This thesis addresses the sampling problem in a high-dimensional space, i.e., the computation of averages with respect to a defined probability density that is a function of many variables. Such sampling problems arise in many application areas, including molecular dynamics, multiscale models, and Bayesian sampling techniques used in emerging machine learning applications. Of particular interest are thermostat techniques, in the setting of a stochastic-dynamical system, that preserve the canonical Gibbs ensemble defined by an exponentiated energy function. In this thesis we explore theory, algorithms, and numerous applications in this setting. We begin by comparing numerical methods for particle-based models. The class of methods considered includes dissipative particle dynamics (DPD) as well as a newly proposed stochastic pairwise Nosé-Hoover-Langevin (PNHL) method. Splitting methods are developed and studied in terms of their thermodynamic accuracy, two-point correlation functions, and convergence. When computational efficiency is measured by the ratio of thermodynamic accuracy to CPU time, we report significant advantages in simulation for the PNHL method compared to popular alternative schemes in the low-friction regime, without degradation of convergence rate. We propose a pairwise adaptive Langevin (PAdL) thermostat that fully captures the dynamics of DPD and thus can be directly applied in the setting of momentum-conserving simulation. These methods are potentially valuable for nonequilibrium simulation of physical systems. We again report substantial improvements in both equilibrium and nonequilibrium simulations compared to popular schemes in the literature. We also discuss the proper treatment of the Lees-Edwards boundary conditions, an essential part of modelling shear flow. We also study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. These methods are important in multiscale modelling and in the design of new machine learning algorithms for inference and parameterization for large datasets, challenges which are increasingly important in "big data" applications. In addition to providing a more comprehensive discussion of the foundations of these methods, we propose a new numerical method for the adaptive Langevin/stochastic gradient Nosé-Hoover thermostat that achieves a dramatic improvement in numerical efficiency over the most popular stochastic gradient methods reported in the literature. We demonstrate that the newly established method inherits a superconvergence property (fourth order convergence to the invariant measure for configurational quantities) recently demonstrated in the setting of Langevin dynamics. Furthermore, we propose a covariance-controlled adaptive Langevin (CCAdL) thermostat that can effectively dissipate parameter-dependent noise while maintaining a desired target distribution. The proposed method achieves a substantial speedup over popular alternative schemes for large-scale machine learning applications.

O estudo de redes complexas tem alavancado um tremendo interesse em anos recentes. Uma das características salientes de redes complexas é a presença de comunidades, ou grupos de nós densamente conectados. A detecção de comunidades pode não apenas ajudar a entender as estruturas topológicas de redes complexas, mas também pode fornecer novas técnicas para aplicações reais, como mineração de dados. Neste trabalho, propomos um novo modelo para detecção de comunidades em redes complexas, no qual várias partículas caminham na rede e competem umas com as outras para marcar seu próprio território e rejeitar partículas intrusas. O processo atinge o equilíbrio dinâmico quando cada comunidade tem apenas uma partícula. Nossa abordagem não apenas pode obter bons resultados na detecção de comunidades, como também apresenta diversas características interessantes: 1) O processo de competição de partículas é similar a muitos processos naturais e sociais, tais como competição de animais por recursos, exploração territorial por humanos (animais), campanhas eleitorais, etc.. Portanto, o modelo proposto neste trabalho pode ser útil para simular a dinâmica evolutiva de tais processos. 2) Neste modelo, nós introduzimos uma regra para controlar o nível de aleatoriedade do passeio da partícula. Descobrimos que uma pequena porção de aleatoriedade pode aumentar bastante a taxa de detecção de comunidades. Nossa descoberta é análoga ao notável fenômeno chamado ressonância estocástica onde o desempenho de um sistema determinístico não-linear pode ser bastante melhorado através da introdução de um certo nível de ruído. É interessante notar que tal fenômeno é observado em uma situação diferente aos sistemas clássicos de ressonância estocástica. 3) Nossa descoberta indica que a aleatoriedade tem um papel importante em sistemas evolutivos. Ela serve para automaticamente escapar de armadilhas não desejáveis e explorar novos espaços, isto é, ela é um descobridor de novidades. 4) Uma análise quantitativa para processo de competição entre duas particulas e duas comunidades foi conduzida, a qual é um passo de avanço para desenvolvimento de teoria fundamental de aprendizado competitivo / Study of complex networks has triggered tremendous interests in recent years. One of the salient features of complex networks is the presence of communities, or groups of densely connected nodes. Community detection can not only help to understand the topological structure of complex networks, but also provide new techniques for real applications, such as data mining. In this work, a new model for complex network community detection is proposed, in which several particles walk in the network and compete with each other to mark their own territory and reject particle intruders. The process reaches dynamics equilibrium when each community has only one particle. This approach not only can get good community detection results, but also presents several interesting features: 1) The particle competition process is rather similar to many natural and social processes, such as resource competition by animals, territory exploration by humans (animal), election campaigns, etc.. Thus, the model proposed in this work may be useful to simulate dynamical evolution of such processes. 2) In this model, a rule to control the level of randomness of particle walking is introduced. We found a small portion of randomness can largely improve the community detection rate. Such a finding is analogous to a remarkable phenomenon called stochastic resonance (SR) where the performance of a nonlinear deterministic system can be largely enhanced by introducing a certain level of noise. Interestingly, such a SR-type phenomenon is observed in quite a different situation from classical SR systems. 3) Our finding indicates that randomness has an important role in evolutionary systems and in machine learning. It serves to automatically escape some undesirable traps and explore new spaces, i.e., it is a novelty finder. 4) A quantitative analysis for two particle competition in two communities is provided. This is a step toward the development of fundamental theory of competitive learning

