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Proeme, Arno. "Nonequilibrium dynamical transition in the asymmetric exclusion process." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5286.
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Over the last few decades the interests of statistical physicists have broadened to include the detailed quantitative study of many systems - chemical, biological and even social - that were not traditionally part of the discipline. These systems can feature rich and complex spatiotemporal behaviour, often due to continued interaction with the environment and characterised by the dissipation of flows of energy and/or mass. This has led to vigorous research aimed at extending the established theoretical framework and adapting analytical methods that originate in the study of systems at thermodynamic equilibrium to deal with out-of-equilibrium situations, which are much more prevalent in nature. This thesis focuses on a microscopic model known as the asymmetric exclusion process, or ASEP, which describes the stochastic motion of particles on a one-dimensional lattice. Though in the first instance a model of a lattice gas, it is sufficiently general to have served as the basis to model a wide variety of phenomena. That, as well as substantial progress made in analysing its stationary behaviour, including the locations and nature of phase transitions, have led to it becoming a paradigmatic model of an exactly solvable nonequilibrium system. Recently an exact solution for the dynamics found a somewhat enigmatic transition, which has not been well understood. This thesis is an attempt to verify and better understand the nature of that dynamical transition, including its relation, if any, to the static phase transitions. I begin in Chapter 2 by reviewing known results for the ASEP, in particular the totally asymmetric variant (TASEP), driven at the boundaries. I present the exact dynamical transition as it was first derived, and a reduced description of the dynamics known as domain wall theory (DWT), which locates the transition at a different place. In Chapter 3, I investigate solutions of a nonlinear PDE that constitutes a mean-field, continuum approximation of the ASEP, namely the Burgers equation, and find that a similar dynamical transition occurs there at the same place as predicted by DWT but in disagreement with the exact result. Next, in Chapter 4 I report on efforts to observe and measure the dynamical transition through Monte Carlo simulation. No directly obvious physical manifestation of the transition was observed. The relaxation of three different observables was measured and found to agree well with each other but only slightly better with the exact transition than with DWT. In Chapter 5 I apply a numerical renormalisation scheme known as the Density Matrix Renormalisation Group (DMRG) method and find that it confirms the exact dynamical transition, ruling out the behaviour predicted by DWT. Finally in Chapter 6 I demonstrate that a perturbative calculation, involving the crossing of eigenvalues, allows us to rederive the location of the dynamical transition found exactly, thereby offering some insight into the nature of the transition.
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FOMINA, Margarita. "THE PHYSICAL ORIGIN OF PROTEIN DYNAMICAL TRANSITION: A LIQUID-LIQUID TRANSITION IN HYDRATION WATER?" Doctoral thesis, Università degli Studi di Palermo, 2015. http://hdl.handle.net/10447/106561.
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In this thesis I study, by means of neutron scattering, calorimetry, and dielectric spectroscopy, the physical origin of protein dynamical transition (PDT) which is usually observed at ~230 K in protein hydrated powders and is deemed necessary for protein function. Measurements reported in this thesis have been performed on hydrated powders of Myoglobin. The combined use of different experimental techniques gives a coherent description of the PDT and reveals a connection with a liquid-liquid crossover occurring in the protein hydration water at about the same temperature. In order to deepen our understanding of this connection and to obtain a direct experimental evidence of the existence of a liquid-liquid transition (LLT) in supercooled water at low temperatures, we investigated a second system, i.e. deeply cooled water confined within the pores of a 3-dimensional disordered SiO2 xerogel. In this system the hydrophilic surface of the matrix pores mimics the protein surface, while water confined within the pores mimics the protein hydration water. Using the same experimental techniques, we obtained evidence for the presence of a LLT, occurring at about 230 K, between a low density liquid (LDL) predominant at lower temperatures and a high density liquid predominant at higher temperatures. In conclusion, we suggest that the LLT in protein hydration shell is the physical origin of the biologically relevant protein dynamical transition.
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Mitchell, Radford. "Transition to turbulence and mixing in a quasi-two-dimensional Lorentz force-driven Kolmogorov flow." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/49045.
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The research in this thesis was motivated by a desire to understand the mixing properties of quasi-two-dimensional flows whose time-dependence arises naturally as a result of fluid-dynamic instabilities. Additionally, we wished to study how flows such as these transition from the laminar into the turbulent regime. This thesis presents a numerical and theoretical investigation of a particular fluid dynamical system introduced by Kolmogorov. It consists of a thin layer of electrolytic fluid that is driven by the interaction of a steady current with a magnetic field produced by an array of bar magnets.
First, we derive a theoretical model for the system by depth-averaging the Navier-Stokes equation, reducing it to a two-dimensional scalar evolution equation for the vertical component of vorticity. A code was then developed in order to both numerically simulate the fluid flow as well as to compute invariant solutions. As the strength of the driving force is increased, we find a number of steady, time-periodic, quasiperiodic, and chaotic flows as the fluid transitions into the turbulent regime.
Through long-time advection of a large number of passive tracers, the mixing properties of the various flows that we found were studied. Specifically, the mixing was quantified by computing the relative size of the mixed region as well as the mixing rate. We found the mixing efficiency of the flow to be a non-monotonic function of the driving current and that significant changes in the flow did not always lead to comparable changes in its transport properties. However, some very subtle changes in the flow dramatically altered the degree of mixing. Using the theory of chaos as it applies to Hamiltonian systems, we were able to explain many of our results.
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Park, Hyunhang. "Spin Systems far from Equilibrium: Aging and Dynamic Phase Transition." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/19323.
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Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems.
Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets.
We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions.Ph. D.
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Brown, Roger Keith. "Triangular proximity-coupled arrays : phase transition in a magnetic field and dynamical properties /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu148726282507655.
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Nájera, Ocampo Oscar. "Study of the dimer Hubbard Model within Dynamical Mean Field Theory and its application to VO₂." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS462/document.
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J'étudie en détail la solution d'un modèle simplifié d'électrons fortement corrélés, à savoir le modèle de Hubbard dimérisé. Ce modèle est la réalisation la plus simple d'un problème de cluster DMFT. Je fournis une description détaillée des solutions dans une région de coexistence où l'on trouve deux états (méta) stables des équations DMFT, l'un métallique et l'autre isolant. De plus, je décris en détail comment ces états disparaissent à leurs lignes critiques respectives. Je clarifie le rôle clé joué par la corrélation intra-dimère, qui agit ici en complément des corrélations de Coulomb.Je passe en revue la question importante du passage continue entre unisolant Mott et un isolant Peierls où je caractérise une variété de régimes physiques. Dans un subtil changement de la structure électronique, lesbandes de Hubbard évoluent des bandes purement incohérentes (Mott) à desbandes purement cohérentes (Peierls) à travers un état inattendu au caractère mixte. Je trouve une température d'appariement singulet T* en-dessous de laquelle les électrons localisés à chaque site atomique peuvent se lier dans un singulet et minimiser leur entropie. Ceci constitue un nouveau paradigme d'un isolant de Mott paramagnétique.Enfin, je discute la pertinence de mes résultats pour l'interprétation de différentes études expérimentales sur VO₂. Je présente plusieurs arguments qui me permettent d'avancer la conclusion que la phase métallique, à vie longue (métastable) induite dans les expériences pompe-sonde, et l'état métallique métastable M₁, thermiquement activé dans des nano-domaines, sont identiques. De plus, ils peuvent tous être qualitativement décrits, dans le cadre de notre modèle, par un métal corrélé dimériséWe study in detail the solution of a basic strongly correlated model,namely, the dimer Hubbard model. This model is the simplest realization ofa cluster DMFT problem.We provide a detailed description of the solutions in the ``coexistentregion'' where two (meta)stable states of the DMFT equations are found, onea metal and the other an insulator. Moreover, we describe in detail howthese states break down at their respective critical lines. We clarify thekey role played by the intra-dimer correlation, which here acts in additionto the onsite Coulomb correlations.We review the important issue of the Mott-Peierls insulator crossoverwhere we characterize a variety of physical regimes. In a subtle change inthe electronic structure the Hubbard bands evolve from purely incoherent(Mott) to purely coherent (Peierls) through a state with unexpected mixedcharacter. We find a singlet pairing temperature T* below which thelocalized electrons at each atomic site can bind into a singlet and quenchtheir entropy, this uncovers a new paradigm of a para-magnetic Mottinsulator.Finally, we discuss the relevance of our results for the interpretation ofvarious experimental studies in VO₂. We present a variety of argumentsthat allow us to advance the conclusion that the long-lived (meta-stable)metallic phase, induced in pump-probe experiments, and the thermallyactivated M₁ meta-stable metallic state in nano-domains are the same.In fact, they may all be qualitatively described by the dimerizedcorrelated metal state of our model
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Tan, Xiao. "Partitioning and Control for Dynamical Systems Evolving on Manifolds." Licentiate thesis, KTH, Reglerteknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-283672.
