Rozprawy doktorskie: „Kinetic Monte Carlo Methods”

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Mandreoli, Lorenzo. "Density based Kinetic Monte Carlo Methods". [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975329111.

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Höök, Lars Josef. "Variance reduction methods for numerical solution of plasma kinetic diffusion". Licentiate thesis, KTH, Fusionsplasmafysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-91332.

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Performing detailed simulations of plasma kinetic diffusion is a challenging task and currently requires the largest computational facilities in the world. The reason for this is that, the physics in a confined heated plasma occur on a broad range of temporal and spatial scales. It is therefore of interest to improve the computational algorithms together with the development of more powerful computational resources. Kinetic diffusion processes in plasmas are commonly simulated with the Monte Carlo method, where a discrete set of particles are sampled from a distribution function and advanced in a Lagrangian frame according to a set of stochastic differential equations. The Monte Carlo method introduces computational error in the form of statistical random noise produced by a finite number of particles (or markers) N and the error scales as αN−β where β = 1/2 for the standard Monte Carlo method. This requires a large number of simulated particles in order to obtain a sufficiently low numerical noise level. Therefore it is essential to use techniques that reduce the numerical noise. Such methods are commonly called variance reduction methods. In this thesis, we have developed new variance reduction methods with application to plasma kinetic diffusion. The methods are suitable for simulation of RF-heating and transport, but are not limited to these types of problems. We have derived a novel variance reduction method that minimizes the number of required particles from an optimization model. This implicitly reduces the variance when calculating the expected value of the distribution, since for a fixed error the optimization model ensures that a minimal number of particles are needed. Techniques that reduce the noise by improving the order of convergence, have also been considered. Two different methods have been tested on a neutral beam injection scenario. The methods are the scrambled Brownian bridge method and a method here called the sorting and mixing method of L´ecot and Khettabi[1999]. Both methods converge faster than the standard Monte Carlo method for modest number of time steps, but fail to converge correctly for large number of time steps, a range required for detailed plasma kinetic simulations. Different techniques are discussed that have the potential of improving the convergence to this range of time steps.
QC 20120314

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Herron, Adam David. "Mesoscale Modeling of Shape Memory Alloys by Kinetic Monte Carlo–Finite Element Analysis Methods". BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/8261.

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A coupled kinetic Monte Carlo – Finite Element Analysis (kMC–FEA) method is developed with a numerical implementation in the Scalable Implementation of Finite Elements at NASA (ScIFEN). This method is presented as a mesoscale model for Shape Memory Alloy (SMA) material systems. The model is based on Transition State Theory and predicts the nonlinear mechanical behavior of the 1st order solid–solid phase transformation between Austenite and Martensite in SMAs. The kMC–FEA modeling method presented in this work builds upon the work of Chen and Schuh [1, 2]. It represents a “bottom-up” approach to materials modeling and could serve as a bridge for future studies that attempt to link ab initio methods with phenomenological findings in SMA systems. This thesis presents the derivation of the kMC–FEA model, which is then used to probe the various responses expected in SMAs and verify the influence of model parameters on simulation behavior. In a departure from the work of Chen and Schuh, the thermodynamic derivation includes an elastic transformation energy term, which is found to be a significant fraction of the total transformation energy and play an important role in the evolution of a simulation. Theoretical predictions of the model behavior can be made from this derivation, including expected transformation stresses and temperatures. A convergence study is presented as verification that the new elastic energy term proposed in this model is a reasonable approximation. A parameter sensitivity study is also presented, showing good agreement between theoretical predictions and the results of a full-factorial numerical exploration of model outputs. Model simulation demonstrates the emergence of the shape memory effect, an important SMA behavior not shown by Chen and Schuh, along with the expected superelastic effect and thermal hysteresis. Further exploration of simulated model outputs presented in this work involves comparison with experimental data and predicted output values obtained from a separate phenomenological constitutive model. This comparison shows that the kMC–FEA method is capable of reproducing qualitative, but not yet quantitative, responses of real SMA material systems. Discussion of each model parameter and its effects on the behavior of the model are presented as guidelines for future studies of SMA materials. A complete implementation of the method is contained in a new finite element software package (ScIFEN) that is available for future

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Schmidt, Daniel. "Kinetic Monte Carlo Methods for Computing First Capture Time Distributions in Models of Diffusive Absorption". Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/97.

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In this paper, we consider the capture dynamics of a particle undergoing a random walk above a sheet of absorbing traps. In particular, we seek to characterize the distribution in time from when the particle is released to when it is absorbed. This problem is motivated by the study of lymphocytes in the human blood stream; for a particle near the surface of a lymphocyte, how long will it take for the particle to be captured? We model this problem as a diffusive process with a mixture of reflecting and absorbing boundary conditions. The model is analyzed from two approaches. The first is a numerical simulation using a Kinetic Monte Carlo (KMC) method that exploits exact solutions to accelerate a particle-based simulation of the capture time. A notable advantage of KMC is that run time is independent of how far from the traps one begins. We compare our results to the second approach, which is asymptotic approximations of the FPT distribution for particles that start far from the traps. Our goal is to validate the efficacy of homogenizing the surface boundary conditions, replacing the reflecting (Neumann) and absorbing (Dirichlet) boundary conditions with a mixed (Robin) boundary condition.

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Gong, Min. "A study of surface growth mechanism by kinetic Monte-Carlo simulation". Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37636194.

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Gong, Min, i 鞏旻. "A study of surface growth mechanism by kinetic Monte-Carlo simulation". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37636194.

