Stochastic models describing how interacting individuals give rise to collective behaviour have become a widely used tool across disciplines—ranging from biology to physics to social sciences. Continuum population-level models based on partial differential equations for the population density can be a very useful tool (when, for large systems, particle-based models become computationally intractable), but the challenge is to predict the correct macroscopic description of the key attributes at the particle level (such as interactions between individuals and evolution rules). In this thesis we consider the simple class of models consisting of diffusive particles with short-range interactions. It is relevant to many applications, such as colloidal systems and granular gases, and also for more complex systems such as diffusion through ion channels, biological cell populations and animal swarms. To derive the macroscopic model of such systems, previous studies have used ad hoc closure approximations, often generating errors. Instead, we provide a new systematic method based on matched asymptotic expansions to establish the link between the individual- and the population-level models. We begin by deriving the population-level model of a system of identical Brownian hard spheres. The result is a nonlinear diffusion equation for the one-particle density function with excluded-volume effects enhancing the overall collective diffusion rate. We then expand this core problem in several directions. First, for a system with two types of particles (two species) we obtain a nonlinear cross-diffusion model. This model captures both alternative notions of diffusion, the collective diffusion and the self-diffusion, and can be used to study diffusion through obstacles. Second, we study the diffusion of finite-size particles through confined domains such as a narrow channel or a Hele–Shaw cell. In this case the macroscopic model depends on a confinement parameter and interpolates between severe confinement (e.g., a single- file diffusion in the narrow channel case) and an unconfined situation. Finally, the analysis for diffusive soft spheres, particles with soft-core repulsive potentials, yields an interaction-dependent non-linear term in the diffusion equation.

Solid state lithium ion electrolytes are important to the development of next generation safer and high power density lithium ion batteries. Perovskite-structured LLT is a promising solid electrolyte with high lithium ion conductivity. LLT also serves as a good model system to understand lithium ion diffusion behaviors in solids. In this thesis, molecular dynamics and related atomistic computer simulations were used to study the diffusion behavior and diffusion mechanism in bulk crystal and grain boundary in lithium lanthanum titanate (LLT) solid state electrolytes. The effects of defect concentration on the structure and lithium ion diffusion behaviors in LLT were systematically studied and the lithium ion self-diffusion and diffusion energy barrier were investigated by both dynamic simulations and static calculations using the nudged elastic band (NEB) method. The simulation results show that there exist an optimal vacancy concentration at around x=0.067 at which lithium ions have the highest diffusion coefficient and the lowest diffusion energy barrier. The lowest energy barrier from dynamics simulations was found to be around 0.22 eV, which compared favorably with 0.19 eV from static NEB calculations. It was also found that lithium ions diffuse through bottleneck structures made of oxygen ions, which expand in dimension by 8-10% when lithium ions pass through. By designing perovskite structures with large bottleneck sizes can lead to materials with higher lithium ion conductivities. The structure and diffusion behavior of lithium silicate glasses and their interfaces, due to their importance as a grain boundary phase, with LLT crystals were also investigated by using molecular dynamics simulations. The short and medium range structures of the lithium silicate glasses were characterized and the ceramic/glass interface models were obtained using MD simulations. Lithium ion diffusion behaviors in the glass and across the glass/ceramic interfaces were investigated. It was found that there existed a minor segregation of lithium ions at the glass/crystal interface. Lithium ion diffusion energy barrier at the interface was found to be dominated by the glass phase.

