Dissertations / Theses on the topic 'Non-equilibrium and Equilibrium Monte Carlo Simulations'
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1
De, Joannis Jason. "Equilibrium properties of polymer solutions at surfaces Monte Carlo simulations /." [Florida] : State University System of Florida, 2000. http://etd.fcla.edu/etd/uf/2000/ane5947/dissertation%5Fdone.pdf.
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Thesis (Ph. D.)--University of Florida, 2000.Title from first page of PDF file. Document formatted into pages; contains ix, 242 p.; also contains graphics. Vita. Includes bibliographical references (p. 232-241).
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Rudzinsky, Michael Steven. "Theoretical and Simulation Studies of a Driven Diffusive System." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/26162.
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We explore steady-state properties of a driven lattice gas, which is a simple model of interacting many-particle systems, driven far from equilibrium by an external field. First, we study a system on a square lattice with periodic boundary conditions (PBC) along both principal lattice axes, while the drive acts along only one of these axes. For such systems, we analyze the full distribution of structure factors. Next, we investigate the effects of imposing other boundary conditions on the system. In particular, we focus on models with shifted periodic boundary conditions (SPBC) along one axis and open boundary conditions (OBC) along the other axis. The OBC allow us to have a steady flux of particles through the system while the SPBC permits us to drive the system in a range of possibilities. Using Monte Carlo simulation techniques, we discover a rich variety of phenomena, especially at low temperatures. A continuum theory for the densities, based on Langevin equations, is formulated and its predictions compared to simulation data. Many large scale properties are described successfully.Ph. D.
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Anderson, Mark Jule Jr. "Cooperative Behavior in Driven Lattice Systems with Shifted Periodic Boundary Conditions." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30606.
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We explore the nature of driven stochastic lattice systems with non-periodic boundary conditions. The systems consist of particle and holes which move by exchanges of nearest neighbor particle-hole pairs. These exchanges are controlled by the energetics associated with an internal Hamiltonian, an external drive and a stochastic coupling to a heat reservoir. The effect of the drive is to bias particle-hole exchanges along the field in such a way that a particle current can be established. Hard-core volume constraints limit the occupation of only one particle (hole) per lattice site. For certain regimes of the overall particle density and temperature, a system displays a homogeneous disordered phase. We investigate cooperative behavior in this phase by using two-point spatial correlation functions and structure factors. By varying the particle density and the temperature, the system orders into a phase separated state, consisting of particle-rich and particle-poor regions. The temperature and density for the co-existence state depend on the boundary conditions. By using Monte Carlo simulations, we establish co-existence curves for systems with shifted periodic boundary conditions.Ph. D.
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Korniss, György. "Non-equilibrium Phase Transitions and Steady States in Biased Diffusion of Two Species." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30607.
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We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbor empty sites, but particle-particle exchange between oppositely charged particles is also allowed on a separate time scale. Controlled by this relative time scale, particle density and drive, the system orders into a charge-segregated state. Using a combination of Monte Carlo simulations and continuum field theory techniques, we study the order of these transitions and map out the steady state phase diagram of the system. On a single sheet of transitions, a line of multicritical points is found, separating the first order and continuous transitions. Furthermore, we study the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. The average structure factors show a discontinuity singularity at the origin which in real space predicts an intricate crossover between power laws of different kinds. We also seek for generic statistical properties of these quantities. The probability distributions of the structure factors are universal asymmetric exponential distributions.
This research was supported in part by grants from the National Science Foundation
through the Division of Materials Research.Ph. D.
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Siretskiy, Alexey. "Monte Carlo Simulations of the Equilibrium Properties of Semi-stiff Polymer Chains : Efficient Sampling from Compact to Extended Structures." Doctoral thesis, Uppsala universitet, Fysikalisk kemi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-151618.
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Polymers is a class of molecules which can have many different structures due to a large number of degrees of freedom. Many biopolymers, e.g. DNA, but also synthetic macromolecules have special structural features due to their backbone stiffness. Since such structural properties are important for e.g. the biological function, a lot of effort has been put into the investigation of the configurational properties of semi-stiff molecules. A theoretical treatment of these systems is often accompanied by computer simulations. The main idea is to compare theoretically derived models with experimental results for real polymers. Using Monte Carlo simulations, I have investigated how this computational technique can build a bridge between theoretical models and experimentally observed phenomena. The effort was mainly directed to develop sampling techniques, for efficiently exploring the configurational space of semi-stiff chains in a wide range of structures. The work was concentrated on compact conformations, since they, as is well known from previous studies, are difficult to sample using conventional methods. In my studies I have shown that the simple and, at a first glance, time consuming method of bead-by-bead regrow as a way of changing the configuration of a semi-stiff chain gave very promising and encouraging results when combined with modern simulation techniques, like Entropic Sampling with the Wang-Landau algorithm. The resulting simulation package was also suitable for parallelization which resulted in a further speed-up of the calculations. In addition to the more elaborate sampling methods, I also investigated external conditions to induce compaction of a semi-stiff polymer. In the case of a polyampholyte the condensing agent could be a multivalent salt, creating effective attraction between the loops of the chain, while for neutral polymers, an external field and the geometry of the confining volume can induce a compaction.
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Patel, Sonal. "Determination of Phase Equilibria and the Critical Point Using Two-Phase Molecular Dynamics Simulations with Monte Carlo Sampling." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3587.
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The two-phase MD technique employed in this work determines the liquid and vapor phase densities from a histogram of molecular densities within phase clusters in the simulation cell using a new Monte Carlo (MC) sampling method. These equilibrium densities are then fitted in conjunction with known critical-point scaling laws to obtain the critical temperature, and the critical density. This MC post-processing method was found to be more easily implemented in code, and it is efficient and easily applied to complex, structured molecules. This method has been successfully applied and benchmarked for a simple Lennard-Jones (LJ) fluid and a structured molecule, propane. Various degrees of internal flexibility in the propane models showed little effect on the coexisting densities far from critical point, but internal flexibility (angle bending and bond vibrations) seemed to affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point. The developed MD+MC method was then used to test the efficacy of two all-atom, site-site pair potential models (with and without point charges) developed solely from the energy landscape obtained from high-level ab initio pair interactions for the first time. Both models produced equivalent phase domes and critical loci. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here. Lastly, the transferability of the ab initio potential model was evaluated by applying it to 1-pentanol. An attempt has been made to separate the errors due to transferability of the potential model from errors due to the use of a true-pair potential. The results suggested a good level of transferability for the site-site model. The lack of multi-body effects appears to be dominant weakness in using the generalized ab initio potential model for determination of the phase dome and critical properties of larger alcohols.
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Krometis, Justin. "Lane Preference in a Simple Traffic Model." Thesis, Virginia Tech, 2004. http://hdl.handle.net/10919/42365.
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We examine the effect of lane preference on a quasi one-dimensional three-state driven lattice gas, consisting of holes and positive and negative particles, and periodic boundary conditions in the longitudinal direction. Particles move via particle-hole and, with a lesser rate, particle-particle exchanges; the species are driven in opposite directions along the lattice, each preferring one of the lanes with a given probability, p. The model can be interpreted as traffic flow on a two-lane beltway, with fast cars preferring the left lane and slow cars preferring the right, viewed in a comoving frame. In steady-sate, the system typically exhibits a macroscopic cluster containing a majority of the particles. At very high values of p, a first order transition takes the system to a spatially disordered state. Using Monte Carlo simulations to analyze the system, we find that the size of the cluster increases with lane preference. We also observe a region of negative response, where increasing the lane preference decreases the number of particles in their favored lane, against all expectations. In addition, simulations show an intriguing sequence of density profiles for the two species. We apply mean-field theory, continuity equations, and symmetries to derive relationships between observables to make a number of predictions verified by the Monte Carlo data.Master of Science
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Li, Linjun. "Systems Driven out of Equilibrium with Energy Input at Interfaces or Boundaries." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/77884.