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Alexander, Kathleen Carmody. "An off-lattice kinetic Monte Carlo method for the investigation of grain boundary kinetic processes". Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/108218.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Materials Science and Engineering, 2016.
"September 2016." Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 155-171).
Kinetic Monte Carlo (Kc) methods have the potential to extend the accessible timescales of off-lattice atomistic simulations beyond the limits of molecular dynamics by making use of transition state theory and parallelization. However, it is a challenge to identify a complete catalog of events accessible to an off-lattice system in order to accurately calculate the residence time for Kc. Possible approaches to some of the key steps needed to address this problem are developed in this thesis. After validating these methods in the study of vacancy diffusion, we implemented our off-lattice Kc method to study the kinetic behavior of the [Sigma]5 (210) grain boundary (GB) in copper. We found that the activation energy associated with intrinsic diffusion at this GB is between the activation energies of interstitial diffusion and vacancy diffusion. We have also measured GB mobility in this system and found the activation energy of GB migration to be similar to that of bulk diffusion. For comparison, we have performed a molecular dynamics study of this target GB and obtained diffusivity and mobility estimates that are sufficiently similar to our Kc results at high temperatures. At low temperatures, the molecular dynamics simulations did not yield meaningful predictions. The results of this case study indicate that the off-lattice Kc method developed herein may provide a means to study GB kinetic properties under conditions and timescales that were previously inaccessible. Towards the end of developing predictive relationships to describe GB kinetic properties, we have begun to assess whether the normalized ground state residence time of a GB is a good predictor of kinetic behavior by analyzing several low-CSL GBs. We see a clear relationship between normalized ground state residence time and kinetic properties for the GBs considered so far. A more thorough investigation will be required to establish whether or not these preliminary findings indicate a more general relationship.
by Kathleen Carmody Alexander.
Ph. D.

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Hay, Aaron M. "Applying massively parallel kinetic Monte Carlo methods to simulate grain growth and sintering in powdered metals". Thesis, Monterey, California. Naval Postgraduate School, 2011. http://hdl.handle.net/10945/5583.

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Approved for public release; distribution is unlimited.
50 nm) can be used to bond materials at dramatically lower temperatures and pressures while maintaining the mechanical properties of nanostructured materials. Despite these promising results, the grain growth and sintering mechanisms of nanostructures are not fully understood. Simulations performed using KMC algorithms can be used to model nanoparticle grain growth and sintering. Sandia National Laboratories' new, massively-parallel, Stochastic Parallel Particle Kinetic Simulator (SPPARKS) code is capable of simulating large-scale problems of grain growth and sintering from the nanoscale to the microscale. This thesis focused on setting up SPPARKS on the Naval Postgraduate School's high performance computing resources. The performance of SPPARKS was assessed for large-scale simulations of grain growth and sintering. Using SPPARKS, the ability to perform coupled grain growth and sintering was demonstrated while controlling variables such as temperature, porosity, and grain size. The results demonstrate the importance of the spatial distribution of porosity on the nanostructure evolution during grain growth and sintering.

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Shi, Feng. "Nucleation and growth in materials and on surfaces : kinetic Monte Carlo simulations and rate equation theory /". Connect to full text in OhioLINK ETD Center, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1216839589.

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Morris, Aaron Benjamin. "Investigation of a discrete velocity Monte Carlo Boltzmann equation". Thesis, [Austin, Tex. : University of Texas, 2009. http://hdl.handle.net/2152/ETD-UT-2009-05-127.

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Nandipati, Giridhar. "Kinetic Monte Carlo simulations of submonolayer and multilayer epitaxial growth over extended time- and length-scales /". Connect to full text in OhioLINK ETD Center, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=toledo1248923011.

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Abraham, Jan Willem [Verfasser]. "Formation of Metal-Polymer Nanocomposites by Plasma-Based Deposition Methods: Kinetic Monte Carlo and Molecular Dynamics Simulations / Jan Willem Abraham". Kiel : Universitätsbibliothek Kiel, 2018. http://d-nb.info/1163603708/34.

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Ramsey, James J. "Exploration of the Use of the Kinetic Monte Carlo Method in Simulation of Quantum Dot Growth". University of Akron / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=akron1302092138.

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Sun, Grace Siswanto. "Simulations of platinum growth on Pt(111) using density functional theory and kinetic monte carlo simulations /". Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/9672.

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Jolley, Kenny. "Multiscale methods for nanoengineering". Thesis, University of Leicester, 2009. http://hdl.handle.net/2381/7809.

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This thesis is presented in two sections. Two different multiscale models are developed in order to increase the computational speed of two well known atomistic algorithms, Molecular Dynamics (MD) and Kinetic Monte Carlo (KMC). In Section I, the MD method is introduced. Following this, a multiscale method of linking an MD simulation of heat conduction to a finite element (FE) simulation is presented. The method is simple to implement into a conventional MD code and is independent of the atomistic model employed. This bridge between the FE and MD simulations works by ensuring that energy is conserved across the FE/MD boundary. The multiscale simulation allows for the investigation of large systems which are beyond the range of MD. The method is tested extensively in the steady state and transient regimes, and is shown to agree with well with large scale MD and FE simulations. Furthermore, the method removes the artificial boundary effects due to the thermostats and hence allows exact temperatures and temperature gradients to be imposed on to an MD simulation. This allows for better study of temperature gradients on crystal defects etc. In Section II, the KMC method is introduced. A continuum model for the KMC method is presented and compared to the standard KMC model of surface diffusion. This method replaces the many discrete back and forth atom jumps performed by a standard KMC algorithm with a single flux that can evolve in time. Elastic strain is then incorporated into both algorithms and used to simulate atom deposition upon a substrate by Molecular Beam Epitaxy. Quantum dot formation due to a mismatch in the lattice spacing between a substrate and a deposited film is readily observed in both models. Furthermore, by depositing alternating layers of substrate and deposit, self-organised quantum dot super-lattices are observed in both models.

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Mossberg, Eva. "Some numerical and analytical methods for equations of wave propagation and kinetic theory". Doctoral thesis, Karlstad : Fakulty of Technology and Science, Mathematics, Karlstads universitet, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-1848.

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Costa, Davide. "Modelling the thermal ageing evolution of Fe-Cr alloys using a lattice kinetic Monte Carlo approach based on DFT calculations". Thesis, Lille 1, 2012. http://www.theses.fr/2012LIL10037/document.