This thesis focuses on option of omitting the stationarity assumption, which is usually used in the financial time series analysis. The theory of semi-stationary processes is introduced. This type of process has time-dependent spectra (the evolutionary spectra) in comparison with stationary process. The evolutionary spectra estimator is derived using a linear filter and then averaged in time to reduce any fluctuations caused by randomness. Predictions and variance estimates are retrieved from the estimated time dependent spectra. The semi-stationary processes theory is applied to the ARMA processes with time-dependent coefficients, a coefficient estimator based on evolutionary spectra is suggested. Calculations are performed in R software. Powered by TCPDF (www.tcpdf.org)

[pt] Nesta dissertação, é apresentado um procedimento estatístico para a estimação de perfis de curvas de carga por aparelhos para consumidores residenciais atendidos na BT (Baixa Tensão). O modelo desenvolvido utiliza informações de duas fontes distintas: PPHs (Pesquisas de Posses e Hábitos de Aparelhos Elétricos) e Medições de consumo com medidores eletrônicos com memória de massa que gravam leituras de consumo por aparelhos a cada 15 minutos. Através das PPHs desenvolvidas por Procel/Eletrobrás em 1996, obtêm-se um perfil aproximado da curva de carga do domicilio por aparelho. Entretanto, esta curva tende a ser imprecisa, pois é obtida por declarações de uso dos aparelhos. Para reduzir esta imprecisão, foi montado um experimento onde uma sub-amostra de domicílios auditados pelas PPHs, teve os principais aparelhos da residência medidos por medidores eletrônicos em intervalos de 15 minutos. A partir das curvas de utilização destes aparelhos, obtidas pelos dois procedimentos, utilizou-se um modelo estatístico de regressão linear para estimar coeficientes de ajustes para correção das curvas declaradas para cada hora do dia, para os principais eletrodomésticos do domicílio. Os resultados foram aplicados a duas distribuidoras do grupo ENDESA: AMPLA e COELCE. / [en] In this thesis, it is presented a statistical based model that allows the estimation of the load shape curve for appliances (end uses) for residential consumers that belong to low voltage group (BT clients), using information from two sources: PPHs (Energy Audit on Ownership and Usage of Electrical Appliances) and household measurements through specific devices that provide not only the total consumption (15 minute intervals) as well as the breakdown of this consumption for each device (end use) existing in the household. Through energy audits (PPHs) developed by Procel/Eletrobrás in 1996, one has a rough idea of the load shape curves by appliance. However, the curves obtained this way tend to be rather imprecise, as they are obtained by the consumer information of usage of the equipments on the surveys, which tend to be rather vague. In order to reduce such imprecision, an experiment was set where a subsample of the original survey sample is selected and the main appliances consumption measured by electronic meters at intervals of 15 minutes. The end use load shape obtained by these meters are then compared with the corresponding curve obtained by usage declaration. Using the linear regression model, the correction coefficients of the declarations are obtained for each hour of the day, for the main appliances. The results were applied to two distribution utilities of the ENDESA group: AMPLA and COELCE.

Orientador: Carlos Roberto Padovani / Banca: Marie Oshiiwa / Banca: Sandra Fiorelli de Almeida Penteado Simeão / Banca: José Carlos Martinez / Banca: Luis Carlos Giarola / Resumo: Objetivou-se a construção de Índices Percentuais de "Status" - IDPS (%) visando à ordenação e classificação de assentamentos rurais, em relação ao desenvolvimento sustentável (IDPSDS (%)), considerando aspectos agronômico, socioeconômico e ambiental, para diagnosticar a realidade dos mesmos. Nesse sentido, consideraram-se procedimentos metodológicos estatísticos analíticos univariados e multivariados para o estabelecimento de descritores analíticos - índices - envolvendo técnicas de Coeficientes de Variação (CV) e Componentes Principais (CP), que foram empregados na construção dos IDPSDS (%). Dados de assentamentos rurais, de sete regiões do Estado de Mato Grosso foram usados na exemplificação da metodologia. A partir de diagnósticos cedidos pela Empresa Mato-Grossense de Pesquisa, Assistência e Extensão Rural S/A - EMPAER-MT, variáveis foram agrupadas em 22 blocos, sendo que seis foram utilizados na construção de índices. As técnicas CP e CV também foram aplicadas em bloco único geral, com 47 variáveis. A variação do Índice Percentual de "Status" (%) - IDPS (%) foi de 0% a 100%. A concordância mínima nos resultados entre as técnicas foi de 6% e máxima de 32%. Os assentamentos com maiores IDPSDS (%) foram considerados de "maior potencial" em relação às variáveis consideradas. A opção de utilização do IDPS (%) pela técnica dos Coeficientes de Variação ou de Componentes Principais é livre e depende exclusivamente do interesse da pesquisa. A fim de comparar os resultados da classificação geral com os grupos formados em função de similaridade do comportamento das variáveis elencadas no bloco único geral, realizou-se o agrupamento dos assentamentos, utilizando-se a técnica de Agrupamento. A classificação e o agrupamento geraram resultados coerentes. O assentamento Vale do Seringal pertencente à região de ...