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With the development and integration of cyber-physical and safety-critical systems, control systems are expected to achieve tasks that include logic rules, receptive decision-making, safety constraints, and so forth. For example, in a persistent surveillance application, an unmanned aerial vehicle might be required to "take photos of areas A and B infinitely often, always avoid unsafe region C, and return to the charging point when the battery level goes low." One possible design approach to achieve such complex specifications is automata-based planning using formal verification algorithms. Central to the existing formal verification of continuous-time systems is the notion of abstraction, which consists of partitioning the state space into cells, and then formulating a certain control problem on each cell. The control problem is characterized as finding a state feedback to make all the closed-loop trajectories starting from one cell reach and enter a consecutive cell in finite time without intruding any other cells. This essentially abstracts the continuous system into a finite-state transition graph. The complex specifications can thus be checked against the simple transition model using formal verification tools, which yields a sequence of cells to visit consecutively. While control algorithms have been developed in the literature for linear systems associated with a polytopic partitioning of the state space, the partitioning and control problem for systems on a curved space is a relatively unexplored research area. In this thesis, we consider $ SO (3) $ and $ \ mathbb {S} ^ 2 $, the two most commonly encountered manifolds in mechanical systems, and propose several approaches to address the partitioning and control problem that in principle could be generalized to other manifolds. Chapter 2 proposes a discretization scheme that consists of sampling point generation and cell construction. Each cell is constructed as a ball region around a sampling point with an identical radius. Uniformity measures for the sampling points are proposed. As a result, the $SO(3)$ manifold is discretized into interconnected cells whose union covers the whole space. A graph model is naturally built up based on the cell adjacency relations. This discretization method, in general, can be extended to any Riemannian manifold. To enable the cell transitions, two reference trajectories are constructed corresponding to the cell-level plan. We demonstrate the results by solving a constrained attitude maneuvering problem with arbitrary obstacle shapes. It is shown that the algorithm finds a feasible trajectory as long as it exists at that discretization level. In Chapter 3, the 2-sphere manifold is considered and discretized into spherical polytopes, an analog of convex polytopes in the Euclidean space. Moreover, with the gnomonic projection, we show that the spherical polytopes can be naturally mapped into Euclidean polytopes and the dynamics on the manifold locally transform to a simple linear system via feedback linearization. Based on this transformation, the control problems then can be solved in the Euclidean space, where many control schemes exist with safe cell transition guarantee. This method serves as a special case that solves the partition-and-control problem by transforming the states and dynamics on manifold to Euclidean space in local charts. In Chapter 4, we propose a notion of high-order barrier functions for general control affine systems to guarantee set forward invariance by checking their higher order derivatives. This notion provides a unified framework to constrain the transient behavior of the closed-loop trajectories, which is essential in the cell-transition control design. The asymptotic stability of the forward invariant set is also proved, which is highly favorable for robustness with respect to model perturbations. We revisit the cell transition problem in Chapter 2 and show that even with a simple stabilizing nominal controller, the proposed high-order barrier function framework provides satisfactory transient performance.QC 20201012
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Kreilos, Tobias [Verfasser], and Bruno [Akademischer Betreuer] Eckhardt. "Turbulence Transition in Shear Flows and Dynamical Systems Theory / Tobias Kreilos. Betreuer: Bruno Eckhardt." Marburg : Philipps-Universität Marburg, 2014. http://d-nb.info/1052995128/34.
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Rusz, Ján, Shunsuke Muto, and Kazuyoshi Tatsumi. "Energy Loss by Channeled Electrons: A Quantitative Study on Transition Metal Oxides." Cambridge University Press, 2013. http://hdl.handle.net/2237/20834.
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Borrero, Daniel. "Subcritical Transition to Turbulence in Taylor-Couette Flow." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53140.
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Turbulence is ubiquitous in naturally-occurring and man-made flows. Despite its importance in scientific and engineering applications, the transition from smooth laminar flow to disorganized turbulent flow is poorly understood. In some cases, the transition can be understood in the context of linear stability theory, which predicts when the underlying laminar solution will become unstable as a parameter is varied. For a large class of flows, however, this approach fails spectacularly, with theory predicting that the laminar flow is stable but experiments and simulations showing the emergence of spatiotemporal complexity. In this dissertation, the direct or subcritical transition to turbulence in Taylor-Couette flow (i.e., the flow between independently rotating co-axial cylinders) is studied experimentally. Chapter 1 discusses different scenarios for the transition to turbulence and recent advances in understanding the subcritical transition within the framework of dynamical systems theory. Chapter 2 presents a comprehensive review of earlier investigations of linearly stable Taylor-Couette flow. Chapter 3 presents the first systematic study of long-lived super-transients in Taylor-Couette flow with the aim of determining the correct dynamical model for turbulent dynamics in the transitional regime. Chapter 4 presents the results of experiments regarding the stability of Taylor-Couette flow to finite-amplitude perturbations in the form of injection/suction of fluid from the test section. Chapter 5 presents numerical investigations of axisymmetric laminar states with realistic boundary conditions. Chapter 6 discusses in detail the implementation of time-resolved tomographic particle image
velocimetry (PIV) in the Taylor-Couette geometry and presents preliminary tomographic PIV measurements of the growth of turbulent spots from finite-amplitude perturbations. The main results are summarized in Chapter 7.
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Gong, Xue. "Dynamical Systems in Cell Division Cycle, Winnerless Competition Models, and Tensor Approximations." Ohio University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1458303716.
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Al-Sawai, Wael. "Non-equilibrium Phase Transitions in Interacting Diffusions." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7660.
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The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific analysis of each model individually. In this thesis, we propose a potential classification method for time-dependent dynamical systems, namely comparing the possible deformations of the original problem, and identifying dynamical systems which share the same deformation space. The specific model on which this procedure is developed is the Kuramoto model for interacting, disordered oscillators. Studied in the mean-field limit by a variety of methods, its associated synchronization phase transition appears as an appropriate model for cooperative phenomena ranging from coupled Josephson junctions to self-ordering patterns in biological and social systems. We investigate the geometric deformation of the dynamical system into the space of univalent maps of the unit disk, related to the Douady-Earle extension and the Denjoy-Wolff theory, and separately the algebraic deformation into the space of nonlinear sigma models for unitary operators. The results indicate that the Kuramoto model is representative for a large class of non-equilibrium synchronization models, with a rich phase-space diagram.
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Restrepo, Lopez Ricardo. "Topics in spatial and dynamical phase transitions of interacting particle systems." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42729.
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In this work we provide several improvements in the study of phase transitions
of interacting particle systems:
- We determine a quantitative relation between non-extremality of the limiting Gibbs measure of a tree-based spin system, and the temporal mixing of
the Glauber Dynamics over its finite projections. We define the concept of 'sensitivity' of a reconstruction scheme to establish such a relation. In particular, we focus on the independent sets model, determining a phase
transition for the mixing time of the Glauber dynamics at the same location of
the extremality threshold of the simple invariant Gibbs version of the model.
- We develop the technical analysis of the so-called spatial mixing conditions for interacting particle systems to account for the connectivity structure of the underlying graph. This analysis leads to improvements regarding the location of the uniqueness/non-uniqueness phase transition for the independent sets model over amenable graphs; among them, the elusive hard-square model in lattice statistics, which has received attention since Baxter's solution of the analogous hard-hexagon in 1980.
- We build on the work of Montanari and Gerschenfeld to determine the existence of correlations for the coloring model in sparse random graphs. In particular, we prove that correlations exist above the 'clustering' threshold of such a model; thus providing further evidence for the conjectural algorithmic 'hardness' occurring at such a point.
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Hiruta, Yoshiki. "Dynamics and subcritical transition focusing on spatially-localized turbulence in two-dimensional Kolmogorov flow." Kyoto University, 2019. http://hdl.handle.net/2433/242590.
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Khapko, Taras. "Transition to turbulence in the asymptotic suction boundary layer." Licentiate thesis, KTH, Stabilitet, Transition, Kontroll, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-141344.
