Submitted by (ana.araujo@ufrpe.br) on 2016-08-12T15:41:19Z No. of bitstreams: 1 Silvio Fernando Alves Xavier Junior.pdf: 1969278 bytes, checksum: 716d98cbb2937cd01be0ff1272ed5033 (MD5) / Made available in DSpace on 2016-08-12T15:41:19Z (GMT). No. of bitstreams: 1 Silvio Fernando Alves Xavier Junior.pdf: 1969278 bytes, checksum: 716d98cbb2937cd01be0ff1272ed5033 (MD5) Previous issue date: 2011-06-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Rainfall can be understood as an end product of a number of complex atmospheric processes, which vary in space and time, and it may be considered one of most important dominant factor of the meteorological-climatic features of an specified investigated area. In this study, we observed if the dynamics of rain in Piracicaba, São Paulo - Brazil is generated by a multifractal process and / or belongs to classes of Self-Organized Criticality systems. To detect long-term correlations and multifractal behavior, we apply MF-DFA method that systematically detect nonstationarities and overcome trends in the data at all timescales. We calculated the generalized Hurst exponent, h(q), and Renyi exponent, (q). The results showed the existence of power-law long-term correlations which are described by a hierarchy of scaling exponents, that is the consequence of an underlying multifractal stochastic process. For smaller scales of about 8 months, the dynamics of rain is generated by a multifractal process (the generalized Hurst exponent, h(q), decreases with the increase in order (q) meaning it can be modeled using the cascade models. For larger scales, the value of h(q) is between 0:35 �� 0:55 indicating a weaker multifractality. The hypothesis that rainfall may be a case of Self-Organized Criticality is assessed. We analyze two events: the daily amount of rain and drought events (days without rain), both are weather phenomena that are strongly linked to rainfall. It appears that the distribution of the daily amount of rain displays two different scaling regimes for small and large intensities. The value of the ratio of these exponents confirms the results that were obtained in regions with tropical and subtropical climates. However, for the distribution of drought events we find two distinct scaling exponents with values that are closer than those observed in the daily amount of rain. The multifractal properties and self-organized criticality should be incorporated into theoretical models and computer simulations of the dynamics of rainfall and related phenomena.Rainfall can be understood as an end product of a number of complex atmospheric processes, which vary in space and time, and it may be considered one of most important dominant factor of the meteorological-climatic features of an specified investigated area. In this study, we observed if the dynamics of rain in Piracicaba, São Paulo - Brazil is generated by a multifractal process and / or belongs to classes of Self-Organized Criticality systems. To detect long-term correlations and multifractal behavior, we apply MF-DFA method that systematically detect nonstationarities and overcome trends in the data at all timescales. We calculated the generalized Hurst exponent, h(q), and Renyi exponent, (q). The results showed the existence of power-law long-term correlations which are described by a hierarchy of scaling exponents, that is the consequence of an underlying multifractal stochastic process. For smaller scales of about 8 months, the dynamics of rain is generated by a multifractal process (the generalized Hurst exponent, h(q), decreases with the increase in order (q) meaning it can be modeled using the cascade models. For larger scales, the value of h(q) is between 0:35 �� 0:55 indicating a weaker multifractality. The hypothesis that rainfall may be a case of Self-Organized Criticality is assessed. We analyze two events: the daily amount of rain and drought events (days without rain), both are weather phenomena that are strongly linked to rainfall. It appears that the distribution of the daily amount of rain displays two different scaling regimes for small and large intensities. The value of the ratio of these exponents confirms the results that were obtained in regions with tropical and subtropical climates. However, for the distribution of drought events we find two distinct scaling exponents with values that are closer than those observed in the daily amount of rain. The multifractal properties and self-organized criticality should be incorporated into theoretical models and computer simulations of the dynamics of rainfall and related phenomena. / A precipitação pode ser entendida como um produto final de processos atmosféricos complexos, os quais variam no tempo e espaço, e pode ser considerada um dos mais importantes fatores dominante das características meteorológicas-climáticas de uma determinada área investigada. Neste trabalho, verificamos se a dinâmica da chuva em Piracicaba, São Paulo - Brasil é gerada por um processo multifractal e/ou pertence as classes dos sistemas com propriedade da criticalidade auto-organizada. Para detectar a correlação