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The purpose of this study was the building of Percentage Indexes of "Status" - PIS (%), seeking the ordination and classification of rural settlements, regarding to the sustainable development (Percentages Indexes of Sustainable Development "Status" - PISDS (%)), considering agronomical, socioeconomic and environmental aspects, to diagnose the reality of rural settlements. In this sense, it was took into consideration univariate and multivariate statistical-analytical methodological procedures to the establishment of analytical descriptors - indexes - involving techniques of Variation Coefficients (VC) and Principal Components (PC), which were used in the construction of PISDS (%). Data of rural settlements, from seven regions of the State of Mato Grosso were used in the exemplification of the methodology. By using diagnosis released by the Enterprise of Research, Assistance and Rural Extension from Mato Grosso Inc. - EMPAER- MT, variables were grouped in 22 blocks, 6 blocks of which were used to construct the indexes. The VC and PC techniques were also applied in a unique general block, with 47 variables. The variation of the Percentage Index of "Status" (%) - PIS (%) was from 0% to 100%. The minimum concordance in the results between the techniques was 6% and the maximum, 32%. The settlements with higher PISDS (%) were considered as "higher potential" regarding the considered variables. The option of usage of the PIS (%) by the technique of the Variation Coefficients or the Principal Components is free and depends only on the interest of the research. In order to compare the results of the general classification with the groups formed in function of the similarities in the behavior of the variables listed in the unique general block, the grouping of settlements has been done, using the technique of Grouping. The classification... (Complete abstract click electronic access below) / Doutor

O Parque Ecológico Tietê (PET), em Ermelino Matarazzo, a leste da região metropolitana de São Paulo, foi criado com o objetivo de preservar as várzeas do rio Tietê. Antes da criação do parque, a região foi palco de várias atividades antrópicas que levaram ao risco de contaminação do solo e águas subterrâneas. A recuperação iniciou-se com o plantio de espécies nativas, o que também promoveu a recolonização da fauna, composta essencialmente de espécies frugívoras. Dentre as espécies de plantas presentes no parque, a palmeira Jerivá (Syagrus romanzoffiana) é importante por sua ampla distribuição geográfica nos ecossistemas brasileiros. O presente estudo teve como objetivo compreender, através de coeficientes de prospecção biogeoquímicos, a interação entre os compartimentos solo, água subterrânea e planta, este último representado pela palmeira Jerivá. Os resultados indicaram que o Jerivá apresentou diferentes coeficientes de absorção entre suas folhas e pecíolos. O estudo também demonstrou que fatores como sazonalidade dentro de um período mínimo de um ano, idade e espécies de plantas devem ser levados em conta em abordagens biogeoquímicas. / The Tietê Ecological Park (PET) in Ermelino Matarazzo, east of the metropolitan area of São Paulo city, was created with the purpose of preserving the floodplains of the Tietê River. Prior to the establishment of the park, the region was scene of several anthropogenic activities which led to high risk of soil and groundwater contamination. Subsequent recovery of the degraded area was aimed through the planting of native plant species, which also promoted the recolonization of the area by the fauna, essentially composed of frugivorous species. Among the plant species introduced in the park, the Jerivá palm tree (Syagrus romanzoffiana) is important for its wide geographical distribution in Brazilian ecosystems. The current study aimed to understand, through biogeochemical prospecting coefficients, the interaction between soil compartments, underground water and plant, the latter represented by the Jerivá palm tree. The results indicated that Jerivá presented different absorption coefficients among its leaves and petioles. The study also demonstrated that factors like seasonality within a minimum period of one year, age and plant species must be taken into account in biogeochemical approaches.

