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1
Malhado, Joaô Pedro Bettencourt Cepêda. „Etudes théoriques de la dynamique impliquant des intersections coniques“. Paris 6, 2009. http://www.theses.fr/2009PA066352.
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En chimie moléculaire, l'approximation de Born-Oppenheimer permet d'utiliser le concept de surface d'énergie potentielle à l'échelle atomique. Les intersections coniques (ICs) correspondent aux points où ces surfaces sont dégénérées, et où cette approximation n'est plus valable; les concepts de la dynamique classique y voient leur application réduite et les transitions non-adiabatiques entre ces surfaces deviennent importantes. Les ICs sont particulièrement d'intérêt en photochimie, puisque elles sont responsables de la relaxation électronique non-radiative du premier état excité vers l'état fondamental. Cette thèse étudie deux aspects théoriques différents de la dynamique associée aux ICs. Dans un premier temps, l'effet de la dynamique du solvant sur la dynamique autour des ICs est abordé. En particulier, nous présentons l'influence d'un solvant polaire sur la réaction photo-isomérisationd'un modèle d'une base de Schiff protonée. L'attention est centrée sur l'introduction d'un terme de friction dépendante du temps dans la description dynamique des coordonnées internes de la molécule et celle du solvant. Nous démontrons que la prise en compte des dissipations est nécessaire à une description correcte de la dynamique du modèle, et que l'échelle de temps du mouvement du solvant détermine la vitesse de relaxation de l'état excité ainsi que le rapport isomérique des produits. Dans une seconde partie, nous nous focalisons sur la formulation d'une description simple, et utilisable dans les applications, pour la dynamique autour des ICs et plus particulièrement, pour décrire la vitesse de relaxation non-adiabatique au voisinage de l'une IC. Un modèle pour le mécanisme de cette relaxation est introduit, en utilisant une description de l'IC comme un double cône, des trajectoires classiques et l'expression de Landau-Zener pour la probabilité de transition non-adiabatique. Deux géométries différentes pour le cône sont considérées. Le cas le plus simple est le double cône vertical circulaire puisqu'une formulation analytique de la constante de vitesse est rendue possible par des propriétés des trajectoires dues à la symétrie du problème. Nous présentons dans un second temps le cas d'un double cône asymétrique penché, pour lequel une constante de vitesse analytique n'a pas été obtenue, mais où les concepts précédemment introduits dans le modèle sont utilisés pour étudier la variation de la vitesse de relaxation en fonction des conditions initiales et de la géométrie de l'IC. Les résultats du modèle sont comparés avec des simulations utilisant la méthode de surface hopping, avec laquelle le modèle partage un certain nombre de points communs.
2
Borgman, Jacob. „Fluctuations of the expansion : the Langevin-Raychaudhuri equation /“. Thesis, Connect to Dissertations & Theses @ Tufts University, 2004.
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Thesis (Ph.D.)--Tufts University, 2004.Adviser: Larry H. Ford. Submitted to the Dept. of Physics. Includes bibliographical references (leaves 117-120). Access restricted to members of the Tufts University community. Also available via the World Wide Web;
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Sachs, Matthias Ernst. „The Generalised Langevin Equation : asymptotic properties and numerical analysis“. Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/29566.
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In this thesis we concentrate on instances of the GLE which can be represented in a Markovian form in an extended phase space. We extend previous results on the geometric ergodicity of this class of GLEs using Lyapunov techniques, which allows us to conclude ergodicity for a large class of GLEs relevant to molecular dynamics applications. The main body of this thesis concerns the numerical discretisation of the GLE in the extended phase space representation. We generalise numerical discretisation schemes which have been previously proposed for the underdamped Langevin equation and which are based on a decomposition of the vector field into a Hamiltonian part and a linear SDE. Certain desirable properties regarding the accuracy of configurational averages of these schemes are inherited in the GLE context. We also rigorously prove geometric ergodicity on bounded domains by showing that a uniform minorisation condition and a uniform Lyapunov condition are satisfied for sufficiently small timestep size. We show that the discretisation schemes which we propose behave consistently in the white noise and overdamped limits, hence we provide a family of universal integrators for Langevin dynamics. Finally, we consider multiple-time stepping schemes making use of a decomposition of the fluctuation-dissipation term into a reversible and non-reversible part. These schemes are designed to efficiently integrate instances of the GLE whose Markovian representation involves a high number of auxiliary variables or a configuration dependent fluctuation-dissipation term. We also consider an application of dynamics based on the GLE in the context of large scale Bayesian inference as an extension of previously proposed adaptive thermostat methods. In these methods the gradient of the log posterior density is only evaluated on a subset (minibatch) of the whole dataset, which is randomly selected at each timestep. Incorporating a memory kernel in the adaptive thermostat formulation ensures that time-correlated gradient noise is dissipated in accordance with the fluctuation-dissipation theorem. This allows us to relax the requirement of using i.i.d. minibatches, and explore a variety of minibatch sampling approaches.
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Birrell, Jeremiah, Scott Hottovy, Giovanni Volpe und Jan Wehr. „Small Mass Limit of a Langevin Equation on a Manifold“. SPRINGER BASEL AG, 2016. http://hdl.handle.net/10150/622782.
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12 month embargo; First Online: 11 July 2016We study damped geodesic motion of a particle of mass m on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as , its solutions converge to solutions of a limiting equation which includes a noise-induced drift term. A very special case of the main result presents Brownian motion on the manifold as a limit of inertial systems.
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Schaudinnus, Norbert [Verfasser], und Gerhard [Akademischer Betreuer] Stock. „Stochastic modeling of biomolecular systems using the data-driven Langevin equation“. Freiburg : Universität, 2015. http://d-nb.info/1122646887/34.
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Siegle, Peter [Verfasser]. „Markovian Embedding of Superdiffusion within a Generalized Langevin Equation Approach / Peter Siegle“. München : Verlag Dr. Hut, 2011. http://d-nb.info/1011441683/34.
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Caballero-Manrique, Esther. „Langevin Equation approach to bridge different timescales of relaxion in protein dynamics /“. view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1276397961&sid=3&Fmt=2&clientId=11238&RQT=309&VName=PQD.
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Thesis (Ph. D.)--University of Oregon, 2006.Typescript. Includes vita and abstract. Includes bibliographical references (leaves 90-99). Also available for download via the World Wide Web; free to University of Oregon users.
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Song, XiaoGeng Ph D. Massachusetts Institute of Technology. „Nonadiabatic electron transfer in the condensed phase, via semiclassical and Langevin equation approach“. Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/49751.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2009.Includes bibliographical references (leaves 127-137).
In this dissertation, we discuss two methods developed during my PhD study to simulate electron transfer systems. The first method, the semi-classical approximation, is derived from the stationary phase approximation to the path integral in the spin-coherent representation. The resulting equation of motion is a classical-like ordinary differential equation subject to a two-ended boundary condition. The boundary value problem is solved using the "near real trajectory" algorithm. This method is applied to three scattering problems to compute the transmission and reflection probabilities. The strength and weakness of this approach is investigated in details. The second approach is based on the generalized Langevin equation, in which the quantum transitions of electronic states are condensed into a linear regression equation. The memory kernel in the regression equation is computed using a second perturbation expansion. The perturbation is optimized to achieve the best convergence of the second order expansion. This procedure results in a tow-hop Langevin equation, the THLE. Results from a spin-boson system validate the THLE in a wide range of parameter regimes. Lastly, we tested the feasibility of using Monte Carlo sampling to compute the memory kernel from the spin-boson system and proposed a smoothing technique to reduce the number of sampling points.
by XiaoGeng Song.
Ph.D.
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Pedchenko, B. O., A. S. Yermolenko, Stanislav Ivanovych Denisov, Станіслав Іванович Денисов und Станислав Иванович Денисов. „Langevin equations for suspended magnetic particles drifting under the Magnus force“. Thesis, Sumy State University, 2017. http://essuir.sumdu.edu.ua/handle/123456789/63757.
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The Magnus effect, i.e., dependence of the trajectory of a body on its rotation, is widely used in sport, science and technical applications. Recently we have shown [1, 2] that due to the Magnus force the single-domain ferromagnetic particles, which are suspended in a viscous fluid and subjected to a harmonic driving force and a non-uniformly rotating magnetic field, can perform drift in a preferred direction. This result has been obtained within the deterministic approach when thermal fluctuations, leading to translational and rotational Brownian motion of particles, are ignored. Our estimations show [2] that it is possible for relatively large particles (> 102 nm). Therefore, to study the drift phenomenon for smaller particles, it is necessary to account for these fluctuations in basic equations.
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Attanasio, Felipe [UNESP]. „Numerical study of the Ginzburg-Landau-Langevin equation: coherent structures and noise perturbation theory“. Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/92029.
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attanasio_f_me_ift.pdf: 793752 bytes, checksum: 490b63eed4bdd7ec83984c78ac824d6d (MD5)Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de sistemas em equilíbrio e próximos a ele e apresentamos como a equação de GLL pode ser usada em sistemas que exibem transições de fase, na quantização estocástica e no estudo da interação de estruturas coerentes com fônons de origem térmica. Também apresentamos um método perturbativo, denominado teoria de perturbação no ruído (TPR), adequado para situações onde a intensidade do ruído estocástico é fraca. Através de simulações numéricas, investigamos a restauração de uma simetria 'Z IND. 2' quebrada, a aplicabilidade da TPR em uma dimensão e efeitos de temperatura finita numa solução topológica do tipo kink - onde apresentamos novos resultados sobre defeitos de dois kinks
In this Dissertation we present a numerical study of the GinzburgLandau-Langevin (GLL) equation in one spatial dimension, with emphasis on the applicability of a stochastic perturbative method and the statistical mechanics of topological defect structures in field-theoretic models of real scalar fields. We briefly review concepts of equilibrium and near-equilibrium statistical mechanics and present how the GLL equation can be used in systems that exhibit phase transitions, in stochastic quantization and in the study of the interaction of coherent structures with thermal phonons. We also present a perturbative method, named noise perturbation theory (NPT), suitable for situations where the stochastic noise intensity is weak. Through numerical simulations we investigate the restoration of a broken 'Z IND. 2' symmetry, the applicability of the NPT in one dimension and finite temperature effects on a topological kink solution - where we present new results on two-kink defects
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Attanasio, Felipe. „Numerical study of the Ginzburg-Landau-Langevin equation : coherent structures and noise perturbation theory /“. São Paulo, 2013. http://hdl.handle.net/11449/92029.