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We study the non-equilibrium behavior of systems that are driven out of equilibrium from the interface. In the first part of this thesis, we study a model of a two-dimensional lattice gas that is in contact with two heat baths that are at different temperatures. Performing Monte Carlo simulations, we find that there are three possible types of non-equilibrium steady states, depending on the values of certain system parameters. They include a disordered phase, a fully phase separated state, and an interesting state with striped patterns in the half of the lattice where the temperature is lower. The last one is a novel non-equilibrium steady state that we study systematically by varying the system parameters. To obtain the non-equilibrium finite-size phase diagram, we perform a spectrum analysis to classify not only the three major states, but also the sub-states of the striped phase. In the second part of the thesis, we study magnetic friction that results when two Potts systems move with respect to each other. In this research, we first study a model that consists of two interacting Potts blocks, where one block moves on top of the other. As a result, the system is driven out of equilibrium constantly. In our research we find for weak interfacial couplings that the contacting surfaces behave rather similar to a free surface. If the interfacial coupling is strong, however, anisotropic spin patterns appear on the contacting surfaces. This study is extended to a three-dimensional Potts wedge with a tip sliding along the surface of a Potts block. It is found that the shape of the Potts lattice influences the surface behavior of the system.Ph. D.
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Binauld, Quentin. "Modélisation et simulation du rayonnement dans les jets de moteurs à propergol solide à haute altitude." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLC090/document.
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Le rayonnement dans les jets issus de moteurs à propergol solide constitue un phénomène essentiel à l’estimation des flux aux parois et à la prédiction de la signature radiative des engins. A haute altitude, de l’ordre de 100 km, ces jets sont caractérisés par des écoulements compressibles diphasiques, à fort aspect raréfié dans certaines régions, compos ´es de particules d’alumine et de gaz de combustion. Le transfert radiatif y joue un rôle important dans la mesure où il influence fortement le refroidissement et le changement de phase des particules. Afin de simuler numériquement les jets et leur rayonnement, différents modèles ont été développés. Le rayonnement des gaz a été pris en compte à l’aide de modèles statistiques à bandes étroites. Le phénomène de surfusion qui régit le changement de phase de l’alumine et les champs de température associés aux différentes tailles de particules, a été pris en compte. Enfin, une méthode de splitting des puissances radiatives a été mise en œuvre afin de permettre le couplage entre le rayonnement et l’écoulement dans des milieux en des ‘équilibre thermique gaz/particules. Ces modèles ont été implémentes dans une plateforme de calcul, permettant de coupler un solveur fluide utilisant une approche Navier-Stokes, un solveur eulérien pour traiter la phase dispersée et un solveur radiatif qui utilise une méthode de Monte Carlo. L’outil numérique développe a été partiellement validé en comparant nos résultats aux mesures obtenues dans le cadre de l’expérience BSUV2. Dans les conditions de cette expérience, le rayonnement des particules est prédominant mais la contribution des gaz s’avère non négligeable. Des simulations sous différentes hypothèses ont permis de mettre en évidence le rôle primordial du transfert radiatif, couplé au phénomène de surfusion, dans l’établissement des champs de température des particules. La dernière partie de ces travaux s’est attachée à l’étude du déséquilibre vibrationnel de la phase gazeuse et de son impact sur le rayonnement dans les jets. Il est montré que le gel partiel des niveaux de vibration de la molécule CO2 durant la détente du jet peut augmenter de façon significative son rayonnementRadiation from solid propellant rocketplumes is important for the prediction of thermalfluxes on vehicle walls and of plume signature. Athigh altitudes, of approximately 100 km, those plumesare characterized by two-phase compressible flows,highly rarefied in some regions, composed of aluminaparticles and exhaust combustion gases. Radiativetransfer plays an important role in the cooling and thephase change of the particles.In order to carry out numerical simulations of rocketplumes and their radiation, several models have beendeveloped. The radiation of the gas phase is takeninto account using statistical narrow bands models.The supercooling phenomenon has been modeled todeal with the phase change of alumina and to obtaincorrect temperature fields for the different size classesof particles. Finally, a splitting method of the radiativepower has been established to enable the couplingbetween radiation and the flow field under gas/particlethermal non-equelibrium. These models have beenimplemented in a calculation platform, enabling tocouple a Navier-Stokes solver for the gas phase, anEulerian solver dealing with the dispersed phase anda radiative solver based on a Monte Carlo method.The developed numerical tool has been partly validatedcomparing our results with the measurementsobtained during the BSUV2 experiment. In the conditionsof this experiment, particle radiation is shownto be predominant but the contribution of the gasphase is found to be non-negligible. Simulations underdifferent hypotheses have put the emphasis onthe importance of radiative transfer, coupled with thesupercooling phenomenon, for an accurate evaluationof particle temperature fields.The last part of this work focuses on the study ofgas vibrational non-equilibrium and its impact on radiationfrom high altitude plumes. It is shown thatthe slow deexcitation of vibrational levels of the CO2molecule during the plume expansion may increasesignificantly its radiation
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Rodrigues, Áttila Leães. "Estudo de transições de fase em sistemas com simetria \"up-down\" e estados absorventes." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-26092014-105955/.
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Neste trabalho estudamos um modelo estocástico com simetria Ising e dois estados absorventes em três dimensões com uma rede cúbica e em duas dimensões através de uma rede triangular. O estudo levou em conta cálculos de aproximação de campo médio e simulações de Monte Carlo. Os resultados mostraram que o modelo tem transição de segunda ordem de uma fase paramagnética para uma fase ferromagnética, uma transição da fase ferromagnética para uma fase absorvente, também de segunda ordem, e ainda uma transição de primeira ordem da fase paramagnética para a fase absorvente. No espaço de parâmetros as três linhas de transição se encontram no diagrama de fases em um ponto onde o modelo se comporta como o modelo do votante.In this work we studied a stochastic model with ising symmetry and two simmetric absorbing configurations in a three-dimensional cubic lattice and in two dimensions using a triangular lattice. The study took into account simple mean-field approximations and Monte Carlo simulations. The results showed that the model has a second-order transition from a paramagnetic phase to a ferromagnetic phase and second-order transition from ferromagnetic phase to the absorbing one. A first-order phase transition from the paramagnetic phase to the absorbing phase is observed too. In the phase diagram the two second-order transition lines aproaches to the point where the model behaves like the voter model.
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Siddique, Shahnewaz. "Failure mechanisms of complex systems." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51831.
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Understanding the behavior of complex, large-scale, interconnected systems in a rigorous and structured manner is one of the most pressing scientific and technological challenges of current times. These systems include, among many others, transportation and communications systems, smart grids and power grids, financial markets etc. Failures of these systems have potentially enormous social, environmental and financial costs. In this work, we investigate the failure mechanisms of load-sharing complex systems. The systems are composed of multiple nodes or components whose failures are determined based on the interaction of their respective strengths and loads (or capacity and demand respectively) as well as the ability of a component to share its load with its neighbors when needed. Each component possesses a specific strength (capacity) and can be in one of three states: failed, damaged or functioning normally. The states are determined based on the load (demand) on the component.
We focus on two distinct mechanisms to model the interaction between components strengths and loads. The first, a Loss of Strength (LOS) model and the second, a Customer Service (CS) model. We implement both models on lattice and scale-free graph network topologies. The failure mechanisms of these two models demonstrate temporal scaling phenomena, phase transitions and multiple distinct failure modes excited by extremal dynamics. We find that the resiliency of these models is sensitive to the underlying network topology. For critical ranges of parameters the models demonstrate power law and exponential failure patterns. We find that the failure mechanisms of these models have parallels to failure mechanisms of critical infrastructure systems such as congestion in transportation networks, cascading failure in electrical power grids, creep-rupture in composite structures, and draw-downs in financial markets. Based on the different variants of failure, strategies for mitigating and postponing failure in these critical infrastructure systems can be formulated.
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Yewande, Emmanuel Oluwole. "Modelling and simulation of surface morphology driven by ion bombardment." Doctoral thesis, [S.l.] : [s.n.], 2006. http://webdoc.sub.gwdg.de/diss/2006/yewande.
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Lee, Ming Ripman, and 李明. "Monte Carlo simulation for confined electrolytes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31240513.
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Lee, Ming Ripman. "Monte Carlo simulation for confined electrolytes /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22055009.
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Bernardin, Frederick E. "Application of Semi-Grand Canonical Monte Carlo (SGMC) methods to describe non-equilibrium polymer systems." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/42428.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2007.Includes bibliographical references.