de longo alcance e o comportamento multifractal, aplicamos o método MF-DFA que sistematicamente detecta não-estacionariedades e tendências nos dados para todas escalas de tempo. Calculamos o expoente generalizado de Hurst, h(q), e o expoente de Renyi, (q). Os resultados mostraram a existência de correlações de longo alcance, caracterizadas por uma hierarquia dos expoentes de escala, consequência de um processo estocástico multifractal. Para as escalas menores, aproximadamente 8 meses, a dinâmica de chuva é gerada por um processo multifractal (o expoente de Hurst generalizado, h(q), diminui com o aumento de ordem q) significando que pode ser modelada utilizando os modelos de cascata. Para as escalas maiores, o valor de h(q) está entre 0,35-0,55 o que indica a multifractalidade mais fraca. A hipótese de que a precipitação pode ser um caso de Self- Organized Criticality é avaliada. Analisamos dois eventos: a quantidade diária de chuva e eventos de seca (dias sem chuva), ambos são fenômenos metereológicos os quais são fortemente ligados à precipitação. Verifica-se que a distribuição da quantidade diária de chuva exibe dois regimes de escala distintos para pequenas e grandes quantidades. O valor da razão desses expoentes encontrados confirmam os resultados que foram obtidos nas regiões com climas tropical e subtropical. No entanto, para a distribuição de eventos de seca encontramos dois expoentes de escala distintos com valores bem mais próximos comparados com os observados na quantidade diária de chuva. As propriedades multifractais e criticalidade auto-organizada deverão ser incorporados em modelos teóricos e simulações computacionais da dinâmica das chuvas e fenômenos relacionados.

La découverte du graphène en 2004 constitue une double avancée en physique de la matière condensée. D'une part, ses propriétés électroniques sont celles d’un gaz de fermions de Dirac sans masse. D'autre part, sa structure fournit le tout premier exemple d’un matériau ordonné à deux dimensions.Cette seconde caractéristique est étudiée dans cette thèse par microscopie à effet tunnel (STM), dans le cas du graphène synthétisé en ultra-haut vide sur la face (0001) du rhénium. A deux dimensions, l’ordre cristallin est en effet impossible, et il est prédit qu’un quasi-ordre à longue distance s’y substitue, où la phase du paramètre d’ordre fluctue. Le substrat de rhénium intervient alors comme une influence extérieure qui peut restaurer l’ordre cristallin, en forçant la structure du graphène à épouser une relation d’épitaxie avec le rhénium.L’étude proposée de la structure du graphène démontre qu’elle est en fait tributaire de contraintes cinétiques héritées de sa croissance. Plusieurs nanostructures caractéristiques ont ainsi été identifiées à l’échelle atomique, permettant de remonter au mécanisme de croissance. Deux chemins réactionnels y entrent ainsi en compétition. Le premier aboutit à une famille d’agrégats de carbone métastables, de structures bien définies, en épitaxie sur le rhénium. Le second mène à la croissance d’îlots de graphène qui s’étendent sur quelques nanomètres. La coalescence de ces îlots et l’incorporation des agrégats en leur sein conduit à des défauts structurels dont la structure atomique est détaillée pour la première fois. Cette étude exhaustive révèle la diversité des chemins réactionnels lors de la croissance de graphène sur rhénium, qui sont autant de compromis entre cinétique et thermodynamique.Au terme de cette croissance, le graphène obtenu n’est pas uniforme, mais constitué de domaines s'étendant sur des distances de l'ordre de 10 nm. Chaque domaine présente une relation d'épitaxie entre le graphène et le rhénium qui lui est propre, où le graphène s'avère à la fois tourné et cisaillé par rapport à son substrat, comme le montre une méthode d’analyse d’images STM développée à cet effet. L’élaboration d’une classification universelle de ces relations d'épitaxie montre leur grande diversité. Deux interprétations se confrontent alors. Les parois entre domaines de graphène peuvent en effet être interprétées comme des défauts topologiques dans l’ordre cristallin imposé au graphène par le substrat de rhénium. Alternativement, ce sont des modes de fluctuations dont la dynamique est gelée par l’interaction avec le substrat. Ces résultats remettent donc en question la notion d’ordre cristallin imposé par son substrat à un matériau bidimensionnel. Ils montrent qu’au lieu de forcer une relation d'épitaxie particulière, l’interaction du graphène avec son substrat donne lieu à une phase dite chaotique. / The discovery of graphene in 2004 is a two-fold breakthrough in condensed matter physics. On the one hand, its electronic properties are that of a massless Dirac fermion gas. On the other hand, its structure is the very first example of an ordered material in two dimensions.This second characteristics is studied in this thesis by scanning tunneling microscopy (STM), in the case of graphene grown in ultra-high vacuum on the (0001) surface of rhenium. In two dimensions, crystalline order is indeed impossible, and it is predicted to be replaced by