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Cette thèse aborde l'étude du vieillissement thermique du système Fe-Cr. Nous avons étudié le mécanisme de diffusion de la lacune dans le cadre de la théorie de la fonctionnelle de la densité (Density Functional Theory - DFT) et examiné la capacité d'un potentiel empirique de la classe EAM (Embedded Atom Method) à reproduire les résultats DFT. Nous avons montré que l'énergie de migration de la lacune dépend fortement de l'environnement atomique du point de col où les interactions chrome-chrome et chrome-lacune déterminent en partie l’énergie de point de col. Nous avons proposé trois approches pour la paramétrisation d'un modèle Monte Carlo Cinétique (MCC) atomique : l’une entièrement basée sur le potentiel EAM, les autres partiellement basées sur nos calculs DFT. Les simulations par MCC du vieillissement thermique des alliages Fe-20% at. Cr et Fe-25% at. Cr à 773 K montrent la formation de précipités riches en chrome dont la croissance avec le temps suit une loi de puissance avec un exposant 1/3, en accord avec la théorie de Lifshitz-Slyozov-Wagner. La paramétrisation des simulations par MCC entièrement basée sur le potentiel EAM prédit une taille moyenne des précipités supérieure à celle observée expérimentalement, alors que cette dernière est sous-estimée par les paramétrisations partiellement basées sur nos calculs DFT. Ce désaccord semble avoir une origine cinétique plutôt que thermodynamique. La composition de la phase riche en chrome varie au cours de la séparation de phase, indiquant ainsi que la démixtion se produit par nucléation non-classique ou par décomposition spinodale. Des précipités interconnectés sont plus susceptibles de se former dans le système Fe-25% at. Cr plutôt que dans l’alliage Fe-20% at. Cr suggérant ainsi que, lorsque la concentration en soluté augmente, le mécanisme de démixtion se rapproche de la décomposition spinodale
In this thesis, we address the study of the microstrucutre evolution of the Fe-Cr system under thermal ageing. The vacancy diffusion mechanism was investigated in the framework of the density functional theory (DFT) and the capability of a recently developed embedded atom method (EAM) empirical cohesive model to reproduce the DFT results was examined. We have shown that the vacancy migration energy strongly depends on the saddle point atomic environment where the chromium-chromium and the chromium-vacancy interactions partially determine the saddle point energy. We proposed three approaches for the parameterisation of an atomistic kinetic Monte Carlo (AKMC) model: one fully based on the EAM potential, the others partially based on our DFT calculations. The AKMC simulations of the thermal ageing of the Fe-20 at.%Cr and Fe-25 at.%Cr alloys at 773 K show the formation of chromium-rich precipitates whose growth with time follows a power law with exponent 1/3. This is consistent with the Lifshitz-Slyozov-Wagner theory of coarsening. The AKMC parameterisation fully based on the EAM potential predicts a mean precipitate size higher than the experimentally observed one, whereas the parameterisations partially based on our DFT calculations underestimate it. This disagreement seems to have a kinetic rather than thermodynamic origin. The composition of the precipitating phase varies during the phase separation thus indicating that the unmixing is driven by either a non-classical nucleation or a spinodal decomposition. Interconnected precipitates are more likely to form in the Fe-25 at.%Cr alloy than in the Fe-20 at.%Cr thus suggesting that, as the solute concentration increases, the spinodal decomposition is more likely to occur

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Mertz, Helene. "Modélisation des réactions chimiques dans un code de simulation par la méthode Monte Carlo". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLV012/document.

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Les méthodes Direct Simulation Monte Carlo (DSMC) sont utilisées par Ariane group pour calculer les torseurs d'efforts aérodynamiques et les flux thermiques sur les engins spatiaux pour des écoulements hypersoniques en milieu raréfié.Afin de pouvoir caractériser la dislocation des étages de lanceurs et donc l'empreinte de retombée de débris, une modélisation précise des mécanismes générateurs de flux thermiques est nécessaire. Les réactions chimiques étant dimensionnantes pour le calcul du flux thermique, l'objectif de cette thèse est de développer l'outil de calcul avec la méthode DSMC nommé IEMC de manière à pouvoir prendre en compte les écoulements réactifs.Deux modèles de chimie sont mis en place pour pouvoir prendre en compte la totalité des réactions. Après leur vérifications sur des cas élémentaires, ils sont appliqués et validés sur des cas tests de rentrée pour différentes atmosphères. Les différents modèles considérés sont testés afin d'évaluer leur influence. Les modèles de chimie dépendent de nouveaux paramètres d'entrée, dont les valeurs numériques sont incertaines. Une étude de quantification de leur incertitude est menée et a permis de vérifier que les grandeurs de sorties de la simulation avec un écoulement réactif, notamment le flux thermique, n'est que peu impacté par ces paramètres incertains
Direct Simulation Monte Carlo (DSMC) methods are used in Ariane group to compute aerodynamic forces and moments and heat fluxes on space objects for hypersonic flows in rarefied regimes.To caracterise the dislocation of the stages and the debris footprints, a precise modelisation of the mechanism that contribute to the heat flux is necessary. The contribution of the chemical reactions is important for the determination of the heat flux. The purpose of this thesis is to develop the in house IEMC tool using the DSMC method so that it can compute reactive flows.The different steps of the developments are presented in this work. The first step is the presentation, implementation and verification of two different chemistry models. They are validated for simulations on real test cases. Different models are tested in order to evaluate their effect. Chemical models implemented in the code depend on new input parameters, whose numerical data are uncertain. Using a uncertainty quantification study, it is shown that the output data of the reactive simulation, especially the heat flux, is weakly impacted by the tested uncertain parameters

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Beh, Ongueng Yves Alain. "Simulation atomistique Monte Carlo Cinétique des processus de croissance de couches passives sur alliage métalliques : cas des alliages Fer-Chrome". Paris 6, 2008. http://www.theses.fr/2008PA066277.