Understanding the structure of materials, and how this structure affects their properties, is an important step towards the understanding that is necessary in order to apply computational methods to the end of designing materials to fit very specific needs. Such needs include specific optical and mechanical properties. In polymers, the ability to easily create orientation through a variety of processes allows the production of materials that, while chemically similar, exhibit a wide variety of optical and mechanical properties. The ability to illuminate the connections between structure and optical or mechanical properties depends on the ability to reliably interpret a wide variety of experimental measurements. I assert that thermodynamic consistency and energy minimization is an integral part of this endeavor; reliable analyses of structure and properties are built upon the foundation of a minimum-free-energy ensemble of configurations that reproduces the experimental results. This project encompasses three goals, which make up this thesis: 1) to show how sets of experimental measurements are integrated into simulations to produce thermodynamically consistent, minimum-free-energy ensembles; 2) to show how these ensembles can characterize the conformations of macromolecules, which are not available from direct simulation; 3) to show how dynamic processes, which create inhomogeneous systems can be incorporated, along with experimental structural measurements, into thermodynamically consistent, minimum-free-energy ensembles. To achieve the first of these goals, we describe the application of the Semi-Grand Canonical Monte Carlo (SGMC) method to analyze and interpret experimental data for non-equilibrium polymer melts and glasses. Experiments that provide information about atomic-level ordering, e.g. birefringence, are amenable to this approach.
(cont.) Closure of the inverse problem of determining the structural detail from limited data is achieved by selecting the lowest-free-energy ensemble of configurations that reproduces the experimental data. The free energy is calculated using the thermodynamic potential of the appropriate semi-grand canonical (SGC) ensemble ... , as defined by the experimental data. To illustrate the method we examine uniaxially oriented polyethylene melts of average chain length up to C400. The simulation results are analyzed for features not explicitly measured by birefringence, such as the density, torsion angle distribution, molecular scale orientation and free energy, to understand more fully the underlying features of these non-equilibrium states. The stress-optical rule for polyethylene is evaluated in this way. The second goal is achieved through multi-scale modeling, which requires the selection and preservation of information crucial to understanding the behavior of a system at appropriate length and time scales. For a description of processed polymers, such a model must successfully link rheological properties with atomic-level structure. We propose a method for the calculation of an important rheological state descriptor, the configuration tensor
(cont.) Because the characteristic relaxation times of processed polymer chains often span several orders of magnitude, it is commonly the case that partial relaxation of the chains is frozen into the final product. We report results of molecular simulations by the Semi-grand Canonical Monte Carlo (SGMC) method to study the orientation-dependent elasticity of glassy polystyrene as a function of both the system-average degree of orientation and the degree of relaxation of chain ends at a constant average degree of orientation, in accord with the tube model of Doi and Edwards. Our simulations reproduce quantitatively the experimentally observed changes in the tensile modulus E33 as a function of both average orientation and inhomogeneity of the orientation due to partial relaxation. The results show that the partial relaxation of the polymer chains is sufficient to explain the observed variation of mechanical properties for samples that differ in processing history, yet have the same observed birefringence.
by Frederick E. Bernardin, III.
Ph.D.
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Daquila, George Lawrence. "Monte Carlo analysis of non-equilibrium steady states and relaxation kinetics in driven lattice gases." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28701.
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We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases, with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations of larger system sizes than previous studies. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay We compare the crossover functions obtained from our simulations with various analytic results in the literature, and analyze the characteristic oscillations that occur in finite systems away from half-filling. As expected, correlations are weak in three dimensions and consequently the mean-field description is adequate. We also investigate the relaxation towards the non-equilibrium steady state in the two-time density-density auto-correlations, starting from strongly correlated initial conditions. We obtain simple aging scaling behavior in one, two, and three dimensions, with the expected power laws.
We numerically investigate the behavior of driven lattice gases with nearest neighbor interactions at half-filling with periodic boundary conditions below and at the critical temperature using Monte Carlo simulations of very large lattices in two dimensions. This work is one of few that explores the relaxation to a non-equilibrium steady state. We obtain data collapse for the finite-size scaling form of density-density auto-correlation function at the critical point. We achieve data collapse using finite-size scaling of the time-dependent order parameter during the transient regime starting from strongly correlated initial conditions. We present simple aging scaling of the density-density auto-correlation function at the critical point starting from strongly correlated initial conditions using Monte Carlo simulations of two different lattice anisotropies. We thus unambiguously confirm the critical exponents determined by renormalization group methods using measurement of dynamic quantities in the transient regime. Measuring these dynamic quantities in the transient regime provides more conclusive measurements of the critical exponents than previous studies measuring static quantities in the stationary state. We provide qualitative arguments that the lattice anisotropy determines the steady-state for sub-critical quenches.Ph. D.
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Johnson, Tomi Harry. "Non-equilibrium strongly-correlated dynamics." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:55d438cc-d9a1-4898-ac05-49299bad6806.
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We study non-equilibrium and strongly-correlated dynamics in two contexts. We begin by analysing quantum many-body systems out of equilibrium through the lens of cold atomic impurities in Bose gases. Such highly-imbalanced mixtures provide a controlled arena for the study of interactions, dissipation, decoherence and transport in a many-body quantum environment. Specifically we investigate the oscillatory dynamics of a trapped and initially highly-localised impurity interacting with a weakly-interacting trapped quasi low-dimensional Bose gas. This relates to and goes beyond a recent experiment by the Inguscio group in Florence. We witness a delicate interplay between the self-trapping of the impurity and the inhomogeneity of the Bose gas, and describe the dissipation of the energy of the impurity through phononic excitations of the Bose gas. We then study the transport of a driven, periodically-trapped impurity through a quasi one-dimensional Bose gas. We show that placing the weakly-interacting Bose gas in a separate periodic potential leads to a phononic excitation spectrum that closely mimics those in solid state systems. As a result we show that the impurity-Bose gas system exhibits phonon-induced resonances in the impurity current that were predicted to occur in solids decades ago but never clearly observed. Following this, allowing the bosons to interact strongly, we predict the effect of different strongly-correlated phases of the Bose gas on the motion of the impurity. We show that, by observing the impurity, properties of the excitation spectrum of the Bose gas, e.g., gap and bandwidth, may be inferred along with the filling of the bosonic lattice. In other words the impurity acts as a probe of its environment. To describe the dynamics of such a strongly-correlated system we use the powerful and near-exact time-evolving block decimation (TEBD) method, which we describe in detail. The second part of this thesis then analyses, for the first time, the performance of this method when applied to simulate non-equilibrium classical stochastic processes. We study its efficacy for a well-understood model of transport, the totally-asymmetric exclusion process, and find it to be accurate. Next, motivated by the inefficiency of sampling-based numerical methods for high variance observables we adapt and apply TEBD to simulate a path-dependent observable whose variance increases exponentially with system size. Specifically we calculate the expected value of the exponential of the work done by a varying magnetic field on a one-dimensional Ising model undergoing Glauber dynamics. We confirm using Jarzynski's equality that the TEBD method remains accurate and efficient. Therefore TEBD and related methods complement and challenge the usual Monte Carlo-based simulators of non-equilibrium stochastic processes.
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Martins, Tiago Dias 1986. "Implementação e testes de Métodos Monte Carlo para simulação de equilíbrio sólido-líquido." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/266900.