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The focus of this thesis is on the numerical study of subcritical transition to turbulence in the asymptotic suction boundary layer (ASBL). Applying constant homogeneous suction prevents the spatial growth of the boundary layer, granting access to the asymptotic dynamics. This enables research approaches which are not feasible in the spatially growing case. In a first part, the laminar–turbulent separatrix of the ASBL is investigated numerically by means of an edge-tracking algorithm. The consideration of spanwise-extended domains allows for the robust localisation of the attracting flow structures on this separatrix. The active part of the identified edge states consists of a pair of low- and high-speed streaks, which experience calm phases followed by high energy bursts. During these bursts the structure is destroyed and re-created with a shift in the spanwise direction. Depending on the streamwise extent of the domain, these shifts are either regular in direction and distance, and periodic in time, or irregular in space and erratic in time. In all cases, the same clear regeneration mechanism of streaks and vor- tices is identified, bearing strong similarities with the classical self-sustaining cycle in near-wall turbulence. Bifurcations from periodic to chaotic regimes are studied by varying the streamwise length of the (periodic) domain. The resulting bifurcation diagram contains a number of phenomena, e.g. multistability, intermittency and period doubling, usually investigated in the context of low-dimensional systems. The second part is concerned with spatio–temporal aspects of turbulent ASBL in large domains near the onset of sustained turbulence. Adiabatically decreasing the Reynolds number, starting from a fully turbulent state, we study low-Re turbulence and events leading to laminarisation. Furthermore, a robust quantitative estimate for the lowest Reynolds number at which turbulence is sustained is obtained at Re QC 20140213
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Moles, Jordan. "On concentration inequalities for equilibrium states in lattice and symbolic dynamical systems." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX102.
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Cette étude traite de l'existence de concentration Gaussienne pour des états d'équilibre suffisamment mélangeant sur réseau. De plus, nous montrons qu'une telle condition assure l'unicité de ceux-ci.Dans le premier chapitre, nous montrons que si un état d'équilibre associé à un potentiel invariant par décalage et absolument sommable satisfait la concentration Gaussienne alors il est à fortiori mélangeant et unique i.e. il ne peut y avoir transition de phase.Par la suite, nous étudions numériquement un modèle physique particulier autorisant une transition de phase à savoir le modèle d'Ising ferromagnétique en dimension deux. Nous évaluons les constantes de la concentration grâce à la simulation d'observables classiques à toute température. Grâce au comportement de ces paramètres, nous mettons spécialement en lumière la divergence de la constante de concentration Gaussienne à la température critique et nous en déduisons qu'une telle propriété ne peut exister.Puis, nous prouvons que l'existence de la concentration Gaussienne est satisfaite pour toute température supérieure à la température critique pour ce modèle.Ensuite, nous étudions un système dynamique symbolique unidimensionnel sur un alphabet fini: les chaînes à liaisons complètes. Nous étudions en particulier les propriétés de concentration de l'unique état d'équilibre associé à un potentiel (ou probabilité de transition) satisfaisant la condition de Walters.Enfin, nous traitons le régime de haut bruit pour des automates cellulaires probabilistes. Nous prouvons notamment que dans ce régime, ils satisfont la concentration Gaussienne pour une certaine classe d'observables spatio-temporellesThis thesis deals with the existence of Gaussian concentration for sufficiently mixing equilibrium states for lattice systems. Moreover, we show that such a property ensures uniqueness.In the first chapter, we show that if an equilibrium state associated to a shift-invariant and absolutely summable potential satisfies a Gaussian concentration bound then it is à fortiori mixing and unique em i.e. there is no phase transition.Thereafter, We study numerically a particular physical model which allows phase transition to occur: the ferromagnetic Ising model in two dimensions. We evaluate concentration constants through classical estimates at all temperature. Thank to the behavior of these parameters, we emphasize divergence of the Gaussian concentration constant at the critical temperature deduce that such property doesn't hold.Later on, we prove that the Gaussian concentration behavior holds for all temperature above the critical one for this model.Then, we dedicate a chapter to the study of an unidimensional symbolic dynamics on a finite alphabet: chains with complete connections. In particular, we study the concentration properties of a unique equilibrium state associated to a potential (or transition probability) satisfying Walters' condition.In the end, we review the high-noise regime in probabilistic cellular automata. In particular, we prove that in this regime, the probabilistic cellular automata satisfies a Gaussian concentration for a certain class of spatio-temporal observables
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Masurel, Robin. "Role des hétérogénéités dynamiques dans la mécanique des polymères amorphes : modélisation et simulations par éléments finis." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066001.
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Les polymères amorphes présentent des hétérogénéités dynamiques à l'échelle de 3 à 5nm proche de la température de transition vitreuse. Leur contribution aux propriétés mécaniques est encore mal connue. Pour ce faire, nous considérons un modèle simple dans lequel chaque hétérogénéité dynamique possède un unique temps de relaxation distribué aléatoirement selon une loi log-normale. Un modèle coarse-grained à l’échelle d’une hétérogénéité dynamique est alors développé dans le cadre de l'approximation des milieux continus. Ainsi, des simulations par éléments finis nous permettent de calculer les propriétés mécaniques macroscopiques des polymères en tenant compte des effets de couplage mécaniques en hétérogénéités. Nous montrons que la transition vitreuse est pilotée par un réseau de percolation des domaines lents. Nous mettons également en évidence les couplages mécaniques intervenant entre hétérogénéités dynamiques. Dans le cas des films minces de polymères confinés à l’échelle de quelques dizaines de nanomètres, nous montrons que les hétérogénéités dynamiques permettent de rendre compte d’un ralentissement de la dynamique macroscopique du film. En considérant que pour de fortes contraintes, la dynamique locale des polymères massifs est accélérée, nous démontrons que les hétérogénéités dynamiques permettent de rendre compte d’un phénomène de contrainte interne à un système, celle-ci étant la cause d’une partie non récupérable de l’énergie élastique stockée un système lors d’une déformation plastiqueAmorphous polymers present dynamical heterogeneities at the scale of 3 to 5nm near Tg. Their contributions to mechanical properties are still not well known. We thus consider a simple model where each dynamical heterogeneities has its own relaxation time randomly drawn is a log-normal time distribution. A coarse –grained model at the dynamical heterogeneity is then developed in the continuous medium approximation. Finite element simulations are performed to calculate macroscopic mechanical properties of amorphous polymers taking account of mechanical couplings between heterogeneities. We show that the glass transition is controlled by a percolation of slow domains. Mechanical couplings result in viscoelastic spectrum highly narrowed as compared to the microscopic one. In thin films of polymers, we evidence a slowdown of the dynamics of relaxation as compared to the bulk one. Considering that a high applied stress increase the dynamics of polymers, we show that dynamical heterogeneities result in an internal stress network. The latter is a consequence a plastic deformation and result in an internal energy which is not released after an unloading
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Griffith, Daniel Todd. "New methods for estimation, modeling and validation of dynamical systems using automatic differentiation." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1408.
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The main objective of this work is to demonstrate some new computational methods
for estimation, optimization and modeling of dynamical systems that use automatic
differentiation. Particular focus will be upon dynamical systems arising in Aerospace
Engineering. Automatic differentiation is a recursive computational algorithm, which
enables computation of analytically rigorous partial derivatives of any user-specified
function. All associated computations occur, in the background without user
intervention, as the name implies. The computational methods of this dissertation are
enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate
Embedding Method). OCEA has been recently developed and makes possible efficient
computation and evaluation of partial derivatives with minimal user coding. The key
results in this dissertation details the use of OCEA through a number of computational
studies in estimation and dynamical modeling.
Several prototype problems are studied in order to evaluate judicious ways to use
OCEA. Additionally, new solution methods are introduced in order to ascertain the
extended capability of this new computational tool. Computational tradeoffs are studied
in detail by looking at a number of different applications in the areas of estimation,
dynamical system modeling, and validation of solution accuracy for complex dynamical
systems. The results of these computational studies provide new insights and indicate
the future potential of OCEA in its further development.
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Vieira, Ewerton Rocha 1987. "Transition matrix theory = Teoria da matriz de transição." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307536.
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Orientador: Ketty Abaroa de RezendeTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Nessa tese, apresentamos uma unificação da teoria das matrizes de transição algébrica, singular, topológica e direcional ao introduzir a matriz de transição (generalizada), a qual engloba todas as quatros citadas anteriormente. Alguns resultados de existência são apresentados bem como a verificação de que cada matriz de transição supracitada são casos particulares da matriz de transição (generalizada). Além disso, nós abordamos como as aplicações das quatros matrizes de transiçao, na teoria do índice de Conley, se traduzem para a matriz de transição (generalizada). Quando a matriz de transição (generalizada) satisfizer o requerimento adicional de cobrir o isomorfismo do índice de Conley F definido pelo fluxo, pode-se provar propriedades de existência e de conexão de órbitas. Essa matriz de transição com a propriedade de cobrir o isomorfismo F é definida como matriz de transição topológica generalizada e a utilizamos para obter conexões de órbitas num fluxo Morse-Smale sem órbitas periódicas bem como para obter conexões de órbitas numa continuação associada à sequência espectral dinâmica
Abstract: In this thesis, we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition matrix existence results are presented as well as the verification that each of the previous transition matrices are cases of the (generalized) transition matrix. Furthermore, we address how applications of the previous transition matrices to the Conley Index theory carry over to the (generalized) transition matrix. When this more general transition matrix satisfies the additional requirement that it covers flow-defined Conley-index isomorphisms, one proves algebraic and connection-existence properties. These general transition matrices with this covering property are referred to as generalized topological transition matrices and are used to consider connecting orbits of Morse-Smale flows without periodic orbits, as well as those in a continuation associated to a dynamical spectral sequence
Doutorado
Matematica
Doutor em Matemática
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Zhoroev, Tilekbek. "Controllability and Observability of Linear Nabla Discrete Fractional Systems." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3156.