Sedimentation is a fundamental operation in wastewater treatment works. A rational design of sedimentation tanks is currently achieved by plotting iso-percentile (iso-percentage) concentration removal profiles from flocculent settling data. A major drawback of the graphical iso-percentage method is that the iso-percentile lines are often manually interpolated and are mere hand drawn estimations. This is because the settling behaviour of sludge particles is highly non-linear. The manual analytical process is therefore very tedious, inaccurate and subjective. Hence, an optimised design of sedimentation tanks is necessary in order to eliminate the errors incurred during data analysis. In this study, a mechanistic iso-percentile flocculent model (referred to as the velocity flocculation model) is developed to simulate the behaviour of flocculating colloidal particles in turbid water. This model is based on the physical meanings of flocculent settling particles and on fractal theory. It is formulated to produce automated iso-percentile curves which are fundamental in the design of sedimentation tanks. The iso-percentile model was vertically integrated into a velocity model to produce a model expressing the velocity of particles as a function of removal rate. The velocity model has an obvious advantage over the iso-percentile model in that it is easy to contextualize. It can be reverted back to the iso-percentile trajectory analysis eliminating the need for extensive data interpolation and may in future eliminate the need for settling column analysis altogether. In the current study, the integrated velocity form is used to predict instantaneous flocculent settling velocity of fine suspended particles under near quiescent conditions. This is vital since it is difficult to obtain velocity values in-situ or directly from sedimentation tanks. Model validity and competency was tested by a direct comparison with existing literature models, such as Ozer’s model and Ramatsoma and Chirwa’s model. Model comparison was based on the goodness of fit, the least sum of square errors and mathematical consistency with known flocculent settling behaviour. The newly developed iso-percentile model achieved a more accurate simulation of physical experimental data, did not violate any of the mathematical constraints and yielded lower sum of square errors than originally achieved by Ozer and Ramatsoma and Chirwa. Notably, the proposed velocity model offers a distinctive advantage over conventional interpolated-iso-percentile based models which are prone to numerical errors during interpolation. Its performance (velocity model) was compared against Je and Chang’s velocity model. Higher velocity values were observed for the new model than for Je and Chang’s model implying that empirically based models would tend to under-predict the velocity values. The model developed in this study brings us one step closer to achieving full automation of the settling tank and clarifier design. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Chemical Engineering / unrestricted

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21350号 / 工博第4509号 / 新制||工||1702(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 後藤 仁志, 教授 KIM Chul-Woo, 准教授 KHAYYER,Abbas / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

No description available.

