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(In,Ga)N/GaN-Leuchtdioden wurden vor mehr als 10 Jahren kommerzialisiert, dennoch ist das Verständnis über den Einfluss von Lokalisierung auf die Rekombinationsdynamik in den (In,Ga)N/GaN Quantengräben (QG) unvollständig. In dieser Arbeit nutzen wir die temperaturabhängige stationäre und zeitaufgelöste Spektroskopie der Photolumineszenz (PL), um diesen Einfluss in einer typischen Ga-polaren, planaren (In,Ga)N/GaN-QG-Struktur zu untersuchen. Zusätzlich dehnen wir unsere Studie auf N-polare, axiale (In,Ga)N/GaN Quantumscheiben, nichtpolare Kern/Mantel GaN/(In,Ga)N µ-Drähte und Ga-polare, submonolage InN/GaN Übergitter aus. Während wir einen einfach exponentiellen Abfall der PL-Intensität in den nichtpolaren QG beobachten (Hinweise auf die Rekombination von Exzitonen), folgen die PL-Transienten in polaren QG asymptotisch einem Potenzgesetz. Dieses Potenzgesetz weist auf eine Rekombination zwischen individuell lokalisierten, räumlich getrennten Elektronen und Löchern hin. Für einen solchen Zerfall kann keine eindeutige PL-Lebensdauer definiert werden, was die Schätzung der internen Quanteneffizienz und die Bestimmung einer Diffusionslänge erschwert. Um nützliche Rekombinationsparameter und Diffusivitäten für die polaren QG zu extrahieren, analysieren wir die PL-Transienten mit positionsabhängigen Diffusionsreaktionsgleichungen, die durch einen Monte-Carlo-Algorithmus effizient gelöst werden. Aus diesen Simulationen ergibt sich, dass das asymptotische Potenzgesetz auch bei effizienter nichtstrahlender Rekombination (z. B. in den Nanodrähten) erhalten bleibt. Zudem stellen wir fest, dass sich die InN/GaN Übergitter elektronisch wie konventionelle (In,Ga)N/GaN QG verhalten, aber mit starkem, thermisch aktiviertem nichtstrahlenden Kanal. Des Weiteren zeigen wir, dass das Verhältnis von Lokalisierungs- und Exzitonenbindungsenergie bestimmt, dass die Rekombination entweder durch das Tunneln von Elektronen und Löchern oder durch den Zerfall von Exzitonen dominiert wird. / (In,Ga)N/GaN light-emitting diodes have been commercialized more than one decade ago. However, the knowledge about the influence of the localization on the recombination dynamics and on the diffusivity in the (In,Ga)N/GaN quantum wells (QWs) is still incomplete. In this thesis, we employ temperature-dependent steady-state and time-resolved photoluminescence (PL) spectroscopy to investigate the impact of localization on the recombination dynamics of a typical Ga-polar, planar (In,Ga)N/GaN QW structure. In addition, we extend our study to N-polar, axial (In,Ga)N/GaN quantum disks, nonpolar core/shell GaN/(In,Ga)N µ-rods, and Ga-polar, sub-monolayer InN/GaN superlattices. While we observe a single exponential decay of the PL intensity in the nonpolar QWs, indicating the recombination of excitons, the decay of the PL intensity in polar QWs asymptotically obeys a power law. This power law reveals that recombination occurs between individually localized, spatially separated electrons and holes. No unique PL lifetime can be defined for such a decay, which impedes the estimation of the internal quantum efficiency and the determination of a diffusion length. In order to extract useful recombination parameters and diffusivities for the polar QWs, we analyze the PL transients with position-dependent diffusion-reaction equations, efficiently solved by a Monte Carlo algorithm. From these simulations, we conclude that the power law asymptote is preserved despite efficient nonradiative recombination in the nanowires. Moreover, we find that the InN/GaN superlattices behave electronically as conventional (In,Ga)N/GaN QWs, but with a strong, thermally-activated nonradiative channel. Furthermore, we demonstrate that the ratio of localization and exciton binding energy, both of which are influenced by the magnitude of the internal electric fields in the QWs, determines the recombination mechanism to be either dominated by tunneling of electrons and holes or by the decay of excitons.