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The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we study the controllability and observability of time-invariant linear nabla fractional systems.We investigate the time-variant case in Chapter 5 and we define the state transition matrix in fractional calculus. In the last chapter, the results are summarized and directions for future work are stated.
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Wesp, Christian [Verfasser], Carsten [Akademischer Betreuer] Greiner, and Jürgen [Akademischer Betreuer] Schaffner-Bielich. "Dynamical simulation of a linear sigma model near the chiral phase transition / Christian Wesp. Gutachter: Carsten Greiner ; Jürgen Schaffner-Bielich." Frankfurt am Main : Univ.-Bibliothek Frankfurt am Main, 2015. http://d-nb.info/1079362495/34.
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van, Rooij Marieke M. J. W. "What Changes When We Change Our Decision Strategy? A Dynamical Account of Transitions between Risk-averse and Risk-seeking Choice Behavior." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1382951052.
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Farano, Mirko. "Using nonlinear optimization to understand coherent structures in turbulence and transition." Thesis, Paris, ENSAM, 2017. http://www.theses.fr/2017ENAM0047/document.
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Cette thèse vise à démêler les principaux mécanismes impliqués dans les écoulements transitoires et turbulents. L’idée centrale est d'utiliser une technique d’optimisation non linéaire pour étudier l’origine et le rôle des structures cohérentes habituellement observées dans ces écoulements. Cette méthode a été utilisée dans trois contextes différents. Tout d’abord, un écoulement laminaire linéairement stable a été considéré et l'optimisation a été utilisée pour calculer les perturbations les plus amplifiées parmi toutes les perturbations capables de déclencher une transition vers la turbulence. Une fois que la turbulence est bien établie, une optimisation non linéaire entièrement 3D maximisant l'énergie cinétique turbulente est utilisée pour étudier les structures cohérentes qui peuplent l’écoulement turbulent et les mécanismes responsables de la croissance et de l’échange d’énergie (optimale) sont étudiés. Ensuite, une approche de type système dynamique est appliquée aux équations du mouvement. La géométrie de l’espace des phases est étudiée en utilisant la théorie de la croissance transitoire pour évaluer l’importance des variétés stable et instable dans la dynamique. Dans le même cadre, un algorithme de minimisation non linéaire est utilisé pour calculer les connexions hétérocliniques parmi les solutions invariantes des équations de Navier-StokesThis thesis aims at unraveling the main mechanisms involved in transitional and turbulent flows. The central idea is that of using a nonlinear optimization technique to investigate the origin and role of coherent structures usually observed in these flows. This method has been used in three different contexts. First, a linearly stable laminar flow has been considered and the optimization has been used to compute the most amplified perturbations among all disturbances able to trigger transition to turbulence. Once turbulence is well established, a fully 3D nonlinear optimization maximizing the turbulent kinetic energy is used to study coherent structures populating turbulent shear flow as well as investigate the mechanisms responsible for the energy (optimally) growth and exchange. Then, a dynamical system approach is applied to fluid flow equations. The geometry of the state space is investigated by using transient growth theory to reveal the importance of the stable and unstable manifold. In the same framework, a nonlinear minimization algorithm is used to compute heteroclinic connections among invariant solutions of the Navier-Stokes equations
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Conte, Riccardo. "A dynamical approach to the calculation of thermal reaction rate constants." Doctoral thesis, Scuola Normale Superiore, 2008. http://hdl.handle.net/11384/85794.
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Ruscher, Céline. "The Voronoi liquid : a new model to probe the glass transition." Thesis, Strasbourg, 2017. http://www.theses.fr/2017STRAE027/document.
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Comprendre l’origine microscopique du ralentissement de la dynamique au voisinage de la transition vitreuse reste l’un des problèmes fondamentaux de la physique de la matière condensée. Au cours de ce travail, nous introduisons un nouveau modèle de liquide, appelé liquide de Voronoï, et dont les interactions sont directement reliées aux propriétés géométriques des tessellations de Voronoï. Pour cette classe de liquides, les interactions sont à plusieurs corps et agissent de telle sorte que le système est toujours sous tension tout en restant stable. Le but de ce travail est d’étudier un mélange binaire du liquide de Voronoï et de voir de quelles façons ces interactions exotiques affectent le scénario habituel de la transition vitreuse. Tout au long de ce travail, nous caractérisons le liquide de Voronoï bidisperse théoriquement et par le biais des simulations numériques. Nous proposons également des comparaisons avec des liquides de Lennard-Jones surfondus bien décrit dans la littératureUnderstanding the origin of the important slowing down of the dynamics near glass transition is still one of the remaining fundamental problems of condensed matter physics. During this work we introduced a brand-new model of liquids named Voronoi liquid, whose interactions are directly related to the geometrical properties of Voronoi tessellations. For these class of liquids interactions are intrinsically manybody and act in such a way that the liquid is always under tension but remains stable. The aim of this work is to use a binary mixture of the Voronoi liquid to see to what extend these exotic interactions may affect the classical scenario of glass transition. Throughout this work we characterize theoretically and by mean of numerical simulation the bidisperse Voronoi liquid. Comparisons with well-known Lennard-Jones glass formers are systematically performed
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Sayer, Ryan Thomas. "Quantum Dynamics Using Lie Algebras, with Explorations in the Chaotic Behavior of Oscillators." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3285.
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We study the time evolution of driven quantum systems using analytic, algebraic, and numerical methods. First, we obtain analytic solutions for driven free and oscillator systems by shifting the coordinate and phase of the undriven wave function. We also factorize the quantum evolution operator using the generators of the Lie algebra comprising the Hamiltonian. We obtain coupled ODE's for the time evolution of the Lie algebra parameters. These parameters allow us to find physical properties of oscillator dynamics. In particular we find phase-space trajectories and transition probabilities. We then search for chaotic behavior in the Lie algebra parameters as a signature for dynamical chaos in the quantum system. We plot the trajectories, transition probabilities, and Lyapunov exponents for a wide range of the following physical parameters: strength and duration of the driving force, frequency difference, and anharmonicity of the oscillator. We identify conditions for the appearance of chaos in the system.
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SANGIOVANNI, GIORGIO. "The electron-phonon interaction in strongly correlated electron systems." Doctoral thesis, La Sapienza, 2004. http://hdl.handle.net/11573/917137.
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Landes, François. "Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112171/document.
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De nombreux systèmes complexes soumis à un ajout continu d'énergie réagissent à cet ajout par une accumulation de tension au cours du temps, interrompue par de soudaines libérations d'énergie appelées avalanches. Récemment, il a été remarqué que plusieurs propriétés élémentaires de la dynamique d'avalanche sont issues de processus de relaxation ayant lieu à une échelle microscopique, processus qui sont négligés dans la plupart des modèles. Lors de ma thèse, j'ai étudié deux modèles classiques d'avalanches, modifiés par l'ajout d'une forme de relaxation la plus simple possible. Le premier système est une interface viscoélastique tirée à travers un milieu désordonné. En champ moyen, nous prouvons que l'interface a un comportement périodique caractérisé par une nouvelle échelle temporelle (émergente), avec des avalanches qui touchent l'ensemble du système. Le calcul semi-analytique de la force de friction agissant sur la surface donne des résultats compatibles avec les expériences de friction classique. En dimension finie (2D), les événements touchant l'ensemble du système (trouvés en champ moyen) deviennent localisés, et les simulations numériques donnent des résultats en bon accord avec plusieurs caractéristiques importantes des tremblements de terre, tant qualitativement que quantitativement. Le second système incluant également une forme très simple de relaxation est un modèle jouet d'avalanche : c'est la percolation dirigée. Dans notre étude d'une variante non-markovienne de la percolation dirigée, nous avons observé que la classe d'universalité était modifiée mais seulement partiellement. En particulier, un exposant change de valeur tandis que plusieurs relations d'échelle sont préservées. Cette idée d'une classe d'universalité étendue, obtenue par l'ajout d'une perturbation non-markovienne offre des perspectives prometteuses pour notre premier systèmeMany complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche dynamics are induced at the microscopic level by relaxation processes, which are neglected by most models. During my thesis, I studied two well-known models of avalanche dynamics, modified minimally by the inclusion of some forms of relaxation. The first system is that of a viscoelastic interface driven in a disordered medium. In mean-field, we prove that the interface has a periodic behaviour (with a new, emerging time scale), with avalanche events that span the whole system. We compute semi-analytically the friction force acting on this surface, and find that it is compatible with classical friction experiments. In finite dimensions (2D), the mean-field system-sized events become local, and numerical simulations give qualitative and quantitative results in good agreement with several important features of real earthquakes. The second system including a minimal form of relaxation consists in a toy model of avalanches: the Directed Percolation process. In our study of a non-Markovian variant of Directed Percolation, we observed that the universality class was modified but not completely. In particular, in the non-Markov case an exponent changes of value while several scaling relations still hold. This picture of an extended universality class obtained by the addition of a non-Markovian perturbation to the dynamics provides promising prospects for our first system
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Holzer, Jenny Rebecca. "Scanning SQUID Microscope Measurements on Josephson Junction Arrays." University of Cincinnati / OhioLINK, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=ucin973710069.