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La croissance de couches minces d’oxydes sur les alliages métalliques et les métaux purs est un phénomène ayant fait l’objet d’un grand nombre d’études expérimentales. Les structures des couches d’oxydes sont bien connues, ainsi que les modèles mathématiques servant à modéliser les aspects macroscopiques de la croissance. Cependant, les détails des mécanismes de germination de la couche d’oxyde dans les premiers stades de la corrosion ainsi que sa croissance ultérieure demeurent peu ou mal connus. La simulation atomistique apparaît comme une alternative pour évaluer les différents mécanismes proposés et appréhender l’influence des différents paramètres physico-chimiques. Le développement d’un tel outil de simulation a démarré au LPCS avec la thèse de M. Legrand. En se basant sur l’exemple de l’alliage FeCr, un modèle informatique tridimensionnel dit «modèle de Legrand», permettant de simuler la dissolution sélective et la passivation des alliages binaires a été réalisé. L’évolution dynamique est basée sur une technique de type Monte Carlo classique. Le logiciel permet de simuler l’évolution d’un alliage quelconque, d’une composition et d’une structure cristallographique donnée. Il prend en compte la diffusion des atomes sur la surface, leur dissolution et le blocage de la dissolution par formation d’une couche de passivation. Cet outil était adapté pour la simulation des premiers stades de la corrosion. L’objectif de ce travail est d’améliorer ce modèle existant, afin de simuler l’évolution de la couche passive sur une échelle de temps plus longue. A l’issue de ce travail, de nombreux apports ont été effectués. Ainsi, l’introduction d’un champ de force MEAM (Modified Embedded Atom Method) pour le calcul des barrières de diffusion et de dissolution, a permis de remplacer les probabilités de diffusion empiriques par des probabilités calculées, et de mettre en évidence la diffusion préférentielle des Cr vers leurs semblables. L’introduction d’une dynamique de simulation Monte Carlo Cinétique (KMC) a permis une prise en compte réaliste de l'évolution cinétique du modèle avec des temps de simulation reliés au temps réel. Enfin Un second réseau cristallographique RVO (réseau virtuel d’oxyde) tridimensionnel, correspondant à celui de la couche passive (Cr2O3) a été implémenté, ainsi qu’une interface graphique pour un meilleur suivi de la simulation. Les résultats obtenus lors des simulations sont en accord avec les observations expérimentales: passivation totale à partir du Fe-16Cr, enrichissement en Cr de la couche passive, allures des courbes cinétiques, influence du champ électrique, mise en évidence l’apparition de cavités sous la couche passive
In last few years, many experimental studies of the growing of thin oxide film on pure metal or alloys have been performed. The structure of these oxides is well known and several macroscopic models have been proposed for the oxide growth. However, the details of the mechanism of the nucleation of the thin film in the early stages and it further growth are little known. Atomistic simulation could be an useful technique to evaluate the proposed growth mechanisms, and to investigate the influence of some physical or chemical parameters. The development of atomistic modelling has been started at the LPCS with M. Legrand thesis. Based on the case of FeCr alloy, a 3D model (“Legrand model”) has been developed for the simulation of the selective dissolution and passivation of binary alloy. Using a classical Monte Carlo algorithm, the code simulates the evolution of any alloy with a well known composition and crystallographic atomic structure. It takes into account surface diffusions, dissolution and the blocking of the dissolution by the formation of a passive monolayer. This code was well adapted to the simulation of the early stages of the corrosion. The goal of this work is to improve the Legrand model, in order to simulate the evolution of the passive layer on longer time. Many improvements have been done. A semi-empirical potential MEAM (Modified Embedded Atom Method) has been introduced to compute energy barriers of diffusion and dissolution. The MEAM potential allow us to replace all empirical diffusion probabilities by calculated values, and also to show the preferential diffusion of chromium toward other chromium atoms. The introduction of the KMC (Kinetic Monte Carlo) has allowed simulations with time scale comparable to the experimental values. A second 3D crystallographic lattice (virtual lattice of oxide :VNO ), corresponding to the passive layer (Cr2O3) have been introduced. A graphical interface allows the monitoring of the structural evolution of the model during the simulation. The results obtained with the new model are in agreement with experimental findings: complete passivation above 16% of Cr content, Cr enrichment in the passive layer, aspect of kinetic curves, influence of electric field, formation of cluster of vacancies under the passive layer

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Garnier, Thomas. "Transfert d'échelle dans la modélisation thermodynamique et cinétique des alliages". Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00784326.

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La prédiction des microstructures représente un enjeu majeur pour l'étude des processus de vieillissement des alliages métalliques, en particulier sous irradiation. Les résultats des calculs ab initio de structure électronique peuvent être utilisés pour paramétrer les méthodes cinétiques de Monte Carlo Atomique et permettent ainsi de simuler quantitativement la diffusion des atomes et l'évolution de la microstructure qui en résulte. Cette méthode est cependant limitée par le temps de calcul qu'elle exige. Les simulations mésoscopiques évitent cet écueil, mais souffrent généralement de ne pouvoir être paramétrées sur les résultats obtenus aux échelles inférieures, limitant ainsi leur pouvoir de prédiction. Dans ce travail, une méthode de simulation appelée Monte Carlo cellulaire cinétique a été développée pour relier les échelles atomiques et mésoscopiques tout en conservant la nature discrète des atomes. Une procédure de paramétrisation basée sur les simulations Monte Carlo à l'échelle atomique a été établie. Elle permet de reproduire quantitativement les propriétés macroscopiques d'équilibre des alliages indépendamment de la taille des cellules utilisées. Une application à l'alliage fer-cuivre est présentée. Afin de décrire les propriétés cinétiques à ces échelles, un outil générique de calcul de la matrice d'Onsager dans les alliages a été mis en place. Il est fondé sur la theorie du Champ Moyen Auto-Cohérent. Les résultats obtenus sur des cinétiques de diffusion et de précipitation dans un alliage modèle sont présentés et validés par une comparaison systématique avec des simulations Monte Carlo à l'échelle atomique.

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Bos, Cornelis [Verfasser]. "Atomistic simulation of interface controlled solid-state phase transformations : development and application of a multi-lattice kinetic Monte Carlo method / Institut für Metallkunde der Universität Stuttgartt ... Vorgelegt von Cornelis Bos". Stuttgart : Max-Planck-Inst. für Metallforschung, 2006. http://d-nb.info/979722705/34.

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Martalo', G. "DIFFERENT SCALE MODELING FOR CROWD DYNAMICS AND MULTI-TEMPERATURE GAS MIXTURES". Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/243643.