The existence of hydrodynamically developed, laminar Viscoelastic Secondary Flows (VSFs) of non-Newtonian fluids in straight ducts of non-circular cross-section was proposed in the 1950's. VSFs have since been observed sporadically, and only once with a velocimetric technique. Using axial and transverse full flow-field velocity-position raster maps made with Rheological Nuclear Magnetic Resonance (Rheo-NMR), Newtonian and non-Newtonian fluid flows were quantified in Hagen-Poiseuille and Power Law contexts, over more than two orders of magnitude of flow rate, in ducts of circle, square, triangle, and pentagon cross-section. VSF was reliably and repeatedly observed to occur at between one part in 130 and one part in 600 of the primary axial flow velocity. Velocity measurements ranged from <10 µm/s to approximately 30 cm/s, suggesting a velocity dynamic range >3E4 without optimization. To obtain VSF flow direction information, a novel flow directional phantom was developed and characterized. Aqueous solutions of Polyethylene Oxide (PEO), Viscarin GP-109NF, Viscarin GP-209NF (V209), Hyaluronan (HA) in a Phosphate-Buffered Saline-like solvent, and an aqueous Polyethylene Glycol/PEO-based Boger fluid were investigated. Axial data was corroborated with related data gathered by an independent method. Basic simulations corroborated the VSF observations. Duct hydraulic diameters (>= 1.6 mm) approached the micro-channel regime. VSF detections in HA --- synovial fluid's principal component --- and V209 were novel, as were observations of some artifacts which were subsequently characterized and corrected. The detection of VSF in HA represents the first experimental evidence suggesting that its second normal stress (N_2) is comparable to that of better-characterized fluids. In the first application of a new VSF-based method, a particular Boger fluid's constant viscosity and, in the square duct, its lack of VSF were used with established criteria to suggest that the fluid's N_2 approached zero. The development of a rudimentary, but versatile and inexpensive home-built velocimetric spectrometer is detailed, as are several new components. An exhaustive VSF literature review is included. The remarkable transverse velocimetric ability of Rheo-NMR in both optically opaque and transparent system is highlighted, suggesting that perhaps the technique might represent, in both micro-channels and conventional ducts, the gold-standard in flow velocimetry.

In present finite element study, the dynamics of incompressible isothermal flows of Newtonian and two generalised non-Newtonian models through complex mixing-separating planar channel and circular pipe filled with and without porous media, including Darcy's term in momentum equation, is presented. Whilst, in literature this problem is solved only for planar channel flows of Newtonian and viscoelastic fluids. The primary aim of this study is to examine the laminar flow behaviour of Newtonian and inelastic non-Newtonian fluids, and investigate the robustness of the numerical algorithm. The rheological properties of non-Newtonian fluids are defined utilising a range of constitutive equations, for inelastic non-Newtonian fluids non-linear viscous models, such as Power Law and Bird-Carreau models are used to capture the shear thinning behaviour of fluids. To simulate such complex flows, steady-state solutions are sought employing time-dependent finite element algorithm. Temporal derivatives are discretised using second order Taylor series expansion, while, spatial discretisation is achieved through Galerkin approximation in combination to deal with incompressibility a pressure-correction scheme adopted. In order to achieve the algorithm of semi-implicit form Darcy's-Brinkman equation is utilized for the conversion in Darcy's terms and diffusion, while Crank-Nicolson approach is adopted for stability and acceleration. Simple and complex flows for various complex flow bifurcations of the combined mixing-separating geometries, for both two-dimensional planar channel in Cartesian coordinates, as well as axisymmetric circular tube in cylindrical polar coordinates system are investigated. These geometries consist of a two-inverted channel and pipe flows connected through a gap in common partitions, initially filled with non-porous materials and later with homogeneous porous materials. Computational domain is having variety it has been investigated with many configurations. These computational domains have been appeared in industrial applications of combined mixing and separating of fluid flows both for porous and non-porous materials. Fully developed velocity profile is applied on both inlets of the domain by imposing analytical solutions found during current study for porous materials. Numerical study has been conducted by varying flow rates and flow direction due to a variety in the domain. The influence of varying flow rates and flow directions are analysed on flow structure. Also