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Vanneuville, Hugo. "Percolation dans le plan : dynamiques, pavages aléatoires et lignes nodales." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1262/document.
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Dans cette thèse, nous étudions trois modèles de percolation planaire : la percolation de Bernoulli, la percolation de Voronoi, et la percolation de lignes nodales. La percolation de Bernoulli est souvent considérée comme le modèle le plus simple à définir admettant une transition de phase. La percolation de Voronoi est quant à elle un modèle de percolation de Bernoulli en environnement aléatoire. La percolation de lignes nodales est un modèle de percolation de lignes de niveaux de champs gaussiens lisses. Deux fils conducteurs principaux ont guidé nos travaux. Le premier est la recherche de similarités entre ces modèles, en ayant à l'esprit que l'on s'attend à ce qu'ils admettent tous la même limite d'échelle. Nous montrons par exemple que le niveau critique de la percolation de lignes nodales est égal au niveau auto-dual (à savoir le niveau zéro) lorsque le champ considéré est le champ de Bargmann-Fock, qui est un champ gaussien analytique naturel. Le deuxième fil conducteur est l'étude de dynamiques sur ces modèles. Nous montrons en particulier que, si on considère un modèle de percolation de Voronoi critique et si on laisse les points se déplacer selon des processus de Lévy stables à très longue portée, alors il existe des temps exceptionnels avec une composante non bornéeWe study three models of percolation in the plane: Bernoulli percolation, Voronoi percolation, and nodal lines percolation. Bernoulli percolation is often considered as the simplest model which admits a phase transition. Voronoi percolation is a Bernoulli percolation model in random environment. Nodal lines percolation is a level lines percolation model for smooth planar Gaussian fields. We have followed two main threads. The first one is the resarch of similarities between these models, having in mind that we expect that they admit the same scaling limit. We show for instance that the critical level for nodal lines percolation is the self-dual level (namely the zero level) if the Gaussian field is the Bargmann-Fock field, which is natural analytical field. The second main thread is the study of dynamics on these percolation models. We show in particular that if we sample a critical Voronoi percolation model and if we let each point move according to a long range stable Lévy process, then there exist exceptional times with an unbounded cluster
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Thompson, Ian. "Dynamic phase transitions in biased ensembles of particle systems with repulsive interactions." Thesis, University of Bath, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.665407.
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We study dynamic phase transitions in the constant-volume and constant- pressure ensembles of two different systems: a one-dimensional system of diffusive hard particles and a three-dimensional glass-former of nearly-hard repulsive particles. The dynamic transitions are observed using ensembles of trajectories biased with respect to their dynamic activity, biasing to greater or lower activities than equilibrium allows us to sample different dynamic phases. We perform finite-size scaling of the transitions with respect to sys- tem size and observation time, and compare them to first-order phase tran- sitions. The two ensembles are not equivalent in the one-dimensional model. We compare our results to analytic predictions for diffusive systems in both the active and inactive phases, there are structural signatures for both dy- namic regimes. The active phases show hyperuniform ordering and the inac- tive regimes show jamming behaviour, local jamming in the constant-volume ensemble is achieved through phase separation. In the three-dimensional sys- tem we observe a dynamic transition to a glassy inactive phase, there is no obvious structural change and the structural relaxation time increases sig- nificantly. We take configurations from the active and inactive phases and subject them to a jamming protocol in order to compare the final density of the jammed packings. Previous work shows that the inactive phase of glass-forming systems have a different distribution of vibrational modes and a higher compressibility, this suggests that the jamming behaviour should differ between the two phases. We show that jammed packings generated from inactive configurations are denser than those generated from active configurations.
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Delange, Pascal. "Many-electron effects in transition metal and rare earth compounds : Electronic structure, magnetic properties and point defects from first principles." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX040/document.
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Le sujet de cette thèse est la théorie à partir des premiers principes de la structure électronique de matériaux présentant de fortes corrélations électroniques. D’importants progrès ont été faits dans ce domaine grâce aux implémentations modernes de Théorie de la Fonctionelle de Densité (DFT). Néanmoins, la méthode DFT a certaines limitations. D’une part, elle est faite pour décrire les propriétés de l’état fondamental mais pas des états excités des matériaux, bien que ces derniers soient également importants. D’autre part, les approximations de la fonctionnelle employées en pratique réduisent la validité de la DFT, conceptuellement exacte : en particulier elles décrivent mal les matériaux aux effets de corrélations les plus importants.Depuis les années 1990, différentes théoriques quantiques à N corps ont été utilisées pour améliorer ou compléter les simulations à base de DFT. Une des plus importantes est la Théorie du Champ Moyen Dynamique (DMFT), dans laquelle un modèle sur réseau est relié de manière auto-cohérente à un modèle plus simple d’impureté, ce qui donne de bons résultats à condition que les corrélations soient principalement locales. Nous présentons brièvement ces théories dans la première partie de cette thèse. Les progrès récents de la DMFT visent, entre autres, à mieux décrire les effets non-locaux, à comprendre les propriétés hors équilibre et à décrire de vrais matériaux plutôt que des modèles.Afin d’utiliser la DMFT pour décrire de vrais matériaux, il faut partir d’un calcul de structure électronique traitant tous les électrons au même niveau, puis appliquer une correction traitant les effets à N corps sur un sous-espace de basse énergie d’orbitales autour niveau de Fermi. La définition cohérente d’un tel sous-espace nécessite de tenir compte de la dynamique des électrons en-dehors de cet espace. Ces derniers, par exemple, réduisent la répulsion de Coulomb entre électrons dans le sous-espace. Néanmoins, combiner la DFT et la DMFT n’est pas aisé car les deux n’agissent pas sur la même observable. Dans la deuxième partie de cette thèse, nous étudions les modèles de basses énergies, comme la technique échange écranté + DMFT récemment proposée. Nous analysons l’importance de l’échange non-local et des interactions de Coulomb retardées, et illustrons cette théorie en l’appliquant aux états semi-cœur dans les métaux d10 Zn et Cd.Dans la dernière partie, nous utilisons ces méthodes pour étudier trois matériaux corrélés importants d’un point de vue technologique. Dans un premier temps, nous nous intéressons à la physique des mono-lacunes dans la phase paramagnétique du fer. De façon surprenante pour un défaut aussi simple, son énergie de formation n’a toujours pas été obtenue de manière cohérente par la théorie et l’expérience. Nous démontrons que cela est dû à de subtils effets de corrélations autour de la lacune dans la phase paramagnétique à haute température : cette phase est plus fortement corrélée que la phase ferromagnétique, où des calculs de DFT ont été faits.Dans un deuxième temps, nous étudions la transition métal-isolant dans la phase métastable VO2 B. Nous montrons que cette transition ressemble à celle entre la phase conventionnelle rutile et la phase M2 de VO2, mettant en jeu à la fois des liaisons covalentes dans les dimères et une transition de Mott sur les atomes V restants. Nous étudions également l’effet de lacunes d’oxygène sur la structure électronique de VO2.Enfin, nous proposons une technique au-delà de la DFT pour calculer le champ cristallin dans les oxydes et alliages de terres rares. Bien que l’amplitude de ce champ soit faible pour les orbitales localisées 4f des lanthanides, il est crucial pour leur caractère d’aimant permanent. En modifiant l’approximation Hubbard I pour résoudre les équations de DMFT, nous évitons une erreur d’auto-interaction faible en valeur absolue mais physiquement importante, démontrant l’importance de modèles de basse énergie correctement définisThe topic of this thesis is the first-principles theory of the electronic structure of materials with strong electronic correlations. Tremendous