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Orientador: Charlles Rubber de Almeida AbreuDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química
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Resumo: O estudo a nível microscópico do Equilíbrio Sólido-Líquido (ESL) só se desenvolveu a partir do século XX e ainda existem aspectos de tal fenômeno que não são bem compreendidos, mesmo para os sistemas mais simples. Por esse motivo, é necessário que métodos eficientes para simular diretamente o ESL sejam formulados. O principal objetivo deste trabalho foi desenvolver e implementar Métodos Monte Carlo Multicanônicos para simular o ESL de sistemas de Lennard-Jones e, então, avaliar a aplicabilidade de tais métodos com base na sua eficiência. Primeiramente, buscou-se melhorar os resultados do método desenvolvido por Muguruma e Okamoto (2008), que visava amostrar a energia do sistema uniformemente e o volume com probabilidade de Boltzmann, enquanto mantinha-se fixo o número de partículas da caixa de simulação cúbica. Em seguida, uma nova abordagem foi proposta, cuja principal característica é não restringir o formato da caixa, embora a amostragem fosse realizada da mesma forma. Em ambos os métodos, a densidade de estados do sistema foi estimada usando a técnica da matriz de transições e uma abordagem de paralelização das simulações foi empregada a fim de se obter uma amostragem mais efetiva. Os resultados obtidos com o primeiro método mostraram que uma simulação como essa depende significativamente do número de partículas. Além disso, a amostragem dos estados de energia ficou presa na fase sólida. Já os resultados obtidos com a nova metodologia foram ligeiramente melhores que os obtidos com o método anterior. A amostragem para o sistema com o menor número de partículas foi equivalente para as duas fases em questão. No entanto, as simulações com sistemas maiores apresentaram o mesmo problema apontado no método anterior. A princípio, sugeriu-se a existência de uma transição polimórfica. No entanto, simulações na fase sólida com a nova metodologia apontam o contrário. Apesar dos resultados insatisfatórios, este trabalho se constitui em um passo importante no estudo de um tema complexo, que é a previsão de Equilíbrio Sólido-Líquido utilizando métodos de simulação direta
Abstract: The study at the microscopic level of Solid-Liquid Equilibrium (SLE) was only developed in the 20th century and still exist some aspects of this phenomenon that are not well understood, even for the simplest systems. Therefore, it is necessary the development of efficient methods to directly simulate the SLE. The main objective of this work was to develop and implement Multicanonical Monte Carlo methods to simulate the SLE of the Lennard-Jones system and then evaluate their applicability based on efficiency. First, we sought to improve the performance of a method used by Muguruma and Okamoto (2008), which aimed to sample the system energy uniformly and the volume with the Boltzmann probability, while keeping fixed the number of particles in a cubic simulation box. Then a new approach was proposed, whose main feature was let the shape of the box free, although the sampling was performed in the same way. In both methods, the density of states of the system was estimated using the transition matrix technique and an approach for parallelization of the simulations was employed to obtain a more effective sampling. The results obtained with the first method showed that such a simulation depends on the number of particles present in the system. Moreover, the sampling of energy states got stuck in the solid phase. The results obtained with the new method were slightly better than those obtained with the previous method. The sampling for the system with the lowest number of particles was equivalent for the two phases concerned. However, simulations with larger systems presented the same problem of the previous method. At first, it was suggested the existence of a polymorphic transition. However, simulations in the solid phase with the new methodology show the opposite. Despite the unsatisfactory results, this work constitutes na important step in studying a complex subject, which is the prediction of Solid-Liquid Equilibrium using direct simulation methods
Mestrado
Engenharia de Processos
Mestre em Engenharia Química
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Triampo, Wannapong. "Non-Equilibrium Disordering Processes In binary Systems Due to an Active Agent." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/26738.
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In this thesis, we study the kinetic disordering of systems
interacting with an agent or a walker. Our studies divide naturally into two
classes: for the first, the dynamics of the walker conserves the total
magnetization of the system, for the second, it does not. These distinct
dynamics are investigated in part I and II respectively.
In part I, we investigate the disordering of an initially
phase-segregated binary alloy due to a highly mobile vacancy which exchanges
with the alloy atoms. This dynamics clearly conserves the total
magnetization. We distinguish three versions of dynamic rules for the
vacancy motion, namely a pure random walk , an ``active' and a biased walk.
For the random walk case, we review and reproduce earlier work by Z.
Toroczkai et. al.,~cite{TKSZ} which will serve as our base-line. To test
the robustness of these findings and to make our model more accessible to
experimental studies, we investigated the effects of finite temperatures
(``active walks') as well as external fields (biased walks). To monitor the
disordering process, we define a suitable disorder parameter, namely the
number of broken bonds, which we study as a function of time, system size
and vacancy number. Using Monte Carlo simulations and a coarse-grained field
theory, we observe that the disordering process exhibits three well
separated temporal regimes. We show that the later stages exhibit dynamic
scaling, characterized by a set of exponents and scaling functions. For the
random and the biased case, these exponents and scaling functions are
computed analytically in excellent agreement with the simulation results.
The exponents are remarkably universal. We conclude this part with some
comments on the early stage, the interfacial roughness and other related
features.
In part II, we introduce a model of binary data corruption induced
by a Brownian agent or random walker. Here, the magnetization is not
conserved, being related to the density of corrupted bits }$
ho ${small .}
{small Using both continuum theory and computer simulations, we study the
average density of corrupted bits, and the
associated density-density correlation function, as well as several other
related quantities. In the second half, we
extend our investigations in three main directions which allow us to make
closer contact with real binary systems. These are i) a detailed analysis of
two dimensions, ii) the case of competing agents, and iii) the cases of
asymmetric and quenched random couplings. Our analytic results are in good
agreement with simulation results. The remarkable finding of this study is
the robustness of the phenomenological model which provides us with the tool,
continuum theory, to understand the nature of such a simple model.Ph. D.
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Düring, H. Gustavo. "Non-equilibrium dynamics of nonlinear wave systems : Turbulent regime, breakdown and wave condensation." Paris 6, 2010. http://www.theses.fr/2010PA066278.
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Dans cette thèse des problèmes relatifs à deux sujets différents ont été étudié. Tous les deux liés à la description statistique des systèmes avec nombreux degrés de liberté, mais d'une nature très différente. La première partie de ce travail est consacrée à l'étude des systèmes d'ondes faiblement non linéaires. La théorie bien établie de la turbulence des ondes est appliquée à différents systèmes, en étudiant la validité et les limites de celle-ci. Les propriétés statistiques à long terme pour les ondes élastiques dans les plaques et coques, et les ondes capillaires dans un fluide ont été considérées en fonction d'une équation cinétique pour la répartition des densités spectrales. Parmi d'autres situations, on analyse le régime turbulent, l'effet de la dissipation et la limite non dispersive. D'autre part, la description de la dynamique d'un condensat d'ondes a été mis en place, cela élargit la théorie de la turbulence d'ondes en incluant cette structure cohérente simple. Dans la deuxième partie on a étudié le problème du signe, qui représente une grosse limitation dans de nombreuses simulations numériques. Une bonne compréhension de la mécanique statistique des échantillonnages de Monte Carlo avec le problème du signe, est réalisée par analogie avec les systèmes vitreux. Une nouvelle approche est également proposée avec l'utilisation du recuit quantique, qui, loin de résoudre le problème du signe donne une compréhension plus approfondie de la structure de celui-ci.
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Long, Garrett Earle. "Comparative Surface Tension Predictions via Grand Canonical Transition Matrix Monte Carlo Simulation." Miami University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=miami1533206970884063.
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Bertrand, Corentin. "Algorithme Monte-Carlo pour les systèmes quantiques à fortes interactions et hors d'équilibre en nanoélectronique." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAY030.
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Les problèmes quantiques à plusieurs corps hors d'équilibre concentrent de plus en plus d'attention en physique de la matière condensée. Par exemple, les systèmes d'électrons en interaction soumis à un champ électrique externe (constant ou variable) sont un sujet d'étude important en nanoélectronique, mais aussi plus récemment en science des matériaux, afin d'identifier de nouveaux états de la matière hors d'équilibre. Dans cette thèse, une nouvelle méthode numérique et générique a été conçue pour ces systèmes, et appliquée au modèle d'impureté d'Anderson. Ce modèle représente fidèlement un point quantique couplé à une ou plusieurs électrodes, et rends compte à l'équilibre de l'effet Kondo : une manifestation des interactions Coulombiennes au sein du point quantique. Cette méthode a permis d'observer la disparition de l'effet Kondo lorsque le point quantique est conduit hors d'équilibre par une différence de potentiel. Le cœur de la méthode utilise un algorithme Monte-Carlo Quantique diagrammatique. Il s'agit d'une version optimisée de l'algorithme de Profumo et al. [Phys. Rev. B 91, 245154 (2015)], qui calcule des observables dépendantes du temps ou des fonctions de corrélations à travers leurs séries de perturbation en puissances de la force de l'interaction U. Le problème de la divergence de ces séries à grand U est traité par une méthode de resommation robuste. Elle analyse la structure analytique des séries dans le plan complexe en U afin de proposer une régularisation sur mesure par transformation conforme du plan complexe. En post-traitement, une technique Bayésienne permet d'inclure des informations non perturbatives pour réduire les barres d'erreurs qui ont été exacerbées par la resommation. Cette méthode pourrait être appliquée à l'étude de matériaux hors d'équilibre grâce aux algorithmes de "quantum embedding", comme la théorie dynamique de champs moyen, qui permettent l'étude de modèles de réseaux par la résolution d'un problème d'impureté autocohérentNon-equilibrium quantum many-body problems are attracting increasingly more attention in condensed matter physics. For instance, systems of interacting electrons submitted to an external (constant or varying) electric field are studied in nanoelectronics, and more recently in materials, for the search of novel non-equilibrium states of matter. In this thesis, we developed a new numerical generic method for these problems, and apply it to the Anderson impurity model. This model is a good representation of a quantum dot coupled to one or several leads, and gives rise at equilibrium to the Kondo effect --- a manifestation of Coulomb interactions within the dot. We apply our method to compute the collapse of the Kondo effect when the quantum dot is driven out of equilibrium by a voltage bias. Our method is based on a diagrammatic Quantum Monte Carlo (QMC) algorithm. The QMC is an optimized version of the algorithm of Profumo et al. [Phys. Rev. B 91, 245154 (2015)], which computes time-dependent observables or correlation functions as perturbation series in the interaction strength U. To address the problem of diverging series at large U, we constructed a robust resummation scheme which analyses the analytical structure of the series in the U complex plane, for proposing a tailor-made regularization method using a conformal transform of the complex plane. As a post-treatment, a Bayesian technique allows to introduce non-perturbative information to tame the exacerbation of error bars caused by the resummation. We emphasize the potential application to study non-equilibrium materials through "quantum embedding" schemes, such as the Dynamical Mean Field Theory (DMFT), which allow to study lattice models through solving a self-consistent impurity model
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Macé, Jean-Sébastien. "Modélisation du fonctionnement d’un gyrolaser He-Ne de très haute précision." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112160/document.
