Networks that self-organize in response to information are one of the most central studies in complex systems theory. A new time series analysis tool for studying self-organizing systems is developed and demonstrated. This method is applied to interacting complex swarms to explore the connection between information transport and group size, providing evidence for Dunbar's numbers having a foundation in network dynamics. A complex network model of information spread is developed. This network infodemic model uses reinforcement learning to simulate connection and opinion adaptation resulting from interaction between units. The model is applied to study polarized populations and echo chamber formation, exploring strategies for network resilience and weakening. The model is straightforward to extend to multilayer networks and networks generated from real world data. By unifying explanation and prediction, the network infodemic model offers a timely step toward understanding global collective behavior.

Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems. Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions. / Ph. D.

No description available.

Dynamical properties of non-equilibrium systems, similar to equilibrium ones, have been shown to obey robust time scaling laws which have enriched the concept of physical universality classes. In the first part of this Dissertation, we present the results of our investigations of some of the critical dynamical properties of systems belonging to the Voter or the Directed Percolation (DP) universality class. To be more precise, we focus on the aging properties of two-state and three-state Potts models with absorbing states and we determine temporal scaling of autocorrelation and autoresponse functions. We propose a novel microscopic model which exhibits non-equilibrium critical points belonging to the Voter, DP and Ising Universality classes. We argue that our model has properties similar to the Generalized Voter Model (GVM) in its Langevin description. Finally, we study the time evolution of the width of interfaces separating different absorbing states. The second part of this Dissertation is devoted to the applications of Machine Learning models in physical systems. First, we show that a trained Convolutional Neural Network (CNN) using configurations from the Ising model with conserved magnetization is able to find the location of the critical point. Second, using as our training dataset configurations of Ising models with conserved or non-conserved magnetization obtained in importance sampling Monte Carlo simulations, we investigate the physical properties of configurations generated by the Restricted Boltzmann Machine (RBM) model. The first part of this research was sponsored by the US Army Research Office and was accomplished under Grant Number W911NF-17-1-0156. The second part of this work was supported by the United States National Science Foundation through grant DMR-1606814. / Doctor of Philosophy / Physical systems with equilibrium states contain common properties with which they are categorized in different universality classes. Similar to these equilibrium systems, non-equilibrium systems may obey robust scaling laws and lie in different dynamic universality classes. In the first part of this Dissertation, we investigate the dynamical properties of two important dynamic universality classes, the Directed Percolation universality class and the Generalized Voter universality class. These two universality classes include models with absorbing states. A good example of an absorbing state is found in the contact process for epidemic spreading when all individuals are infected. We also propose a microscopic model with tunable parameters which exhibits phase transitions belonging to the Voter, Directed Percolation and Ising universality classes. To identify these universality classes, we measure specific dynamic and static quantities, such as interface density at different values of the tunable parameters and show that the physical properties of these quantities are identical to what is expected for the different universal classes. The second part of this Dissertation is devoted to the application of Machine Learning models in physical systems. Considering physical system configurations as input dataset for our machine learning pipeline, we extract properties of the input data through our machine learning models. As a supervised learning model, we use a deep neural network model and train it using configurations from the Ising model with conserved dynamics. Finally, we address the question whether generative models in machine learning (models that output objects that are similar to inputs) are able to produce new configurations with properties similar to those obtained from given physical models. To this end we train a well known generative model, the Restricted Boltzmann Machine (RBM), on Ising configurations with either conserved or non-conserved magnetization at different temperatures and study the properties of configurations generated by RBM. The first part of this research was sponsored by the US Army Research Office and was accomplished under Grant Number W911NF-17-1-0156. The second part of this work was supported by the United States National Science Foundation through grant DMR-1606814.