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Orientador: Gastão Inácio KreinBanca: Raquel Santos Marques de Carvalho
Banca: Ricardo D'Elia Matheus
Resumo: Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de sistemas em equilíbrio e próximos a ele e apresentamos como a equação de GLL pode ser usada em sistemas que exibem transições de fase, na quantização estocástica e no estudo da interação de estruturas coerentes com fônons de origem térmica. Também apresentamos um método perturbativo, denominado teoria de perturbação no ruído (TPR), adequado para situações onde a intensidade do ruído estocástico é fraca. Através de simulações numéricas, investigamos a restauração de uma simetria 'Z IND. 2' quebrada, a aplicabilidade da TPR em uma dimensão e efeitos de temperatura finita numa solução topológica do tipo "kink" - onde apresentamos novos resultados sobre defeitos de dois kinks
Abstract: In this Dissertation we present a numerical study of the GinzburgLandau-Langevin (GLL) equation in one spatial dimension, with emphasis on the applicability of a stochastic perturbative method and the statistical mechanics of topological defect structures in field-theoretic models of real scalar fields. We briefly review concepts of equilibrium and near-equilibrium statistical mechanics and present how the GLL equation can be used in systems that exhibit phase transitions, in stochastic quantization and in the study of the interaction of coherent structures with thermal phonons. We also present a perturbative method, named noise perturbation theory (NPT), suitable for situations where the stochastic noise intensity is weak. Through numerical simulations we investigate the restoration of a broken 'Z IND. 2' symmetry, the applicability of the NPT in one dimension and finite temperature effects on a topological "kink" solution - where we present new results on two-kink defects
Mestre
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Bauke, Francisco Conti [UNESP]. „Portadores quentes: modelo browniano“. Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/91881.
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bauke_fc_me_rcla.pdf: 1413465 bytes, checksum: 5695187aaf8a438767e3a8684e26c073 (MD5)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Neste trabalho estudamos o modelo do movimento Browniano de uma partícula carregada sob a ação de campos elétrico e magnético, externos e homogêneos, no formalismo de Langevin. Calculamos a energia cinética média através do teorema da flutuação-dissipação e obtivemos uma expressão para a temperatura efetiva das partículas Brownianas em função da temperatura do reservatório e dos campos externos. Esta temperatura efetiva mostrou-se sempre maior que a temperatura do reservatório, o que explica a expressão “portadores quentes”. Estudamos essa temperatura efetiva no regime assintótico, ou seja, no estado estacionário atingido em tempos muito longos (quando comparado com o tempo de colisão) e a utilizamos para escrever as equações de transporte em semicondutores, denominadas equações de Shockley generalizadas sendo que incluem nesse caso também a ação do campo magnético. Uma aplicação direta e relevante foi a modelagem para o já conhecido efeito Gunn para portadores assumidos como Brownianos. A temperatura efetiva calculada por nós no regime transiente permitiu estudar também os efeitos do reservatório na relaxação da temperatura efetiva à temperatura terminal (de não equilíbrio e estacionária). Nossos resultados no que diz respeito ao efeito Gunn, embora seja o modelo mais simples de um portador Browniano, mostrou uma surpreendente concordância com resultados experimentais, sugerindo que modelos mais sofisticados devam incluir os elementos apresentados neste estudo
We present a Brownian model for a charged particle in a field of forces, in particular, electric and magnetic external homogeneous fields, within the Langevin formalism. We compute the average kinetic energy via the fluctuation dissipation and obtain an expression for the Brownian particle´s effective temperature. The latter is a function of the heat bath temperature and both external fields. This effective temperature is always greater than the heat bath temperature, therefore the expression “hot carriers”. This effective temperature, in the asymptotic regime, the stationary state at long times (greater than the collision time), is used to write down the transport equations for semiconductors, namely the generalized Shockley equations, now incorporating the magnetic field effect. A direct and relevant application follows: a model for the well known Gunn effect, assuming a Brownian scheme. In the transient regime the computed effective temperature also allow us to probe some features of the heat bath, as the effective temperature relaxes to its terminal stationary value. As for our results in the Gunn effect model, the simplest of all in a Brownian scheme, we obtain a surprisingly good agreement with experimental data, suggesting that more involved models should include our minimal assumptions
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Sposini, Vittoria. „A numerical study of fractional diffusion through a Langevin approach in random media“. Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12494/.
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The study of Brownian motion has a long history and involves many different formulations. All these formulations show two fundamental common results: the mean square displacement of a diffusing particle scales linearly with time and the probability density function is a Guassian distribution.
However standard diffusion is not universal. In literature there are numerous experimental measurements showing non linear diffusion in many fields including physics, biology, chemistry, engineering, astrophysics and others. This behavior can have different physical origins and has been found to occur frequently in spatially disordered systems, in turbulent fluids and plasmas, and in biological media with traps, binding sites or macro-molecular crowding.
Langevin approach describes the Brownian motion in terms of a stochastic differential equation.
The process of diffusion is driven by two physical parameters, the relaxation or correlation time tau and the velocity diffusivity coefficient Dv.
An extension of the classical Langevin approach by means of a population of tau and Dv is here considered to generate a fractional dynamics. This approach supports the idea that fractional diffusion in complex media results from Gaussian processes with random parameters, whose randomness is due to the medium complexity. A statistical characterization of the complex medium in which the diffusion occurs is realized deriving the distributions of these parameters.
Specific populations of tau and Dv lead to particular fractional diffusion processes.
This approach allows for preserving the classical Brownian motion as basis and it is promising to formulate stochastic processes for biological systems that show complex dynamics characterized by fractional diffusion.
A numerical study of this new alternative approach represents the core of the present thesis.
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Townsend, Peter Stephen Morris. „Diffusion of light adsorbates on transition metal surfaces“. Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274001.
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Helium-3 surface spin echo spectroscopy (HeSE) has been used to measure the diffusive dynamics of adsorbates on close-packed metal surfaces, namely hydrogen on Cu(111), Pd(111) and Ru(0001), carbon and oxygen on Ru(0001), and oxygen on Cu(111). Chapter 2 reviews the HeSE technique and describes the relevant dynamical models and statistical methods used to interpret data in later chapters. The performance of the ionizing detector is analysed, with a focus on the signal-to-noise ratio. In Chapter 3 expressions for the classical intermediate scattering function (ISF) are introduced for open and closed systems. The effects of corrugation and surface-perpendicular motion on the amplitude of different components in the ISF are modelled analytically and compared with simulation. The exact ISF for a particle on a flat surface, obeying the Generalized Langevin Equation with exponential memory friction, is calculated analytically. In Chapter 4 the analytical ISF is calculated for quantum Brownian motion and for coherent tunneling dynamics in a tight binding system. The bounce method for calculating quantum mechanical hopping rates in dissipative systems is applied to model diffusion of hydrogen on Ru(0001). Chapter 5 presents the first HeSE measurements of carbon and oxygen diffusion. C/Ru(0001) diffusion is assigned to a small carbon cluster. The jump rate has an activation energy $E_{A}=292\pm7\,$meV in the temperature range $550\,\textrm{K}\leq T \leq 1300\,$K. Oxygen diffusion is significantly slower. By comparison of literature data with the new HeSE results, the activation energy for oxygen diffusion at low coverage is estimated as $650\pm10$meV. Oxygen measurements at high coverage $\theta\approx0.22\,$ML are consistent with strong mutual O-O interactions. Surface diffusion is also observed after exposing Cu(111) to oxygen. Chapter 6 presents low-coverage measurements of protium (H) and deuterium (D) diffusion on Ru(0001), Pd(111) and Cu(111). In the quantum activated regime there is evidence for multiple jumps in all three systems, suggesting a low dynamical friction. The measurements on Ru(0001) indicate that the deep tunneling rate is much slower for D than for H.
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MARTINS, FERNANDO R. „Medidas de parametros nucleares de um reator de potencia zero aplicando a tecnica de analise de ruidos“. reponame:Repositório Institucional do IPEN, 1992. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10294.
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Dissertacao (Mestrado)
IPEN/D
Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP
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Simand, Catherine. „Etude de la turbulence inhomogène au voisinage d'un tourbillon“. Lyon, École normale supérieure (sciences), 2002. http://www.theses.fr/2002ENSL0236.
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Les écoulements fermés entre deux disques coaxiaux corotatifs créés facilement en laboratoire sont turbulents, à hauts Reynolds, et tourbillonnaires à grande échelle, avec une stabilité contrôlée : nous pouvons donc examiner l'interaction entre la vorticité et la turbulence, sur toute la gamme d'échelles de la cascade d'énergie. A grande échelle, des visualisations à l'aide de bulles, de billes et des mesures de vitesse par vélocimétries laser Doppler et à film chaud, permettent la distinction de deux écoulements moyens. Si les disques tournent à la même vitesse, l'écoulement est en rotation globale, avec un tourbillon axial intense, stable temporellement. Si les disques tournent à des vitesses différentes, le disque le plus rapide aspire le fluide au niveau de l'axe de rotation, et le tourbillon est instable. Les outils habituels d'analyse de la turbulence ont été utilisés, et se révèlent toujours pertinents : les cascades sont multiplicatives, infiniment divisibles, et les noyaux des propagateurs sont pratiquement log-normaux. Qualitativement, tout se passe comme si la turbulence étáit homogène. Néanmoins, les inhomogénéités à grande échelle ont des effets quantitatifs sur les évolutions le long des échelles des spectres de puissance et des fonctions de structure, et modulent la profondeur de la cascade. La rotation globale freine le transfert d'énergie des grandes vers les petites échelles, voire même à l'inverse localement, tandis que la rotation différentielle l'accélère. Une description très récente de la cascade turbulente à l'aide d'une équation de Langevin est appliquée à ces signaux de vitesse et à celui d'un jet servant de référence, typique de la turbulence homogène et isotrope. De nombreux liens avec d'autres modèles de turbulence sont établis, qui dévoilent les limites de celui-ci : le coefficient de diffusion est insuffisant pour rendre compte de l'intermittence des signaux. Ceci est clairement prouvé sur les distributions des incréments de vitesse.
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Zeren, Zafer. „Lagrangian stochastic modeling of turbulent gas-solid flows with two-way coupling in homogeneous isotropic turbulence“. Thesis, Toulouse, INPT, 2010. http://www.theses.fr/2010INPT0106/document.