progress has been made in this field thanks to modern implementations of Density Functional Theory (DFT). However, the DFT framework has some limits. First, it is designed to predict ground state but not excited state properties of materials, even though the latter may be just as important for many applications. Second, the approximate functionals used in actual calculations have more limited validity than conceptually exact DFT: in particular, they are not able to describe those materials where many-electron effects are most important.Since the 1990's, different many-body theories have been used to improve or complement DFT calculations of materials. One of the most significant non-perturbative methods is Dynamical Mean-Field Theory (DMFT), where a lattice model is self-consistently mapped onto an impurity model, producing good results if correlations are mostly local. We briefly review these methods in the first part of this thesis. Recent developments on DMFT and its extensions were aimed at better describing non-local effects, understanding out-of-equilibrium properties or describing real materials rather than model systems, among others. Here, we focus on the latter aspect.In order to describe real materials with DMFT, one typically needs to start with an electronic structure calculation that treats all the electrons of the system on the same footing, and apply a many-body correction on a well-chosen subspace of orbitals near the Fermi level. Defining such a low-energy subspace consistently requires to integrate out the motion of the electrons outside this subspace. Taking this into account correctly is crucial: it is, for instance, the screening by electrons outside the subspace strongly reduces the Coulomb interaction between electrons within the subspace. Yet it is a complex task, not least because DFT and DMFT are working on different observables. In the second part of this thesis, we discuss low-energy models in the context of the recently proposed Screened Exchange + DMFT scheme. In particular, we study the importance of non-local exchange and dynamically-screened Coulomb interactions. We illustrate this by discussing semi-core states in the d10 metals Zn and Cd.In the third and last part, we use the methods described above to study the electronic structure of three fundamentally and technologically important correlated materials. First, we discuss the physics of point defects in the paramagnetic phase of bcc Fe, more precisely the simplest of them: the monovacancy. Surprisingly for such a simple point defect, its formation energy had not yet been reported consistently from calculations and experiments. We show that this is due to subtle but nevertheless important correlation effects around the vacancy in the high-temperature paramagnetic phase, which is significantly more strongly correlated than the ferromagnetic phase where DFT calculations had been done.Second, we study the metal-insulator phase transition in the metastable VO2 B phase. We show that this transition is similar to that between the conventional rutile and M2 VO2 phases, involving both bonding physics in the dimer and an atom-selective Mott transition on the remaining V atoms. Motivated by recent calculations on SrVO3, we study the possible effect of oxygen vacancies on the electronic structure of VO2.Finally, we propose a scheme beyond DFT for calculating the crystal field splittings in rare earth intermetallics or oxides. While the magnitude of this splitting for the localized 4f shell of lanthanides does not typically exceed a few hundred Kelvin, it is crucial for their hard-magnetic properties. Using a modified Hubbard I approximation as DMFT solver, we avoid a nominally small but important self-interaction error, stressing again the importance of carefully tailored low-energy models
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Fujiwara, Naoya. "Dynamic phase transition and pattern dynamics in periodic external fields." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/135964.
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Souvatzis, Petros. "Electronic Structure and Lattice Dynamics of Elements and Compounds." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8198.
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Suárez, Villagrán Martha Yolima 1984. "Estudos do modelo de Hubbard desordenado em duas dimensões." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276990.
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Orientador: Eduardo MirandaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: Estudamos nesta tese alguns aspectos da transição metal-isolante de Mott no caso desordenado. O modelo no qual baseamos nosso estudo é o modelo de Hubbard desordenado, que é o modelo mais simples a apresentar a transição metal-isolante de Mott. Analisamos esse modelo através da Teoria Dinâmica de Campo Médio Estatística (StatDMFT). Essa teoria é uma extensão natural da Teoria Dinâmica de Campo Médio (DMFT), que foi usada com relativo sucesso nos últimos anos para analisar a transição de Mott no caso limpo. Como no caso dessa última, a StatDMFT incorpora os efeitos de correlação eletrônica apenas nos seus aspetos locais. A desordem é tratada de maneira a incorporar todos os efeitos de localização de Anderson. Com essa técnica, analisamos a transição de Mott desordenada no caso bi-dimensional, usando o Monte Carlo quântico para resolver os problemas de impureza única de Anderson requeridos pela StatDMFT. Encontramos as linhas espinodais nas quais o metal e o isolante deixam de ser meta-estáveis. Também estudamos os padrões espaciais das flutuações de quantidades locais, como a auto-energia e a função de Green local, e mostramos como há o aparecimento de regiões metálicas dentro do isolante e viceversa. Analisamos efeitos de tamanho finito e mostramos que, em consonância com os teoremas de Imry e Ma, a transição de primeira ordem desaparece no limite termodinâmico. Analisamos as propriedades de transporte desse sistema através de um mapeamento a um sistema de resistores aleatórios clássicos e calculamos a corrente média e sua distribuição através da transição metal-isolante. Finalmente, estudamos o comportamento da parede de domínio que se forma entre o isolante e o metal no caso limpo. Isso foi feito através de um modelo de uma cadeia unidimensional conectada a reservatórios, um metálico e um isolante, cada um em uma de suas extremidades. Nesse caso, utilizamos o método da Teoria de Perturbação Iterada para a solução dos modelos de impureza única. Encontramos o comportamento da parede como função da temperatura e das interações
Abstract: In this thesis, we studied some aspects of the Mott metal-insulator transition in the disordered case. The model on which we based our analysis is the disordered Hubbard model, which is the simplest model capable of capturing the Mott metal-insulator transition. We investigated this model through the Statistical Dynamical Mean-Field Theory (statDMFT). This theory is a natural extension of the Dynamical Mean-Field Theory (DMFT), which has been used with relative success in the last several years with the purpose of describing the Mott transition in the clean case. As is the case for the latter theory, the statDMFT incorporates the electronic correlation effects only incorporate Anderson localization effects.. With this technique, we analyzed the disordered two-dimensional Mott transition, using Quantum Monte Carlo to solve the associated single-impurity problems. We found the spinodal lines at which metal and insulator cease to be meta-stable. We also studied the spatial fluctuations of local quantities, such as the self-energy and the local Green¿s function, and showed the appearance of metallic regions within the insulator and vice-versa. We carried out an analysis of finite-size effects and showed that, in agreement with the theorems of Imry and Ma, the first-order transition is smeared in the thermodynamic limit. We analyzed transport properties by means of a mapping to a random classical resistor network and calculated both the average current and its distribution across the metalinsulator transition. Finally, we studied the behavior of the domain wall which forms between the metal and the insulator in the clean case. This was done by means of a model of a one-dimensional chain connected to two reservoirs, one metallic and the other insulating, each attached to one of the chain¿s ends. In this case, we used the Iterated Perturbation Theory technique in order to solve the associated singleimpurity problems. We then established the behavior of the domain wall width as a function of temperature and interactions
Doutorado
Física
Doutora em Ciências
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Benzid, Khalif. "Etude de l'effet de l'anisotropie magnétique sur la phase dynamique et sur la phase géométrique des bits quantiques de spins électroniques d'ions de métaux de transition Mn2+, Co2+, Fe3+ isolés et des complexes d'ions Fe3+ dans l'oxyde de zinc monocristallin." Thesis, Strasbourg, 2016. http://www.theses.fr/2016STRAE009/document.