Estudou-se nesta pesquisa o processo de lodos ativados para pós-tratamento do efluente proveniente de um reator anaeróbio compartimentado, que recebe esgoto sanitário. Isso se deu em vários ensaios em sistema descontínuo (\"batch\'\') para avaliar a biodegradabilidade dessa água residuária e em um ensaio em sistema contínuo com finalidade de melhorar a qualidade do efluente final e determinar os coeficientes cinéticos, os parâmetros a\' e b \', a taxa de utilização de oxigênio e o coeficiente &#945. Também realizaram-se ensaios hidrodinâmicos para verificação do tipo de reator utilizado. A pesquisa desenvolveu-se com base em uma célula de aeração, em escala de laboratório, composta por quatro câmaras (reatores) que possuíam tanque de aeração e decantador secundário justapostos, separados por uma cortina fixa. Não houve controle de temperatura nos dois sistemas utilizados. No ensaio em sistema contínuo quatro reatores foram operados simultaneamente com as respectivas idades do lodo de 5, 10, 15 e 20 dias durante 35 dias. O tempo de detenção hidráulico foi mantido próximo de 8 horas. Nesse ensaio os reatores quando se encontravam estabilizados dinamicamente, apresentaram remoção superior a 95% para DBO bruta, 90% para DBO filtrada, 87% para DQO bruta, 80% para DQO filtrada e 95% para SST. Mesmo não sendo realizado processo adicional para remoção de nutrientes, os reatores, após a estabilização dinâmica, apresentaram remoção de fosfato de até 28% e de nitrogênio amoniacal até níveis de não serem detectados pelos métodos de análises utilizados. Os ensaios hidrodinâmicos mostraram que os reatores são do tipo mistura completa. / In this work the activated sludge process for post-treatment of effluent anaerobic baffled reactor which receives sanitary sewage was studied. This was established during various experiments in batch system to evaluate the biodegradable of this wastewater and also in an experiment of continuous system aiming to improve the quality of the final effluent and to determine the kinetic coefficients, the a\' and b\' parameters, the oxygen uptake rate and the &#945 coefficient. Hydrodynamic tests to verify the type of reactor used in this research were also perfonned. The work was developed and based on an aeration cell bench-scale, composed of four chambers (reactors) which had an aeration tank and a secondary settling tank in the same chamber, separated by a fixed baffle. Temperature control was not used in both systems. In the experiment of continuous system, four reactors were simultaneously operated with sludge age of 5, 10, 15 and 20 days during 35 days. The hidraulic retention time was maintained at around 8 hours. When the reactors were dynamically stabilized, they showed an average removal superior to 95% for BOD (biochemical oxygen demand), 90% for filtrated BOD, 87% for COD (chemical oxygen demand), 80% for filtrated COD and 95% for TSS (total suspended solids). Without additional process of nutrient removal, after the dynamic stabilization the reactors presented up to 28% of total phosphate removal and ammonia nitrogen up to levels of not being detected by the analyses methods used. The hydrodynamic tests showed that the reactors are of the complete-mix type.