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In the first part of this work we want to propose a model able to reproduce correctly the dynamics of a crowd in bounded domains (for example rooms and corridors) and in presence of obstacles, and also to discuss the emergence of some behaviors induced by panic. Starting from the analysis of a microscopic description for a small crowd one can deduce some mesoscopic and macroscopic models when the number of agents increases and the crowd is more comparable to gases and fluids. In the second part we want to propose some multi-temperature models for gas mixtures by means of standard tools of kinetic theory. Some descriptions are proposed also in presence of chemical reactions and of an internal structure for molecules to take non-translational degrees of freedom into account. The resulting models are tested on the classical problem of the steady shock wave and the occurence of smooth solutions and sub-shocks is discussed for varying parameters.

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Pedersen, Daniel. "Development of a Kinetic Monte Carlo Code". Thesis, Uppsala universitet, Materialteori, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202711.

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A framework for constructing kinetic monte carlo (KMC) simulations of diffusive events on a lattice was developed. This code was then tested by running simulations of Fe adatom diffusion on graphene and graphene-boron nitride surfaces. The results from these simulations was then used to show that the modeled diffusion adheres to the laws of brownian motion and generates results similar to recent research findings.

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Marshall, Timothy Craig. "KINETIC MONTE CARLO SIMULATION OF BINARY ALLOYS". VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5657.

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There are many tools to simulate physical phenomena. Generally, the simulation technique is defined by the size of the simulation area. Two well know techniques for simulating atom dynamics are kinetic Monte Carlo (kMC) and molecular dynamics (MD). In this work we simulate physical vapor deposition of binary metallic systems using the kMC technique. A sufficient quantity of atoms are deposited so that morphological features can be observed. Where kMC has fallen short we have used MD to supplement our results.

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Dickinson, Andrew Samuel. "On the analysis of Monte Carlo and quasi-Monte Carlo methods". Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409715.

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Göncü, Ahmet. "Monte Carlo and quasi-Monte Carlo methods in pricing financial derivatives". Tallahassee, Florida : Florida State University, 2009. http://etd.lib.fsu.edu/theses/available/etd-06232009-140439/.

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Thesis (Ph. D.)--Florida State University, 2009.
Advisor: Giray Ökten, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (viewed on Oct. 5, 2009). Document formatted into pages; contains x, 105 pages. Includes bibliographical references.

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Taft, Keith. "Monte Carlo methods for radiosity". Thesis, University of Liverpool, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272796.

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Strathmann, Heiko. "Kernel methods for Monte Carlo". Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10040707/.

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This thesis investigates the use of reproducing kernel Hilbert spaces (RKHS) in the context of Monte Carlo algorithms. The work proceeds in three main themes. Adaptive Monte Carlo proposals: We introduce and study two adaptive Markov chain Monte Carlo (MCMC) algorithms to sample from target distributions with non-linear support and intractable gradients. Our algorithms, generalisations of random walk Metropolis and Hamiltonian Monte Carlo, adaptively learn local covariance and gradient structure respectively, by modelling past samples in an RKHS. We further show how to embed these methods into the sequential Monte Carlo framework. Efficient and principled score estimation: We propose methods for fitting an RKHS exponential family model that work by fitting the gradient of the log density, the score, thus avoiding the need to compute a normalization constant. While the problem is of general interest, here we focus on its embedding into the adaptive MCMC context from above. We improve the computational efficiency of an earlier solution with two novel fast approximation schemes without guarantees, and a low-rank, Nyström-like solution. The latter retains the consistency and convergence rates of the exact solution, at lower computational cost. Goodness-of-fit testing: We propose a non-parametric statistical test for goodness-of-fit. The measure is a divergence constructed via Stein's method using functions from an RKHS. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, and apply the test to quantifying convergence of approximate MCMC methods, statistical model criticism, and evaluating accuracy in non-parametric score estimation.

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29

Eden-Jones, Kym Denys. "Kinetic Monte Carlo simulations of autocatalytic protein aggregation". Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/9365.

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The self-assembly of proteins into filamentous structures underpins many aspects of biology, from dynamic cell scaffolding proteins such as actin, to the amyloid plaques responsible for a number of degenerative diseases. Typically, these self-assembly processes have been treated as nucleated, reversible polymerisation reactions, where dynamic fluctuations in a population of monomers eventually overcome an energy barrier, forming a stable aggregate that can then grow and shrink by the addition and loss of more protein from its ends. The nucleated, reversible polymerisation framework is very successful in describing a variety of protein systems such as the cell scaffolds actin and tubulin, and the aggregation of haemoglobin. Historically, amyloid fibrils were also thought to be described by this model, but measurements of their aggregation kinetics failed to match the model's predictions. Instead, recent work indicates that autocatalytic polymerisation - a process by which the number of growth competent species is increased through secondary nucleation, in proportion to the amount already present - is better at describing their formation. In this thesis, I will extend the predictions made in this mean-field, autocatalytic polymerisation model through use of kinetic Monte Carlo simulations. The ubiquitous sigmoid-like growth curve of amyloid fibril formation often possesses a notable quiescent lag phase which has been variously attributed to primary and secondary nucleation processes. Substantial variability in the length of this lag phase is often seen in replicate experimental growth curves, and naively may be attributed to fluctuations in one or both of these nucleation processes. By comparing analytic waiting-time distributions, to those produced by kinetic Monte Carlo simulation of the processes thought to be involved, I will demonstrate that this cannot be the case in sample volumes comparable with typical laboratory experiments. Experimentally, the length of the lag phase, or "lag time", is often found to scale with the total protein concentration, according to a power law with exponent γ. The models of nucleated polymerisation and autocatalytic polymerisation predict different values for this scaling exponent, and these are sometimes used to identify which of the models best describes a given protein system. I show that this approach is likely to result in a misidentification of the dominant mechanisms under conditions where the lag phase is dominated by a different process to the rest of the growth curve. Furthermore, I demonstrate that a change of the dominant mechanism associated with total protein concentration will produce "kinks" in the scaling of lag time with total protein concentration, and that these may be used to greater effect in identifying the dominant mechanisms from experimental kinetic data. Experimental data for bovine insulin aggregation, which is well described by the autocatalytic polymerisation model for low total protein concentrations, displays an intriguing departure from the predicted behaviour at higher protein concentrations. Additionally, the protein concentration at which the transition occurs, appears to be affected by the presence of salt. Coincident with this, an apparent change in the fibril structure indicates that different aggregation mechanisms may operate at different total protein concentrations. I demonstrate that a transition whereby the self-assembly mechanisms change once a critical concentration of fibrils or fibrillar protein is reached, can explain the observed behaviour and that this predicts a substantially higher abundance of shorter laments - which are thought to be pathogenic - at lower total protein concentrations than if self-assembly were consistently autocatalytic at all protein concentration. Amyloid-like loops have been observed in electron and atomic-force microscographs, together with non-looped fibrils, for a number of different proteins including ovalbumin. This implies that fibrils formed of these proteins are able to grow by fibrillar end-joining, and not only monomer addition as is more commonly assumed. I develop a simple analytic expression for polymerisation by monomer addition and fibrillar end-joining, (without autocatalysis) and show that this is not sufficient to explain the growth curves obtained experimentally for ovalbumin. I then demonstrate that the same data can be explained by combining fibrillar end-joining and fragmentation. Through the use of an analytic expression, I estimate the kinetic rates from the experimental growth curves and, via simulation, investigate the distribution of lament and loop lengths. Together, my findings demonstrate the relative importance of different molecular mechanisms in amyloid fibril formation, how these might be affected by various environmental parameters, and characteristic behaviour by which their involvement might be detected experimentally.