We study the non-equilibrium behavior of systems that are driven out of equilibrium from the interface. In the first part of this thesis, we study a model of a two-dimensional lattice gas that is in contact with two heat baths that are at different temperatures. Performing Monte Carlo simulations, we find that there are three possible types of non-equilibrium steady states, depending on the values of certain system parameters. They include a disordered phase, a fully phase separated state, and an interesting state with striped patterns in the half of the lattice where the temperature is lower. The last one is a novel non-equilibrium steady state that we study systematically by varying the system parameters. To obtain the non-equilibrium finite-size phase diagram, we perform a spectrum analysis to classify not only the three major states, but also the sub-states of the striped phase. In the second part of the thesis, we study magnetic friction that results when two Potts systems move with respect to each other. In this research, we first study a model that consists of two interacting Potts blocks, where one block moves on top of the other. As a result, the system is driven out of equilibrium constantly. In our research we find for weak interfacial couplings that the contacting surfaces behave rather similar to a free surface. If the interfacial coupling is strong, however, anisotropic spin patterns appear on the contacting surfaces. This study is extended to a three-dimensional Potts wedge with a tip sliding along the surface of a Potts block. It is found that the shape of the Potts lattice influences the surface behavior of the system. / Ph. D.

This thesis reports the results of light-scattering measurements and visual investigations of critical phenomena in the complex mixture 1-propanol (1P) + water (W) + potassium chloride (KCl) which has a special critical point (or a special thermodynamic state) known as the double critical point (DCP). The main theme of the thesis is the critical behavior on approaching a special critical point (i.e., the DCP) in a complex or associating mixture in contrast with that in simple, nonassociating mixtures. The asymptotic critical behavior in complex or associating fluids, such as polymer solutions and blends, ionic and nonionic micellar solutions, microemulsions, aqueous and nonaqueous electrolyte solutions, protein solutions, etc., is now commonly accepted to belong to the 3D-Ising universality class. However, the temperature range of the asymptotic regime in these fluids, with universal behavior, has a nonuniversal width and is, in general, smaller than that in simple or nonassociating fluids. In complex mixtures, which are made up of relatively large molecules or particle clusters of mesoscopic range, the coupling between the conventional correlation length of the critical fluctuations ( ξ) and an additional length scale associated with the mesoscale structures (ξD) is known to modify the approach towards the universal nonclassical critical behavior near their critical points. Nevertheless, the generality of this approach needs to be confirmed. There are also instances of a pure classical or close to classical behavior being observed in the critical domain of complex mixtures, although recent experimental results contradict the earlier observations. Therefore, further experimental evidences than that presently available are necessary before one can say how far the analogy between simple and complex fluids can be pushed. Variations in the effective dielectric constant of a mixture have been known to affect the critical behavior. Furthermore, we anticipate the presence of special critical points in complex mixtures to cause nontrivial modifications in the approach towards the universal asymptotic critical behavior. Special thermodynamic states are characterized by critical fluctuations with exceptionally large correlation length, and are displayed by multicomponent liquid mixtures, in which there are a multitude of thermodynamic paths by which a critical point can be approached, and offers rich information about the critical phenomena. These issues are being addressed in this research work. This thesis is organized into 7 Chapters. Chapter 1 begins with an account of the historical development of the field of critical point phenomena with a brief introduction to critical phenomena in simple fluids. Critical phenomena observed in various complex systems such as aqueous and nonaqueous ionic fluids, polymer solutions and blends, micellar and microemulsion systems, etc., are discussed, with particular attention to investigations into crossover from Ising to mean-field critical behavior observed in these systems, which are relevant to the present work. Theoretical attempts at modeling ionic criticality are cited and summarized. This is followed by a discussion of re-entrant phase transitions in multicomponent liquid systems. An account of the various types of special critical points, such as double critical point, critical double point, critical inflection point, quadruple critical point, etc., highlighting the critical behavior on approaching these special critical points, and some of the models of reentrant miscibility are briefly given. The Chapter ends with a statement on the goals of the present research work. Chapter 2 describes the instrumentation developed and the data acquisition procedures adopted for the study. Details of the thermostats and precision temperature controllers used for visual and light-scattering measurements are provided. The important design considerations relating to the achievement of a high degree of temperature stability (~ ±1 mK in the range 293-383 K) are elucidated clearly. The temperature sensors