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Les gyromètres laser He-Ne sont des senseurs inertiels dont la fiabilité et la précision sont reconnues depuis le milieu des années 1980. Leur grande sensibilité leur permet de mesurer des vitesses de rotation avec une précision qui atteint 10⁻³ °/ h dans le domaine aéronautique. Cependant, du fait d’un fonctionnement complexe basé sur une physique riche et variée, ses performances sont fortement dépendantes des conditions de fonctionnement et de toute modification du processus de fabrication. Dans ce cas, un travail de modélisation prend tout son sens, puisqu’il permet, outre une compréhension claire et précise des différents phénomènes physiques, un accès à des études paramétriques non envisageables expérimentalement. La modélisation globale du fonctionnement d’un gyrolaser He-Ne a ainsi été l’objectif principal de la collaboration entre la société Sagem (groupe Safran), un des leaders mondiaux dans le domaine des senseurs inertiels, et le Laboratoire de Physique des Gaz et des Plasmas (LPGP). Cette modélisation est « multiphysique » du fait de la diversité des domaines que couvre la physique du gyrolaser (Plasma, Physique Atomique, Lasers). C’est pourquoi nous avons développé trois modèles spécifiquement adaptés à chaque domaine. Le premier décrit la modélisation de la colonne positive du plasma de décharge dans une approche fluide. Ce modèle permet une description quantitative du plasma et l’accès aux grandeurs telles que la densité électronique et la fonction de distribution en énergie des électrons. Ces grandeurs sont les entrées nécessaires au second modèle qui traite la cinétique des états excités du plasma He-Ne. Un modèle collisionnel-radiatif à 1 dimension radiale (1D-CRM) a ainsi été développé. L’aspect 1D se justifie par l’importance des phénomènes de transport d’atomes et de rayonnement pouvant influer sur le profil radial de l’inversion de population du laser. Le transfert radiatif par auto-absorption des transitions radiatives résonantes a notamment été modélisé en résolvant l’équation de Holstein-Biberman à partir d’une méthode Monte-Carlo. Cet aspect constitue un élément majeur de ce travail de thèse. La diffusion des atomes excités du mélange He-Ne a également été prise en compte en résolvant l’équation de diffusion avec différentes conditions au bord à la surface du capillaire.A partir des populations et des taux cinétiques de peuplement et dépeuplement calculés par 1D-CRM, l’amplification laser dans la cavité a été modélisée dans le cadre d’une approche Maxwell-Bloch à 2 niveaux (NADIA) en incluant la saturation inhomogène du gain c’est-à-dire en tenant compte de la vitesse des atomes émetteurs dans la direction de propagation des faisceaux lasers. La cinétique de NADIA a été optimisée et les processus de transports dans l’espace des phases ont également été implémentés. Ce modèle a été utilisé pour étudier les performances du gyrolaser liées au milieu amplificateur et pour dériver les paramètres physiques nécessaires au développement d’un simulateur du gyrolaser.Dans ce simulateur, un modèle physique simplifié dérivé de NADIA, a été couplé à des modules « systèmes » dans le but de reproduire en sortie le signal opérationnel d’un gyrolaser. Ceci nous a permis de réaliser des études paramétriques sur les grandeurs caractérisant les performances d’un gyrolaser notamment le biais dynamique et le Random-Walk. Nous montrons en particulier que les performances de notre simulateur sont en bon accord avec celles observées en conditions opérationnelles. De plus, nos résultats montrent que ce simulateur est également un outil puissant pour l’analyse de données expérimentalesRing laser gyros (RLG) are inertial sensors whose reliability and accuracy have been recognised since the mid-1980s. Their high sensitivity enables them to measure angular velocity with an accuracy of 10⁻³ °/ h in aeronautics. However, because of a complex functioning based on a rich and varied physics, their performances are highly dependent on the working conditions and on any modification in the manufacturing process. In this case, a numerical modelling is pertinent since it allows both a clear understanding of the ring laser physics and parametric studies which are not experimentally feasible. The global modelling of a He-Ne RLG has been the main objective of the collaboration between Sagem (Safran group), which is one of the world leader in the inertial sensors field, and the Gas and Plasma Physics Laboratory (LPGP).This modelling is “multi-physics” since RLG physics involves several disciplines (plasma, atomic and laser physics). Therefore we have developed three models specifically adapted to each field. The first one describes the modelling of the positive column of the glow discharge following a fluid approach. This model allows a quantitative description of the plasma and gives access to fundamental quantities like the electron density or the electron energy distribution function. These quantities are the required inputs for the second model which treats the kinetics of the excited states inside the He-Ne plasma. For this, a collisional-radiative model in a radial geometry (1D-CRM) has been developed. The radial geometry is justified by the importance of the transport processes of atoms and radiations which can influence the radial profile of the population inversion. Notably, the radiative transfer by self-absorption of the resonant radiative transitions has been modelled by solving the Holstein-Biberman equation by a Monte-Carlo method. This aspect is a major component of this PhD work. Diffusion of excited atoms inside the plasma has also been taken into account by solving the diffusion equation with different boundary conditions at the capillary surface. From the populations and the kinetic rates computed by 1D-CRM, the laser amplification inside the cavity has been modelled using a two-level Maxwell-Bloch approach (NADIA) taking into account the inhomogeneous gain saturation, which means to consider the thermal speed of the atoms in the direction of propagation of the laser beams. The kinetics of NADIA has been optimized and transport processes in the phase space have also been implemented. This model has been used to study the performances of the RLG linked to the amplifying medium and to derive the physical parameters needed for the development of a simulator.Concerning this simulator, a simplified physical model from NADIA has been coupled to system modules in order to reproduce the operating signal of a RLG. This allows to conduct parametric studies on the quantities defining the RLG performance in particular the dynamic bias and the so-called “Random Walk”. We showed notably that the results of our simulator are in good agreement with experimental measurements in operating conditions. Moreover, our results show that this simulator is a powerful tool for analysing experimental data
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Razavi, Seyed Mostafa. "OPTIMIZATION OF A TRANSFERABLE SHIFTED FORCE FIELD FOR INTERFACES AND INHOMOGENEOUS FLUIDS USING THERMODYNAMIC INTEGRATION." University of Akron / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=akron1481881698375321.
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Neyt, Jean-Claude. "Calcul de la tension interfaciale de mélanges gaz / eau, gaz / huile et huile / eau par simulation moléculaire." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2013. http://tel.archives-ouvertes.fr/tel-00962483.
