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1
Glass, K. „Dynamics of systems of interacting particles“. Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599435.
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In this thesis, we bring together three different problems in studying the equations where ui is a vector of length m, and β is a real parameter restricted to β ≥ -1. The N-body problem concerns N masses attracting one another according to a (1)/(r2) gravitational force. Much work has been done in finding central configurations of the N masses. If a system of masses released from a central configuration, it will remain similar to itself for all time, and can exhibit periodic behaviour.
2
Franz, Benjamin. „Recent modelling frameworks for systems of interacting particles“. Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:ac76d159-4cdd-40c9-b378-6ea1faf48aed.
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In this thesis we study three different modelling frameworks for biological systems of dispersal and combinations thereof. The three frameworks involved are individual-based models, group-level models in the form of partial differential equations (PDEs) and robot swarms. In the first two chapters of the thesis, we present ways of coupling individual based models with PDEs in so-called hybrid models, with the aim of achieving improved performance of simulations. Two classes of such hybrid models are discussed that allow an efficient simulation of multi-species systems of dispersal with reactions, but involve individual resolution for certain species and in certain parts of a computational domain if desired. We generally consider two types of example systems: bacterial chemotaxis and reaction-diffusion systems, and present results in the respective application area as well as general methods. The third chapter of this thesis introduces swarm robotic experiments as an additional tool to study systems of dispersal. In general, those experiments can be used to mimic animal behaviour and to study the impact of local interactions on the group-level dynamics. We concentrate on a target finding problem for groups of robots. We present how PDE descriptions can be adjusted to incorporate the finite turning times observed in the robotic system and that the adjusted models match well with experimental data. In the fourth and last chapter, we consider interactions between robots in the form of hard-sphere collisions and again derive adjusted PDE descriptions. We show that collisions have a significant impact on the speed with which the group spreads across a domain. Throughout these two chapters, we apply a combination of experiments, individual-based simulations and PDE descriptions to improve our understanding of interactions in systems of dispersal.
3
Romanovsky, Igor Alexandrovich. „Novel properties of interacting particles in small low-dimensional systems“. Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-07102006-041659/.
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Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2007.Landman, Uzi, Committee Member ; Yannouleas, Constantine, Committee Member ; Bunimovich, Leonid, Committee Member ; Chou, Mei-Yin, Committee Member ; Pustilnik, Michael, Committee Member.
4
Jacquot, Stéphanie Mireille. „Large systems of interacting particles : the Marcus-Lushnikov process and the β-Laguerre ensemble“. Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610327.
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5
Geiger, Benjamin [Verfasser], und Klaus [Akademischer Betreuer] Richter. „From few to many particles: Semiclassical approaches to interacting quantum systems / Benjamin Geiger ; Betreuer: Klaus Richter“. Regensburg : Universitätsbibliothek Regensburg, 2020. http://d-nb.info/1215906064/34.
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6
Lafleche, Laurent. „Dynamique de systèmes à grand nombre de particules et systèmes dynamiques“. Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLED010.
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On étudie dans cette thèse le comportement en temps long de solutions d’équations aux dérivées partielles. Celles-ci modélisent des systèmes à grand nombre de particules dont la dynamique est due à des forces externes, internes et à l’interaction entre ces particules. Cependant, on considère différentes échelles. On voyage ainsi du niveau quantique des atomes au niveau macroscopique des étoiles, et l’on voit que des différences apparaissent bien que certaines propriétés soient conservées. Dans ce voyage, on croise le chemin de diverses applications telles que l’astrophysique, les plasmas,les semi-conducteurs, la biologie et l’économie. Ce travail est divisé en trois parties.Dans la première, on étudie le comportement semi-classique de l’équation de Hartree en mécanique quantique et sa limite vers l’équation de Vlasov. On quantifie uniformément en la constante de Planck des propriétés telles que la propagation des moments et de normes de Lebesgue à poids et la dispersion. On les utilise ensuite pour établir des estimées de stabilité entre les deux équations au moyen d’un analogue semi-classique des distances de Wasserstein. Dans la deuxième partie, on regarde le comportement en temps long d’équations cinétiques dont l’opérateur de collision est linéaire et a un équilibre local avec peu de moments, tel que l’opérateur de Fokker-Planck, sa version fractionnaire et un opérateur de Boltzmann linéaire. Deux principales techniques sont utilisées, l’une consistant à construire des entropies et la seconde à utiliser la positivité.Enfin, la dernière partie s’intéresse à des modèles macroscopiques inspirés de l’équation de Keller-Segel et l’on regarde les paramètres sous lesquels ce type de système s’effondre sur lui-même, se disperse ou se stabilise. Le premier effet se voit en introduisant des poids appropriés, le deuxième avec des distances de Wasserstein et le troisième au moyen des normes de LebesgueIn this thesis, we study the behavior of solutions of partial differential equations that arise from the modeling of systems with a large number of particles. The dynamic of all these systems is driven by interaction between the particles and external and internal forces. However, we will consider different scales and travel from the quantum level of atoms to the macroscopic level of stars. We will see that differences emerge from the associated dynamics even though the main properties are conserved. In this journey, we will cross the path of various applications of these equations such as astrophysics, plasma, semi-conductors, biology, economy. This work is divided in three parts.In the first one, we study the semi classical behavior of the quantum Hartree equation and its limit to the kinetic Vlasov equation. Properties such as the propagation of moments and weighted Lebesgue norms and dispersive estimates are quantified uniformly in the Planck constant and used to establish stability estimates in a semiclassical analogue of the Wasserstein distance between the solutions of these two equations.In the second part, we investigate the long time behavior of macroscopic and kinetic models where the collision operatoris linear and has a heavy-tailed local equilibrium, such as the Fokker-Planck operator, the fractional Laplacian with a driftor a Linear Boltzmann operator. This let appear two main techniques, the entropy method and the positivity method.In the third part, we are interested in macroscopic models inspired from the Keller-Segel equation, and we study therange of parameters under which the system collapses, disperses or stabilizes. The first effect is studied using appropriate weights, the second using Wasserstein distances and the third using Lebesgue norms
7
Gracar, Peter. „Random interacting particle systems“. Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761028.
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Consider the graph induced by Z^d, equipped with uniformly elliptic random conductances on the edges. At time 0, place a Poisson point process of particles on Z^d and let them perform independent simple random walks with jump probabilities proportional to the conductances. It is well known that without conductances (i.e., all conductances equal to 1), an infection started from the origin and transmitted between particles that share a site spreads in all directions with positive speed. We show that a local mixing result holds for random conductance graphs and prove the existence of a special percolation structure called the Lipschitz surface. Using this structure, we show that in the setup of particles on a uniformly elliptic graph, an infection also spreads with positive speed in any direction. We prove the robustness of the framework by extending the result to infection with recovery, where we show positive speed and that the infection survives indefinitely with positive probability.
8
Deshayes, Aurélia. „Modèles de croissance aléatoire et théorèmes de forme asymptotique : les processus de contact“. Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0168/document.
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Cette thèse s'inscrit dans l'étude des systèmes de particules en interaction et plus précisément dans celle des modèles de croissance aléatoire qui représentent un quantité qui grandit au cours du temps et s'étend sur un réseau. Ce type de processus apparaît naturellement quand on regarde la croissance d'un cristal ou bien la propagation d'une épidémie. Cette dernière est bien modélisée par le processus de contact introduit en 1974 par Harris. Le processus de contact est un des plus simples systèmes de particules en interaction présentant une transition de phase et l'on connaît maintenant bien son comportement sur ses phases. De nombreuses questions ouvertes sur ses extensions, notamment celles de formes asymptotiques, ont motivé ce travail. Après la présentation de ce processus et de certaines de ses extensions, nous introduisons et étudions une nouvelle variante: le processus de contact avec vieillissement où les particules ont un âge qui influence leur capacité à donner naissance à leurs voisines. Nous effectuerons pour ce modèle un couplage avec une percolation orientée inspiré de celui de Bezuidenhout-Grimmett et nous montrerons la croissance d'ordre linéaire de ce processus. Dans la dernière partie de la thèse, nous nous intéressons à la preuve d'un théorème de forme asymptotique pour des modèles généraux de croissance aléatoire grâce à des techniques sous-Additives, parfois complexes à mettre en place à cause de la non 'survie presque sûre' de nos modèles. Nous en concluons en particulier que le processus de contact avec vieillissement, le processus de contact en environnement dynamique, la percolation orientée avec immigration hostile, et le processus de contact avec sensibilisation vérifient des résultats de forme asymptotiqueThis thesis is a contribution to the mathematical study of interacting particles systems which include random growth models representing a spreading shape over time in the cubic lattice. These processes are used to model the crystal growth or the spread of an infection. In particular, Harris introduced in 1974 the contact process to represent such a spread. It is one of the simplest interacting particles systems which exhibits a critical phenomenon and today, its behaviour is well-Known on each phase. Many questions about its extensions remain open and motivated our work, especially the one on the asymptotic shape. After the presentation of the contact process and its extensions, we introduce a new one: the contact process with aging where each particle has an age age that influences its ability to give birth to its neighbours. We build a coupling between our process and a supercritical oriented percolation adapted from Bezuidenhout-Grimmett's construction and we establish the 'at most linear' growth of our process. In the last part of this work, we prove an asymptotic shape theorem for general random growth models thanks to subadditive techniques, which can be complicated in the case of non-Permanent models conditioned to survive. We conclude that the process with aging, the contact process in randomly evolving environment, the oriented percolation with hostile immigration and the bounded modified contact process satisfy asymptotic shape results
9
Wang, Hao Carleton University Dissertation Mathematics and Statistics. „Interacting branching particle systems and superprocesses“. Ottawa, 1995.