the impact of increasing inertia, permeability and power law index on flow behaviour and pressure difference are investigated. From predicted solution of present numerical study, for Newtonian fluids a close agreement is realised between numerical solutions and experimental data. During simulations, it has been noticed that enhancing fluid inertia (flow rates), and permeability has visible effects on the flow domains. When the Reynolds number value increases the size and power of the vortex for recirculation increases. Under varying flow rates an early activity of vortex development was observed. During change in flow directions reversed flow showed more inertial effects as compared with unidirectional flows. Less significant influence of inertia has been observed in domains filled with porous media as compared with non-porous. The power law model has more effects on inertia and pressure as compared with Bird Carreau model. Change in the value of permeability gave significant impact on pressure difference. Numerical simulations for the domain and fluids flow investigated in this study are encountered in the real life of mixing and separating applications in the industry. Especially this purely quantitative numerical investigation of flows through porous medium will open more avenues for future researchers and scientists.

Title: Incompressible fluids with temperature dependent visco- sity, numerical analysis and computational simulations Author: RNDr. Oldřich Ulrych Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., DSc. Abstract: Flows of incompressible fluids connected with significant exchange of ther- mal and mechanical energy and with material moduli varying with the temperature and the shear rate, are described by the balance equations for linear momentum and energy, complemented by suitable constitution equations for the Cauchy stress and the heat flux. Assuming sufficient smoothness of quantities involved, the energy balance equation exhibits several equivalent formulations. However, within the context of weak solution, these formulations are, in general, not equivalent. This thesis is based on the existence theory for the generalized Navier-Stokes-Fourier system describing planar flow of fluids with a shear and temperature dependent vis- cosity. We specify parameters of a generalized power-law model under which weak formulations of balance equations are meaningful and both considered formulations of the energy balance equation are equivalent. Supported by the existence theory, we propose and numerically solve several problems pursuing the aim to systematically compare the...

Le modèle classique de la finance (Markowitz, Sharpe, Black, Scholes, Fama) a, dès le début, été remis en cause par le mathématicien Benoît Mandelbrot (1924-2010). Il démontre que la loi normale ne correspond pas à la réalité des marchés, parce qu’elle sous-estime les risques extrêmes. Il faut au contraire utiliser les lois de puissance, comme la loi de Pareto. Nous montrons ici toutes les implications de ce changement fondamental sur la finance, mais aus-si, ce qui est nouveau, en ce qui concerne la gestion des entreprises (à travers le calcul du coût des capitaux propres). Nous tentons de mettre à jour les raisons profondes de l’existence des lois de puissance en économie à travers la notion d’entropie. Nous présen-tons de nouveaux outils théoriques pour comprendre la formation des prix (la théorie de la proportion diagonale), des bulles (la notion de réflexivité), des crises (la notion de réseau), en apportant une réponse globale à la crise actuelle (un système monétaire diversifié). Toutes ces voies sont très peu, ou pas du tout exploitées. Elles sont surtout, pour la pre-mière fois, mises en cohérence autour de la notion de loi de puissance. C’est donc une nou-velle façon de comprendre les phénomènes économiques que nous présentons ici. / The classical model of finance (Markowitz, Sharpe, Black, Scholes, Fama) has, from the be-ginning, been challenged by the mathematician Benoit Mandelbrot (1924-2010). It shows that the normal distribution does not match the reality of the market, because it underesti-mates the extreme risks. Instead, we must use the power laws, such as the Pareto law. We show the implications of this fundamental change in the finance, but also in the manage-ment of companies (through the calculation of cost of capital). We try to update the underly-ing reasons for the existence of power laws in economics through the concept of entropy. We present new theoretical tools to understand price formation (the theory of diagonal proportion), bubbles (the notion of reflexivity), crisis (network concept), providing a com-prehensive response to the current crisis (a diversified monetary system). All these ways are very little or not at all exploited. They are mostly for the first time, made consistent around the notion of power law. This is a new way of understanding economic phenomena present-ed here.