Adaptive filtering has grown to become a fundamental topic in signal processing, increasingly attracting attention from the community. Important factors in this popularization were their low computational complexity and model-free nature, adapting even to nonstationary characteristics of the systems and/or signals under study. Nevertheless, many adaptive algorithms introduce trade-offs, for instance, between convergence rate, nonstationary signals tracking, and steady-state error, which can hinder their use in practical applications. Furthermore, some adaptive filters can become unstable when word length is reduced and/or the input data are highly correlated. Recently, combination of adaptive filters was put forward as a solution for such issues. This approach consists in combining a pool of filters by means of a supervisor that attempts to make the overall system at least as good (usually in the mean-square sense) as the best filter in the set. Examples of these structures have been shown to successfully solve this problem, although well-known limitations remain to be addressed. Moreover, due to the relative novelty of this topic, developments in combination of adaptive filters are difficult to accommodate into a common theoretical framework. This work studies combination of adaptive filters and addresses the aforementioned issue by (i) classifying the existing combinations and proposing a taxonomy that exposes the similarities and differences in their forms; (ii) proposing new combinations; (iii) devising a general framework for studying combinations of adaptive filters and using such framework in performance analyses. / Filtragem adaptativa vem ganhando destaque desde seu surgimento tornando-se um tópico de estudo fundamental em processamento de sinais. A versatilidade de dispensarem total conhecimento das propriedades estatísticas dos sinais, aliada à simplicidade computacional de seus métodos, foram importantes fatores em sua consagração. Apesar disto, muitos filtros adaptativos apresentam compromissos envolvendo, por exemplo, velocidade de convergência, rastreamento de sinais não-estacionários e erro em regime, que podem dificultar sua aplicação na prática. Ademais, alguns algoritmos adaptativos são instáveis quando suas entradas são altamente correlacionados e/ou a precisão dos cálculos é reduzida. Uma solução recente para estes problemas é o uso de combinações de filtros adaptativos. Esta abordagem baseia-se em combinar um conjunto de filtros por meio de um supervisor que procura fazer com que o sistema global seja pelo menos tão bom (em geral no sentido quadrático médio) quanto o melhor filtro do conjunto. Exemplos destas estruturas já mostraram a eficácia deste método, apesar de ainda existirem reconhecida limitações. Além disso, em se tratando de um tópico relativamente recente, os desenvolvimentos na área de combinação de filtros adaptativos não possuem uma estrutura teórica unificada. Este trabalho propõe abordar estas questões (i) classificando as combinações existentes e criando uma taxonomia que explicite semelhanças e diferenças entre elas; (ii) introduzindo novas combinações; e (iii) desenvolvendo uma forma unificada de descrever combinações de filtros adaptativos e usando-a em análises de desempenho.

In der vorliegenden Arbeit wurden drei unabhängige Problemfelder moderner biophysikalischer und materialwissenschaftlicher Forschung untersucht: Diffusion in binären Legierungen, der Umbauprozess in trabekulärem Knochen und die Voraussage mechanischer Eigenschaften, insbesonders der Biegesteifigkeit, selbstorganisierender, amphiphiler Membrane. Für alle drei Problemfelder wurden Gittermodelle gewählt, um ausgesuchte Fragestellungen zu untersuchen. Für den Fall der Diffusion in Legierungen war dies, inwieweit sich der Diffusionprozess, der sich auf atomarer Ebene als diskrete Platztäusche zwischen Atomen und Leerstellen manifestiert, auf einer größeren, makroskopischen, Ebene mit Hilfe einer kontinuumstheoretischen Theorie beschreiben lässt. Im Fall der Beschreibung des Umbauprozesses in in trabekulärem Knochen wurde die die spongiöse Architektur des Knochens auf ein Gitter abgebildet und mittels einer vereinfachten mechanischen Beschreibung die lokale Belastung in jedem Knochenelement bestimmt. Die zeitliche Entwicklung des Systems wurde mittels eines stochastischen Umbaugesetzes gesteuert, das die Wahrscheinlichkeit für Knochenan- bzw. -abbau als Funktion der lokalen Volumenänderung vorgab. Es wurde gezeigt, dass ein nicht-lineares Umbaugesetz bessere Übereinstimmung mit experimentellen Ergebnissen zeigt, als ein rein lineares. Weiters wurde das Krankheitsbild der Osteoporose untersucht und es konnte eine Unterscheidung zwischen einem normalen Alterungsprozess der Knochenstruktur und einer krankhaften Veränderung gezogen werden. Um die mechanischen Eigenschaften selbstorganisierender Membrane zu bestimmen, wurden linear elastische Federkräfte zwischen benachbarten Molekülen angenommen. Die