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Nous avons étudié, par RPE impulsionnelle, la cohérence quantique et des spins électroniques des ions de transition Mn2+, Co2+, Fe3+, et des complexes Fe3+/Cs+ et Fe3+/Na+, tous présents dans le ZnO monocristallin. Nous avons trouvé que l’anisotropie magnétique peut altérer la cohérence de la phase dynamique des qubits des spins électroniques. Nous avons mesuré une faible décohérence pour les spins d’ions Mn2+et Fe3+ dans ZnO, qui ont tous deux une faible anisotropie magnétique uniaxiale, tandis que les ions Co2+ isolés avec une très forte anisotropie magnétique uniaxiale, une décohérence rapide a été mis en évidence. Nous avons trouvé que les spins électroniques des complexes de type Fe3+/Cs+, ayant un tenseur d’anisotropie magnétique plus complexe que la simple anisotropie uniaxiale des ions Fe3+ isolés, possèdent presque le même temps de décohérence. Par la méthode des perturbations, nous avons mis en évidence théoriquement un terme supplémentaire à la phase habituelle de Berry, dû à l’anisotropie magnétique et qui existe dans tout système ayant un spin S>1/2We studied by pulsed EPR (p-EPR), the quantum coherence of electronic spins qubits of isolated transition metal ions of Mn2+, Co2+, Fe3+ and Fe3+/Cs+ as well as Fe3+/Na+ complexes, all found as traces in mono-crystalline ZnO. Indeed, we experimentally demonstrated that the magnetic anisotropy can alter the coherence of the dynamic phase of electronic spins qubits. We found a small decoherence for Mn2+ and Fe3+, spins having a small uniaxial magnetic anisotropy, and on the contrary, we found a very strong decoherence for Co2+ spins having a very strong uniaxial magnetic anisotropy. We found that the electronic spins of the Fe3+/Cs+ complex, having a more complex tensor magnetic anisotropy compared to the simplest uniaxial one of isolated Fe3+ spins in ZnO, have almost the same coherence time. By the perturbation method, we have found theoretically an additional term to the usual geometric Berry phase, due to the magnetic anisotropy which exists in any system having a spin S>1/2
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Rojas, Molina Constanza. "Etude mathématique des propriétés de transport des opérateurs de Schrödigner aléatoires avec structure quasi-cristalline." Thesis, Cergy-Pontoise, 2012. http://www.theses.fr/2012CERG0565/document.
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Cette thèse est consacrée à l'étude du transport électronique dans des modèles désordonnés non ergodiques, dans le cadre de la théorie des opérateurs de Schrödinger aléatoires.Pour commencer, nous reformulons l'outil principal pour notre étude, l'analyse multi-échelles, dans le cadre non ergodique. Nous établissons les conditions d'homogénéité que l'opérateur doit vérifier pour appliquer cette méthode. Ensuite, nous étudions les propriétés spectrales des opérateurs de Delone-Anderson non ergodiques. Ces systèmes modélisent l'énergie d'une particule en interaction avec un milieu dont la structure atomique est quasi-cristalline et la nature des impuretés est désordonnée. Dans le cas où les mesures de probabilité associées au potentiel de simple site sont régulières, en dimension 2 et sous l'effet d'un champ magnétique, nous établissons une transition métal-isolant et l'existence d'une énergie de mobilité qui sépare les régions de localisation et de délocalisation dynamiques. Pour des mesures de simple site régulières et celle de Bernoulli, nous démontrons la localisation dynamique en bas du spectre. De plus, nous obtenons une description quantitative de la région de localisation dynamique en termes de paramètres géométriques de l'ensemble de Delone de base.Nous concluons ce travail avec l'étude de la densité d'états intégrée pour des modèles de Delone-Anderson, en combinaison avec des outils de la théorie des systèmes dynamiques associés aux quasi-cristaux. Sous certaines conditions sur la géométrie de l'ensemble de Delone sous-jacent, nous montrons l'existence de la densité d'états intégrée. De plus, dans le cas d'une perturbation de Delone-Anderson du Laplacien libre, nous démontrons qu'elle a un comportement asymptotique de Lifshitz en bas du spectreHis thesis is devoted to the study of electronic transport in non ergodic disordered models, in the framework of random Schrödinger operators.We start by reformulating the main tool in our study, the multiscale analysis, in the non ergodic setting. We establish suitable homogeneity conditions on the operator, in order to apply this method.Next, we study the spectral properties of non ergodic Delone-Anderson operators. These models represent a particle interacting with a medium whose atomic structure is quasi-crystalline and the nature of its impurities is disordered. In the case where the probability measures associated to the single-site potential are regular, in dimension 2 and under the effect of a magnetic field, we establish a metal-insulator transition and the existence of a mobility edge that separates the localization and delocalization regions. In arbitrary dimension, for regular and for Bernoulli single-site measures, we show dynamical localization at the bottom of the spectrum. Moreover, we obtain a quantitative lower bound on the size of the localization region in terms of the geometric parameters of the underlying Delone structure.We conclude this essay by studying the integrated density of states for Delone-Anderson models, using tools from the theory of dynamical systems associated to quasicrystals. Under certain conditions on the geometry of the underlying Delone set, we show the existence of the integrated density of states. Furthermore, in the case of a Delone-Anderson perturbation of the free Laplacian, we show it exhibits Lifshitz tails at the bottom of the spectrum
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Khodadadi, Sheila. "Influence of Solvent on Protein Dynamics and Activity." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1247697577.
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Hines, Andrew Peter. "Entanglement, dynamical bifurcations and quantum phase transitions /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19792.pdf.
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Blythe, Richard Alexander. "Nonequilibrium phase transitions and dynamical scaling regimes." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/10834.
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In recent years, the application of statistical mechanics to nonequilibrium systems, and quite specifically the probabilistic modelling of nonequilibrium microscopic dynamics, has become a major research topic. However, in contrast to the equilibrium case, there is currently no general framework within which nonequilibrium systems are understood. Hence the aim of this thesis is to improve our understanding of nonequilibrium systems through the study of a range of systems with probabilistic microscopic dynamics and the collective phenomena - notably phase transitions and the onset of scaling regimes - that arise. In this thesis I briefly review general aspects of mathematical models of probabilistic dynamics (stochastic processes), with a particular emphasis on steady-state properties and the origin of phase transitions. Then I consider separately four specific types of nonequilibrium dynamics. Firstly, I introduce and solve exactly a model of a particle reaction system. The solution which employs commutation properties of the q-deformed harmonic oscillator algebra, reveals that phase transitions in the analytic form of the particle density as a function of time arise as a direct consequence of randomness in the reaction dynamics. I also use similar mathematical techniques to solve the partially asymmetric exclusion process, an important prototype of a physical system that is driven by its environment. This model is also found to exhibit phase transitions, although in this case their origins lies in the nonequilibrium interactions between the system and its surroundings. Then I examine the scaling behaviour associated with the nonequilibrium directed percolation continuous phase transition. This transition is related to the presence of an absorbing state and I provide evidence for such a transition in a wetting model that does not possess an absorbing state. Finally, I generalise the wetting model to two dimensions and study its interfacial scaling behaviour. This is found to belong to the Kardar-Parisi-Zhang universality class, although there are strong crossover effects - which I quantify - that obscure the scaling regime.
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Shakhovoy, Roman. "Structural properties and dynamics of alkali sulfates." Thesis, Orléans, 2015. http://www.theses.fr/2015ORLE2029/document.
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Le sujet de cette thèse est principalement ciblé sur l’étude du transport ionique dans les sulfates d’alcalins de la famille LIMSO₄, où M=Na, K, Rb, Cs. Une attention particulière est portée sur l’étude du système LiNaSO₄, le plus intéressant en termes de dynamique ionique, par RMN en fonction de la température. Dans le cadre de cette étude, nous avons effectué des mesures de temps de relaxation et de largeurs de raie pour toute la série de composés. Des mesures de coefficients d’autodiffusion du ₇li et du ²³Na, ont été menées depuis l’ambiante jusqu’à la température de fusion. Pour la première fois, nous avons pu mesurer la cinétique de transition de phase dans LiNaSO₄, à partir d’une nouvelle méthode basée sur la différence de temps de relaxation dans les deux phases de part et d’autre d e la transition, mais sans mesurer forcément le T₁. Cette technique élaborée dans le cadre de ce travail permet de mesurer l’évolution au cours du temps du volume de la phase qui apparait pour des vitesses de refroidissement contrôlées. Nous avons aussi mené une étude par RMN des réorientations des groupements sulfates dans la phase basse température. L’influence des réorientations des SO ₄² sur les couplages quadripolaires au noyau 7li, a été étudiée par un modèle de réorientation par sauts, qui n’avait encore jamais été utilisé pour les sulfates. La méthode proposée est une méthode à « bas couts » car elle permet d’atteindre l’information sur la dynamique des groupements sulfates sans enrichir l’échantillon en ¹⁷O ou de mener des expériences très longues pour le ³³S, ou sans passer par les mesures de temps de relaxation. Afin d’analyser le rétrécissement par le mouvement (motional narrowing) en fonction de la température dans les solides avec deux sous réseaux cationiques diffusant comme dans le cas du LiNaSO₄ , nous avons élaboré un modèle permettant de fitter l’évolution observée à deux marches de la largeur de raie RMN avec la température. La fonction analytique obtenue a été étendue au cas de distributions de temps de corrélationThe main goal of a present research is a detailed study of ionic transfer in double sulfates belonging to the LIMSO₄ family, where M = Na, K, Rb, Cs. The most attention has been paid to LiNaSO₄ as to the most interesting (in terms of the ion dynamics) compound among other double sulfates. We have carried out magnetic relaxation measurements and line width analysis for all compounds under consideration. Moreover, PGF NMR measurements of ₇li and ²³Na self-diffusion coefficients in LiNaSO4 have been carried out. For the first time, we have measured the phase transition kinetics in LiNaSO₄. For this purpose, we developed a new technique, which is based on the difference of spin-lattice relaxation times in the two phases, but which does not involve the direct measurement of T₁. Elaborated technique allows measuring time evolution of the volume of the appearing phase at controlled cooling rates. We have carried out NMR study of the sulfate ion reorientations in the low-temperature modification of LiNaSO₄. The influence of the SO ₄² reorientational jumps on the quadrupolar interactions of 7Li nuclei was investigated b y a j ump reorientational model, which has not previously been app lied to sulfates. The proposed method is a “low-cost” technique, since it does not require an ¹⁷O enriched sample and dispenses with time-consuming ³³S NMR. Other advantage of a given method is a possibility to probe reorientational motions without NMR relaxation measurements. To analyze motional narrowing in solids with two diffusing spin sublattices (such case occurs, e.g., in LiNaSO₄) we deduced a formula, which can be used for fitting of the two-step temperature dependencies of the NMR line width. The obtained function has been al so ex tended to the case, when a distribution of correlation times takes place. The advantage of this approach is that even in the case of distribution of correlation times, the fitting function could be expressed in the analytical form
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Smith, Kristin Elizabeth. "Full-time motherhood understanding transition dynamics /." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3515.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2006.Thesis research directed by: Sociology. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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González, Gómez Andrés. "Nonlinear dynamics and smooth transition models." Doctoral thesis, Handelshögskolan i Stockholm, Ekonomisk Statistik (ES), 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:hhs:diva-541.