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10
Deshayes, Aurélia. „Modèles de croissance aléatoire et théorèmes de forme asymptotique : les processus de contact“. Electronic Thesis or Diss., Université de Lorraine, 2014. http://www.theses.fr/2014LORR0168.
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Cette thèse s'inscrit dans l'étude des systèmes de particules en interaction et plus précisément dans celle des modèles de croissance aléatoire qui représentent un quantité qui grandit au cours du temps et s'étend sur un réseau. Ce type de processus apparaît naturellement quand on regarde la croissance d'un cristal ou bien la propagation d'une épidémie. Cette dernière est bien modélisée par le processus de contact introduit en 1974 par Harris. Le processus de contact est un des plus simples systèmes de particules en interaction présentant une transition de phase et l'on connaît maintenant bien son comportement sur ses phases. De nombreuses questions ouvertes sur ses extensions, notamment celles de formes asymptotiques, ont motivé ce travail. Après la présentation de ce processus et de certaines de ses extensions, nous introduisons et étudions une nouvelle variante: le processus de contact avec vieillissement où les particules ont un âge qui influence leur capacité à donner naissance à leurs voisines. Nous effectuerons pour ce modèle un couplage avec une percolation orientée inspiré de celui de Bezuidenhout-Grimmett et nous montrerons la croissance d'ordre linéaire de ce processus. Dans la dernière partie de la thèse, nous nous intéressons à la preuve d'un théorème de forme asymptotique pour des modèles généraux de croissance aléatoire grâce à des techniques sous-Additives, parfois complexes à mettre en place à cause de la non 'survie presque sûre' de nos modèles. Nous en concluons en particulier que le processus de contact avec vieillissement, le processus de contact en environnement dynamique, la percolation orientée avec immigration hostile, et le processus de contact avec sensibilisation vérifient des résultats de forme asymptotiqueThis thesis is a contribution to the mathematical study of interacting particles systems which include random growth models representing a spreading shape over time in the cubic lattice. These processes are used to model the crystal growth or the spread of an infection. In particular, Harris introduced in 1974 the contact process to represent such a spread. It is one of the simplest interacting particles systems which exhibits a critical phenomenon and today, its behaviour is well-Known on each phase. Many questions about its extensions remain open and motivated our work, especially the one on the asymptotic shape. After the presentation of the contact process and its extensions, we introduce a new one: the contact process with aging where each particle has an age age that influences its ability to give birth to its neighbours. We build a coupling between our process and a supercritical oriented percolation adapted from Bezuidenhout-Grimmett's construction and we establish the 'at most linear' growth of our process. In the last part of this work, we prove an asymptotic shape theorem for general random growth models thanks to subadditive techniques, which can be complicated in the case of non-Permanent models conditioned to survive. We conclude that the process with aging, the contact process in randomly evolving environment, the oriented percolation with hostile immigration and the bounded modified contact process satisfy asymptotic shape results
11
Stoica, Cristina. „Particle systems with quasihomogeneous interaction“. Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ52774.pdf.
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12
Ahmed, Hashim Abdalla. „Particle interactions in multicomponent systems“. Thesis, University of Bath, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235560.
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13
Xu, Lihu. „Nonlinear problems in infinite interacting particle systems“. Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444071.
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14
Moreira, Adriana Gomes. „Nonequilibrium phase transitions in interacting particle systems“. Universidade Federal de Minas Gerais, 1996. http://hdl.handle.net/1843/BUOS-9GJQ9K.
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We study the two-dimensional contact process (CP) with quenched disorder in the form of random dilution of a fraction x. A qualitative picture of the phase diagram is obtained through mean-¯eld theory (MFT). Monte Carlo simulations show that the relative shift in the critical point, [¸c(x)¡¸c(0)]=¸c(0) is in reasonable agreement with MFT, for small values of x. As expected on the basis of the Harris criterion, the critical exponents governing the order parameter and the survival probability take values
different from those of the pure model. We also study the critical spreading dynamics of the diluted model. In the pure model, spreading from a single particle at the critical point ¸c(0) is characterized by the critical exponents of directed percolation: in 2+1 dimensions, ± = 0:46, ´ = 0:214, and z = 1:13. Disorder causes a dramatic change in the critical behavior of the contact process.We also study the one-dimensional pair-contact process via time-dependent series expansions. Numerical results provide easonable estimates for the location of the critical point.Estudamos o processo de contato diluído (DCP) bidimensional. Desordem é introduzida na forma de diluição, com uma fração x de sítios sendo removida aleatoriamente da rede. Uma descrição qualitativa do diagrama de fases é obtida através da teoria de campo médio na aproximação de blocos. Simulações de Monte Carlo mostram que o deslocamento relativo do ponto crítico, [c(x) - c(0)]/c(0), para x pequeno, está de acordo com os resultados obtidos por campo médio. Os expoentes críticos relacionados com o parâmetro de ordem e a probabilidade de sobrevivência do modelo diluído são diferentes dos expoentes do modelo puro, como era esperado pelo critério de Harris. Usando simulações dependentes do tempo estudamos a evolução do modelo a partir de uma única semente. No modelo puro, o comportamento crítico é caracterizado por leis de potência descritas pelos expoentes críticos de percolação dirigida: em 2+1 dimensões, = 0,46, = 0,214, e z = 1,13. A presença de desordem causa uma mudan»ca drástica no comportamento crítico do modelo.Estudamos também o processo de contato de pares unidimensional utilizando o método de expansão em séries dependente do tempo. Estimativas razoáveis para a localização do ponto crítico foram obtidas.
15
Tran, Hong Quan. „Cutoff phenomenon for some interacting particle systems“. Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. http://www.theses.fr/2024UPSLD007.
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Sur un espace d’états fini, une chaîne de Markov irréductible à temps continu converge vers sa mesure stationnaire unique, ou en d’autres termes, se mélange. La convergence est mesurée par rapport à la distance en variation totale. Dans la théorie moderne des chaînes de Markov, nous nous intéressons aux chaînes où l’espace d’états devient grand. En étudiant certains modèles de mélange de cartes, Aldous, Diaconis et Shashahani ont découvert le phénomène remarquable maintenant connu sous le nom de cutoff : lorsque l’espace d’états devient grand, la distance entre la chaîne et l’équilibre reste proche de sa valeur maximale pendant une longue période, puis chute soudainement vers zéro sur une échelle de temps beaucoup plus courte. Depuis, le phénomène de cutoff a été observé dans de nombreux contextes différents, tels que les chaînes de naissance et de mort, les systèmes de spin à haute température, les systèmes de particules en interaction, etc. Malgré l’accumulation de modèles, il n’existe pas encore de théorie générale permettant de prédire efficacement cutoff. Au lieu de cela, le cutoff est montré modèle par modèle. Dans cette thèse, nous étudions trois systèmes de particules en interaction: le processus d’exclusion unidimensionnel avec réservoirs, le processus de Glauber-Exclusion dans le régime à haut température, et le processus de Zero-Range à champ-moyen avec potentiel croissant sous-linéairement. Pour chaque modèle, nous établissons cutoff et fournissons une estimation fine pour le trou spectral. Nous nous concentrons particulièrement sur le cadre de la percolation de l’information introduit par Lubetzky et Sly, qui nous permet de montrer le cutoff même sans connaître la formule explicite de la mesure invarianteOn a finite state space, an irreducible continuous-time Markov chain converges to its unique stationary measure, or in other words, mixes. The convergence is often measured by the total variation distance. In the modern theory of Markov Chains, we are interested in the case where the state space becomes large. When studying some models of card shuffling, Aldous, Diaconis, and Shashahani discovered a remarkable phenomenon now known as cutoff: as the state space becomes large, the distance between the chain and equilibrium stays close to its maximal value for a long time and then suddenly drops to near zero in a much shorter time scale. Since then, the cutoff phenomenon has been observed in many different contexts, such as birth and death chains, high-temperature spin systems, interacting particle systems, etc. Despite the accumulation of models, there is not yet a general theory to effectively predict cutoff. Instead, cutoff is proved model by model.In this thesis, we study three models : the one-dimensional Exclusion process with reservoirs, the Glauber-Exclusion process in the high-temperature regime, and the mean-field Zero-Range process with increasing sublinear potential. These three models all fall under the category of interacting particle systems. For each model, we establish cutoff and provide a sharp estimate on the spectral gap. We particularly focus on the information percolation framework introduced by Lubetzky and Sly, which allows us to show cutoff even without knowing the explicit formula of the invariant measure
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Blanco-Mantecon, Mireia. „Interactions, particle size and surface effects in magnetic nanoparticle systems“. Thesis, Bangor University, 2000. https://research.bangor.ac.uk/portal/en/theses/interactions-particle-size-and-surface-effects-in-magnetic-nanoparticle-systems(2f7d3ef7-ef4c-43b0-b3ad-9e5c68f629e5).html.