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Dans ce travail de thèse, réalisé à l'IMFT, nous nous sommes intéressés aux écoulements turbulents diphasiques gaz-solides et plus particulièrement au phénomène de couplage inverse qui correspond à la modulation de la turbulence par la phase dispersée. Ce mécanisme est crucial pour les écoulements à forts chargements massiques. Dans cette thèse, nous avons considéré une turbulence homogène isotrope stationnaire sans gravité dans laquelle des particules sont suivies individuellement d'une façon Lagrangienne. La turbulence du fluide porteur est obtenue par des simulations directes (DNS). Les particules sont sphériques, rigides et d'une taille inférieure aux plus petites échelles de la turbulence. Leur densité est bien plus grande que la densité du fluide. Dans ce cadre, la force la plus importante agissant sur les particules est celle de traînée. Les interactions inter-particules ainsi que la gravité ne sont pas prises en compte. Pour modéliser ce type d'écoulement, une approche stochastique est utilisée pour laquelle l'accélération du fluide est modélisée par une équation de Langevin. L'originalité de ce travail est la prise en compte de l'effet de la modulation de la turbulence par un terme additionnel. Nous avons proposé deux modèles : une force de couplage moyenne qui est définie à partir des vitesses moyennes des phases, et une force instantanée qui est définie à l'aide du formalisme mésoscopique Eulérien. La fermeture des modèles s’appuie sur la fonction d’autocorrélation Lagrangienne et l’équation de transport de l’énergie cinétique. Les modèles sont testés en terme de prédiction de la vitesse de dérive et des corrélations fluide-particule. Les résultats montrent que le modèle moyen, plus simple, prend en compte les effets principaux du couplage inverse. Cependant, le problème de fermeture pratique est reporté sur la modélisation de l’échelle intégrale Lagrangienne et l’énergie cinétique de la turbulence du fluide vue par les particulesIn this thesis, performed in IMFT, we are interested in the turbulent gas-solid flows and more specifically, in the phenomenon of turbulence modulation which is the modification of the structure of the turbulence due to the solid particles. This mechanism is crucial in flows with high particle mass-loadings. In this work, we considered a homogeneous isotropic turbulence without gravity kept stationary with stochastic type forcing. Discrete particles are tracked individually in Lagrangian manner. Turbulence of the carrier phase is obtained by using DNS. The particles are spherical, rigid and of a diameter smaller than the smallest scales of turbulence. Their density is very large in comparison to the density of the fluid. In this configuration the only force acting on the particles is the drag force. Volume fraction of particles is very small and inter-particle interactions are not considered. To model this type of flow, a stochastic approach is used where the fluid element accel- eration is modeled using stochastic Langevin equation. The originality in this work is an additional term in the stochastic equation which integrates the effect of the particles on the trajectory of fluid elements. To model this term, we proposed two types of modeling: a mean drag model which is defined using the mean velocities from the mean transport equations of the both phases and an instantaneous drag term which is written with the help of the Mesoscopic Eulerian Approach. The closure of the models is based on the Lagrangian auto- correlation function of the fluid velocity and on the transport equation of the fluid kinetic energies. The models are tested in terms of the fluid-particle correlations and fluid-particle turbulent drift velocity. The results show that the mean model, simple, takes into account the principal physical mechanism of turbulence modulation. However, practical closure problem is brought forward to the Lagrangian integral scale and the fluid kinetic energy of the fluid turbulence viewed by the particles
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Bauke, Francisco Conti. „Portadores quentes : modelo browniano /“. Rio Claro : [s.n.], 2011. http://hdl.handle.net/11449/91881.
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Orientador: Roberto E. Lagos MonacoBanca: José Antonio Roversi
Banca: Bernardo Laks
Resumo: Neste trabalho estudamos o modelo do movimento Browniano de uma partícula carregada sob a ação de campos elétrico e magnético, externos e homogêneos, no formalismo de Langevin. Calculamos a energia cinética média através do teorema da flutuação-dissipação e obtivemos uma expressão para a temperatura efetiva das partículas Brownianas em função da temperatura do reservatório e dos campos externos. Esta temperatura efetiva mostrou-se sempre maior que a temperatura do reservatório, o que explica a expressão "portadores quentes". Estudamos essa temperatura efetiva no regime assintótico, ou seja, no estado estacionário atingido em tempos muito longos (quando comparado com o tempo de colisão) e a utilizamos para escrever as equações de transporte em semicondutores, denominadas equações de Shockley generalizadas sendo que incluem nesse caso também a ação do campo magnético. Uma aplicação direta e relevante foi a modelagem para o já conhecido efeito Gunn para portadores assumidos como Brownianos. A temperatura efetiva calculada por nós no regime transiente permitiu estudar também os efeitos do reservatório na relaxação da temperatura efetiva à temperatura terminal (de não equilíbrio e estacionária). Nossos resultados no que diz respeito ao efeito Gunn, embora seja o modelo mais simples de um portador Browniano, mostrou uma surpreendente concordância com resultados experimentais, sugerindo que modelos mais sofisticados devam incluir os elementos apresentados neste estudo
Abstract: We present a Brownian model for a charged particle in a field of forces, in particular, electric and magnetic external homogeneous fields, within the Langevin formalism. We compute the average kinetic energy via the fluctuation dissipation and obtain an expression for the Brownian particle's effective temperature. The latter is a function of the heat bath temperature and both external fields. This effective temperature is always greater than the heat bath temperature, therefore the expression "hot carriers". This effective temperature, in the asymptotic regime, the stationary state at long times (greater than the collision time), is used to write down the transport equations for semiconductors, namely the generalized Shockley equations, now incorporating the magnetic field effect. A direct and relevant application follows: a model for the well known Gunn effect, assuming a Brownian scheme. In the transient regime the computed effective temperature also allow us to probe some features of the heat bath, as the effective temperature relaxes to its terminal stationary value. As for our results in the Gunn effect model, the simplest of all in a Brownian scheme, we obtain a surprisingly good agreement with experimental data, suggesting that more involved models should include our minimal assumptions
Mestre
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Miserocchi, Andrea. „The Fokker-Planck equation as model for the stochastic gradient descent in deep learning“. Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18290/.
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La discesa stocastica del gradiente (SGD) è alla base degli algoritmi di
ottimizzazione di reti di Deep Learning più usati in AI, dal riconoscimento
delle immagini all’elaborazione del linguaggio naturale. Questa tesi si propone di descrivere un modello basato sull’equazione di Fokker-Planck della dinamica del SGD. Si introduce la teoria dei processi stocastici, con particolare enfasi sulle equazioni di Langevin e sull’equazione di Fokker-Planck. Si mostra come il SGD minimizzi un funzionale sulla densità di probabilità dei pesi, non dipendente direttamente dalla funzione di costo. Infine si discutono le implicazioni di questa inferenza variazionale ottenuta dal SGD.
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Brännlund, Niklas. „Modeling and implementation of dense gas effects in a Lagrangian dispersion model“. Thesis, Umeå universitet, Institutionen för fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-105203.
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The use of hazardous toxic substances is very common in the industrial sector. The substances are often stored in tanks in storage compartments or transported between industrial premises. In case of an accident involving these substances, severe harm can affect both population and the environment. This leaves a demand for an accurate prediction of the substance concentration distribution to mitigate the risks as much as possible and in advance create suitable safety measures. Toxic gases and vapors are often denser than air making it affected by negative buoyancy forces. This will make the gas descend and spread horizontally when reaching the ground. Swedish Defence Research Agency (FOI) carries today a model called LillPello for simulating the dispersion of gases, yet it does not account for the specific case of a dense gas. Therefore, this thesis aims to implement the necessary effects needed to accurately simulate the dispersion of a dense gas. These effects were implemented in Fortran 90 by solving five conservation equations for energy, momentum (vertical and horizontal) and mass. The model was compared against experimental data of a leak of ammonia (NH3). By analyzing the result of the simulations in this thesis, we can conclude that the overall result is satisfactory. We can notice a small concentration underestimation at all measurement points and the model produced a concentration power law coefficient which lands inside the expected range. Two out of the three statistical quantities Geometric Mean (MG), Geometric Variance (VG) and Factor of 2 (FA2) produced values within the ranges of acceptable values. The drawback of the model as it is implemented today is its efficiency, so the main priority for the future of this thesis is to improve this. The model should also be analyzed on more experiments to further validate its accuracy.Användandet av giftiga ämnen är vanligt inom den industriella sektorn. Ämnena är oftast lagrade i behållare positionerade i lagringsutrymmen eller så transporteras ämnena mellan industrilokaler. I samband med en olycka innehållande dessa substanser kan stora skador drabba både befolkning och miljön. Detta leder till ett behov av att noggrant kunna förutspå koncentrationsfördelningen för att minska riskerna, samt i förväg kunna skapa lämpliga säkerhetsåtgärder. Giftiga gaser och ångor är oftast tyngre än luft vilket gör att gasen blir påverkad av negativ bärkraft. Detta gör att gasen sjunker och sprids horisontalt när den når marken. Totalförsvarets Forskningsinstitut (FOI) besitter idag en modell kallad LillPello som simulerar spridning av gaser, men den hanterar inte det specifika fallet av en tunggas. Därför siktar detta projekt på att, in i LillPello, implementera de nödvändiga effekterna som behövs för att korrekt kunna simulera spridningen av en tunggas. Dessa effekter är implementerad i Fortran 90 genom att lösa fem konserveringsekvationer för energi, momentum (vertikal och horisontell) samt massa. Modellen jämfördes mot data från ett fältexperiment där ammoniak (NH3) släpptes ut. Genom att analysera resultatet från simuleringar kan vi dra slutsatsen att det övergripande resultatet är tillfredsställande. Vi kan notera en underskattning för alla koncentrationsmätningar i simuleringarna och modellen producerade en potenslagsexponent vars värde hamnade innanför den accepterade gränsen. Två utav de tre beräknade statistiska kvantiteterna: Geometriskt medelvärde (MG), Geometrisk varians (VG) och Faktor av 2 (FA2) producerade värden inom de acceptabla gränserna. Största nackdelen med modellen är dess effektivitet och därför är största prioritet för det fortsatta arbetet inom detta projekt att effektivisera implementeringen. Modellen ska även bli vidare analyserad mot fler experiment för att validera dess noggrannhet.
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Dangerfield, C. E. „Stochastic models of ion channel dynamics and their role in short-term repolarisation variability in cardiac cells“. Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:cd0be850-1ff0-4792-8171-438ff8fc0161.