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La prédiction de valeurs de tension interfaciale des fluides est capitale dans de nombreuses applications industrielles. Les techniques de simulation moléculaire et l'évolution rapide des moyens de calcul intensif permettent depuis quelques années de prédire des valeurs de tension interfaciale pour des systèmes complexes. Des travaux concernant des équilibres liquide / vapeur des corps purs SO2, O2, N2 et Ar montrent que les modèles choisi pour chaque molécule peuvent influencer la qualité des prédictions de tension interfaciale. Des simulations d'équilibres gaz acide / alcane de type CO2 / n-butane, CO2 / n-décane et H2S / n-pentane ont ensuite été réalisées. Elles ont mis en évidence l'efficacité des méthodes de simulation de type Monte Carlo pour la prédiction des tensions interfaciales pour de tels systèmes. L'étude de systèmes ternaires H2O / N2+CH4 et H2O / CO2+H2S a par ailleurs montré que le recourt à la dynamique moléculaire pouvait faciliter l'équilibration des systèmes simulés, rendant plus efficace la prédiction des tensions interfaciales. L'étude d'équilibres liquide / vapeur de saumures de chlorure de sodium a permis de mettre en évidence l'efficacité de certains potentiels non-polarisables pour la prédiction de l'évolution de la tension interfaciale avec la molarité de sel. Les modèles polarisables de type core-shell choisis ne permettent de prédire ni les masses volumiques, ni les tensions interfaciales. Enfin, l'étude d'équilibres eau / alcane en présence de sel ou de méthanol a montré que les méthodes de dynamique moléculaire permettaient de prédire quantitativement des valeurs de tension interfaciale pour ce type d'interface. L'effet de l'alcool abaissant la tension interfaciale a bien été observé, tout comme son placement préférentiel à l'interface.
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Acharya, Arjun R. "Free energy differences : representations, estimators, and sampling strategies." Thesis, University of Edinburgh, 2004. http://hdl.handle.net/1842/602.
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In this thesis we examine methodologies for determining free energy differences (FEDs) of phases via Monte Carlo simulation. We identify and address three generic issues that arise in FED calculations; the choice of representation, the choice of estimator, and the choice of sampling strategy. In addition we discuss how the classical framework may be extended to take into account quantum effects. Key words: Phase Mapping, Phase Switch, Lattice Switch, Simulated Tempering, Multi-stage, Weighted Histogram Analysis Method, Fast Growth, Jarzynski method, Umbrella, Multicanonical, Path Integral Monte Carlo, Path Sampling, Multihamiltonian, fluctuation theorem.
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Kaiser, Vojtech. "The Wien Effect in Electric and Magnetic Coulomb systems - from Electrolytes to Spin Ice." Thesis, Lyon, École normale supérieure, 2014. http://www.theses.fr/2014ENSL0942/document.
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Les gaz ou fluides de Coulomb sont composés de particules chargées couplées entre elles par interaction coulombienne à longue portée. De part la nature de ces interactions, la physique du gaz de Coulomb est très riche, comme par exemple dans des électrolytes plus ou moins complexes, mais aussi à travers l'émergence de monopôles magnétiques dans la glace de spin. Dans cette thèse nous nous intéressons au comportement hors d'équilibre des gaz de Coulomb et de la glace de spin. Au centre de cette étude se trouve le deuxième effet de Wien, qui est une croissance linéaire de la conductivité en fonction du champ électrique appliqué à un électrolyte faible. Ce phénomène est une conséquence directe de l'interaction coulombienne qui pousse les charges à se lier par paires ; le champ électrique va alors aider à dissocier ces paires et créer des charges mobiles qui amplifient la conductivité. Le deuxième effet de Wien est un processus hors-équilibre non-linéaire, remarquablement décrit par la théorie de Onsager. Nos simulations sur réseau permettent de découvrir le rôle de l'environnement ionique qui agit contre le deuxième effet de Wien, ainsi que de caractériser la mobilité du système et sa dépendance en fonction du champ externe. Les simulations nous ont aussi donné accès aux corrélations de charges qui décrivent le processus microscopique à la base de l'effet Wien. Enfin, nous regardons plus précisément le gaz émergent de monopôles dans la glace de spin, aussi appelé « magnétolyte », capable de décrire de manière remarquable les propriétés magnétiques de glace de spin. Nous décrivons la dynamique complète hors-équilibre de cette magnétolyte soumise à une forçage périodique ou une trempe dans un champ magnétique en incluant à la fois le deuxième effet de Wien et la réponse du réseau de spins qui est à la base de l'émergence des monopôles magnétiques. Tout au long, nous utilisons une simple extension des simulations de gaz de Coulomb sur réseau pour préciser nos prédictions. Il est très rare de trouver une théorie analytique du comportement hors-équilibre d'un système hautement frustré au-delà de la réponse linéaireA Coulomb gas or fluid comprises charged particles that interact via the Coulomb interaction. Examples of a Coulombic systems include simple and complex electrolytes together with magnetic monopoles in spin ice. The long-range nature of the Coulomb interaction leads to a rich array of phenomena.This thesis is devoted to the study of the non-equilibrium behaviour of lattice based Coulomb gases and of the quasi-particle excitations in the materials known as spin ice which constitute a Coulomb gas of magnetic charges. At the centre of this study lies the second Wien effect which describes the linear increase in conductivity when an electric field is applied to a weak electrolyte. The conductivity increases due to the generation of additional mobile charges via a field-enhanced dissociation from Coulombically bound pairs.The seminal theory of Onsager gave a detailed analysis of the Wien effect. We use numerical simulations not only to confirm its validity in a lattice Coulomb gas for the first time but mainly to study its extensions due to the role of the ionic atmosphere and field-dependent mobility. The simulations also allow us to observe the microscopic correlations underlying the Wien effect.Finally, we look more closely at the emergent gas of monopoles in spin ice—the magnetolyte. The magnetic behaviour of spin ice reflects the properties of the Coulomb gas contained within. We verify the presence of the Wien effect in model spin ice and in the process predict the non-linear response when exposed to a periodic driving field, or to a field quench using Wien effect theory. We use a straightforward extension of the lattice Coulomb gas simulations to refine our predictions. It is a highly unusual result to find an analytic theory for the non-equilibrium behaviour of a highly frustrated system beyond linear response
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Klamser, Juliane Uta. "Transitions de phase en basse dimension à l’équilibre et hors d’équilibre." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS333.
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Bien que la nature soit tridimensionnelle, il existe de nombreux systèmes dont les dimensions effectives sont inférieures, offrant une nouvelle physique. Cette thèse porte sur les transitions de phase dans les systèmes de faibles dimensions, en particulier sur les phases hors équilibre dans la matière active (MA) bidimensionnelle (2D). À la différence des systèmes passifs, les particules actives sont entraînées par de l'énergie injectée à l'échelle microscopique à partir de degrés de liberté internes, entraînant une dynamique irréversible, et donnant souvent lieu à des phases macroscopiques contrastant avec l'équilibre. Dans une première partie, ce travail propose une caractérisation quantitative des phases hors équilibre en s'appuyant sur un modèle minimal de MA. Ce modèle repose sur des particules 2D autopropulsées avec des interactions de paires. La dynamique (Monte Carlo cinétique persistante) est une variante des disques passifs et diffère des modèles bien connus de MA. Un diagramme de phase quantitatif complet est présenté, incluant la séparation de phase induite par motilité (SPIM). De plus, le scénario de fusion en deux étapes avec la phase hexatique se retrouve aussi hors équilibre. L'activité peut fondre un solide 2D et les lignes de fusion restent séparées de SPIM. La deuxième partie explore l'existence de transitions de phase dans les modèles 1D classiques avec des interactions courtes portées à température non nulle. Une idée largement partagée est que de telles transitions sont impossibles. Un contre-exemple clair est présenté où la non-analyticité de l'énergie libre émerge d'un nouveau mécanisme d'origine géométrique, établi de manière rigoureuseAlthough nature is three-dimensional, lower dimensional systems are often effectively realized offering fascinating new physics. The subject of this thesis is phase transitions in low dimensions, with its primary focus on non-equilibrium phases in two-dimensional active matter. Unlike passive systems, active particles are driven by energy injected at the microscopic scale from internal degrees of freedom resulting in an irreversible dynamics, often giving rise to macroscopic phases in striking contrast to equilibrium. A goal is to give a quantitative characterization of such non-equilibrium phases and to capture these in simplest realizations of active matter. The thesis explores two-dimensional self-propelled particles with isotropic pair-wise interactions. The dynamics (persistent kinetic Monte Carlo) is a variant of passive disks and different from well-known models of active matter. A full quantitative phase diagram is presented including motility induced phase separation (MIPS) as seen in other active systems. Additionally, the famous two-step melting scenario with the hexatic phase extends far from equilibrium. In this non-equilibrium scenario, the activity can melt a 2D solid and the melting lines remain separated from MIPS. The second part explores a frequently debated issue of the existence of phase transitions in classical one-dimensional models with short-range interactions at non-zero temperature. A widely shared misconception is that such transitions are not possible. A clear counterexample to this belief is given where non-analyticity in the free energy emerges from a new mechanism with a geometrical origin, which is then established on a rigorous ground
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Zhang, Kai. "Equilibrium and Non-equilibrium Monte Carlo Simulations of Microphases and Cluster Crystals." Diss., 2012. http://hdl.handle.net/10161/5856.