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This work has involved the study of the magnetic behaviour of small magnetic nanoparticle systems. Due to the reduced size of magnetic nanoparticles they present distinctive properties, such as size and surface effects, that have been analysed in this work, as well as the effect of interactions in such systems. The samples chosen for the study were magnetite particles in the form of a ferrofluid and Co nanoclusters in a nonmagnetic matrix of Cu. Both systems present very narrow particle size distributions, which facilitates the interpretation of the data. The samples have been subjected to basic characterisation, which includes the determination of the distribution of magnetic particle sizes using the magnetisation curves at room temperatures, TEM microscopy and X-ray diffraction, in the case of the ferrofluid samples. For the nanoclusters, a time of flight spectrometer has been used to obtain the number of atoms per cluster. Many of the measurements have been performed at low temperatures, where thermal effects are minimised. For such measurements the samples have been frozen in a zero applied field, so that they have a random distribution of magnetic moments prior to the measurement. The energy barrier distributions have been calculated via the temperature decay of remanence (TDR). From this study, an effective anisotropy constant has been calculated. For the study of the interactions, surface and size effects, magnetisation, susceptibility (ZFC), remanence and delta-M curves, as well as the time dependence of magnetisation have been studied. The attempt frequency of the different particle size systems has been calculated using different techniques. The basic magnetic behaviour can be explained on the basis of the Neel blocking model. It has been found that the systems with the smaller particles have significant surface effects, which are enhanced at lower temperatures. Interactions, which are weak due to the low concentration of magnetic material in the samples (<10%), have been found to be overall demagnetising and the evolution of the magnetic properties with dilution has been explained. As is the case for the surface effects, interaction effects are stronger at low temperatures due the reduction of thermal effects. The experimental results have been compared with calculations from a Montecarlo model for fine particles, which includes the effects of concentration, anisotropy, particle size and temperature.
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Stamm, Matthew T. „Particle Dynamics and Particle-Cell Interaction in Microfluidic Systems“. Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/308886.
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Particle-laden flow in a microchannel resulting in aggregation of microparticles was investigated to determine the dependence of the cluster growth rate on the following parameters: suspension void fraction, shear strain rate, and channel-height to particle-diameter ratio. The growth rate of an average cluster was found to increase linearly with suspension void fraction, and to obey a power-law relationships with shear strain rate as S^0.9 and channel-height to particle-diameter ratio as (h/d)^-3.5. Ceramic liposomal nanoparticles and silica microparticles were functionalized with antibodies that act as targeting ligands. The bio-functionality and physical integrity of the cerasomes were characterized. Surface functionalization allows cerasomes to deliver drugs with selectivity and specificity that is not possible using standard liposomes. The functionalized particle-target cell binding process was characterized using BT-20 breast cancer cells. Two microfluidic systems were used; one with both species in suspension, the other with cells immobilized inside a microchannel and particle suspension as the mobile phase. Effects of incubation time, particle concentration, and shear strain rate on particle-cell binding were investigated. With both species in suspension, the particle-cell binding process was found to be reasonably well-described by a first-order model. Particle desorption and cellular loss of binding affinity in time were found to be negligible; cell-particle-cell interaction was identified as the limiting mechanism in particle-cell binding. Findings suggest that separation of a bound particle from a cell may be detrimental to cellular binding affinity. Cell-particle-cell interactions were prevented by immobilizing cells inside a microchannel. The initial stage of particle-cell binding was investigated and was again found to be reasonably well-described by a first-order model. For both systems, the time constant was found to be inversely proportional to particle concentration. The second system revealed the time constant to obey a power-law relationship with shear strain rate as τ∝S^.37±.06. Under appropriate scaling, the behavior displayed in both systems is well-described by the same exponential curve. Identification of the appropriate scaling parameters allows for extrapolation and requires only two empirical values. This could provide a major head-start in any dosage optimization studies.
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Fernández, Lafuerza Luis Gonzalo. „Fluctuations in interacting-particle systems: a theoretical study“. Doctoral thesis, Universitat de les Illes Balears, 2012. http://hdl.handle.net/10803/104264.
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La presente tesis doctoral, se centra en el desarrollo de métodos matemáticos para el estudio de
procesos estocásticos de interés en física y otras ciencias naturales. Fundamentalmente se
consideran sistemas de particulas en interacción, prestando especial atención al efecto de la
heterogeneidad entre los componentes del sistema, así como el retraso en las interacciones. También
se estudian propiedades de sincronización en sistemas de elemenentos excitables no identicos. Se
desarrollan diversos métodos analíticos para estudiar este tipo de sistemas y se derivan diversos
resultados mátematicos, algunos exactos y otros aproximados, relevantes para el entendimiento
general de este tipo de sitemas. Los métodos desarrollados son aplicados al estudio de diversos
sistemas concretos, de interés en expresión genética, epidemiología o economía.
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Fearon, Michael. „Theoretical studies of strongly interacting fine particle systems“. Thesis, University of Central Lancashire, 1990. http://clok.uclan.ac.uk/20347/.
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A theoretical analysis of the time dependent behaviour of a system of fine magnetic particles as a function of applied field and temperature was carried out. The model used was based on a theory assuming Neel relaxation with a distribution of particle sizes. This theory predicted a linear variation of 5max with temperature and a finite intercept, which is not reflected by experimental observations. The remanence curves of strongly interacting fine-particle systems were also investigated theoretically. It was shown that the Henkel plot of the dc demagnetisation remanence vs the isothermal remanence is a useful representation of interactions. The form of the plot was found to be a reflection of the magnetic and physical microstructure of the material, which is consistent with experimental data. The relationship between the Henkel plot and the noise of a particulate recording medium, another property dependent on the microstructure, is also considered. The Interaction Field Factor (1FF), a single parameter characterising the non-linearity of the Henkel plot, is investigated. These results are consistent with a previous experimental study. Finally the results of the noise power spectral density for erased and saturated recording media are presented, so that characterisation of interparticle interactions may be carried out with greater accuracy.
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Klauß, Tobias. „An Interacting Particle System for Collective Migration“. Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1228074229228-77328.
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Kollektive Migration und Schwarmverhalten sind Beispiele für Selbstorganisation und können in verschiedenen biologischen Systemen beobachtet werden, beispielsweise in Vogel-und Fischschwärmen oder Bakterienpopulationen. Im Zentrum dieser Arbeit steht ein räumlich diskretes und zeitlich stetiges Model, welches das kollektive Migrieren von Individuen mittels eines stochastischen Vielteilchensystems (VTS) beschreibt und analysierbar macht. Das konstruierte Modell ist in keiner Klasse gut untersuchter Vielteilchensysteme enthalten, sodass der größte Teil der Arbeit der Entwicklung von Methoden zur Untersuchung des Langzeitverhaltens bestimmter VTS gewidmet ist. Eine entscheidende Rolle spielen hier Gibbs-Maße, die zu zeitlich invarianten Maßen in Beziehung gesetzt werden. Durch eine Simulationsstudie und die Analyse des Einflusses der Parameter Migrationsgeschwindigkeit, Sensitivität der Individuen und (räumliche) Dichte der Anfangsverteilung können Eigenschaften kollektiver Migration erklärt und Hypothesen für weitere Analysen aufgestellt werdenCollective migration and swarming behavior are examples of self-organization and can be observed in various biological systems, such as in flocks of birds, schools of fish or populations of bacteria. In the center of this thesis lies a stochastic interacting particle system (IPS), which is a spatially discrete model with a continuous time scale that describes collective migration and which can be treated using analytical methods. The constructed model is not contained in any class of well-understood IPS’s. The largest part of this work is used to develop methods that can be used to study the long-term behavior of certain IPS’s. Thereby Gibbs-Measures play an important role and are related to temporally invariant measures. One can explain the properties of collective migration and propose a hypothesis for further analyses by a simulation study and by analysing the parameters migration velocity, sensitivity of individuals and (spatial) density of the initial distribution
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Emerson, Zachery Ian. „Particle and bubble interactions in flotation systems“. Auburn, Ala., 2007. http://repo.lib.auburn.edu/2007%20Spring%20Dissertations/EMERSON_ZACHERY_45.pdf.
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22
Garrod, Barnaby G. „One-dimensional interacting particle systems as Pfaffian point processes“. Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/81054/.
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A wide class of one-dimensional continuous-time discrete-space interacting particle systems are shown to be Pfaffian point processes at fixed times with kernels characterised by the solutions to associated two-dimensional ODEs. The models comprise instantaneously coalescing or annihilating random walks with fully spatially inhomogeneous jump rates and deterministic initial conditions, including additional pairwise immigration or branching in the pure interaction regimes. We formulate convergence of Pfaffian point processes via their kernels, enabling investigation of diffusive scaling limits, which boils down uniform convergence of lattice approximations to two-dimensional PDEs. Convergence to continuum point processes is developed for a subset of the discrete models. Finally, in the case of annihilating random walks with pairwise immigration we extend the picture to multiple times, establishing the extended Pfaffian property for the temporal process.