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During the last few years nonlinear models have been a very active area of econometric research: new models have been introduced and existing ones generalized. To a large extent, these developments have concerned models in which the conditional moments are regime-dependent. In such models, the different regimes are usually linear and the change between them is governed by an observable or unobservable variable. These specifications can be useful in situations in which it is suspected that the behaviour of the dependent variable may vary between regimes. A classical example can be found the business cycle literature where it is argued that contractions in the economy are not only more violent but also short-lived than expansions. Unemployment, which tends to rise faster during recessions than decline during booms, constitutes another example. Two of the most popular regime-dependent models are the smooth transition and the threshold model. In both models cases the transition variable is observable but the specification of the way in which the model changes from one regime to the other is different. Particularly, in the smooth transition model the change is a continuous whereas in the threshold model it is abrupt. One of the factors that has influenced the development of nonlinear models are improvements in computer technology. They have not only permitted an introduction of more complex models but have also allowed the use of computer-intensive methods in hypothesis testing. This is particularly important in nonlinear models because there these methods have proved to be practical in testing statistical hypothesis such as linearity and parameter constancy. In general, these testing situation are not trivial and their solution often requires computer-intensive methods. In particular, bootstrapping and Monte Carlo testing are now commonly used. In this thesis the smooth transition model is used in different ways. In the first chapter, a vector smooth transition model is used as a device for deriving a test for parameter constancy in stationary vector autoregressive models. In the second chapter we introduce a panel model whose parameters can change in a smooth fashion between regimes as a function of an exogenous variable. The method is used to investigate whether financial constraints affect firms' \ investment decisions. The third chapter is concern with linearity testing in smooth transition models. New tests are introduced and Monte Carlo testing techniques are shown to be useful in achieving control over the size of the test. Finally, the last chapter is devoted to the Smooth Permanent Surge model. This is a nonlinear moving average model in which a shock can have transitory or permanent effects depending on its sign and magnitude. Test for linearity and random walk hypothesis are introduced.Diss. Stockholm : Handelshögsk., 2004
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Furukawa, Akira. "Phase Transition Dynamics of Complex Fluids." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/147797.
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Grote, Christoph. "Dynamic theories of the glass transition." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318104.
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Hung, Jui-Hsiang. "Efficient computational strategies enabling insights into the glass transition." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1512640511831277.
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Millanes, Romero Alba 1986. "Heterochromatin dynamics during epithelial-to-mesenchymal transition." Doctoral thesis, Universitat Pompeu Fabra, 2014. http://hdl.handle.net/10803/129339.
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Although heterochromatin is enriched with repressive traits, it is actively transcribed, giving
rise to large amounts of non-coding RNAs. These transcripts are responsible for the formation
and maintenance of heterochromatin, but little is known about how their transcription is
regulated. In this thesis we show that Snail1 transcription factor represses mouse
pericentromeric transcription and regulates heterochromatin organization through the action
of the H3K4 deaminase LOXL2. Snail1 has a key role in epithelial-to-mesenchymal transition
(EMT). We show that, also during this process, Snail1 is responsible for pericentromeric
transcription regulation. At the onset of EMT, one of the major structural heterochromatin
proteins, HP1α, is transiently released from heterochromatin foci in a Snail1/LOXL2 dependent
manner, concomitantly with a down-regulation of major satellite transcription. Moreover,
prevention of major satellite transcripts down-regulation compromises the migratory and
invasive behaviour of EMT resulting mesenchymal cells. We propose that Snail1 and LOXL2
regulate heterochromatin during this process, which may be crucial to allow the genome
reorganization required to complete EMT.Tot i estar enriquida en marques repressores, l’heterocromatina es transcriu activament i dóna lloc a grans quantitats d’ARNs no codificants. Aquests trànscrits són responsables de la formació i el manteniment de l’heterocromatina, però com es regula la seva transcripció segueix sent quelcom poc clarificat. En aquesta tesi demostrem que el factor de transcripció Snail1 reprimeix la transcripció pericentromèrica en cèl·lules de ratolí i regula l’organització de l’heterocromatina a través de l’acció de la LOXL2, que deamina l’H3K4. Snail1 té un paper clau en la transició epiteli-mesènquima (EMT). Aquí demostrem que, també durant aquest procés, Snail1 és responsable de la regulació de la transcripció pericentromèrica. A l’inici de l’EMT, l’HP1α, una de les principals proteïnes estructurals de l’heterocromatina, es desprèn de forma transitòria de l’heterocromatina. Aquest esdeveniment està regulat per Snail1 i LOXL2 i coincideix amb una disminució de la transcripció pericentromèrica. El bloqueig de la baixada dels trànscrits durant l’EMT compromet les capacitats migratòries i invasives de les cèl·lules mesenchimals que en resulten. Així doncs, proposem que Snail1 i LOXL2 regulen l’heterocromatina durant aquest procés, i així permeten que tingui lloc la reorganització genòmica que deu ser necessària per tal que es completi la EMT.
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Moon, Chang Man. "Molecular dynamics study of phase transition phenomena." Thesis, University of Edinburgh, 2000. http://hdl.handle.net/1842/12675.
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This computer simulation study carried out by classical the molecular dynamics technique (MD) investigates structural phase transitions of various atomic and molecular condensed matter systems. Particularly, our attention is focused on the signals for their observation. Classical nucleation theory is briefly reviewed in relation to the present study. An overall review is made on the methodology of the MD simulation technique such as the integration of the equations of motion, the rotational motion of molecules which is dealt with the four-component quaternion, and other various techniques involved with the simulation of atomic clusters, the simulation of bulk molecular systems using periodic boundary conditions, and isobaric molecular dynamics. There are also reviews on measurements of thermodynamic quantities which are monitored during the simulation including the pressure, the kinetic energy, and the potential energy as well as their corrections due to the spherical cutoff. In addition, various analysis techniques for the observation of the signals of structural phase transitions are discussed. All the potential functions used in this study are of the pairwise additive atom-atom Lennard-Jones interaction for both the atomic and the molecular systems. A small cluster of a binary mixture of krypton and argon atoms is studied by triggered breathing motions to investigate anharmonic motion which involves the structural phase transitions. A small cluster of krypton atoms is also simulated and discussed in detail concerning the very first moment of nucleation in relation to five-fold symmetric structures. In simulations of sulphurhexafluoride molecule systems, artifacts of finite size and periodic boundary conditions are investigated. Freezing the system by MD is investigated since it is known to supercool in computer simulations. Furthermore, accelerating the nucleation process by various methods such as shear flow, accelerated layer, inclusion of defect molecules, and pressure fluctuations is investigated.
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Valiev, Damir. "Flame Dynamics and Deflagration-to-Detonation Transition." Doctoral thesis, Stockholm : Industriell teknik och management, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4875.
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Heyl, Markus Philip Ludwig [Verfasser], and Stefan [Akademischer Betreuer] Kehrein. "Nonequilibrium phenomena in many-body quantum systems : dynamics, thermodynamics, and dynamical phase transitions / Markus Philip Ludwig Heyl. Betreuer: Stefan Kehrein." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2012. http://d-nb.info/1024658619/34.
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