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Soft matter systems exhibiting spatially modulated patterns on a mesoscale are characterized by many long-lived metastable phases for which relaxation to equilibrium is difficult and a satisfactory thermodynamic description is missing. Current dynamical theories suffer as well, because they mostly rely on an understanding of the underlying equilibrium behavior. This thesis relates the study of two canonical examples of modulated systems: microphase and cluster crystal formers. Microphases are the counterpart to gas-liquid phase separation in systems with competing short-range attractive and long-range repulsive interactions. Periodic lamellae, cylinders, clusters, etc., are thus observed in a wide variety of physical and chemical systems, such as multiblock copolymers, oil-water surfactant mixtures, charged colloidal suspensions, and magnetic materials. Cluster crystals in which each lattice site is occupied by multiple particles are formed in systems with steep soft-core repulsive interactions. Dendrimers have been proposed as a potential experimental realization. In order to access and understand the equilibrium properties of modulated systems, we here develop novel Monte Carlo simulation methods. A thermodynamic integration scheme allows us to calculate the free energy of specific modulated phases, while a [N]pT ensemble simulation approach, in which both particle number and lattice spacing fluctuate, allows us to explore their phase space more efficiently. With these two methods, we solve the equilibrium phase behavior of five schematic modulated-phase-forming spin and particle models, including the axial next-nearest-neighbor Ising (ANNNI) model, the Ising-Coulomb (IC) model, the square-well linear (SWL) model, the generalized exponential model of index 4 (GEM-4) and the penetrable sphere model (PSM). Interesting new physics ensues. In the ANNNI layered regime, simple phases are not found to play a particularly significant role in the devil's flowers and interfacial roughening plays at most a small role. With the help of generalized order parameters, the paramagnetic-modulated critical transition of the ANNNI model is also studied. We confirm the XY universality of the paramagnetic-modulated transition and its isotropic nature. With our development of novel free energy minimization schemes, the determination of a first phase diagram of a particle-based microphase former SWL is possible. We identify the low temperature GEM-4 phase diagram to be hybrid between the Gaussian core model (GCM) and the PSM. The system additionally exhibits S-shaped doubly reentrant phase sequences as well as critical isostructural transitions between face-centered cubic (FCC) cluster solids of different integer occupancy. The fluid-solid coexistence in the PSM phase diagram presents a crossover behavior around T~0.1, below which the system approaches the hard sphere limit. Studying this regime allows us to correct and reconcile prior DFT and cell theory work around this transition.
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Alhakeem, Eyad Ali. "Dosimetry at extreme non-charged particle equilibrium conditions using Monte Carlo and specialized dosimeters." Thesis, 2018. https://dspace.library.uvic.ca//handle/1828/10123.
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Radiotherapy is used in clinics to treat cancer with highly energetic ionizing particles. The radiation dose can be measured indirectly by means of radiation detectors or dosimeters. The dose deposited in a detector can be related to dose deposited in a point within the patient. In theory, however, this is only possible under charged particle equilibrium (CPE). The motivation behind the dissertation was driven by the difficult, yet crucial, dosimetry in non-CPE regions. Inaccurate dose assessment performed with standard dosimetry using ionization chambers may significantly impact the outcomes of radiotherapy treatments. Therefore, advanced dosimetry methods tailored specifically to suit non-CPE conditions must be used. This work aims to improve dosimetry in two types of non-CPE conditions that pose dosimetric challenges: regions near interfaces of tissues with low- and high- density media and in small photon fields.
To achieve the main dissertation objectives, an enhanced film dosimetry protocol with a novel film calibration approach was implemented. This calibration method is based on the percent depth dose (PDD) tables and was shown to be efficient and accurate. As a result, the PDD calibration method was used for the film dosimetry process throughout the dissertation work.
Monte Carlo (MC) calculations for the small field dosimetry were performed using phase-space files (PSFs) provided by Varian for TrueBeam linac. The MC statistical uncertainty in these types of calculations is limited by the number of particles (due to latent variance) in the used PSFs. This study investigated the behaviour of the latent variances (LV) with beam energy, depth in phantom, and calculation resolution (voxel size). LV was evaluated for standard 10x10 cm2 fields as well as small fields (down to 1.3 mm diameter). The results showed that in order to achieve sub-percent LV in open 10x10 cm2 field MC simulations a single PSF can be used, whereas for small SRS fields (1.3—10 mm) more PSFs (66—8 PSFs) would have to be summed.
The first study in this dissertation compared the performance of several dosimetric methods in three multi-layer heterogeneous phantoms with water/air, water/lung, and water/steel interfaces irradiated with 6 and 18 MV photon beams. MC calculations were used, along with Acuros XB, anisotropic analytical algorithm (AAA), GafChromic EBT2 film, and MOSkin dosimeters. PDDs were calculated and measured in these heterogeneous phantoms. The result of this study showed that Acuros XB, AAA, and MC calculations were within 1% in the regions with CPE. At media interfaces and buildup regions, differences between Acuros XB and MC were in the range of +4.4% to -12.8%. MOSkin and EBT2 measurements agreed to MC calculations within ~ 2.5%-4.5%. AAA did not predict the backscatter dose from the high-density heterogeneity. For the third, multilayer lung phantom, 6 MV beam PDDs calculated by all treatment planning system (TPS) algorithms were within 2% of MC. 18 MV PDDs calculated by Acuros XB and AAA differed from MC by up to 3.2 and 6.8%, respectively. MOSkin and EBT2 each differed from MC by up to 3%. All dosimetric techniques, except AAA, agreed within 3% in the regions with particle equilibrium. Differences between the dosimetric techniques were larger for the 18 MV than the 6 MV beam. This study provided a comparative performance evaluation of several advanced dosimeters in heterogeneous phantoms. This combination of experimental and calculation dosimetry techniques was used for the first time to evaluate the dose near these interfaces.
The second study in the dissertation aims to improve dose measurement accuracy in small radiotherapy fields. Field output factors of 6 MV beams from TrueBeam linear accelerator (linac) collimated with 1.27-40 mm diameter cones were calculated and measured using MC and EBT3 films. A set of detector specific correction factors for two widely used dosimeters (EFD-3G diode and PTW-60019 microDiamond detectors) were determined based on GafChromic EBT3 film measurements and calculated using MC methods. MC calculations were performed for microDiamond detector in parallel and perpendicular orientations relative to the beam axis. The result of this study showed that the measured OFs agreed within 2.4% for fields ≥10 mm. For the cones of 1.27, 2.46, and 3.77 mm diameter maximum differences were 17.9%, 1.8% and 9.0%, respectively. MC calculated OF in water agreed with those obtained using EBT3 film within 2.2% for all fields. MC calculated output correction factors for microDiamond detector in fields ≥10 mm ranged within 0.975-1.020 for perpendicular and parallel orientations. MicroDiamond detector correction factors calculated for the 1.27, 2.46 and 3.77 mm fields were 1.974, 1.139 and 0.982 with detector in parallel orientation, and these factors were 1.150, 0.925 and 0.914 in perpendicular orientation. EBT3 and MC obtained correction factors agreed within 3.7% for fields of ≥3.77 mm and within 5.9% for smaller cones. This work provided output correction factors for microDiamond and EFD-3G detectors in very small fields of 1.27 – 3.77 mm diameter and demonstrated over and under-response of these detectors in such fields. These correction factors allow improve the accuracy of dose measurements in small photon fields using these detectors.Graduate
2019-08-30
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Langenberg, Marcel Simon. "Energy dissipation and transport in polymeric switchable nanostructures via a new energy-conserving Monte-Carlo scheme." Doctoral thesis, 2018. http://hdl.handle.net/11858/00-1735-0000-002E-E3BB-7.
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Nag, Shubhadeep. "Novel and Fundamental Studies of Separation Methods Leading to Very High Degree of Separation of Molecular Mixtures and Related Studies." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5224.