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Sudden cardiac death due to the development of lethal arrhythmias is the dominant cause of mortality in the UK, yet the mechanisms underlying their onset, maintenance and termination are still poorly understood. Therefore biomarkers are used to determine arrhythmic risk within patients and of new drug compounds. In recent years, the magnitude of variations in the length of successive beats, measured over a short period of time, has been shown to be a powerful predictor of arrhythmic risk. This beat-to-beat variability is thought to be the manifestation of the random opening and closing dynamics of individual ion channels that lie within the membrane of cardiac cells. Computational models have become an important tool in understanding the electrophysiology of the heart. However, current state-of-the-art electrophysiology models do not incorporate this intrinsic stochastic behaviour of ion channels. Those that do use computationally costly methods, restricting their use in complex tissue scale simulations, or employ stochastic simulation methods that result in negative numbers of channels and so are inaccurate. Therefore, using current stochastic modelling techniques to investigate the role of stochastic ion channel behaviour in beat-to-beat variability presents difficulties. In this thesis we take a mathematically rigorous and novel approach to develop accurate and computationally efficient models of stochastic ion channel dynamics that can be incorporated into existing electrophysiology models. Two different models of stochastic ion channel behaviour, both based on a system of stochastic differential equations (SDEs), are developed and compared. The first model is based on an existing SDE model from population dynamics called the Wright-Fisher model. The second approach incorporates boundary conditions into the SDE model of ion channel dynamics that is obtained in the limit from the discrete-state Markov chain model, and is called a reflected SDE. Of these two methods, the reflected SDE is found to more accurately capture the stochastic dynamics of the discrete-stateMarkov chain, seen as the ‘gold-standard’ model and also provides substantial computational speed up. Thus the reflected SDE is an accurate and efficient model of stochastic ion channel dynamics and so allows for detailed investigation into beat-to-beat variability using complex computational electrophysiology models. We illustrate the potential power of this method by incorporating it into a state-of-the-art canine cardiac cell electrophsyiology model so as to explore the effects of stochastic ion channel behaviour on beat-to-beat variability. The stochastic models presented in this thesis fulfil an important role in elucidating the effects of stochastic ion channel behaviour on beat-to-beat variability, a potentially important biomarker of arrhythmic risk.
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Денисов, Станіслав Іванович, Станислав Иванович Денисов, Stanislav Ivanovych Denysov, Тарас Володимирович Лютий, Тарас Владимирович Лютый, Taras Volodymyrovych Liutyi und В. В. Рева. „Эффективная система уравнений Ланжевена для вращательного движения однодоменных ферромагнитных частиц“. Thesis, Сумский государственный университет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/39677.
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При описании открытых систем влияние внешней среды часто моделируется гауссовским белым шумом. Если в уравнениях Ланжевена, описывающих такие системы, шум мультипликативный, тогда возникает проблема выбора его интерпретации, поскольку от этого могут зависеть статистические свойства изучаемой системы. С этой проблемой тесно связана и другая – нахождение приведенных уравнений
Ланжевена, которые гораздо проще исходных, но имеют эквивалентные (в статистическом смысле) решения. В данной работе отмеченные выше проблемы решены для векторного уравнения Ланжевена.
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Wu, Yong. „Relaxation Effects in Magnetic Nanoparticle Physics: MPI and MPS Applications“. Case Western Reserve University School of Graduate Studies / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1370865200.
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Mélykúti, Bence. „Theoretical advances in the modelling and interrogation of biochemical reaction systems : alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination“. Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:d368c04c-b611-41b2-8866-cde16b283b0d.
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This thesis is concerned with methodologies for the accurate quantitative modelling of molecular biological systems. The first part is devoted to the chemical Langevin equation (CLE), a stochastic differential equation driven by a multidimensional Wiener process. The CLE is an approximation to the standard discrete Markov jump process model of chemical reaction kinetics. It is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. We observe that the CLE is not a single equation, but a family of equations with shared finite-dimensional distributions. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m_1 pairs of reversible reactions and m_2 irreversible reactions, there is another, simple formulation of the CLE with only m_1+m_2 Wiener processes, whereas the standard approach uses 2m_1+m_2. Considerable computational savings are achieved with this latter formulation. A flaw of the CLE model is identified: trajectories may leave the nonnegative orthant with positive probability. The second part addresses the challenge when alternative, structurally different ordinary differential equation models of similar complexity fit the available experimental data equally well. We review optimal experiment design methods for choosing the initial state and structural changes on the biological system to maximally discriminate between the outputs of rival models in terms of L_2-distance. We determine the optimal stimulus (input) profile for externally excitable systems. The numerical implementation relies on sum of squares decompositions and is demonstrated on two rival models of signal processing in starving Dictyostelium amoebae. Such experiments accelerate the perfection of our understanding of biochemical mechanisms.
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Evola, Salvatore. „Modelling of the sedimentation phenomenon of solid particles immersed in a turbulent fluid“. Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20077/.
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Settling phenomenon of solid particles immersed in a turbulent fluid has been investigated, in a condition of free-stream turbulence.
Since structures formed onto this condition are complex, it is difficult to predict exactly how particles move. It is thus appropriate to conduct deepen studies of the phenomenon and carry out simulations to describe particles’ settling velocity.
In order to define a new correlation for the evaluation of particles’ settling velocity, different literature correlations and parameters have been exploited.
Langevin dynamics has been used to describe fluid’s motion, and by considering several forces acting on particles (buoyancy, drag, gravitational and virtual mass), it has been possible to evaluate their settling velocity, through a computational approach. Data have been obtained by varying characteristic properties, such as kinetic energy, its rate of dissipation, and physical properties of fluid and particles.
Aiming to find a reliable correlation which best explains the settling phenomenon, results in output from simulations have been compared with that deriving from proposed correlation. Encouraging results have been obtained over the range of operating conditions examined.
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Lagache, Thibault. „Modeling the early steps of viral infection : a stochastic approach“. Paris 6, 2009. http://www.theses.fr/2009PA066470.
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Kopec, Marie. „Quelques contributions à l'analyse numérique d'équations stochastiques“. Electronic Thesis or Diss., Rennes, École normale supérieure, 2014. http://www.theses.fr/2014ENSR0002.
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Ce travail présente quelques résultats concernant le comportement en temps fini et en temps long de méthodes numériques pour des équations stochastiques. On s'intéresse d'abord aux équations différentielles stochastiques de Langevin et de Langevin amorti. On montre un résultat concernant l'analyse d'erreur faible rétrograde de ses équations par des schémas numériques implicites. En particulier, on montre que l'erreur entre le générateur associé au schéma numérique et la solution d'une équation de Kolmogorov modifiée est d'ordre élevé par rapport au pas de discrétisation. On montre aussi que la dynamique associée au schéma numérique est exponentiellement mélangeante. Dans un deuxième temps, on étudie le comportement en temps long d'une discrétisation en temps et en espace d'une EDPS semi-linéaire avec un bruit blanc additif, qui possède une unique mesure invariante . On considère une discrétisation en temps par un schéma d'Euler et en espace par une méthode des éléments finis. On montre que la moyenne, par rapport aux lois invariantes (qui n'est pas forcément unique) associées à l'approximation, par des fonctions tests suffisamment régulières est proche de la quantité correspondante pour µ. Plus précisément, on étudie la vitesse de convergence par rapport aux différents paramètres de discrétisation. Enfin, on s'intéresse à une EDPS semi-linéaire avec un bruit blanc additif dont le terme non-linéaire est un polynôme. On étudie la convergence au sens faible d'une approximation en temps par un schéma de splitting impliciteThis work presents some results about behavior in long time and in finite time of numerical methods for stochastic equations.In a first part, we are considered with overdamped Langevin Stochastic Differential Equations (SDE) and Langevin SDE. We show a weak backward error analysis result for its numerical approximations defined by implicit methods. In particular, we prove that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamic associated with the implicit scheme considered is exponentially mixing.In a second part, we study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure μ. We focus on the discretization in time thanks to a scheme of Euler type, and on a Finite Element discretization in space and we show that the average of regular enough test functions with respect to the (possibly non unique) invariant laws of the approximations are close to the corresponding quantity for μ.More precisely, we analyze the rate of the convergence with respect to the different discretization parameters. Finally, we are concerned with semilinear SPDEs with additive space-time white noise, which the nonlinear term is a polynomial function. We analyze the rate of the weak convergence for discretization in time with an implicit splitting method
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Angeletti, Andrea. „Collective dynamics of active particles“. Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16772/.
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Il nostro scopo è lo studio e il confronto della dinamica di particelle passive e attive in un fluido. Vengono inoltre introdotti i modelli matematici che permettono di simulare il loro comportamento. Sono studiate le propietà e la soluzione numerica dell'equazione di Langevin nella sua approsimazione in regime 'overdamped'. Mostriamo come lo spostamento quadratico medio delle particelle passive sia diffusivo, i.e. lineare nel tempo, e proporzionale al coefficiente di diffusione lineare, mentre quello di particelle attive quadratico per un tempo minore dell'inverso del coefficiente di diffusione rotazionale e diffusivo per un tempo maggiore. Con la presenza di una parete repulsiva e osservando la distribuzione di probabilità della posizione delle particelle, notiamo come quelle attive tendano ad accumularsi su di essa. Infine osserviamo che sotto l'azione di un potenziale repulsivo particelle attive tendono a formare agglomerati.
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Ющенко, Ольга Володимирівна, Ольга Владимировна Ющенко, Olha Volodymyrivna Yushchenko und М. А. Руденко. „Дослідження колективних ефектів при обертальному русі наночастинок“. Thesis, Сумський державний університет, 2018. http://essuir.sumdu.edu.ua/handle/123456789/67932.
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Останнім часом увагу вчених все частіше привертають проблеми, пов’язані з описом руху наночастинок. Це пов’язано з новітніми технологічними розробками із застосуванням наночастинок. Завдяки контрольованому руху наночастинок можна створювати нові матеріали із заданими властивостями та архітектурою, збирати мікро-
та нано-пристрої, контролювати різні каталітичні реакції, організовувати доставку ліків в конкретні точки живих організмів.
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Garofalo, Marco. „Dynamics of numerical stochastic perturbation theory“. Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31086.
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Numerical Stochastic Perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice quantum field theory. The standard algorithm based on the Langevin equation, however, suffers from several limitations which in practice restrict the potential of this technique: first of all it is not exact, a sequence of simulations with finer and finer discretization of the relevant equations have to be performed in order to extrapolate away the systematic errors in the results; and, secondly, the numerical simulations suffer from critical slowing down as the continuum limit of the theory is approached. In this thesis I investigate some alternative methods which improve upon the standard approach. In particular, I present a formulation of Numerical Stochastic Perturbation theory based on the Generalised Hybrid Molecular Dynamics algorithm and a study of the recently proposed Instantaneous Stochastic Perturbation Theory. The viability of these methods is investigated in φ4 theory.
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Radtke, Paul Kaspar. „Mesoscopic Models of Stochastic Transport“. Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19152.
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Transportphänomene treten in biologischen und künstlichen Systemen auf allen Längenskalen auf. In dieser Arbeit untersuchen wir sie für verschiedene Systeme aus einer mesoskopischen Perspektive, in der Fluktuationen physikalischer Größen um ihre Mittelwerte eine wichtige Rolle spielen.