used in the present experiments and their calibration procedures are discussed. The light-scattering instrumentation is discussed in depth. The problems associated with the light-scattering techniques when it is used to study critical point phenomena, and the strategies adopted to overcome them are discussed. The sample cells used for visual investigations and light- scattering experiments, along with the procedure adopted for cleaning and filling of sample cells are also described. Chapter 3 essentially deals with the characterization of the system 1P + W + KCl. It begins with a brief introduction to the critical behavior in complex mixtures, and the motivation behind choosing the present system. The phase behavior in the present mixture, the generation of the coexistence curves and the line of critical points in the mixture, and the method used for preparation of the samples are described. The criticality of the samples is judged by the equal volume phase separation criterion through visual investigations. Addition of a small amount of salt (i.e., KCl) to the 1P + W solution induces phase separation in the mixture as a result of a salting-out process. Decreasing the salt concentration has the same effect as that of increasing pressure on the liquid-liquid demixing of this mixture. Therefore, KCl may be considered as an appropriate field variable analogous to pressure in this mixture. The mixture 1P + W + KCl exhibits reentrant phase transitions and has an array of lower (TL) and upper (TU) critical solution temperatures. It is found that the line of TL’s and TU’s, known as the line of critical points, merge (TU - TL = ΔT → 0) to form a special thermodynamic state known as the DCP. The DCP is approached as close as 509 mK (i.e., ΔT ~ 509 mK) in this work. An analysis of the critical line shows that it is roughly parabolic in shape, which is in consonance with the predictions of the lattice models and the Landau-Ginzburg theory of phase transition. In addition to the presence of a special critical point, various structure probing techniques like small angle X-ray scattering (SAXS), small angle neutron scattering (SANS), etc., indicate the presence of large-scale density inhomogeneities or clusters in 1P + W solution and its augmentation on adding small amount of KCl. Therefore, the present mixture provides a unique possibility to investigate the combined effects of molecular structuring as well as a special critical point on the critical behavior. Only a section of the coexistence surface of the mixture could be generated, owing to various experimental limitations and other problems inherent to the system. This limited further studies on the coexistence curves in the mixture. Chapter 4 reports the critical behavior of osmotic susceptibility in the present mixture. The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths by varying t [ =| (T - T TL)/ TL|] from the lower one-phase region. The light-scattering data analysis emphasizes the need for correction-to-scaling terms for a proper description of the data over the investigated t range. Renormalization of the critical exponents is observed as the critical line is approached along certain special paths. Experimental evidence for the doubling of the extended scaling exponent Δ1 near the DCP is shown. There is no signature of Fisher renormalization in the values of the critical exponents. The data analysis yields very large magnitudes for the correction amplitudes A1 and A2, with the first-correction amplitude A1 being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. The magnitudes of the correction amplitudes are observed to increase gradually as TL approaches the DCP. The increasing need for extended scaling in the neighborhood of special critical points has been noted earlier in several aqueous electrolyte solutions, in polymer-solvent systems, etc. However, the magnitudes of the correction amplitudes were not as large as that in the present case. Analysis of the effective susceptibility exponent γeff in terms of t indicate that, for the TL far away from the DCP, γeff displays a nonmonotonic crossover from its single limit 3D Ising value (~ 1.24) towards its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value (~ 2.39) towards its nearly doubled mean-field value (~ 1.84) with increase in t. For the in-between TL’s, the limiting value of γeff in the asymptotic as well as nonasymptotic regimes gradually increases towards the DCP. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend towards shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover behavior to the mean-field limit extends well beyond t > 10¯2 for the TL’s studied. The crossover behavior is discussed in terms of the emergence of a new lengthscale ξD associated with the enhanced ion-induced clustering seen in the mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover is discussed in terms of the varying influence of the DCP on the critical behavior along the TL line. The discussion is extended to explain the observed critical behavior in various re-entrant systems having other special critical points. The extended renormalized Ising regime towards the DCP is also reflected in a decrease in the correlation length amplitude (ξ0) as TL approaches the DCP. It is observed that the first-correction amplitude A1 corresponding to fit using two correction terms becomes more negative as TL approaches the DCP, implying an increase in the value of the parameter ū of the crossover model [by Anisimov et al., Phys. Rev. Lett. 75, 3146 (1995)] as the DCP is approached. This increase in reflected in a trend towards a relatively sharp crossover behavior of γeff as TL shifts towards the DCP, i.e., towards the high temperature critical points. The significance of the field variable tUL in understanding different aspects of reentrant phase transitions is manifested in the present system as well. Analysis of the data in terms of tUL led to the retrieval of universal values of the exponents for all TL’s. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1. The limited (TL _ T) range restricted such a behavior of the effective exponent (in terms of t as well as tUL) for the lowest TL. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic, high tUL region, as foreseen earlier in micellar systems. The effective susceptibility exponent in terms of tUL also indicates an increase in the sharpness of crossover towards the high temperature TL’s. An increase in the sharpness of crossover with polymer chain length has been observed in polymer solutions. Therefore, our results suggest the need for further composition and temperature-dependent study of molecular structuring in the present mixture. There is also a large decrease in the dielectric constant of the mixture towards the high temperature TL’s. In Chapter 5 the light-scattering measurements are performed on approaching the DCP along the line of the upper critical solution temperatures (i.e., TU’s), by varying t [ = (T - TU )/ TU ] from the high temperature one-phase region in the mixture. A trend towards shrinkage in the simple scaling region is observed as TU shifts away from the DCP. Such a trend was not visible in the data analysis of the TL’s using the correction terms, due to the varying (TL - T) ranges. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. As with the TL’s, for the TU closest to the DCP, γeff displays a nonmonotonic crossover from its 3D-Ising value towards its nearly doubled mean-field value with increase in t. While for that far away from the DCP, γeff displays a nonmonotonic crossover from its single limit Ising value towards a value slightly lower than its mean-field value of 1 with increase in t. The limited (TL – T) range restricted such a behavior of γeff for the TL far away from the DCP, This feature of γeff in the nonasymptotic, high t region is yet again interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from below. Unlike TL’s, the crossover behavior in the present case is pronounced and more sharp for all TU’s. However, the variation in the width of the renormalized Ising regime on approaching the DCP along the TU line is quite similar to that observed along the TL line. The crossover behavior is attributed to the strong ion-induced structuring seen in the mixture, while the observed trend in the crossover as TU shifts towards/away from the DCP is attributed to the varying influence of the DCP. The influence of the DCP on the critical behavior along the TU (or TL) line decreases as TU (or TL) shifts away from the DCP. Our observations indicate an increase in the sharpness of crossover as the critical temperature shifts from TL towards TU, or in other words, as the critical point shifts towards higher temperatures. SANS measurements on the present mixture indicate no difference in the growth of mesoscale clusters in the lower and upper one-phase regions in the mixture. Hence, the observed increase in the sharpness of crossover towards the TU’s is very puzzling. The dielectric constant of the major constituent (i.e., water, ~ 62 %) of the present mixture decreases from around 80 to 63 as the critical temperature shifts from TL towards TU. Therefore, our results suggest the need to look at the crossover phenomena probably from two perspectives, namely, the solvent or dielectric effect and the clustering effect. The increase in the sharpness of the crossover behavior on approaching the high temperature critical points is probably related to the macroscopic property of the mixture, i.e., to the decrease in the dielectric constant of the mixture, while the actual nonmonotonic character of the crossover behavior is related to the microscopic property of the mixture, i.e., to the clustering effects, the extent of which determines the width of the asymptotic critical domain. However, this conclusion is somewhat subtle and calls for rigorous theoretical and experimental efforts to unravel the exact dependence of the crossover behavior on the dielectric constant. Analysis using the field variable tUL in lieu of the conventional variable t led to the retrieval of unique, universal exponents for all TU’s irrespective of the ΔT value. For all TU’s, the effective susceptibility exponent in terms of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis of the effective exponent for the TU far away from the DCP. Like with the TL’s, the crossover behavior extends over nearly the same tUL range for the TU’s studied. However, the crossover is again sharper when compared to the TL’s. Chapter 6 reports light-scattering measurements (by heating as well as cooling) on a non phase-separating 1P + W + KCl mixture in the vicinity of the DCP. The results indicate that despite the lack of phase-separation or critical points, critical-phenomena-like fluctuations can still occur in homogeneous mixtures if they reside in some other direction than temperature or composition (like, pressure or salt concentration) of the phase diagram. Unlike earlier studies on non phase-separating mixtures, our results indicate a crossover behavior of the effective susceptibility exponent, in addition to the power-law behavior. Chapter 7 sums up the major findings of the work reported in this thesis. It also presents a range of open problems that need to be explored further in order to fully understand the results that are reported in this thesis, especially, regarding the exact dependence of dielectric constant of the mixture on the character of the crossover behavior.