Nous proposons deux nouvelles approches pour les systèmes de recommandation et les réseaux. Dans la première partie, nous donnons d’abord un aperçu sur les systèmes de recommandation avant de nous concentrer sur les approches de rang faible pour la complétion de matrice. En nous appuyant sur une approche probabiliste, nous proposons de nouvelles fonctions de pénalité sur les valeurs singulières de la matrice de rang faible. En exploitant une représentation de modèle de mélange de cette pénalité, nous montrons qu’un ensemble de variables latentes convenablement choisi permet de développer un algorithme espérance-maximisation afin d’obtenir un maximum a posteriori de la matrice de rang faible complétée. L’algorithme résultant est un algorithme à seuillage doux itératif qui adapte de manière itérative les coefficients de réduction associés aux valeurs singulières. L’algorithme est simple à mettre en œuvre et peut s’adapter à de grandes matrices. Nous fournissons des comparaisons numériques entre notre approche et de récentes alternatives montrant l’intérêt de l’approche proposée pour la complétion de matrice à rang faible. Dans la deuxième partie, nous présentons d’abord quelques prérequis sur l’approche bayésienne non paramétrique et en particulier sur les mesures complètement aléatoires et leur extension multivariée, les mesures complètement aléatoires composées. Nous proposons ensuite un nouveau modèle statistique pour les réseaux creux qui se structurent en communautés avec chevauchement. Le modèle est basé sur la représentation du graphe comme un processus ponctuel échangeable, et généralise naturellement des modèles probabilistes existants à structure en blocs avec chevauchement au régime creux. Notre construction s’appuie sur des vecteurs de mesures complètement aléatoires, et possède des paramètres interprétables, chaque nœud étant associé un vecteur représentant son niveau d’affiliation à certaines communautés latentes. Nous développons des méthodes pour simuler cette classe de graphes aléatoires, ainsi que pour effectuer l’inférence a posteriori. Nous montrons que l’approche proposée peut récupérer une structure interprétable à partir de deux réseaux du monde réel et peut gérer des graphes avec des milliers de nœuds et des dizaines de milliers de connections. / We propose two novel approaches for recommender systems and networks. In the first part, we first give an overview of recommender systems and concentrate on the low-rank approaches for matrix completion. Building on a probabilistic approach, we propose novel penalty functions on the singular values of the low-rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an expectation-maximization algorithm to obtain a maximum a posteriori estimate of the completed low-rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values. The algorithm is simple to implement and can scale to large matrices. We provide numerical comparisons between our approach and recent alternatives showing the interest of the proposed approach for low-rank matrix completion. In the second part, we first introduce some background on Bayesian nonparametrics and in particular on completely random measures (CRMs) and their multivariate extension, the compound CRMs. We then propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with overlapping block-structure to the sparse regime. Our construction builds on vectors of CRMs, and has interpretable parameters, each node being assigned a vector representing its level of affiliation to some latent communities. We develop methods for simulating this class of random graphs, as well as to perform posterior inference. We show that the proposed approach can recover interpretable structure from two real-world networks and can handle graphs with thousands of nodes and tens of thousands of edges.