[pt] Suspensões correspondem a uma classe de materiais amplamente utilizada em uma grande variedade de aplicações e indústrias. Devido à sua extrema versatilidade, elas têm sido foco de inúmeros estudos nas últimas décadas. Suspensões também são muito flexíveis e podem apresentar diferentes propriedades reológicas e respostas macroscópicas dependendo da escolha dos parâmetros usados como entrada no sistema. Mais especificamente, a resposta reológica de suspensões está intimamente associada ao arranjo microestrutural das partículas que compõem o meio e a fatores externos, como o quão confinadas elas se encontram e a rigidez das partículas. No presente estudo, o efeito da rigidez, confinamento e vazão na microestrutura de suspensões altamente concentradas é avaliado usando Dinâmica Dissipativa de Partículas com Núcleo Modificado. Precedento este estudo principal, foram necessárias outras duas etapas para garantir um sistema de simulação confiável e representativo, que consistiu, essencialmente, na realização de estudos paramétricos para compreender e estimar os valores adequados para os parâmetros de interacção parede-partícula. O presente trabalho aborda estudos paramétricos realizados para auxiliar na escolha dos parâmetros de entrada para evitar a penetração de partículas em um sistema delimitado por paredes. Inicialmente um sistema mais simples, composto por solvente e paredes é construído e os parâmetros de interação e densidades de parede foram ajustados. Em seguida as interações são definidas para suspensões. Neste último caso, vários parâmetros desempenham um papel na penetração e a maneira tradicional de investigar esses efeitos seria exaustiva e demorada. Por isso, optamos por usar uma abordagem de Machine Learning para realizar este estudo. Uma vez ajustados os parâmetros, o estudo de confinamento pôde ser realizado. O objetivo principal deste estudo foi entender como a microestrutura de suspensões concentradas é afetada pela vazão, rigidez das partículas e confinamento. Verificou-se que partículas muito flexíveis sempre formam um aglomerado gigante independente da razão de confinamento; a diferença está em quão compactadas são as partículas. No caso de partículas rígidas, um confinamento mais forte leva à formação de aglomerados maiores. O estudo final aborda um estudo de aprendizado de máquina realizado para prever a reologia de suspensões não confinadas. Com este trabalho foi possível entender e ajustar parâmetros de simulação e desenvolver um domínio computacional que permite estudar sistematicamente efeitos do confinamento em suspensões. / [en] Suspensions correspond to a class of materials vastly used in a large set of applications and industries. Due to its extreme versatility, they have been the focus of numerous studies over the past decades. Suspensions are also very flexible and can display different rheological properties and macroscopic responses depending on the choice of parameters used as input in the system. More specifically, the rheological response of suspensions is intimately associated to the microstructural arrangement of the particles composing the medium and external factors, such as how strongly they are confined and particle rigidity. In the present study, the effect of particle rigidity, confinement and flow rate on the microstructure of highly concentrated suspensions is studied using CoreModified Dissipative Particle Dynamics. Preceding this main study, two other steps were necessary to guarantee a reliable and realistic simulation system, which consisted, essentially, on performing parametric studies to understand and estimate the appropriate values for wall-particle interaction parameters. The present work address parametric studies performed to assist the input parameters choice to prevent particle penetration in a wall-bounded system. Initially a simpler system, composed of solvent and walls, is built and the interaction parameters and wall densities were adjusted. Following, the interactions are set for suspensions. In the latter case multiple parameters play a role in penetration and the traditional way to investigate these effects would be exhaustive and time consuming. Hence, we choose to use a Machine Learning approach to perform this study. Once the parameters were adjusted, the study of confinement could be carried out. The main goal of this study was to understand how the microstructure of concentrated suspensions is affected by flow rate, particle rigidity and confinement. It was found that very soft particles always form a giant cluster regardless the confinement ratio; the difference being on how packed the particles are. In the rigid case, a stronger confinement leads the formation of larger clusters. The final study addresses a machine learning study carried out to predict the rheology of unconfined suspensions. The main contribution of this work is that it was possible to understand and adjust simulation parameters and develop a computational domain that enables to systematically study confinement effects on suspensions.

No description available.