Dans cette thèse nous avons étudié de nombreux aspects de la théorie des systèmes désordonnés. En particulier, nous avons étudié les systèmes vitreux. La description détaillée des systèmes désordonnés et vitreux est un problème ouvert en physique de la matière condensée. Dans le cadre de la théorie de champ moyen pour les verres structuraux nous avons étudié la théorie des fluctuations proche de la transition vitreuse dynamique. L’étude des fluctuations peut etre fait avec le formalisme statique de la théorie de répliques. Nous avons fait cela en introduisant une théorie des champs pour la transition vitreuse à partir du potentiel microscopique entre les particules. Nous avons étudié dans ce cadre les fluctuations au niveau gaussien et nous avons évalués les exposants critiques dans ces approximations. Nous avons aussi étudié la région de validité de la prédiction gaussienne avec l’introduction d’un critère de Ginzburg pour la transition vitreuse. Les résultats que nous avons obtenues ne sont valides que dans la région β. Pour obtenir des resultats dans la région α nous avons étudié la pseudodynamique de Boltzmann que a été introduit par Franz and Parisi. Nous sommes parti des équations de Ornstein-Zernike et nous avons obtenu un ensemble d’équations dynamiques. En utilisant l’approximation Hypernetted Chain nous avons obtenu un ensemble complet d’équations qui sont très similaires aux équations de la théorie de mode-coupling. La troisième partie de la thèse porte sur l’étude des états amorphes des sphères dures en hautes dimensions. Pour obtenir les exposants dynamique dans ce cas, nous avons étudié la stabilité du diagramme de phase 1RSB (one-step-replica-symmetry-breaking). Nous avons découvert que ce diagramme de phase possède une région où la solution 1RSB est instable. La région où la solution 1RSB est instable est connectée avec la description théorique de la physique de jamming des sphères dures et nous avons montré que l’instabilité 1RSB est responsable d’une transition de phase en haute densité. Cette transition s’appelle la transition de Gardner. Nous avons cherché une solution 2RSB et nous avons vu qu’il existait un point en densité après lequel on peut avoir une solution 2RSB (et aussi fullRSB). Nous avons étudié le diagramme de phase 2RSB dans la limite de jamming où la pression devient infini. Après la solution 2RSB nous avons cherché à décrire la solution fullRSB. Nous avons écrit les équations fullRSB et nous avons découvert qu’elles sont identiques aux equations que l’on a dans le cas de un modèle de verres de spins qui s’appelle modèle de Sherrington et Kirkpatrick. Nous avons aussi étudié la solution numerique des équations fullRSB dans la limite de jamming. Cette solution montre beaucoup des choses intéressantes. La plus importante est le comportement du mean square displacement dans la limite de jamming. Si l’on regard les résultats numériques et éxperimentaux, il semble que le plateau de le mean square displacement s’approche a zero comme la pression à un exposant proche de −3/2. Nous avons vu que la solution numérique des équations fullRSB est en mesure de reproduire ce comportement. La quatrième partie de la thése a porté sur la dynamique de mode-coupling dans le régime où la transition vitreuse devient continue. / In this thesis we have studied many aspects of the physics of disordered and glassy systems. The first part of the work is about the theory of dynamical fluctuations in the beta regime. When a system undergoes a dynamical arrest, it can be studied by introducing an appropriate dynamical correlation function that plays the role of the order parameter of the transition. To understand the collective effects underlying the glass transition we have studied the fluctuations of the order parameter on a time scale where the system is relaxed in a typical metastable glassy state. To do this we have seen that coming from the glass phase the system develops critical fluctuations with a diverging correlation length at the mean field level. We have thus derived an effective field theory by focusing only on them. This field theory can be used firstly to derive the mode-coupling exponent parameter that controls the relaxation of the dynamical correlation function when the system relaxes in a metastable glassy state. Moreover we can give a Ginzburg Criterion that can be used to determine the region of validity of the Gaussian approximation. These considerations are valid in the beta regime. To clarify what happens in the alpha regime we have studied a quasi-equilibrium construction, called Boltzmann-Pseudodynamics, recently introduced in order to describe with static techniques the long time regime of glassy dynamics. We have extended this formalism to structural glasses by producing a new set of dynamical equations. We have done this in the simplest approximation scheme that is called Hypernetted Chain. Two results have been obtained : firstly, we have computed the mode-coupling exponent parameter and we have shown that it coincides with the one obtained with the formalism of the first part of the thesis ; secondly we have studied the aging regime and we have derived that the condition that determines the fluctuation-dissipation ratio is a marginal stability one. In the third part of