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Rau, Sebastian [Verfasser]. „Optimal Control of interacting Quantum Particle Systems / Sebastian Rau“. München : Verlag Dr. Hut, 2013. http://d-nb.info/1042308470/34.
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24
Kerner, Joachim Friedrich. „Interacting many-particle systems on general compact quantum graphs“. Thesis, University of London, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603454.
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In this thesis, we discuss many-particle systems on general compact quantum graphs. The results cover systems of distinguishable particles as well as systems of bosons or fermions. The main focus lies on the introduction of many-particle interactions in order to establish a useful model regarding many-particle quantum chaos 811d onc-dimensional Bose-Einstein condensation (BEC). Using suitable quadratic forms, we will characterise self-adjoint realisations of the two- and many-particle Laplacian which incorporate two different types of interactions, i.e. singular interactions localised at the vertices of the graph and contact interactions which are also present along the edges. In that context, we will establish regularity results in order to characteristic the domains of the self-adjoint realisations explicitly. We will also discuss spectral properties of the constructed operators by establishing discreteness of their spectra and Weyl laws for the corresponding eigenvalue counts. Finally, based on the introduced models of interacting particles, we discuss BoseEinstein condensation on general quantum graphs. We will distinguish between systems of bosons for which BEC occurs and such for which no BEC is present at any finite temperature. As a final result, we prove that no Bose-Einstein condensation occurs (in the sense of phase transitions) in a system of bosons interacting via repulsive hard-core interactions.
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Matveev, Konstantin. „q-deformed Interacting Particle Systems, RSKs and Random Polymers“. Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493453.
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We introduce and study four $q$-randomized Robinson--Schensted--Knuth (RSK) insertion tableau dynamics. Each of them is a discrete time Markov dynamics on two-dimensional interlacing particle arrays (these arrays are in a natural bijection with semistandard Young tableaux). For $0
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Bashiri, Kaveh [Verfasser]. „Gradient Flows, Metastability and Interacting Particle Systems / Kaveh Bashiri“. Bonn : Universitäts- und Landesbibliothek Bonn, 2020. http://d-nb.info/1218301406/34.
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27
Oduwole, Olayinka. „Particle interactions in a magnetophoretic system“. Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:f01cbb33-4dd4-4057-8891-7097e6493bce.
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The continuous flow separation of magnetic particles from a mixture of particles could improve the performance of magnetic bead based assays but the formation of agglomerates limit the separation efficiency. Bead agglomerates are formed as a result of magnetic binding forces while the hydrodynamic fluid environment strongly influences their movement. The ability to predict the interaction between nearby beads will help to determine a threshold separation distance which will be recommended for use when obtaining measurement within a magnetic bead assay for a specified time interval. The introductory part of this thesis explored the development of a two dimensional numerical model in Matlab which predicts the trajectory pattern as well as magnetic induced velocities between a pair of super-paramagnetic beads suspended in water within a uniform field. The movement of a bead pair interacting due to both magnetic and hydrodynamic forces within a magnetophoretic system was recorded using an optical system; the beads' movements were compared with the simulated trajectories and gave a good agreement. The model was used to predict the shortest agglomeration time for a given separation distance which is of practical benefit to users of bead based assays. The concluding part of this thesis expanded the simulation into a three dimensional model to predict the interactions among three super-paramagnetic beads within a magnetophoretic system. In order to determine the height of the magnetic beads, a Huygens-Fresnel model was implemented in Matlab which was compared with off-focused diffracted images of the beads viewed under an optical system. A good comparison was obtained by comparing the simulated three-dimensional trajectories with experimental data.
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Cepeda, Chiluisa Eduardo. „Contribution à l'étude probabiliste et numérique d'équations homogènes issues de la physique statistique : coagulation-fragmentation“. Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00952117.
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Cette thèse est consacrée à l'étude de systèmes subissant des coagulations et fragmentations successives. Dans le cas déterministe, on travaille avec des solutions mesures de l'équation de coagulation - multifragmentation. On étudie aussi la contrepartie stochastique de ces systèmes : les processus de coalescence - multifragmentation qui sont des processus de Markov à sauts. Dans un premier temps, on étudie le phénomène de coagulation seul. D'un côté, l'équation de Smoluchowski est une équation intégro-différentielle déterministe. D'un autre côté, on considère le processus stochastique connu sous le nom de Marcus-Lushnikov qui peut être regardé comme une approximation de la solution de l'équation de Smoluchowski. Nous étudions la vitesse de convergence par rapport à la distance de type Wassertein $d_{lambda}$ entre les mesures lorsque le nombre de particules tend vers l'infini. Notre étude est basée sur l'homogénéité du noyau de coagulation $K$.On complémente les calculs pour obtenir un résultat qui peut être interprété comme une généralisation de la Loi des Grands Nombres. Des conditions générales et suffisantes sur des mesures discrètes et continues $mu_0$ sont données pour qu'une suite de mesures $mu_0^n$ à support compact existe. On a donc trouvé un taux de convergence satisfaisant du processus Marcus-Lushnikov vers la solution de l'équation de Smoluchowski par rapport à la distance de type Wassertein $d_{lambda}$ égale à $1/sqrt{n}$.Dans un deuxième temps on présente les résultats des simulations ayant pour objectif de vérifier numériquement le taux de convergence déduit précédemment pour les noyaux de coagulation qui y sont étudiés. Finalement, on considère un modèle prenant en compte aussi un phénomène de fragmentation où un nombre infini de fragments à chaque dislocation est permis. Dans la première partie on considère le cas déterministe, dans la deuxième partie on étudie un processus stochastique qui peut être interprété comme la version macroscopique de ce modèle. D'abord, on considère l'équation intégro-partielle différentielle de coagulation - multifragmentation qui décrit l'évolution en temps de la concentration $mu_t(x)$ de particules de masse $x>0$. Le noyau de coagulation $K$ est supposé satisfaire une propriété de $lambda$-homogénéité pour $lambdain(0,1]$, le noyau de fragmentation $F$ est supposé borné et la mesure $beta$ sur l'ensemble de ratios est conservative. Lorsque le moment d'ordre $lambda$ de la condition initial $mu_0$ est fini, on est capable de montrer existence et unicité d'une solution mesure de l'équation de coagulation - multifragmentation. Ensuite, on considère la version stochastique de cette équation, le processus de coalescence - fragmentation est un processus de Markov càdlàg avec espace d'états l'ensemble de suites ordonnées et est défini par un générateur infinitésimal donné. On a utilisé une représentation Poissonienne de ce processus et la distance $delta_{lambda}$ entre deux processus. Grâce à cette méthode on est capable de construire une version finie de ce processus et de coupler deux processus démarrant d'états initiaux différents. Lorsque l'état initial possède un moment d'ordre $lambda$ fini, on prouve existence et unicité de ces processus comme la limite de suites de processus finis. Tout comme dans le cas déterministe, le noyau de coagulation $K$ est supposé satisfaire une propriété d'homogénéité. Les hypothèses concernant la mesure $beta$ sont exactement les mêmes. D'un autre côté, le noyau de fragmentation $F$ est supposé borné sur tout compact dans $(0,infty)$. Ce résultat est meilleur que celui du cas déterministe, cette amélioration est due à la propriété intrinsèque de masse totale non-explosive que possède un système avec un moment fini d'ordre $lambda$
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Birmpa, Panagiota. „Quantification of mesoscopic and macroscopic fluctuations in interacting particle systems“. Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/76622/.
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The purpose of this PhD thesis is to study mesoscopic and macroscopic fluctuations in Interacting Particle Systems. The thesis is split into two main parts. In the first part, we consider a system of Ising spins interacting via Kac potential evolving with Glauber dynamics and study the macroscopic motion of an one-dimensional interface under forced displacement as the result of large scale fluctuations. In the second part, we consider a diffusive system modelled by a Simple Symmetric Exclusion Process (SSEP) which is driven out of equilibrium by the action of current reservoirs at the boundary and study the non-equilibrium fluctuations around the hydrodynamic limit for the SSEP with current reservoirs. We give a brief summary of the first part. In recent years, there has been significant effort to derive deterministic models describing two-phase materials and their dynamical properties. In this context, we investigate the law that governs the power needed to force a motion of a one dimensional macroscopic interface between two different phases of a given ferromagnetic sample with a prescribed speed V at low temperature. We show that given the mesoscopic deterministic non-local evolution equation for the magnetisation (a non local version of the Allen-Cahn equation), we consider a stochastic Ising spin system with Glauber dynamics and Kac interaction (the underlying microscopic stochastic process) whose mesoscopic scaling limit (intermediate scale between microscale and macroscale) is the given PDE, and we calculate the corresponding large deviations functional which would provide the action functional. We obtain that by deriving upper and lower bounds of the large deviation cost functional. Concepts from statistical mechanics such as contours, free energy, local equilibrium allow a better understanding of the structure of the cost functional. Then we characterise the limiting behaviour of the action functional under a parabolic rescaling, by proving that for small values of the ratio between the distance and the time, the interface moves with a constant speed, while for larger values the occurrence of nucleations is the preferred way to make the transition. This led to a production of two published papers [12] and [14] with my supervisor D. Tsagkarogiannis and N. Dirr. In the second part we study the non-equilibrium fluctuations of a system modelled by SSEP with current reservoirs around its hydrodynamic limit. In particular, we prove that, in the limit, the appropriately scaled fluctuation field is given by a Generalised Ornstein- Uhlenbeck process. For the characterisation of the limiting fluctuation field we implement the Holley-Stroock theory. This is not straightforward due to the boundary terms coming from the nature of the model. Hence, by following a martingale approach (martingale decomposition) and the derivation of the equation of the variance for this model combined with “good” enough correlation estimates (the so-called v-estimates), we reduce the problem to a form whose Holley-Stroock result in [45] is now applicable. This is work in progress jointly with my supervisor and P. Gonçalves, [13].