La thèse est consacrée à la modélisation discrète et continue des écoulements sanguins et des phénomènes connexes tels que la coagulation du sang et l'athérosclérose. Ce travail comprend l'élaboration des modèles mathématiques et numériques de la coagulation du sang, des simulations numériques et l'analyse mathématique d'un modèle d'inflammation chronique au cours d'athérosclérose. Une partie importante de la thèse est liée à la programmation, la mise en œuvre et l'optimisation des codes numériques. La partie principale de la thèse concerne la modélisation de la coagulation du sang in vivo tenant compte des écoulements sanguins, les réactions biochimiques dans le plasma et l'agrégation de plaquettes. La nouveauté principale de ce travail est l'élaboration d'un modèle hybride (discret-continu) de la coagulation du sang et de la formation de caillot sanguin dans le flux. La partie théorique de la thèse est consacrée à l'analyse mathématique d'un modèle d'inflammation chronique liée à l'athérosclérose. Les simulations numériques réalisées dans le cadre de cette thèse impliquent l'élaboration des algorithmes numériques pour les modèles mathématiques et le d´développement des logiciels. Vu le fait que les simulations numériques ont été coûteuse en temps de calcul, des efforts considérables ont été consacrés à la parallélisation des logiciels et à leur optimisation / The thesis is devoted to discrete and continuous modelling of blood flows and related phenomena such as blood coagulation and atherosclerosis. It includes the development of mathematical and numerical models of blood coagulation, numerical simulations and the mathematical analysis of a model problem of chronic inflammation during atherosclerosis. The main part of the thesis concerns modelling of blood coagulation in vivo which takes into account blood flows, biochemical reactions in plasma and platelet aggregation. The main novelty of this work is the development of a hybrid (discrete-continuous) model of blood coagulation and clot formation in flow. The model is used to study several aspects of blood coagulation in flow : platelet aggregation and its interaction with coagulation pathways, influence of the flow speed on the clot development, a possible mechanism by which clot stops growing. The theoretical part of the thesis is devoted to the mathematical analysis of a model of chronic inflammation related to atherosclerosis. In this thesis we study a model problem which describes the propagation of a reaction-diffusion wave in the 2D case with non-linear boundary conditions. For that we use the Leray-Schauder method and a priori estimates of solutions in order to prove the existence of waves in the bistable case. Numerical simulations carried out in the framework of this thesis were based on the numerical implementation of the corresponding models and on the software development. Since the numerical simulations were computationally expensive, a substantial effort was directed to software parallelization and optimization

Un fondu de polymères est un liquide complexe constitué de chaînes macromoléculaires. Ces chaînes présentent la particularité d'offrir une distribution de temps caractéristiques extrêmement importante. L'ensemble de ces différentes échelles représente donc un défi pour la simulation numérique de polymères longs et sont bien au-delà des capacités des ordinateurs actuels. Un thème actuel de recherche porte donc sur le développement de modèles mésoscopiques (modèle gros grains). La construction d'un tel modèle consiste à éliminer les degrés de liberté rapide en regroupant un certain nombre d'atomes en un monomère. Ce monomère est représenté par une sphère molle évoluant dans un bain thermique créé par les degrés de liberté rapides éliminés au cours du processus de nivellement. La dynamique des particules créées est donc stochastique. La dynamique particulaire dissipative qui intègre ces idées est une combinaison de dynamique moléculaire, de Lattice Gas Automata ainsi que de dynamique Brownienne. Le champ de force DPD est constitué d'une interaction molle et d'un thermostat (force dissipative et bruit) et les paramètres de ce champ de force sont généralement calibrés sur des données expérimentales (compressibilité et diffusion). Cette approche est difficilement applicable aux mélanges de polymères. Pour surmonter cette difficulté, l'intégralité du champ de force DPD est construit à partir d'une dynamique moléculaire pour des corps purs ainsi que pour des mélanges. Nous montrons également que pour calculer correctement la force dissipative, la dynamique moléculaire doit être altérée en contraignant la position des monomères. Les coefficients de transport sont calculés par DPD et comparés à ceux obtenus par dynamique moléculaire. Ce travail s'achève par une étude de la transferabilité du champ de force du monomère vers toute une chaîne de polymères. / A molten polymer is a complex liquid consisting of macromolecular chains. These chains have many different time scales. All these scales present a real challenge to numerical simulations and exceed the computational capabilities of today's computers. A current topic of research therefore focuses on the development of mesoscopic models. The main idea behind coarse-graining is to eliminate fast degrees of freedom grouping atoms or molecules into clusters (or monomers). This monomer is represented by a soft sphere operating in a thermal bath generated by the fast degrees of freedom eliminated during the coarse-graining. Particle dynamics is therfore stochastic. Dissipative particle dyna-mics, which includes these ideas, is a combination of molecular dynamics, Lattice Gas Automata and Brownian dynamics. DPD force field consist of a soft interaction and a thermostat (dissipative and random force) and parameters of DPD interaction are generally optimized to match some macroscopic properties like compressibility or self-diffusion coefficient. This approach is difficult to apply to polymer melt. To overcome this problem, we apply an operational procedure available in the literature to the cons-truction of conservative and dissipative forces of DPD force field for pure substances and mixtures. We also show that in order to calculate the dissipative forces, the underlying molecular dynamics must be altered by constraining the position of the mo-nomers. Transport coefficients are calculated by DPD and compared with those obtained by molecular dynamics. This work concludes with a study of the transferability of the force field of the monomer to a chain of polymers.