Im ersten Teil untersuchen wir die persistente Bewegung aktiver Brownscher Teilchen mit zusätzlichem Drehmoment, wie sie z.B. für Spermien oder Janus Teilchen auftritt. Wird ihre Bewegung auf einen Tunnel variierender Breite beschränkt, so setzt im thermischen Nichtgleichgewicht Transport ein; ungerichtete Fluktuationen des rauschhaften Antriebs werden gleichgerichtet. Hierdurch wird ein neuer Ratschentyp realisiert.
Im zweiten Teil untersuchen wir den intrazellulären Cargotransport in den Axonen von Nervenzellen mithilfe molekularer Motoren. Sie werden als asymmetrischer Ausschlussprozess simuliert. Zusätzlich können die Cargos zwischen benachbarten Motoren ausgetauscht werden. Dadurch lassen sich charakteristische Eigenschaften des langsamen axonalen Transports mit einer einzigen Motorspezies reproduzieren. Bewerkstelligt wird dies durch die transiente Anbindung der Cargos an rückwärtslaufende Motorstaus.
Im dritten Teil diskutieren wir resistive switching, die nicht volatile Widerstandsänderung eines Dielektrikums durch elektrische Impulse. Es wird für Anwendungen im Computerspeicher ausgenutzt, dem resistive RAM. Wir schlagen ein auf Sauerstoffvakanzen basierendes stochastisches Gitterhüpfmodell vor. Wir definieren binäre logische Zustände mit Hilfe der zugrunde liegenden Vakanzenverteilung und definieren Schreibe- und Leseoperationen durch Spannungsimpulse für ein solches Speicherelement. Überlegungen über die Unterscheidbarkeit dieser Operationen unter Fluktuationen zusammen mit der Deutlichkeit der unterschiedlichen Widerstandszustände selbst ermöglichen es uns, eine optimale Vakanzenzahl vorherzusagen.Transport phenomena occur in biological and artificial systems at all length scales. In this thesis, we investigate them for various systems from a mesoscopic perspective, in which fluctuations around their average properties play an important role. In the first part, we investigate the persistent diffusive motion of active Brownian particles with an additional torque. It can appear in many real life systems, for example in sperm cells or Janus particles. If their motion is confined to a tunnel of varying width, transport arises out of thermal equilibrium; unbiased fluctuations of the noisy drive are rectified. This way, we have realized a novel kind of ratchet. In the second part, we study intracellular cargo transport in the axons of nerve cells by molecular motors. They are modeled by an asymmetric exclusion process. In a new approach, we add a cargo exchange interaction between the motors. This way, the characteristics of slow axonal transport can be accounted for with a single motor species. It is explained by the transient attachment of cargos to reverse walking motors jams. In the third part, we discuss resistive switching, the non-volatile change of resistance in a dielectric due to electric pulses. It is exploited for applications in computer memory, the resistive random access memory (ReRAM). We propose a stochastic lattice hopping model based on the on oxygen vacancies. We define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such a memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the resistive switching effect itself enable us to predict an optimal vacancy number.
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Jen, Hsiang-Hua. „Theory of light-matter interactions in cascade and diamond type atomic ensembles“. Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/37288.
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In this thesis, we investigate the quantum mechanical interaction of light with matter in the form of a gas of ultracold atoms: the atomic ensemble. We present a theoretical analysis of two problems, which involve the interaction of quantized electromagnetic fields (called signal and idler) with the atomic ensemble (i) cascade two-photon emission in an atomic ladder configuration, and (ii) photon frequency conversion in an atomic diamond configuration. The motivation of these studies comes from potential applications in long-distance quantum communication where it is desirable to generate quantum correlations between telecommunication wavelength light fields and ground level atomic coherences. In the two systems of interest, the light field produced in the upper arm of an atomic Rb level scheme is chosen to lie in the telecom window. The other field, resonant on a ground level transition, is in the near-infrared region of the spectrum. Telecom light is useful as it minimizes losses in the optical fiber transmission links of any two long-distance quantum communication device.
We develop a theory of correlated signal-idler pair correlation. The analysis is complicated by the possible generation of multiple excitations in the atomic ensemble. An analytical treatment is given in the limit of a single excitation assuming adiabatic laser excitations. The analysis predicts superradiant timescales in the idler emission in agreement with experimental observation. To relax the restriction of a single excitation, we develop a different theory of cascade emission, which is solved by numerical simulation of classical stochastic differential equation using the theory of open quantum systems. The simulations are in good qualitative agreement with the analytical theory of superradiant timescales. We further analyze the feasibility of this two-photn source to realize the DLCZ protocol of the quantum repeater communication system.
We provide a quantum theory of near-infrared to telecom wavelength conversion in the diamond configuration. The system provides a crucial part of a quantum-repeater memory element, which enables a "stored" near-infrared photon to be converted to a telecom wavelength for transmission without the destruction of light-atom quantum correlation. We calculate the theoretical conversion efficiency, analyzing the role of optical depth of the ensemble, pulse length, and quantum fluctuations on the process.
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Katz, Roland. „A quantum approach to dynamical quarkonia suppression in high energy heavy ion collisions“. Thesis, Nantes, Ecole des Mines, 2015. http://www.theses.fr/2015EMNA0227/document.
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La chromodynamique quantique (QCD) prédit l'existence d'un nouvel état de la matière : le plasma de quarks et de gluons (PQG). Celui-ci aurait existé dans les premiers instants suivant le Big Bang et peut en principe être produit sous les conditions extrêmes de température et de densité atteintes lors de collisions d'ions lourds à haute énergie (au LHC par exemple). Un des marqueurs de sa présence est la suppression des quarkonia (états liés de quark/antiquark lourds), caractérisée par une production inférieure de ces états dans les collisions d'ions lourds relativement aux collisions proton-proton où le PQG ne pourrait être créé. Cette suppression a bien été observée expérimentalement, mais l'évolution de ses tendances aux énergies du RHIC et du LHC est un véritable défi qui requiert une meilleure compréhension théorique. La présente thèse a pour but d’étudier l’évolution en temps réel de paires corrélées de quark/antiquark lourds considérées comme des systèmes quantiques ouverts en interaction permanente avec un PQG en refroidissement. Explicitement, l'interaction continue entre le milieu et les degrés de liberté internes de la paire est obtenue par 1) un écrantage de couleur dit « de Debye » dû à la présence de charges de couleur dans leur voisinage et 2) des mécanismes de fluctuation/dissipation qui reflètent les collisions permanentes. Cela mène à une image dynamique et continue de la dissociation des quarkonia, de leur recombinaison et des transitions entre états liés. L'étude est transversale à différents cadres théoriques : semi-classique, quantique et quantique des champs. Les prédictions du modèle sont comparées aux résultats expérimentaux et aux résultats d'autres modèles théoriquesThe theory of quantum chromodynamics (QCD) predicts the existence of a new state of matter: the Quark-GluonPlasma (QGP). The latter may have existed at the first moments of the Universe following the Big Bang and can be, in theory, re-produced under the extreme conditions of temperature and density reached in high energy heavy ion collisions (at the LHC for instance). One of the QGP observables is the suppression of the quarkonia (heavy quark/antiquark bound states), characterised by a smaller production of these states in heavy ion collisions in comparison to proton-protoncollisions, in which no QGP production would be possible. This suppression has indeed been observed experimentally, but the puzzling evolution of its trend from RHIC to LHC energies requires a better theoretical understanding. The present thesis aims at studying the real-time evolution of correlated heavy quark/antiquark pairs described as open quantum systems which permanently interact with a cooling QGP. More explicitly, the continuous interaction between the medium and the pair internal degrees of freedom is obtained through 1) a temperature dependent color screening (“Debye” like) due to color charges in the irvicinity and 2) some fluctuation/dissipation mechanisms reflecting the continuous collisions. It leads to a dynamical and continuous picture of the dissociation, recombination and possible transitions to other bound states. This investigation is at the crossroads of different theoretical frameworks: semi-classic, quantum and quantum fields. The deduced predictions are compared to experimental data and to the results of other theoretical models
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Silva, Leandro Alexandre da. „Processos estocásticos em teoria de campos e aplicação ao universo inflacionário“. Universidade do Estado do Rio de Janeiro, 2009. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=7006.
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Conselho Nacional de Desenvolvimento Científico e TecnológicoÉ conhecido que derivações microscópicas obtidas através de métodos de teoria quântica de campos (TQC) podem conduzir a complicadas equações de movimento (EdM) que possuem um termo dissipativo com memória e um termo de ruído colorido. Um caso particularmente interessante é o modelo que escreve a interação entre um sistema e um banho térmico a temperatura T. Motivado por isso, usamos uma prescrição que nos permite reescrever EdMs não-markovianas semelhantes as obtidas em TQC em termos de um sistema de equações locais, para então confrontarmos a solução desse sistema com a solução aproximada usada correntemente na literatura, a chamada aproximação markoviana. A pergunta chave a qual se pretende responder aqui é: dado um conjunto de parâmetros que descrevem o modelo, a aproximação markoviana é suficientemente boa para descrever a dinâmica do sistema se comparada a dinâmica obtida atravéS da EdM não-markoviana? Além disso, consideramos uma versão linear da ELG de forma que pudéssemos determinar o nível de confiança da nossa metodologia numérica, procedimento este realizado comparando-se a solução analítica com a solução numérica. Como exemplo de aplicação prática do tema discutido aqui, comparamos a evolução não-markoviana do inflaton com a evolução markoviana do mesmo num modelo de universo primordial denominado inflação não-isentrópica (warm inflation).
It is known that microscopic derivations based on quantum field theory (QFT)methods can lead to quite complicated equations of motion (EoM) with a dissipation term with memory and a colored noise term. A very interesting particular case is the model that describes the interaction between a system and a thermal bath at some temperature T. Motivated by this, we use a prescription that allow us to rewrite similar non-Markovian EoMs to that obtained in QFT in terms of a set of local equations, so that we can contrast the solution of this system of equations with the approximated solution currently used in the literatury, the so-called Markovian approximation. The key question we want to address here is: given a set of parameters that characterizes the system and the bath, is the Markovian approximation good enough to represent the system's dynamics? We also have considered a linear version of the non-Markovian equation in order to check the confiability of our numerical approach. For that, we have compared the analytical solution with the numerical one. As an example of practical application of the theme discussed here, we contrast the non-Markovian and the Markovian evolution of the inflaton field in an early universe model called warm in inflation.
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Alves, Claudia Marins. „Stochastic models for the treatment of dispersion in the atmosphere“. Laboratório Nacional de Computação Científica, 2006. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=135.