a quasi-long-range order, for which the phase of the order parameter fluctuates. The rhenium substrate then acts as an outside influence that can restore crystalline order, as it forces graphene's structure to adopt an epitaxial relation with rhenium.The study of graphene's structure proposed here proves it actually originates from kinetic constraints inherited from its growth. Many typical nanostructures have indeed been identified at the atomic scale, giving access to the growth mechanism. Two reaction pathways compete. The first one gives rise to a family of metastable carbon clusters with well-defined structures in epitaxy on rhenium. The second one leads to growing graphene islands of a few nanometers in size. The coalescence of these islands and the incorporation of the carbon clusters ends up forming structural defects whose atomic structure is detailed for the first time. This exhaustive study reveals reaction pathways in the growth of graphene on rhenium are diverse, and constitute compromises between kinetics and thermodynamics.At the end of that growth, the obtained graphene is not uniform, but made of roughly 10 nm-large domains. Each domain displays a specific epitaxial relation with rhenium, in which graphene is both twisted and sheared with respect to rhenium, as revealed a STM image analysis method developed for this purpose. Elaborating a universal classification of such epitaxial relations shows they are very diverse. Two interpretations of this morphology are possible. The graphene domain walls can indeed be interpreted as topological defects in the crystalline order set in graphene by the rhenium substrate. Otherwise, they are fluctuation modes whose dynamics is frozen by the interaction with the substrate. These results put into question the notion of crystalline order set by a substrate to a two-dimensional material. They show that instead of forcing a specific epitaxial relationship, the graphene-substrate interaction gives rise to a so-called chaotic phase.

Mon travail traite des propriétés géométriques de domaines présents dans un modèle magnétique simple, le modèle d'Ising. Par domaines nous entendons des régions où les spins prennent des valeurs similaires. En plus des propriétés telles que l'aimantation ou la susceptibilité magnétique, il est intéressant d'étudier la structure des domaines qu'il est naturel de décrire dans le cadre de la percolation. Dans cette thèse je me suis intéressé à plusieurs problèmes liés aux domaines de spins à l'équilibre et hors d'équilibre. J'ai ainsi étudié la dynamique des amas après des trempes critiques ou sous-critiques. Dans le cas de trempes cyritiques, le scaling dynamique a été étudié finement et l'influence des propriétés d'équilibre sur la dynamique mise en avant. Pour les trempes sous-critiques, nous avons considéré comme conditions initiales l'équilibre à une température critique ou infinie. Nous avons montré que dans le cas d'une température initiale critique la probabilité que le système finisse son évolution dans un état avec des bandes est exactement celle qu'un amas percole initialement. Concernant une température initiale infinie nous avons mis en évidence un régime transitoire conduisant le système vers le point critique de percolation. À l'équilibre à la température critique, nous avons obtenu une formule exacte pour la probabilité qu'un amas s'enroule autour d'un système avec des conditions aux bords périodiques. Nous avons aussi étudié le comportement critique du modèle d'Ising avec des interactions à longue portée en nous intéressant au passage des comportements longue portée à courte portée. / In this work I have considered the geometrical properties of the domains found in the Ising model. Those domains are regions where the spins have the same value. In addition to the properties such as magnetisation and magnetic susceptibility, it is interesting to study the domains' structure and this is done naturally within percolation theory. In this thesis, I considered several situations concerning spin domains be it in equilibrium or out of equilibrium. I studied the dynamics of domains after critical or sub-critical quenches. For critical quenches the dynamical scaling has been carefully checked and the influence of the equilibrium properties on the dynamics has been shown. For sub-critical quenches we have considered both critical and infinite temperature initial conditions. We have shown that for critical initial condition the probability that the system ends up in a stripe state is exactly the probability that a spin cluster percolates initially. For the infinite temperature initial condition, we have discovered a transient regime which brings very quickly the system to a state similar to critical percolation. In equilibrium at the critical temperature we obtained an exact formula for the wrapping probabilities of Ising spin clusters on a system with periodic boudary conditions. We have also studied the critical behaviour of the Ising model with long-range interactions with a special interest to the cross-over between the long-range and short-range regimes.