Submitted by Celso Magalhaes (celsomagalhaes@ufrrj.br) on 2017-09-18T11:33:32Z No. of bitstreams: 1 2016 - Jo?o M?rcio Sutana Alvim.pdf: 4276113 bytes, checksum: 115487153abb7bab43e2a012959a64e4 (MD5) / Made available in DSpace on 2017-09-18T11:33:34Z (GMT). No. of bitstreams: 1 2016 - Jo?o M?rcio Sutana Alvim.pdf: 4276113 bytes, checksum: 115487153abb7bab43e2a012959a64e4 (MD5) Previous issue date: 2016-12-21 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / In the classic set of unit operations of solid-liquid separation, sedimentation and filtration techniques stand out as critical processing steps for a broad spectrum of industrial activities. In this context, the proper knowledge of the properties and characteristics of the particulate systems directly involved represents an important aspect for the safe and efficient design of equipment and processes. Over the past 20 years, several methodologies were developed to study such phenomena, resulting in a huge library of sedimentation and filtration models available in the literature. This work presents a study based on the use of a particle-scale numerical simulation technique called Discrete Element Method (DEM), to describe the deposition of particulate solids in liquids. Tridimensional simulations of the sedimentation and filtration processes were carried out in a previously known flow field, as a way to test the applicability of the code and its capacity to virtually describe such processes. Cake properties, such as thickness, porosity and permeability were quantified over time and compared qualitatively and quantitatively with literature data. The effects of operational conditions, solids and liquid properties on the particulate model?s response were also investigated through a series of controlled numerical tests. The packing fraction values obtained in this work for the sedimentation process, when compared to the values found in the literature on similar conditions, showed a satisfactory agreement, with deviations smaller than 12% for all the points assessed / Dentro do conjunto cl?ssico das opera??es unit?rias de separa??o s?lido?l?quido, as t?cnicas de sedimenta??o e filtra??o se destacam como etapas de processamento cruciais para um amplo espectro de atividades da ind?stria. Neste contexto, o conhecimento adequado das propriedades e caracter?sticas dos sistemas particulados diretamente envolvidos representa um aspecto importante para o projeto seguro e eficiente de equipamentos e processos. Ao longo dos ?ltimos 20 anos, diversas metodologias foram desenvolvidas para estudar tais fen?menos, resultando em uma ampla biblioteca de modelos de sedimenta??o e filtra??o dispon?vel na literatura. O presente trabalho apresenta um estudo baseado no uso da simula??o num?rica em escala de part?cula, atrav?s do M?todo de Elementos Discretos ou DEM (do ingl?s ?Discrete Element Method?), para descrever a deposi??o de s?lidos particulados em suspens?es. Foram realizadas simula??es da sedimenta??o e filtra??o em tr?s dimens?es como forma de testar o funcionamento do c?digo e a sua capacidade de reproduzir virtualmente tais processos. As propriedades da torta, tais como espessura, porosidade e permeabilidade foram quantificadas ao longo do tempo e comparadas qualitativa e quantitativamente com dados da literatura. A sensibilidade do modelo desenvolvido a varia??es nas condi??es operacionais de simula??o e nas propriedades f?sicas do s?lido e do l?quido tamb?m foi analisada. Os dados de fra??o de s?lidos obtidos nas simula??es da sedimenta??o apresentaram uma concord?ncia satisfat?ria, quando comparados aos valores encontrados na literatura em condi??es similares, apresentando desvios menores do que 12% para todos os pontos avaliados.