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Dauchet, Jérémi. "Analyse radiative des photobioréacteurs". Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2012. http://tel.archives-ouvertes.fr/tel-00914315.

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L'ingénierie de la photosynthèse est une voie prometteuse en vue de produire à la fois des vecteurs énergétiques et des molécules plateformes pour palier la raréfaction des ressources fossiles. Le défi à relever est de taille car il faut réussir à mettre au point des procédés solaires de production de biomasse à constante de temps courte (quelques jours), là où une centaine de millions d'années a été nécessaire à la formation du pétrole. Cet objectif pourrait être atteint en cultivant des micro-organismes photosynthétiques dans des photobioréacteurs dont les performances cinétiques en surface et en volume seraient optimales. Une telle optimisation nécessite avant tout une analyse fine des transferts radiatifs au sein du procédé. L'analyse radiative des photobioréacteurs qui est ici proposée s'ouvre sur la détermination des propriétés d'absorption et de diffusion des suspensions de micro-organismes photosynthétiques, à partir de leurs caractéristiques morphologiques, métaboliques et structurales. Une chaîne de modélisation est construite, mise en oeuvre et validée expérimentalement pour des micro-organismes de formes simples ; à terme, la démarche développée pourra directement être étendue à des formes plus complexes. Puis, l'analyse du transfert radiatif en diffusion multiple est introduite et illustrée par différentes approximations qui apparaissent pertinentes pour une conceptualisation des photobioréacteurs, menant ainsi à la construction d'un intuitif nécessaire à leur optimisation. Enfin, la méthode de Monte Carlo est mise en oeuvre afin de résoudre rigoureusement la diffusion multiple en géométries complexes (géométries qui découlent d'une conception optimisée du procédé) et afin de calculer les performances cinétiques à l'échelle du photobioréacteur. Ce dernier calcul utilise une avancée méthodologique qui permet de traiter facilement le couplage non-linéaire du transfert radiatif à la cinétique locale de la photosynthèse (et qui laisse entrevoir de nombreuses autres applications dans d'autres domaines de la physique du transport). Ces outils de simulation mettent à profit les développements les plus récents autour de la méthode de Monte Carlo, tant sur le plan informatique (grâce à une implémentation dans l'environnement de développement EDStar) que sur le plan algorithmique : formulation intégrale, algorithmes à zéro-variance, calcul de sensibilités (le calcul des sensibilités aux paramètres géométriques est ici abordé d'une manière originale qui permet de simplifier significativement sa mise en oeuvre, pour un ensemble de configurations académiques testées). Les perspectives de ce travail seront d'utiliser les outils d'analyse développés durant cette thèse afin d'alimenter une réflexion sur l'intensification des photobioréacteurs, et d'étendre la démarche proposée à l'étude des systèmes photoréactifs dans leur ensemble.

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Zhang, Kai. "Monte Carlo methods in derivative modelling". Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/35689/.

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This thesis addresses issues in discretization and variance reduction methods for Monte Carlo simulation. For the discretization methods, we investigate the convergence properties of various Itˆo-Taylor schemes and the strong Taylor expansion (Siopacha and Teichmann [77]) for the LIBOR market model. We also provide an improvement on the strong Taylor expansion method which produces lower pricing bias. For the variance reduction methods, we have four contributions. Firstly, we formulate a general stochastic volatility model nesting many existing models in the literature. Secondly, we construct a correlation control variate for this model. Thirdly, we apply the model as well as the new control variate to pricing average rate and barrier options. Numerical results demonstrate the improvement over using old control variates alone. Last but not least, with the help of our model and control variate, we explore the variations in barrier option pricing consistent with the implied volatility surface.

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32

Maggio, Emilio. "Monte Carlo methods for visual tracking". Thesis, Queen Mary, University of London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497791.

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Crosby, Richard S. "Monte Carlo methods for lattice fields". Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/77699.

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Wang, Junxiong. "Option Pricing Using Monte Carlo Methods". Digital WPI, 2011. https://digitalcommons.wpi.edu/etd-theses/331.

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This project is devoted primarily to the use of Monte Carlo methods to simulate stock prices in order to price European call options using control variates, and to the use of the binominal model to price American put options. At the end, we can use the information to form a portfolio position using an Interactive Brokers paper trading account. This project was done as a part of the masters capstone course Math 573: Computational Methods of Financial Mathematics.

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35

Lu, Mengliu. "Option Pricing Using Monte Carlo Methods". Digital WPI, 2011. https://digitalcommons.wpi.edu/etd-theses/380.

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This paper aims to use Monte Carlo methods to price American call options on equities using the variance reduction technique of control variates and to price American put options using the binomial model. We use this information to form option positions. This project was done a part of the masters capstone course Math 573: Computational Methods of Financial Mathematics.

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36

Fang, Youhan. "Efficient Markov Chain Monte Carlo Methods". Thesis, Purdue University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10809188.