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Liang, Shu-Chien. „Studies on hydrodynamic interactions between particles in liquid-solid systems /“. The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487930304685987.
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Taggi, Lorenzo. „Absorptionsphasenubergang für Irrfahrten mit Aktivierung und stochastische Zelluläre Automaten“. Doctoral thesis, Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-208644.
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This thesis studies two Markov processes describing the evolution of a system of many interacting random components. These processes undergo an absorbing-state phase transition, i.e., as one variates the parameter values, the process exhibits a transition from a convergence regime to one of the absorbing-states to an active regime. In Chapter 2 we study Activated Random Walk, which is an interacting particle system where the particles can be of two types and their number is conserved. Firstly, we
provide a new lower bound for the critical density on Z as a function of the jump distribution and of the sleeping rate and we prove that the critical density is not a constant function of the jump distribution. Secondly, we prove that on Zd in the case of biased jump distribution the critical density is strictly less than one, provided that the sleeping rate is small enough. This answers a question that has been asked by Dickman, Rolla, Sidoravicius [9, 28] in the case of biased jump distribution. Our results have been presented in [33].
In Chapter 3 we study a class of probabilistic cellular automata which are related by a natural coupling to a special type of oriented percolation model. Firstly, we consider the process on a finite torus of size n, which is ergodic for any parameter value. By employing dynamic-renormalization techniques, we prove that the average absorption time grows exponentially (resp. logarithmically) with n when the model on Z is in the active (resp. absorbing) regime. This answers a question that has been asked by Toom [37]. Secondly, we study how the neighbourhood of the model affects the critical probability for the process on Z. We provide a lower bound for the critical probability as
a function of the neighbourhood and we show that our estimates are sharp by comparing them with our numerical estimates. Our results have been presented in [34, 35].
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Pérez, Jérôme. „Stabilite des systemes de particules en interactions gravitationnelle“. Paris 7, 1995. http://www.theses.fr/1995PA077067.
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L'etude de la dynamique et de la stabilite des systemes auto-gravitants est abordee sous le jour nouveau de la mecanique symplectique. D'un point de vue analytique une approche de la stabilite par des methodes d'energie permet de simplifier un certain nombre de resultats classiques, de mettre sur pied un schema d'investigation des problemes ouverts dans ce domaine, et de proposer des conjectures sur la stabilite des systemes auto-gravitants non collisionels spheriques. La mise en uvre de simulations numeriques de tels systemes sur une connexion machine permet alors de confirmer ces conjectures en proposant un parametre de stabilite universel des objets auto-gravitants non collisionels spheriques
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Chung, Eunhyea. „Colloidal particle-surface interactions in atmospheric and aquatic systems“. Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/43728.
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Colloidal particles suspended in a liquid or gas phase often interact with a solid-liquid or solid-gas interface. In this study, experimental data through atomic force microscopy and neutron reflectometry and theoretical results of colloidal particle-surface interactions were obtained and compared. Atmospheric and aquatic environments were considered for the interactions of microbial colloidal particles and nano-sized silica particles with planar surfaces. Spores of Bacillus thuringiensis, members of the Bacillus cereus group, were examined as the microbial particles, simulating the pathogens Bacillus cereus and Bacillus anthracis which are potentially dangerous to human health. Model planar surfaces used in this study include gold which is an electrically conductive surface, mica which is a highly charged, nonconductive surface, and silica.
In atmospheric systems, the interaction forces were found to be strongly affected by the relative humidity, and the total adhesion force of a particle onto a surface was modeled as the addition of the capillary, van der Waals, and electrostatic forces. Each component is influenced by the properties of the particle and surface materials, including hydrophobicity and surface roughness, as well as the humidity of the surrounding atmosphere. In aquatic systems, the interaction forces are mainly affected by the solution chemistry, including pH and ionic strength. The main components of the interaction force between a microbial colloidal particle and a planar surface were found to be the van der Waals and electrostatic forces.
The results obtained in this research provide insights into the fundamental mechanisms of colloidal particle interactions with environmental surfaces in both atmospheric and aquatic systems, contributing to the understanding of the phenomena driving such interfacial processes as deposition, aggregation, and sedimentation. Thus, the results can help us describe the behavior of contaminant colloidal particles in environmental systems and subsequently devise better means for their removal from environmental surfaces.
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Restrepo, Lopez Ricardo. „Topics in spatial and dynamical phase transitions of interacting particle systems“. Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42729.
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In this work we provide several improvements in the study of phase transitions
of interacting particle systems:
- We determine a quantitative relation between non-extremality of the limiting Gibbs measure of a tree-based spin system, and the temporal mixing of
the Glauber Dynamics over its finite projections. We define the concept of 'sensitivity' of a reconstruction scheme to establish such a relation. In particular, we focus on the independent sets model, determining a phase
transition for the mixing time of the Glauber dynamics at the same location of
the extremality threshold of the simple invariant Gibbs version of the model.
- We develop the technical analysis of the so-called spatial mixing conditions for interacting particle systems to account for the connectivity structure of the underlying graph. This analysis leads to improvements regarding the location of the uniqueness/non-uniqueness phase transition for the independent sets model over amenable graphs; among them, the elusive hard-square model in lattice statistics, which has received attention since Baxter's solution of the analogous hard-hexagon in 1980.
- We build on the work of Montanari and Gerschenfeld to determine the existence of correlations for the coloring model in sparse random graphs. In particular, we prove that correlations exist above the 'clustering' threshold of such a model; thus providing further evidence for the conjectural algorithmic 'hardness' occurring at such a point.
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Louis, Pierre-Yves, und Jean-Baptiste Rouquier. „Time-to-Coalescence for interacting particle systems : parallel versus sequential updating“. Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2011/4945/.
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Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too.
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Mujal, Torreblanca Pere. „Interacting ultracold few-boson systems“. Doctoral thesis, Universitat de Barcelona, 2019. http://hdl.handle.net/10803/668191.
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In this thesis, we study the physical properties of several ultracold few-boson systems depending on the interactions between their constituents. Nowadays, experimentally, it is possible to have great control with high precision over the geometry and the interactions between the particles, making them an excellent setup to test directly the principles of quantum mechanics. A very interesting point is to study the evolution of their properties with the number of particles. The theoretical study of these systems pretends to microscopically understand the current experimental results and give support to new experimental developments.
The method that will be used is the exact diagonalization of the Hamiltonian of the system. As we will see, in spite of the attempts to improve it, the method is limited by the fact that, in practice, it is only useful to study few-particle systems. The method has several advantages. First of all, one has access to both the ground and the excited states. In second place, the method is variational and converges to the exact solution as long as the Hilbert space in which we diagonalize is enlarged.
Moreover, since we have access to the states of the system, it is possible to calculate any observable quantity of interest.
First, we will study a system of spinless bosons trapped in a two-dimensional harmonic potential. The effect of the trap is to keep the system bound. It will be seen how the presence of a repulsive interaction changes the energy spectrum and other properties of the system. For instance, the density profile, which is usually measurable, and also the two-body distribution function, which is intimately related to the existence of correlations.
Afterwards, the focus will be on the particular case of having only two bosons in the system interacting through a strong repulsive force. Inspired by the one-dimensional case where the fermionization phenomenon takes place in the strongly-interacting limit, we will study whether in two dimensions there is a resembling reminiscent effect. In other words, we will analyze if there are properties of the two strongly-interacting bosons in two dimensions that are like the ones of two noninteracting fermions.
After that, we will tackle the localization phenomenon in a one-dimensional system that is caused by an external speckle potential that introduces disorder in the system. We will show that the localization is a robust phenomenon against repulsive contact interactions.
