and is shown to be suitable to run in real-time. The result is presented in form of a visual demonstration. In conclusion, even though the final simulation is still in its first iteration, it clearly highlights what can be accomplished by utilizing the GPU and the benefits of using a texture-based approach. The appropriate simulation approach will however always depend on the characteristics of the problem and the limitations of the hardware.

Current commercial Virtual Reality (VR) headsets give viewers immersion in virtual space with stereoscopic graphics and positional tracking. Developers can create VR applications in a working pipeline similar to creating 3D games using game engines. However, the characteristics of VR headsets give disadvantages to the rendering technique particle system with billboard sprites. In our study, we propose a rendering technique called FOggy-LAser Rendering method (FOLAR), which renders realistic laser in fog on billboard sprites. With this method, we can compensate for the disadvantages of using particle systems and still render the graphics in interactive performance for VR. We studied the characteristics of this method by performance benchmarks and comparing the rendered result to a baseline ray-casting method. User study and image similarity metrics are involved in the comparison study. As a result, we observed a satisfying performance and a similar rendering result compared to ray-casting. However, the user study still shows a significant difference in the rendered result between methods. These results imply that FOLAR is an acceptable method for its performance and ness in the rendered result, but still have inevitable trade-offs‌‌‌ in the graphics. / Nuvarande kommersiella Virtual Reality (VR) headset ger användare immersion i virtuellt utrymme med stereoskopisk grafik och positionsspårning. Utvecklare kan skapa VR-applikationer i en fungerande pipeline på ett liknande sätt som att skapa 3D-spel med hjälp av spelmotorer. Egenskaperna hos VR-headset ger emellertid nackdelar med renderingstekniken av billboard sprite partikelsystem. I vår studie föreslår vi en renderingsteknik som kallas FOggy-LAser Rendering method (FOLAR), som renderar realistiska lasrar i dimma på billboard sprites. Med denna metod kan vi kompensera för nackdelarna med att använda partikelsystem och fortfarande göra grafiken i interaktiv prestanda för VR. Vi studerade egenskaperna hos denna metod genom prestanda benchmarks och jämförde renderade resultatet med en baseline ray-cast metod. Användarstudie och image similarity mätvärden är involverade i jämförelsestudien. Som resultat observerade vi en tillfredsställande prestanda och liknande renderings resultat jämfört med ray-casting. Dock visar användarstudien fortfarande en signifikant skillnad i det gjorda resultaten mellan metoderna. Dessa resultat pekar på att FOLAR är en acceptabel metod för dess prestanda och korrekthet i det renderade resultatet, men har fortfarande oundvikliga avvägningar i grafiken.

O propósito desta dissertação é combinar tópicos de percolação e processo de contato para formular e obter resultados em um modelo de sistema de partículas que é inspirado no fenômeno de difusão de uma inovação em uma população estruturada. Mais precisamente, propomos uma cadeia de Markov a tempo contínuo definida na rede hipercúbica d-dimensional. Cada indivíduo da população deve estar em algum dos três estados pertencentes ao conjunto {0; 1; 2}. Nesse modelo, 0 representa ignorante, 1 consciente e 2 adotador. Serão estudados argumentos que permitam encontrar condições suficientes nas quais a inovação se espalha ou não com probabilidade positiva. Isto envolve o estudo de modelos de percolação e do processo de contato. / The purpose of this work is to combine percolation and contact process topics to formulate and achieve results in a particle system model that is inspired by the diffusion phenomenon of an innovation in a structured population. More precisely, we proposed a continuous time Markov chain defined in a population represented by the d-dimensional integer lattice. Each agent of population may be in any of the three states belonging to the set {0; 1; 2}. In this model, 0 stands for ignorant, 1 for aware and 2 for adopter. The arguments, that allow to obtain sufficient conditions under which the innovation either becomes extinct or survives with positive probability, will be studied. This involves the study of percolation models and contact process.

O propósito desta dissertação é combinar tópicos de percolação e processo de contato para formular e obter resultados em um modelo de sistema de partículas que é inspirado no fenômeno de difusão de uma inovação em uma população estruturada. Mais precisamente, propomos uma cadeia de Markov a tempo contínuo definida na rede hipercúbica d-dimensional. Cada indivíduo da população deve estar em algum dos três estados pertencentes ao conjunto {0; 1; 2}. Nesse modelo, 0 representa ignorante, 1 consciente e 2 adotador. Serão estudados argumentos que permitam encontrar condições suficientes nas quais a inovação se espalha ou não com probabilidade positiva. Isto envolve o estudo de modelos de percolação e do processo de contato. / The purpose of this work is to combine percolation and contact process topics to formulate and achieve results in a particle system model that is inspired by the diffusion phenomenon of an innovation in a structured population. More precisely, we proposed a continuous time Markov chain defined in a population represented by the d-dimensional integer lattice. Each agent of population may be in any of the three states belonging to the set {0; 1; 2}. In this model, 0 stands for ignorant, 1 for aware and 2 for adopter. The arguments, that allow to obtain sufficient conditions under which the innovation either becomes extinct or survives with positive probability, will be studied. This involves the study of percolation models and contact process.

Kollektive Migration und Schwarmverhalten sind Beispiele für Selbstorganisation und können in verschiedenen biologischen Systemen beobachtet werden, beispielsweise in Vogel-und Fischschwärmen oder Bakterienpopulationen. Im Zentrum dieser Arbeit steht ein räumlich diskretes und zeitlich stetiges Model, welches das kollektive Migrieren von Individuen mittels eines stochastischen Vielteilchensystems (VTS) beschreibt und analysierbar macht. Das konstruierte Modell ist in keiner Klasse gut untersuchter Vielteilchensysteme enthalten, sodass der größte Teil der Arbeit der Entwicklung von Methoden zur Untersuchung des Langzeitverhaltens bestimmter VTS gewidmet ist. Eine entscheidende Rolle spielen hier Gibbs-Maße, die zu zeitlich invarianten Maßen in Beziehung gesetzt werden. Durch eine Simulationsstudie und die Analyse des Einflusses der Parameter Migrationsgeschwindigkeit, Sensitivität der Individuen und (räumliche) Dichte der Anfangsverteilung können Eigenschaften kollektiver Migration erklärt und Hypothesen für weitere Analysen aufgestellt werden. / Collective migration and swarming behavior are examples of self-organization and can be observed in various biological systems, such as in flocks of birds, schools of fish or populations of bacteria. In the center of this thesis lies a stochastic interacting particle system (IPS), which is a spatially discrete model with a continuous time scale that describes collective migration and which can be treated using analytical methods. The constructed model is not contained in any class of well-understood IPS’s. The largest part of this work is used to develop methods that can be used to study the long-term behavior of certain IPS’s. Thereby Gibbs-Measures play an important role and are related to temporally invariant measures. One can explain the properties of collective migration and propose a hypothesis for further analyses by a simulation study and by analysing the parameters migration velocity, sensitivity of individuals and (spatial) density of the initial distribution.