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Separation of molecular mixtures will often require in chemistry, biology, physics and material science. Existing methods of separation can at best yield a separation factor of 10^4 . They also incur huge expenditure of energy. A new and novel method of separation is proposed in the thesis based on Levitation and Blowtorch effects. This method has been applied for the separation of the four different mixtures, (i) n-pentane-neopentane, (ii) 2,2-dimethyl butane-n-pentane, (iii) n-hexane-neopentane, and (iv) 2,2-dimethyl butane-n-pentane. The results based on Non-Equilibrium Monte Carlo simulations suggest that this method can yield very high separation factors (10^16) with very little consumption of energy. The experimental approach to be employed for the realization of separation is discussed. The changes to the potential energy landscape in the presence of a hot zone are discussed for (i) one-dimensional and three-dimensional systems, (ii) interacting and non-interacting systems, and (iii) hydrocarbons in zeolite system, and compared with Landauer’s suggestion. Extremely small diffusivity of monoatomic species in zeolite NaCaA as a function of diameter of diffusant has been computed with the help of Replica Exchange Transition Interface Sampling (RETIS) technique. Diffusion of a small solute in the body centered cubic lattice is seen to exhibit maxima as a function of the solute diameter. This observation explains the existence of solutes with high diffusivity (for example Co in γ-U and β-Zr, Cu in Pr, or Au in Th). A new potential as a function of Si/Al ratio for modelling zeolite Y and A has been proposed and shown to predict lattice parameter, bulk modulus, infrared spectra, etc in agreement with the experiment.Institute Scholarship (Ministry of Education, Govt. of India)
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(9674882), Sayan Basak. "Hysteresis and Pattern Formation in Electronic Phase Transitions in Quantum Materials." Thesis, 2020.
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We propose an order parameter theory of the quantum Hall nematic in high fractional Landau levels in terms of an Ising description. This new model solves a couple of extant problems in the literature: (1) The low-temperature behavior of the measured resistivity anisotropy is captured better by our model than previous theoretical treatments based on the electron nematic having XY symmetry. (2) Our model allows for the development of true long-range order at low temperature, consistent with the observation of anisotropic low-temperature transport.
We furthermore propose new experimental tests based on hysteresis that can distinguish whether any two-dimensional electron nematic is in the XY universality class (as previously proposed in high fractional Landau levels), or in the Ising universality class (as we propose). Given the growing interest in electron nematics in many materials, we expect our proposed test of universality class to be of broad interest.
Whereas the XY model in two dimensions does not have a long-range ordered phase, the addition of uniaxial random field disorder induces a long-range ordered phase in which the spontaneous magnetization points perpendicular to the random field direction, via an order-by-disorder transition. We have shown that this spontaneous magnetization is robust against a rotating driving field, up to a critical driving field amplitude. Thus we have found evidence for a new non-equilibrium phase transition that was unknown before in this model. Moreover, we have discovered an incredible anomaly at this nonequilibrium phase transition: the critical region is accompanied by a cascade of period multiplication events. This physics is reminiscent of the period bifurcation cascade signaling the transition to chaos in nonlinear systems, and of the approach to the irreversibility transition in models of yield in amorphous solids~\cite{reichhardt-dahmen,leishangthem_yielding_2017}. This period multiplication cascade is surprising to be present in a statistical mechanics model, and suggests that the non-equilibrium transition as a function of driving field amplitude is part of a larger class of transitions in dynamical systems.
Moreover, we show that this multi-period behavior represents a new emergent classical discrete time-crystal, since the new period is robust against changes to initial conditions and low-temperature fluctuations over hundreds of driving period cycles.
We expect this work to be of broad interest, further encouraging cross-fertilization between the rapidly growing field of time-crystals with the well-established fields of nonequilibrium phase transitions and dynamical systems.
Geometrical configurations gave us a better understanding of the multi-period behavior of the limit-cycles.
Moreover, surface probes are continually evolving and generating vast amounts of spatially resolved data of quantum materials, which reveal a lot of detail about the microscopic and macroscopic properties of the system.
Materials undergoing a transition between two distinct states, phase separate.
These phase-separated regions form intricate patterns on the observable surface, which can encode model-specific information, including interaction, dimensionality, and disorder.
While there are rigorous methods for understanding these patterns, they turn out to be time-consuming as well as requiring expertise.
We show that a well-tuned machine learning framework can decipher this information with minimal effort from the user.
We expect this to be widely used by the scientific community to fast-track comprehension of the underlying physics in these materials.
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Moodley, Suren. "Monte Carlo molecular simulation of binary fluid-phase equilibrium using heterogeneous mixing parameters." Thesis, 2012. http://hdl.handle.net/10413/8984.
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Du, Preez Nicholas Bruce. "Determination of phase equilibria for long-chain linear hydrocarbons by Monte Carlo simulation." Thesis, 2005. http://hdl.handle.net/10413/2846.
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The focus of this study was to determine the coexistence phase equilibria for three groups of long-chain linear hydrocarbons (n-alkanes, 1-alkenes and 1-alcohols) using Monte Carlo simulation. Three common transferable united-atom force fields were used in the simulations: OPLS-UA (Jorgensen et al., 1984), TraPPE-UA (Martin and Siepmann, 1998) and NERD (Nath, Escobedo, de Pablo and Patramai, 1998). Isothermal phase equilibria was calculated over a temperature range from approximately the normal boiling point up to just below the critical temperature. The liquid and vapour densities and vapour pressures were determined from the simulations. The density results were then fitted using least-squares regression to the scaling law and the law of rectilinear diameters in order to estimate the critical properties. The vapour pressure data were fitted using least-squares to the Clausius-Clapeyron equation to estimate the normal boiling points. The NVT-Gibbs ensemble method was used to simulate the pure-component coexistence of the vapour and liquid phases. The NPT-Gibbs ensemble was used to simulate the n-alkane binary mixtures. Two forms of configurational-bias Monte Carlo (standard CBMC and coupled-decoupled CBMC) were used to increase the number of swap moves accepted during the simulations. Dual-cutoff CBMC was implemented with a second cut-off of sA in order to speed up the CBMC calculations. Minimum image and a spherical potential truncation after 14A were implemented with standard tail corrections. BICMAC and TOWHEE were the two Fortran-77 codes used to simulate the hydrocarbon compounds. BICMAC was used in the simulations of non-polar molecules and TOWHEE was used in the simulations of polar molecules. System sizes ranged from 300 (for the CB'S) down to 100 molecules (for the Czo's). The simulations were typically equilibrated for at least 30000 cycles and production runs ranged from 50000 to 120000 cycles for the different hydrocarbon groups. Standard deviations of the calculated thermophysical properties were between 1-3% for the liquid densities and 10-20% for the vapour densities and vapour pressures. It was found that the coexistence density curves were generally in good agreement with experiment for all the hydrocarbon groups investigated (the OPL5-UA force field being the exception). The chain-length appeared to have littl e effect on the quality of the calculated thermophysical properties. The chain-length did however increase the time required to perform the simulations substantially. The va pour pressures were consistently over-predicted by NERD and TraPPE-UA. The normal boiling pOints were typically under-predicted by 2-5%. The critical tempe ratures and densities were predicted to within 1-5% of experimental values. The n-alkane mixtures were satisfactorily predicted using the NPT-Gibbs ensemble. While both the NERD and TraPPE-UA force fields were shown to be substantially more accurate compared to the OPLS-UA force field, there was little difference between their predictions. Thus, it is likely that the added complexity of using the bond-stretching potential (used by NERD) is unnecessary. The results of this study show that Monte Carlo simulation may be used to predict vapour-liquid coexistence properties of long-chain hydrocarbons and to approximate critical properties. However, current force fields require more refinement in ord er to accurately predict the hydrocarbon thermophysical properties. Plus, faster computing speeds are required before Monte Carlo simulation becomes an industrially viable method.Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.
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"Molecular simulation of vapour-liquid equilibrium using beowulf clusters." Thesis, 2010. http://hdl.handle.net/10413/1541.
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Düren, Tina. "Molecular modelling of equilibrium adsorption and transport diffusion in microporous solids /." 2002. http://www.gbv.de/dms/ilmenau/toc/35242303X.PDF.
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Liu, Cheng-Wei. "Computational studies of thermal and quantum phase transitions approached through non-equilibrium quenching." Thesis, 2015. https://hdl.handle.net/2144/15436.
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Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions.
The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process.
I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling.
For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system.
To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.
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Blaschke, Johannes Paul. "Entropic Motors." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0022-5E50-C.
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