Finally, we will study the influence of the spin-orbit coupling in a system of bosons with two possible pseudospin components, associated, for instance, to two hyperfine levels, confined in a two-dimensional harmonic trap. We will present an exhaustive analysis of the combined effects of the interaction and the spin-orbit coupling in the spectrum and the properties of the system. In particular we show the existence of a crossover in the ground state of the system susceptible to be experimentally identified.En aquesta tesi, estudiarem les propietats físiques de diversos sistemes de pocs bosons ultrafreds depenent de les interaccions entre els seus constituents. Avui dia, a nivell experimental, es té un gran control amb una gran precisió de la geometria i les interaccions entre les partícules, fet que fa aquest sistemes excel·lents per comprovar de forma directa els principis de la mecànica quàntica. Un punt d'interès és comprovar l'evolució de les seves propietats amb el nombre de partícules. L'estudi teòric d'aquests sistemes pretén entendre a nivell microscòpic els resultats experimentals actuals i donar suport pels nous avenços experimentals. El mètode que farem servir serà la diagonalització exacta del hamiltonià del sistema. Com veurem, malgrat les millores que es poden implementar, ens trobarem amb la limitació de no poder estudiar sistemes de més d'unes quantes partícules. Els avantatges d'aquest mètode són diversos. En primer lloc, podrem obtenir no només l'estat fonamental del sistema sinó que també els primers estats excitats. En segon lloc, el mètode és variacional i sabem que convergeix cap a la solució exacta a mesura que ampliem l'espai de Hilbert en que diagonalitzem. A més a més, en tenir accés als estats del sistema, podem calcular qualsevol quantitat observable que sigui d'interès. Primerament, estudiarem un sistema de bosons sense espín atrapats en un potencial harmònic bidimensional. L'efecte de la trampa és de mantenir el sistema lligat. En haver-hi una interacció repulsiva, veurem com canvia l'espectre d'energia del sistema i també altres propietats. Per exemple, la seva densitat, que habitualment es pot mesurar, i també la funció de distribució de dos cossos, que va íntimament lligada a l'existència de correlacions. Tot seguit, ens centrarem en el cas particular de tenir només dos bosons en el sistema interaccionant a través d'una gran força repulsiva. Inspirats pel cas unidimensional en que té lloc el fenomen de la fermionització en el limit d'interacció molt forta, estudiarem si en el cas bidimensional hi queda cap reminiscència d'aquest efecte. En altres paraules, analitzarem si hi ha propietats dels dos bosons fortament interactuants en dues dimensions que siguin com les de fermions no interactuants en el mateix sistema. A continuació, tractarem el fenomen de la localització en un sistema unidimensional en el qual hi ha un potencial extern de tipus speckle que introdueix desordre en el sistema. Veurem que la localització és un fenomen robust en front de les interaccions repulsives. Per últim, estudiarem la influència de l'espín-òrbita en un sistema de bosons amb dues components de pseudoespín, associades, per exemple, a dos nivells hiperfins, atrapats en un potencial harmònic bidimensional. Presentarem un anàlisi exhaustiu dels efectes conjunts de la interacció i l'espín- òrbita en l'espectre i en les propietats del sistema. En particular, mostrarem l'existència d'un encreuament en l'estat fonamental del sistema susceptible de ser identificat experimentalment.
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Kemgang, Ebenezer. „Dipolar particles under external fields“. Electronic Thesis or Diss., Université de Lorraine, 2022. https://docnum.univ-lorraine.fr/ulprive/DDOC_T_2022_0099_KEMGANG.pdf.
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Ce travail de thèse théorique vise à comprendre l'influence des stimuli externes (champ magnétique, gravité, confinement) ainsi que des effets thermiques sur l'auto-assemblage d'un ensemble de particules dipolaires magnétiques. L'intérêt fondamental des particules dipolaires réside sur le caractère anisotropique et de longue portée des interactions dipôle-dipôle. Différentes échelles de grandeur caractérisent ces systèmes (moléculaire, colloïdale et granulaire). Nos modèles concernent des sphères dures dipolaires, systèmes de référence en physique de la matière condensée. Un premier objectif vise à prédire les comportements de structures des état fondamentaux de l'assemblé de N billes magnétiques en fonction des champs extérieurs appliqués. Le manuscrit débute avec un chapitre bibliographique rassemblant une brève littérature sur les propriétés de systèmes de particules magnétiques et les méthodes numériques développées afin d'atteindre le premier objectif de thèse. Après cela, nous abordons un modèle à deux corps où deux particules magnétiques sont exposées aux champs gravitationnel et magnétique au voisinage d'un substrat. Dans ce modèle, les orientations des moments magnétiques des états fondamentaux sont aussi explorées. Les conditions de dimérisation sont prédites à travers un riche diagramme de phases. Une nouvelle phase dimérique est trouvée où le dimère partiellement en contact avec le substrat forme un angle fini avec la normale de celui-ci. Un régime interdit correspondant aux forts champs gravitationnel et magnétique se généralise au cas à N corps où deux chaînes de polymères restent séparer. Par ailleurs, il est montré que la fragmentation à champ magnétique fort d'une chaîne verticale formée sur le substrat induite par la gravité donne lieu à des plus petites chaînes qui peuvent être séparées ou non. Une mono couche apparaît comme le dernier état de fragmentation de ces structures colonnaires à très forte gravité. Un second axe de recherche est consacré à l'étude de l'influence des fluctuations thermiques sur l'agrégation des particules confinées grâce à la théorie et des simulations. Nous montrons que les fluctuations thermiques sont cruciales pour la formation du ruban. Le rôle du confinement longitudinal y est aussi décisive. L'effet de la longue de chaîne sur la stabilité des rubans formés est discuté. Un nouveau mécanisme d'agrégation (rubanisation) est mis en avant. Ce mécanisme est basé sur des interactions effectives interchain d'ordre quadrupolaire induites par des fluctuations des courbures corréléesThis theoretical thesis work aims to understand the influence of external stimulus (magnetic field, gravity, confinement) as well as thermal effects on the self-assembly of magnetic dipolar particles. The fundamental interest of dipolar particles relies on the anisotropic and long range character of dipole-dipole interactions. Dipolar particles can be found on different length scales (molecular, colloidal or granular). Our models concern dipolar hard spheres, a reference system in condensed matter physics. A first goal is to predict the structure behaviors of the ground states of an assembly of N magnetic beads as the function of applied external fields. The manuscript starts with a bibliographic chapter gathering a brief background of the properties of magnetic particle systems and efficient optimization methods developed to achieve the first goal of the thesis. Afterward, we address a two-body problem where two magnetic particles are exposed to gravity and external magnetic fields near a substrate. There, the orientations of the magnetic moments are explored too. The dimerization conditions are predicted through a richphase diagram. A new dimeric phase is found where the dimer partially in contact with the substrate, forms a finite angle with the normal of the latter. The hindered dimerization regime seen at high gravity and magnetic fields can be generalized to the case where two polymer chains remain separate. Furthermore, it is shown that the fragmentation at high magnetic field of a single standing chain due to the gravity gives rise to many shorter chains that can be separate (or not). A monolayer appears as the final state of fragmentation of these columnar clusters at very large gravity. A second research axis is dedicated to the study of the influence of thermal fluctuations on the aggregation of confined particles by theory and simulations. It is shown that thermal fluctuations are crucial to drive ribbonizaton. The role of longitudinal confinement is decisive there too. The effect of chain length on the stability of the formed ribbons is discussed. Anew aggregation (ribbonization) mechanism is highlighted. This mechanism relies on quadrupolar effective inter-chain interactions stemming from correlated fluctuating curvatures
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Brackstone, Mark Andrew. „Dynamic properties of models of modulated systems in condensed matter“. Thesis, University of Southampton, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.255764.
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Ghezzi, Flavio. „Experimental studies of two-dimensional colloidal systems“. Thesis, Queen's University Belfast, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266705.
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Spiteri, Ludovic. „Self-assembly of dipolar particles“. Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0261/document.