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Lagrangian stochastic models are a largely used tool in the study of passive substances dispersion inside the Atmospheric Boundary Layer.
Its application is related to the trajectory computation of thousands of particles, that numerically simulate the dispersion of suspense substances in the atmosphere. In this study, the basic concepts related to the Lagrangian stochastic modelling are presented and discussed together with its main characteristics and its computational implementation,
to the study of particles dispersion in the atmosphere. In a computational experiment, the obtained results are compared with observational data from the TRACT experiment, that took place in Europe in 1992.
The input data needed for the dispersion model are extracted from simulations with the numerical weather forecast model RAMS. Dispersion over Rio de Janeiro region is also tested in a second experiment.Modelos Lagrangianos estocásticos constituem ferramenta muito utilizada no estudo da dispersão de substâncias passivas na Camada Limite Atmosférica. Sua aplicação consiste em calcular a trajetória de milhares de partículas, que simulam numericamente a dispersão de uma substância em suspensão na atmosfera. Nesta tese, são apresentados e discutidos os conceitos básicos relacionados à Modelagem Lagrangiana Estocástica de Partículas, bem como suas principais características e sua implementação computacional, para o estudo da dispersão de partículas na atmosfera. Numa experimentação computacional, comparam-se os resultados obtidos com dados observacionais provenientes do experimento TRACT, realizado na Europa em 1992. Os dados de entrada necessários ao modelo de dispersão são extraídos de simulações do modelo de previsão numérica do tempo RAMS. A dispersão sobre o Estado do Rio de Janeiro é também testada em um segundo experimento.
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Francisquini, Elton. „Caracterização das propriedades morfológicas, estruturais e magnéticas de nanopartículas Fe3O4 e Fe2CoO4 em matriz orgânica“. reponame:Repositório Institucional da UFABC, 2013.
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Heidernätsch, Mario. „On the diffusion in inhomogeneous systems“. Doctoral thesis, Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-169979.
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Ziel dieser Arbeit ist die Untersuchung des Einflusses der stochastischen Interpretation der Langevin Gleichung mit zustandsabhängigen Diffusionskoeffizienten auf den Propagator des zugehörigen stochastischen Prozesses bzw. dessen Mittelwerte. Dies dient dem besseren Verständnis und der Interpretation von Messdaten von Diffusion in inhomogenen Systemen und geht einher mit der Frage der Form der Diffusionsgleichung in solchen Systemen. Zur Vereinfachung der Fragestellung werden in dieser Arbeit nur Systeme untersucht die vollständig durch einen ortsabhängigen Diffusionskoeffizienten und Angabe der stochastischen Interpretation beschrieben werden können. Dazu wird zunächst für mehrere experimentell relevante eindimensionale Systeme der jeweilige allgemeine Propagator bestimmt, der für jede denkbare stochastische Interpretation gültig ist. Der analytisch bestimmte Propagator wird dann für zwei exemplarisch ausgewählte stochastische Interpretationen, hier für die Itô und Klimontovich-Hänggi Interpretation, gegenübergestellt und die Unterschiede identifiziert. Für Mittelwert und Varianz der Prozesse werden die drei wesentlichen stochastischen Interpretationen verglichen, also Itô, Stratonovich und Klimontovich-Hänggi Interpretation. Diese systematische Untersuchung von inhomogenen Diffusionsprozessen kann zukünftig helfen diese Art von, in genau einer stochastischen Interpretation, driftfreien Systemen einfacher zu identifizieren. Ein weiterer wesentlicher Teil der Arbeit erweitert die Frage auf mehrdimensionale inhomogene anisotrope Systeme. Dies wird z.B. bei der Untersuchung von Diffusion in Flüssigkristallen mit inhomogenem Direktorfeld relevant. Obwohl hier, im Gegensatz zu eindimensionalen Systemen, der Propagator nicht allgemein berechnet werden kann, wird dennoch der Einfluss der Inhomogenität auf Messgrößen, wie die mittlere quadratische Verschiebung oder die Verteilung der Diffusivitäten, bestimmt. Anhand eines Beispiels wird auch der Einfluss der stochastischen Interpretation auf diese Messgrößen demonstriertThe aim of this thesis is to investigate the influence of the stochastic interpretation of the Langevin equation with state-dependent diffusion coefficient on the propagator of the related stochastic process, or its averages, respectively. This helps to obtain a deeper understanding and to interpret measurement data of diffusion in inhomogeneous systems and is accompanied with the question of the proper form of the diffusion equation in such systems. To simplify the question, in this thesis only systems are considered which can be fully described by a spatially dependent diffusion coefficient and a given stochastic interpretation. Therefore, for several experimentally relevant one-dimensional systems, the respective general propagator is determined, which is valid for any possible stochastic interpretation. Then, the propagator for two exemplary stochastic interpretations, here the Itô and Klimontovich-Hänggi interpretation, are compared and the differences are identified. For mean and variance of the processes three major interpretations are compared, namely the Itô, the Stratonovich and the Klimontovich-Hänggi interpretation. This systematic research on inhomogeneous diffusion process may help in future to identify these kind of, in exactly one stochastic interpretation, drift-free systems more easily. Another important part of this thesis extends this question to multidimensional inhomogeneous anisotropic systems. This is of high relevance, for instance, for the research of diffusion in liquid crystalline systems with an inhomogeneous director field. Although, in contrast to one-dimensional systems, the propagator may not be calculated generally, the influence of the inhomogeneity on measurement data like the mean squared displacement or the distribution of diffusivities is determined. Based on one example, also the influence of the stochastic interpretation on these quantities is demonstrated
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Hannay, Jonathan David. „Computational simulations of thermally activated magnetisation dynamics at high frequencies“. Thesis, Bangor University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367315.
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Cohen, Jack Andrew. „Active colloids and polymer translocation“. Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e8fd2e5d-f96f-4f75-8be8-fc506155aa0f.
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This thesis considers two areas of research in non-equilibrium soft matter at the mesoscale. In the first part we introduce active colloids in the context of active matter and focus on the particular case of phoretic colloids. The general theory of phoresis is presented along with an expression for the phoretic velocity of a colloid and its rotational diffusion in two and three dimensions. We introduce a model for thermally active colloids that absorb light and emit heat and propel through thermophoresis. Using this model we develop the equations of motion for their collective dynamics and consider excluded volume through a lattice gas formalism. Solutions to the thermoattractive collective dynamics are studied in one dimension analytically and numerically. A few numerical results are presented for the collective dynamics in two dimensions. We simulate an unconfined system of thermally active colloids under directed illumination with simple projection based geometric optics. This system self-organises into a comet-like swarm and exhibits a wide range of non- equilibrium phenomena. In the second part we review the background of polymer translocation, including key experiments, theoretical progress and simulation studies. We present, discuss and use a common model to investigate the potential of patterned nanopores for stochastic sensing and identification of polynucleotides and other heteropolymers. Three pore patterns are characterised in terms of the response of a homopolymer with varying attractive affinity. This is extended to simple periodic block co-polymer heterostructures and a model device is proposed and demonstrated with two stochastic sensing algorithms. We find that mul- tiple sequential measurements of the translocation time is sufficient for identification with high accuracy. Motivated by fluctuating biological channels and the prospect of frequency based selectivity we investigate the response of a homopolymer through a pore that has a time dependent geometry. We show that a time dependent mobility can capture many features of the frequency response.
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Вітренко, Андрій Миколайович, Андрей Николаевич Витренко und Andrii Mykolaiovych Vitrenko. „Стабилизация равновесного состояния динамической системы при воздействии взаимно-коррелированных шумов“. Thesis, Сумский государственный университет, 2018. http://essuir.sumdu.edu.ua/handle/123456789/67928.
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Рассматривается стохастическая динамическая система, которая описывается уравнением Ланжевена с линейной возвращающей силой и двумя взаимно-коррелированными гауссовскими белыми шумами, один из которых – аддитивный, другой – мультипликативный. Система имеет равновесное состояние в x = 0. При отрицательной взаимной корреляции каждый из шумов характеризуется критической амплитудой, при которой в системе индуцируется унимодальный-бимодальный
переход.
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Arenas, Zochil González. „Formulação supersimétrica de processos estocásticos com ruído multiplicativo“. Universidade do Estado do Rio de Janeiro, 2012. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4684.
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Centro Latino-Americano de FísicaOs processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi.
Multiplicativewhite-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its characterization. In this thesis, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for this kind of processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. We deduce a functional formalism to derive a generating functional for correlation and response functions of a multiplicative stochastic process represented by a Langevin equation. Representing the stochastic process in this functional (Grassmann) formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicativeMarkovian white-noise process and study some of the constraints it imposes on correlation functions using Ward-Takahashi identities.
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Alves, Claudia Marins. „Modelos estocásticos para tratamento da dispersão de material particulado na atmosfera“. Laboratório Nacional de Computação Científica, 2006. https://tede.lncc.br/handle/tede/62.
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Previous issue date: 2006-11-13Lagrangian stochastic models are a largely used tool in the study of passive substances dispersion inside the Atmospheric Boundary Layer. Its application is related to the trajectory computation of thousands of particles, that numerically simulate the dispersion of suspense substances in the atmosphere. In this study, the basic concepts related to the Lagrangian stochastic modelling are presented and discussed together with its main characteristics and its computational implementation, to the study of particles dispersion in the atmosphere. In a computational experiment, the obtained results are compared with observational data from the TRACT experiment, that took place in Europe in 1992. The input data needed for the dispersion model are extracted from simulations with the numerical weather forecast model RAMS. Dispersion over Rio de Janeiro region is also tested in a second experiment.
Modelos Lagrangianos estocásticos constituem ferramenta muito utilizada no estudo da dispersão de substâncias passivas na Camada Limite Atmosférica. Sua aplicação consiste em calcular a trajetória de milhares de partículas, que simulam numericamente a dispersão de uma substância em suspensão na atmosfera. Nesta tese, são apresentados e discutidos os conceitos básicos relacionados à Modelagem Lagrangiana Estocástica de Partículas, bem como suas principais características e sua implementação computacional, para o estudo da dispersão de partículas na atmosfera. Numa experimentação computacional, comparam-se os resultados obtidos com dados observacionais provenientes do experimento TRACT, realizado na Europa em 1992. Os dados de entrada necessários ao modelo de dispersão são extraídos de simulações do modelo de previsão numérica do tempo RAMS. A dispersão sobre o Estado do Rio de Janeiro é também testada em um segundo experimento.
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Yilmaz, Bulent. „Stochastic Approach To Fusion Dynamics“. Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608517/index.pdf.