the thesis we have studied the theory of amorphous states of hard spheres in high dimensions. Hard spheres provide simple models of glasses and they are extensively studied for the jamming transition. In our framework jammed states can be thought as infinite pressure limit of metastable glassy states. During the last years it has been derived a mean field theory of hard spheres based on the 1RSB assumption on the structure of the free energy landscape. However it has been realized that this construction is inconsistent for what concerns the property of the packings at jamming. In the present work we have firstly investigated the possibility of an instability of the 1RSB solution and we have actually found that the 1RSB solution is unstable in the jamming part of the phase diagram. At the same time we have been able to compute the mode-coupling exponent parameter for this system. In order to go beyond the 1RSB solution we have first tried a 2RSB ansatz and then a fullRSB solution. We have derived a set of variational equations that are very close to the ones that have been derived in the Sherrington-Kirkpatrick model. We have solved numerically the equations and we have shown that the fullRSB solution seems to predict that the plateau value of the mean square displacement scale as the pressure to a power close to 3/2 as it seems to be predicted by scaling arguments and in contrast with the 1RSB predictions that show a scaling with the inverse of the pressure. The last chapter of the thesis is on the mode-coupling theory when the glass transition is becoming continuous. We have been able to show that in such a situation a detailed characterization of the solution of the equations can be obtained in the long time regime.

A capacidade de um sistema sensorial detectar estímulos eficientemente é tradicionalmente dimensionada pela faixa dinâmica, que é simplesmente uma medida da extensão do intervalo de intensidades de estímulo para as quais a rede é suficientemente sensível. Muitas vezes, sistemas biológicos exibem largas faixas dinâmicas, que abrangem diversas ordens de magnitude. A compreensão desse fenômeno não é trivial, haja vista que todos os neurônios apresentam janelas de sensibilidade muito estreitas. Tentativas de explicação baseadas em argumentos de recrutamento sequencial dos neurônios sensoriais, com efeitos essencialmente aditivos, simplesmente não são realísticas, haja vista que seria preciso que os limiares de ativação das unidades também apresentassem um escalonamento por várias ordens de magnitude, para cobrir a faixa dinâmica empiricamente observada em nível macroscópico. Notavelmente, o modelo Kinouchi-Copelli (KC), que carrega o nome de seus idealizadores, mostrou que aquele comportamento pode ser um efeito coletivo (não aditivo) do conjunto de neurônios sensoriais. O modelo KC é uma rede de unidades excitáveis com dinâmicas estocásticas e acoplados segundo uma topologia de grafo aleatório. Kinouchi e Copelli mostraram que a taxa espontânea de disparo dos neurônios (ou atividade média) sinaliza uma transição de fase fora do equilíbrio do tipo ordem-desordem, e que exatamente no ponto crítico desta transição (em termos de um parâmetro ligado às características estruturais da rede) a sensibilidade a estímulos externos é máxima, ou seja, a faixa dinâmica exibe uma otimização crítica. Neste trabalho, investigamos como o ponto crítico depende da topologia, utilizando os modelos mais comuns das chamadas redes complexas. Além disso, estudamos computacionalmente os padrões de atividade (avalanches neuronais) exibidos pelo modelo, com especial atenção às mudanças qualitativas de comportamento devido às mudanças de topologia. Comentaremos também a relação desses resultados com experimentos recentes de monitoramento de dinâmicas neurais. / The capacity of a sensory system in efficiently detecting stimuli is usually given by the dynamic range, a simple measure of the range of stimulus intensity over which the network is sensible enough. Many times biological systems exhibit large dynamic ranges, covering many orders of magnitude. There is no easy explanation for that, since individual neurons present very short dynamic ranges isolatedly. Arguments based on sequential recruitment are doomed to failure since the corresponding arrangement of the limiar thresholds of the units over many orders of magnitude is unrealistic. Notably the so-called Kinouchi-Copelli (KC) model strongly suggested that large dynamic range should be a collective effect of the sensory neurons. The KC model is a network of stochastic excitable elements coupled as a random graph. KC showed the spontaneous activity of the network signals an order-disorder nonequilibrium phase transition and that the dynamic range exhibits an optimum precisely at the critical point (in terms of a control parameter related to structural properties of the network). In this work, we investigate how the critical point depends on the topology, considering the alternatives among the standard complex networks. We also study the burts of activity (neuronal avalanches) exhibited by the model, focusing on the qualitative changes due to alternative topologies. Finally we comment on possible connections among our results and recent observations of neural dynamics.