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Cette thèse couvre l'auto-assemblage de particules dipolaires (magnétiques/électriques). Ces systèmes sont abondants en physique de la matière condensée (molécules et nanoparticules magnétiques, particules colloïdales magnétiques, bactérie magnétotactique, etc.). Sur un plan fondamental, ils représentent un défi important en raison de l'anisotropie et de la longue portée de l'interaction de paire. Le principal objectif de ce travail de recherche est de prédire les microstructures de ces systèmes en tenant compte de façon adéquate de l'interaction complexe dipôle-dipôle ainsi que des effets stériques et ceux dus à un éventuel confinement. Comprendre et revisiter les interactions de filaments dipolaires tels que des aiguilles et des chaînes faites de billes dipolaires est une première étape importante de cette thèse. En effet, les chaînes sont les constituants élémentaires de nombreux systèmes dipolaires, notamment sous l'effet d'un champ magnétique extérieur appliqué. Ensuite, l'agrégation colonnaire des chaînes dipolaires est examinée, ce qui conduit aussi naturellement à l'étude des cristaux dipolaires massifs où une nouvelle phase est découverte. Le cas plus générique des chaînes hélicoïdales est discuté en considérant les situations limites que sont les chaînes linéaires droites et en zigzag. L'association des chaînes dipolaires, dans le cas bidimensionnel, forme des rubans, puis une monocouche avec un réseau hexagonal. La réponse non triviale d'un tel réseau à un champ magnétique perpendiculaire imposé est aussi étudiée. Il est démontré qu'un réseau rhombique peut être induit de cette façon. Finalement, la sédimentation de particules paramagnétiques dans une monocouche inclinée en présence d'un champ magnétique est explorée via une étude mêlant expériences, théorie et simulations. L'ordre induit par gravité s'avère être une voie prometteuse pour l'élaboration contrôlée de réseaux bidimensionnelsThis thesis covers the self-assembly of dipolar (magnetic/dielectric) particles. These systems are abundant in condensed matter physics (magnetic molecules and nanoparticles, magnetic colloidal particles, magnetotactic bacteria, etc). They also represent a fundamental challenge owing to the both long range and anisotropic nature of the pair interaction. The main objective of this research work is to predict the microstructures of these systems by properly handling the intricate dipole-dipole interaction combined with steric and possibly confinement effects. Understanding and revisiting the interaction of dipolar filaments such as needles or chains made up of dipolar beads is a first important achievement in this thesis. Indeed, the chains are the fundamental building blocks of many dipolar systems especially under applied external magnetic field. Then, the columnar aggregation of dipolar chains is investigated which naturally leads to the study of the bulk dipolar crystals. A new phase is discovered there. The more generic case of helical chains is discussed by considering limiting situations such as straight linear chains and zigzag chains. The association of dipolar chains in two-dimensions forms ribbons then a monolayer with triangular lattice symmetry. The interesting response of such a layer to an imposed perpendicular magnetic is addressed as well. It is demonstrated that rhombicity can be induced that way. Finally, sedimenting paramagnetic particles in a tilted monolayer in presence of a magnetic field are investigated by experiments, theory and simulations. The gravity-mediated ordering is found to be a promising route to elaborate tailored two-dimensional patterns
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Philipowski, Robert. „Stochastic interacting particle systems and nonlinear partial differential equations from fluid mechanics“. [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=986005622.
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Patil, Deepak C. „Particle Interactions in Industrial Granular Systems: Experiments, Theory, and Simulations“. Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/915.
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Granular media continue to be among the most manipulated materials found in various industries. Particle interactions in granular flow has fundamental importance in analyzing the performance of a wide range of key engineering applications such as hoppers, tumblers, and mixers etc. In spite of such ubiquitous presence, till date, our understanding of the granular flow is very limited. This restricts our ability to design efficient and optimal granular processing equipment. Additionally, the existing design abilities are also constrained by the number of particles to be analyzed, where, a typical industrial application involves millions of particles. This motivated the current research where investigations on the above limitations are pursued from three different angles: experimental, theoretical, and simulation. More specifically, this work aims to study particle-wall interaction and developing a computationally efficient cellular automata simulation framework for industrial granular applications. Towards this end, the current research is divided into two part: (I) energy dissipation during particle-wall interaction (II) cellular automata modeling. In part I, detailed experiments are performed on various sphere-thin plate combinations to measure the coefficient of restitution (COR) which is a measure of energy dissipation and it is one of the most important input parameters in any granular simulation. Alternatively, the energy dissipation measure also used to evaluate the elastic impact performance of superelastic Nitinol 60 material. Explicit finite element simulations are performed to gain detail understanding of the contact process and underlying parameters such as contact forces, stress-strain fields, and energy dissipation modes. A parametric study reveals a critical value of plate thickness above which the effect of plate thickness on the energy dissipation can be eliminated in the equipment design. It is found that the existing analytical expressions has limited applicability in predicting the above experimental and numerical results. Therefore, a new theoretical model for the coefficient of restitution is proposed which combines the effect of plastic deformation and plate thickness (i.e. flexural vibrations). In part II, in order to advance the existing granular flow modeling capabilities for the industry (dry and slurry flows) a cellular automata (CA) modeling framework is developed which can supplement the physically rigorous but computationally demanding discrete element method (DEM). These include a three-dimensional model which takes into account particle friction and spin during collision processing, which provides the ability to handle flows beyond solely the kinetic regime, and a multiphase framework which combines computational fluid dynamics (CFD) with CA to model multi-million particle count applications such as particle-laden flows and slurry flows.
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Rawling, M. Carl. „Particle-water interactions of hydrophobic organic micropollutants in marine systems“. Thesis, University of Plymouth, 1998. http://hdl.handle.net/10026.1/1926.
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An understanding of the reactivity of hydrophobic organic micropollutants (HOMs) is of paramount importance to water quality managers because of their toxicity, persistence, and liability to bioaccumulate. In this study, the role played by the main estuarine variables (organic matter, suspended particulate matter [SPM], particle type and salinity) on HOM behaviour was investigated by employing samples from estuaries with different geochemical signatures (Chupa, Russia, and the Dart, Plym, Beaulieu and Carnon, U K ) . A laboratory-based technique was developed for the determination of the solubility and sorptive behaviour of HOMs using 14C-labelled, beta-emitting organic compounds (2,2\5,5'-tetrachlorobiphenyl (2,2’5,5'-TCB), bis(2-ethylhexyl)phthalate ester (DEHP), and benzo[a]pyrene (BaP)) coupled with liquid scintillation counting. The results indicate that relative solubility is mainly dependent upon the type of dissolved organic carbon (DOC) present, not its concentration, and is reduced with increasing salinity. The uptake of 2,2’5,5'-TCB and BaP by particles is time dependent with a system response time (the time required to achieve 63% of the new equilibrium) of about 0.37 hours for 2,2',5,5’-TCB and 0.02 hours for BaP. The adsorption, expressed as particle-water partition coefficients, KDS, is to a varying extent dependent on DOC, salinity and particle characteristics (iron/manganese hydroxides, particulate carbon and specific surface area). Adsorption is best defined by a linear isotherm and is enhanced in sea water compared with river water owing to a reduction in charge on particle surfaces at high ionic strengths. This effect has been quantified using an adsorption salting constant, Gp, whose values are typically in the range 0.4-2 L mol-2 The inverse relationship between KD and SPM concentration, an effect well documented in the literature, has been defined by a simple power law (KD = a SPM-b where a and b are site and compound-specific constants). Typical values for a and b are approximately 4x10^ and 0.6 for 2,2',5,5'- TCB, 50x105 and 1.0 for DEHP, and 2x105 and 0.5 for BaP, respectively. Empirical parameterisation of these effects are extremely useful for encoding into numerical transport and distribution models, and their application is demonstrated in this thesis by calculating the retention of HOMs by estuaries.
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Spiteri, Ludovic. „Self-assembly of dipolar particles“. Electronic Thesis or Diss., Université de Lorraine, 2018. http://www.theses.fr/2018LORR0261.
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Cette thèse couvre l'auto-assemblage de particules dipolaires (magnétiques/électriques). Ces systèmes sont abondants en physique de la matière condensée (molécules et nanoparticules magnétiques, particules colloïdales magnétiques, bactérie magnétotactique, etc.). Sur un plan fondamental, ils représentent un défi important en raison de l'anisotropie et de la longue portée de l'interaction de paire. Le principal objectif de ce travail de recherche est de prédire les microstructures de ces systèmes en tenant compte de façon adéquate de l'interaction complexe dipôle-dipôle ainsi que des effets stériques et ceux dus à un éventuel confinement. Comprendre et revisiter les interactions de filaments dipolaires tels que des aiguilles et des chaînes faites de billes dipolaires est une première étape importante de cette thèse. En effet, les chaînes sont les constituants élémentaires de nombreux systèmes dipolaires, notamment sous l'effet d'un champ magnétique extérieur appliqué. Ensuite, l'agrégation colonnaire des chaînes dipolaires est examinée, ce qui conduit aussi naturellement à l'étude des cristaux dipolaires massifs où une nouvelle phase est découverte. Le cas plus générique des chaînes hélicoïdales est discuté en considérant les situations limites que sont les chaînes linéaires droites et en zigzag. L'association des chaînes dipolaires, dans le cas bidimensionnel, forme des rubans, puis une monocouche avec un réseau hexagonal. La réponse non triviale d'un tel réseau à un champ magnétique perpendiculaire imposé est aussi étudiée. Il est démontré qu'un réseau rhombique peut être induit de cette façon. Finalement, la sédimentation de particules paramagnétiques dans une monocouche inclinée en présence d'un champ magnétique est explorée via une étude mêlant expériences, théorie et simulations. L'ordre induit par gravité s'avère être une voie prometteuse pour l'élaboration contrôlée de réseaux bidimensionnelsThis thesis covers the self-assembly of dipolar (magnetic/dielectric) particles. These systems are abundant in condensed matter physics (magnetic molecules and nanoparticles, magnetic colloidal particles, magnetotactic bacteria, etc). They also represent a fundamental challenge owing to the both long range and anisotropic nature of the pair interaction. The main objective of this research work is to predict the microstructures of these systems by properly handling the intricate dipole-dipole interaction combined with steric and possibly confinement effects. Understanding and revisiting the interaction of dipolar filaments such as needles or chains made up of dipolar beads is a first important achievement in this thesis. Indeed, the chains are the fundamental building blocks of many dipolar systems especially under applied external magnetic field. Then, the columnar aggregation of dipolar chains is investigated which naturally leads to the study of the bulk dipolar crystals. A new phase is discovered there. The more generic case of helical chains is discussed by considering limiting situations such as straight linear chains and zigzag chains. The association of dipolar chains in two-dimensions forms ribbons then a monolayer with triangular lattice symmetry. The interesting response of such a layer to an imposed perpendicular magnetic is addressed as well. It is demonstrated that rhombicity can be induced that way. Finally, sedimenting paramagnetic particles in a tilted monolayer in presence of a magnetic field are investigated by experiments, theory and simulations. The gravity-mediated ordering is found to be a promising route to elaborate tailored two-dimensional patterns
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Olsson, Martin Wexö. „GPU based particle system“. Thesis, Blekinge Tekniska Högskola, Sektionen för datavetenskap och kommunikation, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-3761.