Neste trabalho, foram utilizadas técnicas e conceitos tipicamente encontrados em estudos de Redes Complexas, uma sub-área da Física Estatística, para caracterizar a Internet e sua evolução em uma década, de 1998 a 2007. Foi considerada como unidade básica de análise, a estrutura Sistema Autônomo. Nesta caracterização, foram utilizadas várias ferramentas computacionais desenvolvidas em linguagem C/C++, que permitiram classificar, simular e modelar propriedades dinâmicas. Dentre estas propriedades podemos destacar o coeficiente de conectividade, fundamental para os estudos topológicos, e o parâmetro menor caminho médio, ambos baseados nas propriedades da matriz adjacência. Os dados experimentais foram inicialmente obtidos nos roteadores de borda da RedeRio de Computadores - FAPERJ e posteriormente, os dados relativos ao intervalo de estudo, foram retirados da base de dados disponibilizada pela Universidade de Oregon. Foi proposto um modelo de crescimento de uma rede complexa baseado nas premissas de crescimento contínuo e conexão preferencial não linear com suporte aos mecanismos de rearranjo e novas conexões entre nós já existentes. Este modelo se mostrou bastante adequado no estudo das propriedades consideradas. Foi desenvolvido um método para cálculo do menor caminho médio que apresentou performance superior àqueles normalmente utilizados pela comunidade acadêmica. O comportamento da topologia sob o ponto de vista da distribuição de probabilidades de conexão e do ranque de conectividade, apresentaram comportamento linear constante no período estudado com coeficientes médios iguais a -2,0 e -0,93, respectivamente. O parâmetro menor caminho médio global da Internet permaneceu praticamente inalterado e igual a 4, 2 ao longo da década estudada. / Connection networks are observed in many areas of human knowledge. The characterization and topological studies of these networks may be performed through distribution of connectivity degrees, rank properties, shortest path length between nodes, adjacency matrix etc, typical concepts from Complex networks, a filed of study of Statistical Physics domain. In this thesis we characterize the Internet connections evolution from 1998 to 2007. The Internet may be seen under several levels of reach and complexity considering different basic units. A wide vision is to consider the Internet basic element as an Autonomous System - AS, which is defined as a cluster of LANs or routers submitted to the same policy of usage, connectivity and technically administrated by the same network management group. The complex network considered in this work is composed by Autonomous Systems (vertices) and the established tra connection (edges) between them obtained from the BGP routing table. Many interesting property of this networks is analyzed, e.g. degree distribution (the rank and outdegree exponents) from 1998 to 2007 and the shortest path length (L), obtained by a proposed computational method (Friburgo algorithm) among each pair of ASs represented in the adjacency matrix. Finally, we present the behavior of the power law function and the shortest path length of the Internet for each year. Simulations of the connections network were carried out by a proposed model developed from continuous growth premises, possibilities of new and rearranging connections. This model was based on the concept of potential preferable connection showing a stable exponential factor that reproduces the true shortest path parameter over the decade.