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This doctoral study consists of two parts. In the first part, the quantum statistical effects on the formation process of the heavy ion fusion reactions have been investigated by using the c-number quantum Langevin equation approach. It has been shown that the quantum effects enhance the over-passing probability at low temperatures. In the second part, we have developed a simulation technique for the quantum noises which can be approximated by two-term exponential colored noise.
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Mostefai, Mohamed Sadek. „Déduction rigoureuse de l'équation de Reynolds à partir d'un système modélisant l'écoulement à faible épaisseur d'un fluide micropolaire, et étude de deux problèmes à frontière libre : Hele-Shaw généralisé et Stephan à deux phases pour un fluide non newtonien“. Saint-Etienne, 1997. http://www.theses.fr/1997STET4019.
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Dans le chapitre 1, on considère le modèle micropolaire de Navier-Stokes avec conditions de bords de type Dirichlet non homogènes en dimension deux. On donnera un résultat d'existence d'une solution faible en utilisant le théorème du point fixe de Leray-Schauder, puis on prouvera l'unicité de la solution faible du problème sous certaines hypothèses. On établiera une justification mathématique de l’équation de Reynolds généralisé à partir de ce modèle là. On étudiera ensuite la forme de l'équation de Reynolds suivant le choix de la viscosité et des données initiales. Dans le chapitre 2, nous considérons le modèle de Hele-Shaw généralisé dans une cellule laminaire, qui consiste à injecter du fluide, avec un débit non constant w 0, à travers un trou de frontière 1, situé sur l'une des deux surfaces ; et à tenir compte que l'une des surfaces a une géométrie quelconque et animée d'un mouvement relatif vertical. En introduisant un changement de variable de type Baiocchi, le problème initial se ramène à l'étude d'une inéquation variationnelle avec terme de Volterra. L'existence d'une solution pour cette dernière est donnée par le théorème du point fixe de Banach. Des résultats de régularité en espace pour la solution seront prouvés en introduisant un problème pénalisé et en utilisant la méthode de Rothe (semi-discrétisation en temps), puis on montrera que la dérivée par rapport à t de la solution de l'inéquation variationnelle est dans l#(0, t, h#2()), ce dernier résultat nous permet de revenir au problème initial. Dans le chapitre 3, on considère un problème de Stefan à deux phases avec convection. Le problème est gouverné par un système couple non linéaire, comprenant la loi de Darcy pour un fluide non newtonien et l'équation d'équilibre d'énergie avec second membre dans l#1. Pour prouver l'existence de solutions du problème faible on introduira une famille de solutions approchées (#, p#), > 0, définies sur le domaine entier , en insérant une fonction de pénalité convenable dans l'équation de pression. On considère ensuite séparement les problèmes en # et p#, respectivement, et en utilisant le principe de point fixe de Schauder, on montre l'existence de couples solutions (#, p#) du problème approché, pour tout > 0. En faisant tendre vers zéro, on montre que les solutions du problème approché convergent vers une limite (, p) qui est une solution faible du problème variationnel. On montre aussi que la fonction est continue d'où le domaine où > 0 est un ensemble ouvert, et l'interface des deux phases est définie a posteriori comme l'ensemble de niveau = 0. On établira, enfin, quelques relations entre les solutions faibles et classiques, dans le cas d’une courbe assez régulière
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Santos, Joao Rafael Lucio dos. „Tópicos em defeitos deformados e o movimento Browniano“. Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/5748.
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Previous issue date: 2013-11-20Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The non-linear science is a central topic covering several investigation areas, such as biology, chemistry, mathematics and physics. In the first part of this thesis, we studied the non-linearity in the scope of classical field theory. The discussions are based on static solutions in (1, 1) space-time dimensions, and they are focused on kinks and lumps defects. In the related procedures, we show several techniques which allowed us to determine new models with their respective analytical solutions. The main mathematical tool to obtain these results is the so called deformation method, which was also an essential piece in the construction of a new extension method. This method presents the determination of new two scalar fields models from the coupling between two one scalar field systems. The method was analyzed carefully, as well as the linear stability, the zero modes, the total energy and the superpotentials, related with the new families of potentials. Furthermore, in the second part we presented the basics concepts about the Brownian Motion, where we analised the features of the solution of the Langevin Equation, and we also introduced a path integral approach to this problem in a quantum field theory way.
A ciência não-linear é tema central de diversas linhas de investigação, cobrindo áreas como a biologia, a física, a matemática e a química. Nossa primeira vertente de trabalho nesta tese, consiste no estudo de não-linearidades via abordagem de teoria clássica de campos. As discussões estão baseadas em soluções estáticas em (1, 1) dimensões, com destaque para o chamados defeitos tipo kink e lump. Nos procedimentos relatados, discorremos a respeito de diversas técnicas para a determinação de novos modelos com suas respectivas soluções analíticas. Um ferramental fundamental para a obtenção desses resultados é o chamado método de deformação, o qual também foi parte essencial para a criação de um método de extensão de modelos, onde visamos a construção de modelos de dois campos reais a partir do acoplamento entre dois modelos de um campo. Tal método também foi exposto em detalhes, bem como as análises sobre estabilidade linear, cálculo de modos zeros, determinação da energia total e dos superpotenciais, relativos às novas famílias de potenciais. Já a segunda linha de pesquisa, refere-se aos conceitos básicos do movimento browniano, onde analisamos as propriedades da solução da equação de Langevin, e na introdução de uma abordagem via integrais de trajetória para descrevê-lo nos moldes de teoria de quântica de campos.
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Le, Thanh Binh. „Sur le problème de coefficient et la multifractalité de whole-plane SLE“. Thesis, Orléans, 2016. http://www.theses.fr/2016ORLE2028/document.
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Le point de départ de cette thèse est la conjecture de Bieberbach : sa démonstration par De Branges utilise deux ingrédients, à savoir la théorie de Loewner des domaines plans croissants et une inégalité de Milin qui concerne les coefficients logarithmiques. Nous commençons par étudier les coefficients logarithmiques du whole-plane SLE en utilisant une méthode combinatoire, assistée par ordinateur. Nous retrouvons les résultats en utilisant une équation aux dérivées partielles analogue à celle obtenue par Beliaev et Smirnov. Nous généralisons ces résultats en définissant le spectre généralisé du whole-plane SLE, que nous calculons par la même méthode, à savoir en dérivant, par le calcul d’Itô, une EDP parabolique satisfaite par les quantités que nous moyennons. Cette famille à deux paramètres d’EDP admet une riche structure algébrique que nous étudions en détail. La dernière partie de la thèse concerne l’opérateur de Grunsky et ses généralisations. Plus expérimentale, nous y mettons à jour, grâce à un logiciel de calcul formel, une structure assez complexe dont nous avons commencé l’explorationThe starting point of this thesis is Bieberbach’s conjecture: its proof, given by De Branges, uses two ingredients, namely Loewner’s theory of increasing plane domains and an inequality from Milin about the logarithmic coefficients. We start with a study of the logarithmic coefficients of the whole-plane SLE by using a combinatorial method, assisted by computer. We find the results by using a partial differential equation similar to that obtained by Beliaev and Smirnov. We generalize these results by defining the generalized spectrum of the whole-plane SLE, that we calculate by the same method, namely by deriving, thanks to Itô calculus, a parabolic PDE satisfied by the quantities of which we take the average. This two-parameter family of PDEs admits a rich algebraic structure that we study in detail. The last part of this thesis is about the Grunsky operator and its generalizations. In this part that is more experimental we update, thanks to a computer algebra system, a rather complex structure of which we began the exploration
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Ceccato, Alessandro. „Approaches to dimensionality reduction and model simplification of dynamics in the chemical context“. Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3426709.
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Much of the effort in the modern chemical and physical sciences is devoted to the study of complex dynamical phenomena. Such a study is often hampered by the considerable complexity (i.e., the high dimensionality) exhibited by the systems of interest.
In this research project, of theoretical and methodological character, we explore some facets of the topics of model reduction and simplification of complex dynamics, both deterministic and stochastic.
In particular, in the first part of the work (chs. 2-5), we focus on deterministic systems. In chapter 2, starting from the findings of two previous works [P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234101 (2013) and P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234102 (2013)] we introduce the concept of "canonical format" of the evolution law for mass-action-based chemical kinetics, and show that the study of such a type of formats could lead to the discovery of new interesting features and to a rationalization of already well-known ones. Specifically, we unveil the existence of "attracting subspaces" in an abstract "hyper-spherical" representation of the dynamics of a reacting system. In chapter 3, based on the theory devised in ch. 2, we develop an algorithm (implemented in the companion software DRIMAK, acronym of Dimensional Reduction for Isothermal Mass-Action Kinetics) aimed at detecting the neighborhood of the Slow Manifold, which is a hypersurface, in the concentration space, in the proximity of which the slow evolution takes place. The detection of the Slow Manifold for a reacting system is a potential key-step to elaborate dimensionality reduction strategies. In chapter 4 we extend the theory to open reaction networks, i.e., reaction networks with one or more reactants continuously injected in the reaction environment. Finally, in chapter 5 we further generalize the theory to general phase-space dynamics, possibly damped.