Cette thèse porte sur l'étude de deux systèmes critiques hors-équilibre par les outils du groupe de renormalisation non-perturbatif (NPRG).Le premier système est le processus de diffusion épidémique, qui modèle la propagation d'une épidémie avec guérison sans immunisation. Ce modèle exhibe une transition de phase continue lorsque l'épidémie subit une extinction. Nous avons utilisé une approximation du NPRG nommée l'approximation du potentiel local modifiée pour l'étude cette transition de phase. Nous avons été conduit à nous interroger sur les résultats antérieurs, obtenus dans le cadre du groupe de renormalisation perturbatif. En particulier, l'appartenance de cette transition de phase à la classe d'universalité de la percolation dirigée avec quantité conservée en basse dimension est remise en question.Le second système est la turbulence pleinement développée isotrope et homogène, décrite par l'équation de Navier-Stokes. L'état stationnaire de ce système dissipatif possède une cascade d'énergie dont la phénoménologie est typique des systèmes invariants d'échelle, tel qu'un spectre d'énergie en loi de puissance. Une examen plus approfondie révèle que l'invariance d'échelle est brisée de manière subtile, ce qui donne lieu à des phénomènes d'intermittence. Nous avons utilisé un développement à grand nombre d'onde du NPRG pour étudier la dépendance temporelle des fonctions de corrélations dans ce système et la possibilité d''intermittence dans la cascade directe en turbulence bidimensionnelle. / This thesis focus on the study of two critical systems out of equilibrium using the tools of the non-perturbative renormalization group (NPRG).The first system is the diffusive epidemic process. This stochastic process models the propagation of an epidemic within a population, where the infected individuals recover without immunization. This model exhibit a phase transition when the epidemic goes extinct. The study consisted in applied an approximate form of the NPRG named the modified local potential approximation to this transition. It led us to take a new look at the standard lore for this model, obtained through a perturbative renormalization group analysis. In particular, whether the phase transition belongs to the universality class of the directed percolation with a conserved quantity is called into question.The second system is fully developed homogeneous isotropic turbulence, as described by the Navier-Stokes equation. The stationary state of this driven-dissipative system shows a energy cascade whose phenomenology is typical of scale-invariant systems. A more in depth examination disclose that scale invariance is broken in a subtle way. This is the origin of intermittence phenomena in turbulence. We used a large wave-number expansion of the NPRG to study the temporal dependency of correlation functions in this system and whether the direct cascade in bidimensional turbulence could develop intermittency.

Made available in DSpace on 2017-07-21T19:26:08Z (GMT). No. of bitstreams: 1 Yuri Aparecido Opata.pdf: 4954287 bytes, checksum: c870711b60baa7a02a2a9d07afe3f6bd (MD5) Previous issue date: 2014-03-21 / This work presents an experimental study of changes in structural, electrical, magnetic, and mechanical properties / No presente trabalho é apresentado um estudo experimental das mudanças nas propriedades estruturais, elétricas, magnéticas e mecânicas