Made available in DSpace on 2015-03-03T15:15:26Z (GMT). No. of bitstreams: 1 EliangelaPB_DISSERT.pdf: 614353 bytes, checksum: 050737d0ef158e6082d81254619adac0 (MD5) Previous issue date: 2011-09-19 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / Considering a non-relativistic ideal gas, the standard foundations of kinetic theory are investigated in the context of non-gaussian statistical mechanics introduced by Kaniadakis. The new formalism is based on the generalization of the Boltzmann H-theorem and the deduction of Maxwells statistical distribution. The calculated power law distribution is parameterized through a parameter measuring the degree of non-gaussianity. In the limit = 0, the theory of gaussian Maxwell-Boltzmann distribution is recovered. Two physical applications of the non-gaussian effects have been considered. The first one, the -Doppler broadening of spectral lines from an excited gas is obtained from analytical expressions. The second one, a mathematical relationship between the entropic index and the stellar polytropic index is shown by using the thermodynamic formulation for self-gravitational systems / Considerando um g?s ideal n?o relativ?stico, os fundamentos da teoria cin?tica padr?o s?o investigados no contexto da mec?nica estat?stica n?o-gaussiana introduzida por Kaniadakis. O novo formalismo ? baseado na generaliza??o do teorema-H de Boltzmann e na dedu??o de Maxwell da distribui??o estat?stica. A distribui??o lei de pot?ncia calculada ? parametrizada por um par?metro medindo o grau de n?o-gaussianidade do sistema. No limite = 0, a teoria gaussiana de Maxwell-Boltzmann ? recuperada. Duas aplica??es dos efeitos n?o-gaussiano s?o estudados. Na primeira, o -alargamento Doppler das linhas espectrais de um g?s excitado ? obtido a partir das express?es anal?ticas. Na segunda, uma rela??o matem?tica entre o ?ndice entr?pico e o ?ndice politr?pico estelar ? mostrada usando uma formula??o termodin?mica para sistemas autogravitantes

Neste trabalho, foram utilizadas técnicas e conceitos tipicamente encontrados em estudos de Redes Complexas, uma sub-área da Física Estatística, para caracterizar a Internet e sua evolução em uma década, de 1998 a 2007. Foi considerada como unidade básica de análise, a estrutura Sistema Autônomo. Nesta caracterização, foram utilizadas várias ferramentas computacionais desenvolvidas em linguagem C/C++, que permitiram classificar, simular e modelar propriedades dinâmicas. Dentre estas propriedades podemos destacar o coeficiente de conectividade, fundamental para os estudos topológicos, e o parâmetro menor caminho médio, ambos baseados nas propriedades da matriz adjacência. Os dados experimentais foram inicialmente obtidos nos roteadores de borda da RedeRio de Computadores - FAPERJ e posteriormente, os dados relativos ao intervalo de estudo, foram retirados da base de dados disponibilizada pela Universidade de Oregon. Foi proposto um modelo de crescimento de uma rede complexa baseado nas premissas de crescimento contínuo e conexão preferencial não linear com suporte aos mecanismos de rearranjo e novas conexões entre nós já existentes. Este modelo se mostrou bastante adequado no estudo das propriedades consideradas. Foi desenvolvido um método para cálculo do menor caminho médio que apresentou performance superior àqueles normalmente utilizados pela comunidade acadêmica. O comportamento da topologia sob o ponto de vista da distribuição de probabilidades de conexão e do ranque de conectividade, apresentaram comportamento linear constante no período estudado com coeficientes médios iguais a -2,0 e -0,93, respectivamente. O parâmetro menor caminho médio global da Internet permaneceu praticamente inalterado e igual a 4, 2 ao longo da década estudada. / Connection networks are observed in many areas of human knowledge. The characterization and topological studies of these networks may be performed through distribution of connectivity degrees, rank properties, shortest path length between nodes, adjacency matrix etc, typical concepts from Complex networks, a filed of study of Statistical Physics domain. In this thesis we characterize the Internet connections evolution from 1998 to 2007. The Internet may be seen under several levels of reach and complexity considering different basic units. A wide vision is to consider the Internet basic element as an Autonomous System - AS, which is defined as a cluster of LANs or routers submitted to the same policy of usage, connectivity and technically administrated by the same network management group. The complex network considered in this work is composed by Autonomous Systems (vertices) and the established tra connection (edges) between them obtained from the BGP routing table. Many interesting property of this networks is analyzed, e.g. degree distribution (the rank and outdegree exponents) from 1998 to 2007 and the shortest path length (L), obtained by a proposed computational method (Friburgo algorithm) among each pair of ASs represented in the adjacency matrix. Finally, we present the behavior of the power law function and the shortest path length of the Internet for each year. Simulations of the connections network were carried out by a proposed model developed from continuous growth premises, possibilities of new and rearranging connections. This model was based on the concept of potential preferable connection showing a stable exponential factor that reproduces the true shortest path parameter over the decade.