Les interactions à longue portée concernent de nombreux systèmes naturels. Un exemple notable est celui de la gravitation newtonienne qui est pertinent dans le cas de l'étude de systèmes d'étoiles ou d'amas de galaxies. Ces systèmes ont notamment la particularité de ne pas respecter l'additivité des potentiels thermodynamiques et présentent une dynamique dominée par les effets collectifs. Une caractéristique remarquable est qu'après une évolution très rapide, ces systèmes restent piégés dans des états quasi-stationnaires pendant un temps qui peut être extrêmement grand (divergeant avec la taille du système). C'est seulement sur des échelles de temps plus longue que les simulation montre que ces systèmes relaxent à l’équilibre thermodynamique.Les états quasi-stationnaire sont interprétés théoriquement comme les solution stationnaires de l'équation de Vlasov. Cette équation de champs moyen représente un très bonne approximation de la dynamique macroscopique des systèmes en interaction à longue portée dans la limite ou le nombre de particule tend vers l'infini. Dans une premier temps, nous nous attacherons à comprendre, en fonction de la portée de la force de paire et de sa régularisation à court distance, quel est le champs de validité de cette équation, et en particulier, dans quelle cas le phénomène d'état quasi-stationnaire est attendu.Dans une seconde partie, combinant les approches théoriques et numériques, nous étudions la modification de la dynamique des systèmes à longue portée soumis à différentes sortes de perturbation non-Hamiltonienne. La robustesse des états quasi-stationnaires en présence des différentes perturbation est analysée en détails. / Long range interactions concern numerous natural systems. A notable example is the one of the gravitation which is relevant in the case of the study of a stars system or galaxy clusters. In particular, these systems does not respect the additivity of thermodynamical potential and present a dynamics dominated by collective effects. One of the most remarkable feature is that, after a very rapid evolution, these systems remains trapped into quasi-stationary states up to a very long time (diverging with the system size). It is only on longer time scales, that simulations have shown that the system relaxes to thermal equilibrium.Quasi-stationary states are theoretically interpreted as solutions of the Vlasov equation. This mean filed equation represents a very good approximation of the dynamics of long range systems in the limit of a large number of particles. Firstly we give a limit on the validity of the Vlasov equation depending of the range of the pair force and on its short scales regularisation. In a second part, using theoretical an numerical approach, we study the modification of the dynamics of long range systems when subjected to different kinds of non-Hamiltonian perturbations. In particular, the robustness of quasi-stationary states, in presence of this different perturbations is analysed in details.

Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possible definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive understanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. 1

Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possi- ble definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive un- derstanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. Method for Hurst index estimation for fractional Gaussian noise and it's application on logarithmic returns of shares of selected produ- cers of beer are included in this work. 1

Att detektera ljudnivå ger mycket information i stadsområde såsom bullernivå, antal skottlossningar, antal kollisioner och detekterar plats på en ljudkälla. I detta projekt monteras en ljuddetektor som kommunicera via LoRa Long Range när ljudet överstiger ett tröskelvärde. Ljuddetektorn implementeras som en fristående modul bestående av tre befintliga moduler. Modulerna som används i projektet innefattar: Lopy4 med Expansionskort 3.1, GPS modul och Ljud sensor  Ljudnivån, batterinivå, koordinater, datum och tid överförs via LoRa-nät till en gateway och vidare till The Thing of Network, TTN websidan och samtidigt sparas data lokalt i ett SD minneskort när ljudet överstiger ett tröskelvärde. Tröskelvärdet kan modifieras efter användarens önskningar. / Detecting noise levels explains a lot in urban areas such as noise levels, number of shots, and number of collisions. In this project, a sound detector is installed that communicates via LoRa, Long Range when the sound exceeds a threshold value. The sound detector is implemented as a stand-alone module consisting of three existing modules. The modules used in the project include Lopy4 with Expansion Card 3.1, GPS module, and Sound sensor. The sound level, battery level, coordinates, date, and time are transferred via LoRa to a gateway and on to The Thing of Network, TTN website, and at the same time data is saved locally in an SD memory card when the sound exceeds a threshold. The threshold can be modified according to the user's wishes.

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One of the most important aspects for all life on this planet is theact to keep their cellular processes in a state where they do notreach equilibrium. One part in the upholding of this imbalanced stateis the barrier between the cells and their surroundings, created bythe cell membrane. In addition to experiments, the investigation ofprocesses occuring in the cell membrane can be performed by usingmolecular dynamics simulations. Through this method we can obtain anatomistic description of the dynamics associated with events that arenot accessible to experimental setups. Molecular dynamics relies onthe integration of Newton's equations of motion in order to sample therelevant parts of phase-space for the system, and therefore it isdependent on a correct description of the interactions between all thesimulated particles. In this thesis I first present an improved methodfor the calculation of long-range interactions in molecular dynamicssimulations, followed by a study of cholesterol's impact on thepermeation of small solutes across a lipid bilayer. The first paper presents a previously derived modification to theparticle-mesh Ewald method, which makes it possible to apply thisto long-range Lennard-Jones interactions. Old implementations of themethod have been haunted by an extreme performance degradation andhere I propose a solution to this problem by applying a modifiedinteraction potential. I further show that the historical treatmentof long-range interactions in simulations of lipid bilayers hasnon-negligible effects on their structural properties.In the second paper, this modification is improved such that the smallerrors introduced by the modified interaction potential becomenegligible. Furthermore, I demonstrate that I have also improved theimplementation of the method so that it now only incurs a performanceloss of roughly 15% compared to conventional simulations using theGromacs simulation package.The third paper presents a simulation study of cholesterol's effect onthe permeation of six different solutes across a variety of lipidbilayers. I analyze the effect of different head groups, tail lengths,and tail saturation by performing simulations of the solutes in fourdifferent bilayers, with cholesterol contents between 0% and50%. Analysis of the simulations shows that the impact of the surfacearea per lipid on the partitioning of the solute could be lower thanpreviously thought. Furthermore, a model with a laterallyinhomogeneous permeability in cholesterol-containing membranes isproposed, which could explain the large differences betweenpermeabilities from experiments and calculated partition coefficientsin simulations. / <p>QC 20140609</p>

<div>In spatio-temporal data analysis, the problem of non-separable space-time covariance functions is important and hard to deal with. Most of the famous constructions of these covariance functions are fully symmetric, which is inappropriate in many spatiotemporal processes. The Non-Fully Symmetric Space-Time (NFSST) Matern model by Zhang, T. and Zhang, H. (2015) provides a way to construct a non-fully symmetric non-separable space-time correlation function from marginal spatial and temporal Matern correlation functions.</div><div>In this work we use the relationship between the spatial Matern and temporal Cauchy correlation functions and their spectral densities, and provide a modification to their Bochner’s representation by including a space-time interaction term. Thus we can construct a non-fully symmetric space-time Matern-Cauchy model, from any given marginal spatial Matern and marginal temporal Cauchy correlation functions. We are able to perform computation and parameter estimate on this family, using the Taylor expansion of the correlation functions. This model has attractive properties: it has much faster estimation compared with NFSST Matern model when the spatio-temporal data is large; it enables the existence of temporal long-range dependence (LRD), adding substantially to the flexibility of marginal correlation function in the time domain. Several spatio-temporal meteorological data sets are studied using our model, including one case with temporal LRD.</div>