The second part of the work (chs. 6-8) is devoted to stochastic systems. In chapter 6 we move the first steps towards the model reduction of stochastic chemical kinetics. Specifically, we show the existence of geometric structures (in the space of the number of molecules of each species) analogous to the Slow Manifold in the macroscopic counterpart. Still in the context of stochastic chemical kinetics, in chapter 7 we make a critical study of two common continuous approximations of the chemical master equation and of the associated Gillespie's stochastic simulation algorithm; namely, we investigate on the physical reliability of the chemical Fokker-Planck and chemical Langevin equations. In particular, we prove that both the approximations suffer from nonphysical probability currents at equilibrium, even for fully reversible and detailed-balanced chemical reaction networks. Finally, in chapter 8 we focus on general overdamped fluctuating systems, which, apart from very simple and low-dimensional cases, are often mathematically intractable. In this context, given the well-known difficulties for the mathematical treatment of such systems, we aim only at achieving a partial, but easily computable, information. Namely, we devise a set of mathematical time-dependent bounds for key-quantities describing the systems of interest.Nelle moderne scienze fisiche e chimiche, uno sforzo considerevole è dedicato allo studio di fenomeni dinamici complessi. Tale studio è spesso ostacolato dalla considerevole complessità (dovuta all'elevata dimensionalità) dei sistemi di interesse. In questo progetto di ricerca, di carattere teorico e metodologico, esploriamo alcuni aspetti riguardanti la riduzione della dimensionalità e la semplificazione di dinamiche complesse, sia deterministiche che stocastiche. In particolare, la prima parte del lavoro (capitoli 2-5), si concentra su sistemi deterministici. Nel capitolo 2, partendo dai risultati ottenuti in due precedenti lavori [P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234101 (2013) and P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234102 (2013)] introduciamo il concetto di "forma canonica" della legge di evoluzione per cinetiche chimiche basate sulla legge di azione di massa, e mostriamo che lo studio di tali forme può condurre alla scoperta di nuove interessanti proprietà e alla razionalizzazione di altre già note. Specificamente, mostriamo l'esistenza di "sottospazi attrattivi" in una rappresentazione astratta (ipersferica) della dinamica del sistema reagente. Nel capitolo 3, basandoci sulla teoria formulata nel capitolo 2, sviluppiamo un algoritmo (implementato nel software DRIMAK, acronimo di Dimensional Reduction for Isothermal Mass-Action Kinetics) finalizzato alla localizzazione di punti prossimi allo Slow Manifold, ossia all’ipersuperficie, nello spazio delle concentrazioni, in prossimità della quale ha luogo la parte lenta dell'evoluzione. L'individuazione dello Slow Manifold per un sistema reagente è potenzialmente un passaggio chiave per elaborare strategie di riduzione di dimensionalità. Nel capitolo 4 estendiamo la teoria a network aperti di reazioni chimiche, ossia a casi in cui uno o più reagenti sono continuamente immessi nell'ambiente di reazione. Infine, nel capitolo 5 generalizziamo ulteriormente la teoria a dinamiche (anche smorzate) nello spazio delle fasi. La seconda parte del lavoro (capitoli 6-8) è dedicata ai sistemi stocastici. Nel capitolo 6 muoviamo i primi passi verso la riduzione di dimensionalità di cinetiche chimiche stocastiche. Specificamente, mostriamo l'esistenza di strutture geometriche (nello spazio dei numeri di molecole per ogni specie) analoghe agli Slow Manifold nella controparte macroscopica. Ancora nel contesto delle cinetiche chimiche stocastiche, nel capitolo 7 mostriamo i risultati di uno studio critico di due comuni approssimazioni continue della ‘chemical master equation’ e dell'algoritmo di simulazione di Gillespie, ossia, le cosiddette equazioni di Fokker-Planck e di Langevin “chimiche”. In particolare, dimostriamo che entrambe le approssimazioni soffrono di una inconsistenza fisica che si manifesta nella presenza di correnti di probabilità spurie all'equilibrio, anche per network di reazioni chimiche completamente reversibili e verificanti il bilancio dettagliato. Infine, nel capitolo 8 ci concentriamo su sistemi fluttuanti sovrasmorzati di tipo generale, i quali, a parte casi molto semplici e a bassa dimensionalità, sono spesso matematicamente intrattabili. In questo contesto miriamo ad ottenere solo un'informazione parziale, ma con basso costo computazionale, sullo stato futuro del sistema. In particolare, otteniamo una serie di disuguaglianze che consentono di vincolare alcune quantità rilevanti del sistema.
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Weiß, Richard Gregor. „The role of water in the kinetics of hydrophobic molecular recognition investigated by stochastic modeling and molecular simulations“. Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/18814.
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Die Assoziation kleiner Moleküle (Liganden) in hydrophobe Bindungstaschen spielt eine fundamentale Rolle in der Biomolekularerkennung und den Selbstassemblierungsprozessen der physikalischen Chemie wässriger Lösungen. Während der Einfluss des Wassers auf die freie Energie der Bindung (die Bindungsaffinität) im thermischen Gleichgewicht in den letzten Jahren auf immer stärkere Aufmerksamkeit stößt, ist die Rolle des Wassers in der Kinetik und der Bestimmung der Bindungsraten noch weitestgehend unverstanden. Welche nanoskaligen Effekte des Wassers beeinflussen die Dynamik des Liganden in der Nähe der Bindungstasche, und wie lassen sie sich durch die chemischen Eigenschaften der Tasche steuern?
Neuste Forschungen haben mithilfe von molekularen Computersimulationen eines einfachen Modells gezeigt, dass Hydrationsfluktuationen in der hydrophoben Bindungstasche an die Dynamik des Liganden koppeln und damit seine Bindungsrate beeinflussen. Da die Wasserfluktuationen wiederum durch die Geometrie und Hydrophobizität der Bindungstasche beeinflusst werden, entsteht die Möglichkeit, kontrollierte Fluktuation zu kreieren, um die Bindungsraten des Liganden zu steuern. In dieser Arbeit wird diese Perspektive mithilfe eines theoretischen Multiskalenansatzes für prototypische Schlüssel-Schloss-Systeme aufgegriffen. Wir untersuchen den Einfluss der physikochemischen Eigenschaften der Bindungstasche auf die Diffusivität und die Bindungsraten des Liganden, und wie die Orientierung eines anisotropen Liganden an die Hydrationsfluktuationen der Tasche koppelt. Damit stellen wir fest, dass kleine Änderungen der Taschentiefe eine extreme Beschleunigung der Bindungsraten bewirken kann und, dass gleichzeitig die Bindung in konkave Taschen vorteilhaft für die Reorientierungsdynamik des Liganden ist. Die Resultate dieses Projekts sollen somit helfen, maßgeschneiderte Lösungen für funktionale „Host-Guest“-Systeme sowie pharmazeutische Moleküle in biomedizinischen Anwendungen zu entwickeln.The association of small molecules (ligands) to hydrophobic binding pockets plays an integral role in biochemical molecular recognition and function, as well as in various self-assembly processes in the physical chemistry of aqueous solutions. While the investigation of water contributions to the binding free energy (affinity) in equilibrium has attracted a great deal of attention in the last decade, little is known about the role of water in determining the rates of binding and kinetic mechanisms. For instance, what are the nanoscale water effects on ligand diffusion close to the hydrophobic docking site, and how can they be steered by the chemical composition of the pocket? Recent studies used molecular simulations of a simple prototypical pocket-ligand model to show that hydration fluctuations within the binding pocket can couple to the ligand dynamics and influence its binding rates. Since the hydration fluctuations, in turn, can be modified by the pocket’s geometry and hydrophobicity, the possibility exists to create well-controlled solvent fluctuations to steer the ligand’s binding rates. In this work, we pick up this appealing notion employing a theoretical multi-scale approach of a generic key-lock system in aqueous solution. We explore the influence of the physicochemical properties of the pocket on local ligand diffusivities and binding rates and demonstrate how the orientation of a (non-spherical) ligand couples to a pocket’s hydration fluctuations. We find that minor modulation in pocket depth can drastically speed up the binding rate and that, concurrently, binding to molded binding sites is advantageous for the rotational dynamics of the ligand. The results and discussion of this work shall, therefore, imply generic design principles for tailored solutions of functional host-guest systems as well as optimized drugs in biomedical applications.
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Pereira, Mike. „Champs aléatoires généralisés définis sur des variétés riemanniennes : théorie et pratique“. Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEM055.
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La géostatistique est la branche des statistiques s’intéressant à la modélisation des phénomènes ancrés dans l’espace au travers de modèles probabilistes. En particulier, le phénomène en question est décrit par un champ aléatoire (généralement gaussien) et les données observées sont considérées comme résultant d’une réalisation particulière de ce champ aléatoire. Afin de faciliter la modélisation et les traitements géostatistiques qui en découlent, il est d’usage de supposer ce champ comme stationnaire et donc de supposer que la structuration spatiale des données se répète dans le domaine d’étude.Cependant, lorsqu’on travaille avec des jeux de données spatialisées complexes, cette hypothèse devient inadaptée. En effet, comment définir cette notion de stationnarité lorsque les données sont indexées sur des domaines non euclidiens(comme des sphères ou autres surfaces lisses)? Quid également du cas où les données présentent structuration spatiale qui change manifestement d’un endroit à l’autre du domaine d’étude? En outre, opter pour des modèles plus complexes,lorsque cela est possible, s’accompagne en général d’une augmentation drastique des coûts opérationnels (calcul et mémoire), fermant alors la porte à leur application à de grands jeux de données. Dans ce travail, nous proposons une solution à ces problèmes s’appuyant sur la définition de champs aléatoires généralisés sur des variétés riemanniennes. D’une part, travailler avec des champs aléatoires généralisés permet d’étendre naturellement des travaux récents s’attachant à tirer parti d’une caractérisation des champs aléatoires utilisés en géostatistique comme des solutions d’équations aux dérivées partielles stochastiques. D’autre part, travailler sur des variétés riemanniennes permet à la fois de définir des champs sur des domaines qui ne sont que localement euclidiens, et sur des domaines vus comme déformés localement (ouvrant donc la porte à la prise en compte du cas non stationnaire). Ces champs généralisés sont ensuite discrétisés en utilisant une approche par éléments finis, et nous en donnons une formule analytique pour une large classe de champs généralisés englobant les champs généralement utilisés dans les applications. Enfin, afin de résoudre le problème du passage à l’échelle pour les grands jeux de données, nous proposons des algorithmes inspirés du traitement du signal sur graphe permettant la simulation, la prédiction et l’inférence de ces champs par des approches "matrix-free"Geostatistics is the branch of statistics attached to model spatial phenomena through probabilistic models. In particular, the spatial phenomenon is described by a (generally Gaussian) random field, and the observed data are considered as resulting from a particular realization of this random field. To facilitate the modeling and the subsequent geostatistical operations applied to the data, the random field is usually assumed to be stationary, thus meaning that the spatial structure of the data replicates across the domain of study. However, when dealing with complex spatial datasets, this assumption becomes ill-adapted. Indeed, how can the notion of stationarity be defined (and applied) when the data lie on non-Euclidean domains (such as spheres or other smooth surfaces)? Also, what about the case where the data clearly display a spatial structure that varies across the domain? Besides, using more complex models (when it is possible) generally comes at the price of a drastic increase in operational costs (computational and storage-wise), rendering them impossible to apply to large datasets. In this work, we propose a solution to both problems, which relies on the definition of generalized random fields on Riemannian manifolds. On one hand, working with generalized random fields allows to naturally extend ongoing work that is done to leverage a characterization of random fields used in Geostatistics as solutions of stochastic partial differential equations. On the other hand, working on Riemannian manifolds allows to define such fields on both (only) locally Euclidean domains and on locally deformed spaces (thus yielding a framework to account for non-stationary cases). The discretization of these generalized random fields is undertaken using a finite element approach, and we provide an explicit formula for a large class of fields comprising those generally used in applications. Finally, to solve the scalability problem,we propose algorithms inspired from graph signal processing to tackle the simulation, the estimation and the inference of these fields using matrix-free approaches
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Schlichting, André. „The Eyring-Kramers formula for Poincaré and logarithmic Sobolev inequalities“. Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-97965.
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The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory.
The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation.
The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.