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Generating random samples from a prescribed distribution is one of the most important and challenging problems in machine learning, Bayesian statistics, and the simulation of materials. Markov Chain Monte Carlo (MCMC) methods are usually the required tool for this task, if the desired distribution is known only up to a multiplicative constant. Samples produced by an MCMC method are real values in N-dimensional space, called the configuration space. The distribution of such samples converges to the target distribution in the limit. However, existing MCMC methods still face many challenges that are not well resolved. Difficulties for sampling by using MCMC methods include, but not exclusively, dealing with high dimensional and multimodal problems, high computation cost due to extremely large datasets in Bayesian machine learning models, and lack of reliable indicators for detecting convergence and measuring the accuracy of sampling. This dissertation focuses on new theory and methodology for efficient MCMC methods that aim to overcome the aforementioned difficulties.

One contribution of this dissertation is generalizations of hybrid Monte Carlo (HMC). An HMC method combines a discretized dynamical system in an extended space, called the state space, and an acceptance test based on the Metropolis criterion. The discretized dynamical system used in HMC is volume preserving—meaning that in the state space, the absolute Jacobian of a map from one point on the trajectory to another is 1. Volume preservation is, however, not necessary for the general purpose of sampling. A general theory allowing the use of non-volume preserving dynamics for proposing MCMC moves is proposed. Examples including isokinetic dynamics and variable mass Hamiltonian dynamics with an explicit integrator, are all designed with fewer restrictions based on the general theory. Experiments show improvement in efficiency for sampling high dimensional multimodal problems. A second contribution is stochastic gradient samplers with reduced bias. An in-depth analysis of the noise introduced by the stochastic gradient is provided. Two methods to reduce the bias in the distribution of samples are proposed. One is to correct the dynamics by using an estimated noise based on subsampled data, and the other is to introduce additional variables and corresponding dynamics to adaptively reduce the bias. Extensive experiments show that both methods outperform existing methods. A third contribution is quasi-reliable estimates of effective sample size. Proposed is a more reliable indicator—the longest integrated autocorrelation time over all functions in the state space—for detecting the convergence and measuring the accuracy of MCMC methods. The superiority of the new indicator is supported by experiments on both synthetic and real problems.

Minor contributions include a general framework of changing variables, and a numerical integrator for the Hamiltonian dynamics with fourth order accuracy. The idea of changing variables is to transform the potential energy function as a function of the original variable to a function of the new variable, such that undesired properties can be removed. Two examples are provided and preliminary experimental results are obtained for supporting this idea. The fourth order integrator is constructed by combining the idea of the simplified Takahashi-Imada method and a two-stage Hessian-based integrator. The proposed method, called two-stage simplified Takahashi-Imada method, shows outstanding performance over existing methods in high-dimensional sampling problems.

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Waldeckerová, Naďa. "Option pricing using Monte Carlo methods". Master's thesis, Vysoká škola ekonomická v Praze, 2015. http://www.nusl.cz/ntk/nusl-206936.

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This thesis aims to analyse different Monte Carlo methods when applied to the problem of option pricing. Closer attention is paid to three variance reduction techniques, namely control variathes, importance sampling and antithetic variables, and two different approaches, least-squares Monte Carlo and quasi-Monte Carlo methods. The detailed analysis of the differences and improvements is done on a problem of plain vanilla option pricing. At the end the methods are each applied to valuation of different exotic options.

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Yam, Chiu Yu. "Quasi-Monte Carlo methods for bootstrap". HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/272.

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Ye, Haocheng. "Monte Carlo Methods in Option Pricing". Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2122.

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This article investigates several variance reduction techniques in Monte Carlo simulation applied in option pricing. It first shows how Monte Carlo simulation could be leveraged in the field of option pricing by demonstrating the quality of Monte Carlo methods and properties of stock options. Then the articles simulate stock price trajectories to infer the optimal option price by averaging the payoff at maturity. The article shows in depth the effect of control variates and antithetic variates, and importance sampling in reducing variance. The last part of the article shows how the same variance reduction techniques could be used in more exotic options such as Asian and Bermuda options. In these cases, their closed-form expressions are more difficult to derive compared to the European options, and thus simulation is widely practiced in the industry.

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Bon, Joshua J. "Advances in sequential Monte Carlo methods". Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/235897/1/Joshua%2BBon%2BThesis%284%29.pdf.

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Estimating parameters of complex statistical models and their uncertainty from data is a challenging task in statistics and data science. This thesis developed novel statistical algorithms for efficiently performing statistical estimation, established the validity of these algorithms, and explored their properties with mathematical analysis. The new algorithms and their associated analysis are significant since they permit principled and robust fitting of statistical models that were previously intractable and will thus facilitate new scientific discoveries.

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Vancea, Ioan. "Pattern formation in nanoparticle suspensions : a Kinetic Monte Carlo approach". Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/8420.

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Various experimental settings that involve drying solutions or suspensions of nanoparticles often called nano-fluids have recently been used to produce structured nanoparticle layers. In addition to the formation of polygonal networks and spinodal-like patterns, the occurrence of branched structures has been reported. After reviewing the experimental results, the work presented in this thesis relies only on simulations. Using a modified version of the Monte Carlo model first introduced by Rabani et al. [95] the study of structure formation in evaporating films of nanoparticle solutions for the case that all structuring is driven by the interplay of evaporating solvent and diffusing nanoparticles is presented. The model has first been used to analyse the influence of the nanoparticles on the basic dewetting behaviour, i.e., on spinodal dewetting and on dewetting by nucleation and growth of holes. We focus, as well, on receding dewetting fronts which are initially straight but develop a transverse fingering instability. One can analyse the dependence of the characteristics of the resulting branching patterns on the driving effective chemical potential, the mobility and concentration of the nanoparticles, and the interaction strength between liquid and nanoparticles. This allows to understand the underlying fingering instability mechanism. We describe briefly how the combination of a Monte Carlo model with a Genetic Algorithm (GA) can be developed and used to tune the evolution of a simulated self-organizing nanoscale system toward a predefined nonequilibrium morphology. This work has presented evolutionary computation as a method for designing target morphologies of self-organising nano-structured systems. Finally, highly localised control of 2D pattern formation in colloidal nanoparticle arrays via surface inhomogeneities created by atomic force microscope (AFM) induced oxidation is presented and some simulations are shown. Furthermore, the model can be extended further, and by including the second type of nanoparticle, the binary mixture behaviour can be captured by simulations. We conclude that Kinetic Monte Carlo simulations have allowed the study of the processes that lead to the production of particular nanoparticle morphologies.