volle elastische Matrix und daraus die gewünschten Eigenschaften wurden für unterschiedliche Zusammensetzungen der Membrane bestimmt. Es wurde gezeigt, dass die Biegesteifigkeit solcher Membrane in einem begrenzten Konzentrationsbereich um mehrere Größenordnungen variieren kann. / This thesis presents the results of investigations on three independent research topics of modern biophysical and materials science research: substitutional diffusion in binary alloys, the remodelling process in trabecular bone and the prediction of mechanical properties of self assembling, amphiphilic bilayers. The basic description of all three projects is based on lattice models, a highly successful class of models that are used in several fields of modern physics to describe physical processes. For the diffusional process in alloys, which on a microscopic scale manifests in a discrete site exchange between one atom and a neighbouring vacancy, it was investigated how this microscopic description can be reconciled with a macroscopic continuum model. For the investigations on remodelling of trabecular bone, the architecture of bone was mapped onto a lattice and the local mechanical state of each element was determined by a simplified mechanical model. A stochastic description was chosen to model the time evolution of the system, relating the probability of bone formation and resorption, respectively, to the local volume changes of the bone elements. It was shown that a non-linear remodelling law is a better candidate to describe the remodelling process in real bone than a linear one. Furthermore, applying the model to osteoporosis - a wide spread bone disease - it was shown that in the features attributed to osteoporosis one has to distinguish between normal ageing of bone''s architecture and additional changes that stem from pathological alterations in the regulatory system. A simple concept was introduced to model the mechanical properties of self-assembled membranes. The molecules forming the membrane are assumed to occupy a triangular lattice, nearest neighbours are connected by linear elastic springs. It was shown that the bending rigidity exhibits a pronounced concentration dependence, varying over orders of magnitude in a narrow concentration regime.

Orientador: Samuel da Silva / Resumo: O principal objetivo deste trabalho é usar métodos de extrapolação em coeficientes de modelos autorregressivos (AR), para fornecer informações futuras de condições de estruturas na existência de mecanismo de danos pré-definidos. Os modelos AR são estimados considerando a predição de um passo à frente, verificados e validados a partir de dados de vibração de uma estrutura na condição não danificada. Os erros de predição são usados para extrair um indicador para classificar a condição do sistema. Então, um novo modelo é identificado se qualquer variação de índices de dano ocorrer, e seus coeficientes são comparados com os do modelo de referência. A extrapolação dos coeficientes de AR é realizada através das splines cúbicas por partes que evitam possíveis instabilidades e alterações indesejáveis dos polinômios, obtendo aproximações adequadas através de polinômios de baixa ordem. Uma curva de tendência para o indicador capaz de predizer o comportamento futuro pode ser obtida a partir da extrapolação direta dos coeficientes. Uma estrutura de três andares com um para-choque e uma coluna de alumínio colocada no centro do último andar são analisados com diferentes cenários de dano para ilustrar a abordagem. Os resultados indicam a possibilidade de estimar a condição futura do sistema a partir dos dados de vibração nas condições de danos iniciais. / Abstract: The main purpose of this work is to apply extrapolation methods upon coefficients of autoregressive models (AR), to provide future condition information of structures in the existence of predefined damage mechanism. The AR models are estimated considering one-step-ahead prediction, verified and validated from vibration data of a structure in the undamaged condition. The prediction errors are used to extract an indicator to classify the system state condition. Then, a new model is identified if any variation of damage indices occurs, and its coefficients are compared to the ones from the reference model. The extrapolation of the AR coefficients is performed through the piecewise cubic splines that avoid possible instabilities and undesirable changes of the polynomials, obtaining suitable approximations through low-order polynomials. A trending curve for the indicator capable of predicting future behavior can be obtained from direct coefficient extrapolation. A benchmark of a three-story building structure with a bumper and an aluminum column placed on the center of the top floor is analyzed with different damage scenarios to illustrate the approach. The results indicate the feasibility of estimating the future system state from the vibration data in the initial damage conditions. / Mestre