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GPGPU (General purpose computing on graphics processing unit) is quite common in today's modern computer games when doing heavy simulation calculations like game physics or particle systems. GPU programming is not only used in games but also in scientific research when doing heavy calculations on molecular structures and protein folding etc. The reason why you use the GPU for these kinds of tasks is that you can gain an incredible speedup in performance to your application. Previous research shows that particle systems scale very well to the GPU architecture. When simulating very large particle-system on the GPU it can run up to 79 times faster than the CPU. But for some very small particle systems the CPU proved to be faster. This research aims to compare the difference between the GPU and CPU when it comes to simulating many smaller particle-systems and to see what happen to the performance when the particle-systems become smaller and smaller.
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Ezanno, François. „Systèmes de particules en interaction et modèles de déposition aléatoire“. Phd thesis, Aix-Marseille Université, 2012. http://tel.archives-ouvertes.fr/tel-00796271.
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Les résultats de cette thèse sont composés de trois parties relativement indépendantes. Dans la première partie, nous reprenons le problème de la définition d'une classe de processus markoviens à une infinité de coordonnées (systèmes de particules en interaction). Nous en proposons une construction ne mettant en jeu ni d'analyse fonctionnelle (ou peu), ni de problème de martingale. Ceci est fait en utilisant des outils probabilistes élémentaires, notamment des couplages adéquats. On fait pour cela une certaine hypothèse sur les taux individuels de transition, qui a été déjà exploitée dans la construction de T. M. Liggett (1972) notamment. Notre construction a l'avantage d'expliquer, plus concrètement que dans les autres constructions, le caractère naturel de cette hypothèse. \\Dans une seconde partie, nous considérons un modèle de croissance cristalline introduit par D. J. Gates et M. Westcott en 1987, où des particules du milieu environnant s'agrègent à la surface d'un cristal à maille carrée. Le modèle est caractérisé par des taux de déposition en chaque site qui prennent une certaine forme. Nos résultats portent principalement sur la question de la récurrence et de la récurrence positive de la surface du cristal en fonction de certains paramètres. Nous montrons notamment l'existence d'une zone de paramètres dans laquelle transience et récurrence positive coexistent, et suspectée de présenter un phénomène critique. La troisième partie porte sur la question de la convergence en loi pour le processus de contact (sur Z) sous-critique vu du bord, partant d'une demi-droite de sites occupés. Nous donnons dans un premier temps une démonstration alternative d'un résultat récent de E. D. Andjel, pour la convergence en loi dans la percolation 2D orientée qui est un équivalent discret du contact. Nous établissons un résultat en relation : le processus de contact vu du bord, sur les configurations finies, admet une limite de Yaglom. Enfin nous mettons en évidence les difficultés à surmonter pour adapter le résultat d'Andjel au temps continu.
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Putan, Diana [Verfasser]. „Uniqueness of equilibrium states in some models of interacting particle systems / Diana Putan“. Bielefeld : Universitätsbibliothek Bielefeld, 2014. http://d-nb.info/1057957062/34.
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Borrello, Davide. „Interacting particle systems : stochastic order, attractiveness and random walk on small world grahs“. Rouen, 2009. http://www.theses.fr/2009ROUES032.
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Le sujet principal de la thèse sont les systèmes de particules en interaction, qui sont des classes de processus spatio-temporels. Ces systèmes décrivent l'évolution de particules en interaction les unes avec les autres sur un espace discret fini ou infini. Dans la partie I, nous examinons l'ordre stochastique dans un système de particules avec multiples naissances, morts et sauts sur l'espace d-dimensionnel à coordonnées entières. Nous donnons des applications pour des modèles biologiques de diffusion d'épidémies et de systèmes de dynamiques de métapopulations. Dans la partie II, nous analysons la marche aléatoire coalescente dans une classe de graphes aléatoires finis qui modèlent les réseaux sociaux, les graphes "small word"The main subject of the thesis is concerned with interacting particle systems, which are classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other on a finite or infinite discrete space. In part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice. We give applications on biological models of spread of epidemics and metapopulations dynamics systems. In part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs
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BORRELLO, DAVIDE. „Interacting particle systems: stochastic order, attractiveness and random walks on small world graphs“. Doctoral thesis, Università degli Studi di Milano-Bicocca, 2009. http://hdl.handle.net/10281/7467.
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The main subject of the thesis is concerned with interacting particle systems, which are
classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other.
The particles move on a finite or infinite discrete space and on each element of this space the state of the configuration is integer valued. Configurations of particles evolve in continuous
time according to a Markov process. Here the space is either the infinite deterministic
d-dimensional lattice or a random graph given by the finite d-dimensional torus with random matchings. In Part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice: stochastic order is a key tool to understand the ergodic properties of a system. We give applications on biological models of spread of epidemics and metapopulation dynamics systems. In Part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs. We derive the law of the meeting time of two random walks on small world graphs and we use this result to understand the role
of random connections in meeting time of random walks and to investigate the behavior
of coalescing random walks.
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Dworaczek, Guera Charlie. „Analyse asymptotiques d'intégrales multiples : au-delà des beta-ensembles classiques“. Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0036.
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Cette thèse vise à étendre les techniques mathématiques qui permettent d’extraire le comportement asymptotique de certaines intégrales multiples quand le nombre d’intégrales tend vers l’infini. Un cas très bien compris est celui de la fonction de partition des beta-ensembles classiques. Les techniques probabilistes de grandes déviations et d’analyse des équations de boucles forment l’arsenal classique pour son étude et permettent de comprendre son comportement asymptotique dans une large généralité. Des généralisations non-triviales de cette intégrale multiple sont étudiés dans ce manuscrit: le régime haute température des beta-ensembles et le modèle sinh. Dans ce premier modèle, la température proportionnelle au nombre de particules permet de rendre l’entropie du même ordre que le potentiel confinant et l’interaction à deux corps. Cela a de multiples conséquences: un support non-borné pour la mesure d’équilibre contrairement au régime classique des beta-ensembles et un opérateur master beaucoup plus délicat à gérer. Une étude fine de son comportement permet de démontrer un théorème central limite et le comportement asymptotique à toute du logarithme de sa fonction de partition. Ce premier résultat permet d’étudier certains aspects de systèmes physiques dits intégrables comme la chaîne de Toda et plus particulièrement sa limite hydrodynamique. Ce deuxième résultat permet enfin d’étendre l’application de la méthode des équations de boucle dans le cas où les particules ne se concentrent pas sur un compact. Finalement, un dernier modèle est étudié, le modèle sinh. L’étude de ce modèle est motivée par la méthode de séparation des variables quantique où ce genre d’intégrales apparaît. Il constitue une généralisation des beta-ensembles classiques où l’effet confinant est plus faible que l’interaction et où cette dernière est plus compliqué. La mesure d’équilibre y est étudié et permet d’obtenir une certaine vérification d’une conjecture de Lukyanov sur le modèle sinh-Gordon quantique en 1+1 dimensions et volume finiThis thesis aims to extend mathematical techniques that extract the asymptotic behavior of certain multiple integrals as the number of integrals tends to infinity. A well-understood case is the partition function of classical beta-ensembles. Probabilistic techniques of large deviations and analysis of loop equations form the classical arsenal for its study and allow for a broad understanding of its asymptotic behavior. Non-trivial generalizations of this multiple integral are studied in this manuscript: the high-temperature regime of beta-ensembles and the sinh model. In the first model, the temperature proportional to the number of particles makes the entropy of the same order as the confining potential and the two-body interaction. This has multiple consequences: an unbounded support for the equilibrium measure contrary to the classical regime of beta-ensembles, and a much more delicate master operator to handle. A detailed study of its behavior allows for the demonstration of a central limit theorem and the asymptotic behavior of the logarithm of its partition function. This first result permits the study of certain aspects of so-called integrable physical systems like the Toda chain, and more specifically, its hydrodynamic limit. This second result finally extends the application of the method of loop equations to cases where particles do not concentrate on a compact set. Lastly, another model is studied, the sinh model. The study of this model is motivated by the quantum separation of variables method where such integrals appear. It constitutes a generalization of classical beta-ensembles where the confining effect is weaker than the interaction, and the latter is more complicated. The equilibrium measure is studied, leading to a certain verification of Lukyanov's conjecture on the quantum sinh-Gordon model in 1+1 dimensions and finite volume