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42

Leung, Suet-ying, i 梁雪瑩. "A study of step kinetics by kinetic Monte Carlo simulation". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31226322.

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Jia, Quiyi. "Pricing American options using Monte Carlo methods". Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119854.

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Zhang, Hongbin. "Pricing Asian Options using Monte Carlo Methods". Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119855.

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45

Wang, Bing, i Ling Wang. "Pricing Barrier Options using Monte Carlo Methods". Thesis, Uppsala universitet, Analys och tillämpad matematik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-152632.

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46

Wang, Liangliang. "Bayesian phylogenetic inference via Monte Carlo methods". Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42935.

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A main task in evolutionary biology is phylogenetic tree reconstruction, which determines the ancestral relationships among di erent species based on observed molecular sequences, e.g. DNA data. When a stochastic model, typically continuous time Markov chain (CTMC), is used to describe the evolution, the phylogenetic inference depends on unknown evolutionary parameters (hyper-parameters) in the stochastic model. Bayesian inference provides a general framework for phylogenetic analysis, able to implement complex models of sequence evolution and to provide a coherent treatment of uncertainty for the groups on the tree. The conventional computational methods in Bayesian phylogenetics based on Markov chain Monte Carlo (MCMC) cannot e ciently explore the huge tree space, growing super exponentially with the number of molecular sequences, due to di culties of proposing tree topologies. sequential Monte Carlo (SMC) is an alternative to approximate posterior distributions. However, it is non-trivial to directly apply SMC to phylogenetic posterior tree inference because of its combinatorial intricacies. We propose the combinatorial sequential Monte Carlo (CSMC) method to generalize applications of SMC to non-clock tree inference based on the existence of a flexible partially ordered set (poset) structure, and we present it in a level of generality directly applicable to many other combinatorial spaces. We show that the proposed CSMC algorithm is consistent and fast in simulations. We also investigate two ways of combining SMC and MCMC to jointly estimate the phylogenetic trees and evolutionary parameters, particle Markov chain Monte Carlo (PMCMC) algorithms with CSMC at each iteration and an SMC sampler with MCMC moves. Further, we present a novel way to estimate the transition probabilities for a general CTMC, which can be used to solve the computing bottleneck in a general evolutionary model, string-valued continuous time Markov Chain (SCTMC), that can incorporate a wide range of molecular mechanisms.

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Leung, Wing-Kai. "Applications of continuum quantum Monte Carlo methods". Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411231.

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Fearnhead, Paul. "Sequential Monte Carlo methods in filter theory". Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299043.

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Murray, Iain Andrew. "Advances in Markov chain Monte Carlo methods". Thesis, University College London (University of London), 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487199.

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Probability distributions over many variables occur frequently in Bayesian inference, statistical physics and simulation studies. Samples from distributions give insight into their typical behavior and can allow approximation of any quantity of interest, such as expectations or normalizing constants. Markov chain Monte Carlo (MCMC), introduced by Metropolis et al. (1953), allows r sampling from distributions with intractable normalization, and remains one of most important tools for approximate computation with probability distributions. I While not needed by MCMC, normalizers are key quantities: in Bayesian statistics marginal likelihoods are needed for model comparison; in statistical physics many physical quantities relate to the partition function. In this thesis we propose and investigate several new Monte Carlo algorithms, both for evaluating normalizing constants and for improved sampling of distributions. Many MCMC correctness proofs rely on using reversible transition operators; this can lead to chains exploring by slow random walks. After reviewing existing MCMC algorithms, we develop a new framework for constructing non-reversible transition operators from existing reversible ones. Next we explore and extend MCMC-based algorithms for computing normalizing constants. In particular we develop a newMCMC operator and Nested Sampling approach for the Potts model. Our results demonstrate that these approaches can be superior to finding normalizing constants by annealing methods and can obtain better posterior samples. Finally we consider 'doubly-intractable' distributions with extra unknown normalizer terms that do not cancel in standard MCMC algorithms. We propose using several deterministic approximations for the unknown terms, and investigate their interaction with sampling algorithms. We then develop novel exact-sampling-based MCMC methods, the Exchange Algorithm and Latent Histories. For the first time these algorithms do not require separate approximation before sampling begins. Moreover, the Exchange Algorithm outperforms the only alternative sampling algorithm for doubly intractable distributions.

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Teckentrup, Aretha Leonore. "Multilevel Monte Carlo methods and uncertainty quantification". Thesis, University of Bath, 2013. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.577753.

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We consider the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such equations arise, for example, in stochastic groundwater ow modelling. Models for random coefficients frequently used in these applications, such as log-normal random fields with exponential covariance, lack uniform coercivity and boundedness with respect to the random parameter and have only limited spatial regularity. To give a rigorous bound on the cost of the multilevel Monte Carlo estimator to reach a desired accuracy, one needs to quantify the bias of the estimator. The bias, in this case, is the spatial discretisation error in the numerical solution of the partial differential equation. This thesis is concerned with establishing bounds on this discretisation error in the practically relevant and technically demanding case of coefficients which are not uniformly coercive or bounded with respect to the random parameter. Under mild assumptions on the regularity of the coefficient, we establish new results on the regularity of the solution for a variety of model problems. The most general case is that of a coefficient which is piecewise Hölder continuous with respect to a random partitioning of the domain. The established regularity of the solution is then combined with tools from classical discretisation error analysis to provide a full convergence analysis of the bias of the multilevel estimator for finite element and finite volume spatial discretisations. Our analysis covers as quantities of interest several spatial norms of the solution, as well as point evaluations of the solution and its gradient and any continuously Fréchet differentiable functional. Lastly, we extend the idea of multilevel Monte Carlo estimators to the framework of Markov chain Monte Carlo simulations. We develop a new multilevel version of a Metropolis Hastings algorithm, and provide a full convergence analysis.

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