Publications (126)224.88 Total impact
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ABSTRACT: We discuss the use of Langevin molecular dynamics in the investigation of the nonequilibrium properties of disordered vortex matter. Our special focus is set on values of system parameters that are realistic for disordered high$T_c$ superconductors such as YBCO. Using a discretized elastic line model, we study different aspects of vortices far from thermal equilibrium. On the one hand we investigate steadystate properties of driven magnetic flux lines in a disordered environment, namely the currentvoltage characteristics, the gyration radius, and the pinning time statistics. On the other hand we study the complex relaxation processes and glassylike dynamics that emerge in typeII superconductors due to the intricate competition between the longrange vortexvortex repulsion and flux pinning due to randomly placed point defects. To this end we consider different types of sudden perturbations: temperature, magnetic field, and external current quenches.  [Show abstract] [Hide abstract]
ABSTRACT: Vortex lines in typeII superconductors display complicated relaxation processes due to the intricate competition between their mutual repulsive interactions and pinning to attractive point or extended defects. We perform extensive Monte Carlo simulations for an interacting elastic line model with either pointlike or columnar pinning centers. From measurements of the space and timedependent heightheight correlation function for lateral flux line fluctuations, we extract a characteristic correlation length that we use to investigate different nonequilibrium relaxation regimes. The specific time dependence of this correlation length for different disorder configurations displays characteristic features that provide a novel diagnostic tool to distinguish between pointlike pinning centers and extended columnar defects.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the laws of coarsening of a twodimensional system of Ising spins evolving under singlespinflip irreversible dynamics at low temperature from a disordered initial condition. The irreversibility of the dynamics comes from the directedness, or asymmetry, of the influence of the neighbours on the flipping spin. We show that the main characteristics of phase ordering at low temperature, such as selfsimilarity of the patterns formed by the growing domains, and the related scaling laws obeyed by the observables of interest, which hold for reversible dynamics, are still present when the dynamics is directed and irreversible, but with different scaling behaviour. In particular the growth of domains, instead of being diffusive as is the case when dynamics is reversible, becomes ballistic. Likewise, the autocorrelation function and the persistence probability (the probability that a given spin keeps its sign up to time $t$) have still powerlaw decays but with different exponents.  [Show abstract] [Hide abstract]
ABSTRACT: We study the effects of rapid temperature and magnetic field changes on the nonequilibrium relaxation dynamics of magnetic vortex lines in disordered typeII superconductors by employing an elastic line model and performing Langevin molecular dynamics simulations. In a previously equilibrated system, either the temperature is suddenly changed, or the magnetic field is instantaneously altered which is reflected in adding or removing flux lines to or from the system. The subsequent aging properties are investigated in samples with either randomly distributed pointlike or extended columnar defects, which allows to distinguish the complex relaxation features that result from either type of pinning centers. Onetime observables such as the radius of gyration and the fraction of pinned line elements are employed to characterize steadystate properties, and twotime correlation functions such as the vortex line height autocorrelations and their meansquare displacement are analyzed to study the nonlinear stochastic relaxation dynamics in the aging regime.  [Show abstract] [Hide abstract]
ABSTRACT: We consider cyclic LotkaVolterra models with three and four strategies where at every interaction agents play a strategy using a timedependent probability distribution. Agents learn from a loss by reducing the probability to play a losing strategy at the next interaction. For that, an agent is described as an urn containing $\beta$ balls of three respectively four types where after a loss one of the balls corresponding to the losing strategy is replaced by a ball representing the winning strategy. Using both meanfield rate equations and numerical simulations, we investigate a range of quantities that allow us to characterize the properties of these cyclic models with timedependent probability distributions. For the threestrategy case in a spatial setting we observe a transition from neutrally stable to stable when changing the level of discretization of the probability distribution. For large values of $\beta$, yielding a good approximation to a continuous distribution, spatially synchronized temporal oscillations dominate the system. For the fourstrategy game the system is always neutrally stable, but different regimes emerge, depending on the size of the system and the level of discretization.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss relaxation and aging processes in the one and twodimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized by a logarithmic growth of ordered domains that take the form of stripes. From the timedependent length, derived from the equaltime spatial correlator, and from the mean displacement of individual particles different regimes in the formation and growth of these domains can be identified. Analysis of twotimes correlation and response functions reveals dynamical scaling in the asymptotic logarithmic growth regime as well as complicated finitetime and finitesize effects in the early and intermediate time regimes. 
Article: Nonequilibrium statistical mechanics of a twotemperature Ising ring with conserved dynamics
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ABSTRACT: The statistical mechanics of a onedimensional Ising model in thermal equilibrium is wellestablished, textbook material. Yet, when driven far from equilibrium by coupling two sectors to two baths at different temperatures, it exhibits remarkable phenomena, including an unexpected 'freezing by heating.' These phenomena are explored through systematic numerical simulations. Our study reveals complicated relaxation processes as well as a crossover between two very different steadystate regimes. 
Article: Equilibrium and nonequilibrium properties of synthetic metamagnetic films: A Monte Carlo study
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ABSTRACT: Synthetic antiferromagnets with strong perpendicular anisotropy can be modeled by layered Ising antiferromagnets. Accounting for the fact that in the experimental systems the ferromagnetic layers, coupled antiferromagnetically via spacers, are multilayers, we propose a description through Ising films where ferromagnetic stacks composed of multiple layers are coupled antiferromagnetically. We study the equilibrium and nonequilibrium properties of these systems where we vary the number of layers in each stack. Using numerical simulations, we construct equilibrium temperature$$magnetic field phase diagrams for a variety of cases. We find the same dominant features (three stable phases, where one phase boundary ends in a critical end point, whereas the other phase boundary shows a tricritical point at which the transition changes from first to second order) for all studied cases. Using timedependent quantities, we also study the ordering processes that take place after a temperature quench. The nature of longlived metastable states are discussed for thin films, whereas for thick films we compute the surface autocorrelation exponent.  [Show abstract] [Hide abstract]
ABSTRACT: We study the pinning dynamics of magnetic flux (vortex) lines in a disordered typeII superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repulsive or purely attractive, and whose strengths are drawn from a Gaussian distribution; as well as continuous Gaussian random potential landscapes. We find that both schemes yield power law distributions in the pinned phase as predicted by extremeevent statistics, yet they differ significantly in their effective scaling exponents and their shorttime behavior.  [Show abstract] [Hide abstract]
ABSTRACT: We employ Monte Carlo simulations to investigate the nonequilibrium relaxation properties of the two and threedimensional Coulomb glass with different longrange repulsive interactions. Specifically, we explore the aging scaling laws in the twotime density autocorrelation function. We find that in the time window and parameter range accessible to us, the scaling exponents are not universal, depending on the filling fraction and temperature: As either the temperature decreases or the filling fraction deviates more from halffilling, the exponents reflect markedly slower relaxation kinetics. In comparison with a repulsive Coulomb potential, appropriate for impurity states in strongly disordered semiconductors, we observe that for logarithmic interactions, the soft pseudogap in the density of states is considerably broader, and the dependence of the scaling exponents on external parameters is much weaker. The latter situation is relevant for flux creep in the disorderdominated Bose glass phase of typeII superconductors subject to columnar pinning centers.  [Show abstract] [Hide abstract]
ABSTRACT: In order to model real ecological systems one has to consider many species that interact in complex ways. However, most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions. The few studies dealing with larger number of species and/or more complex interaction schemes are mostly restricted to numerical explorations. In this paper we determine, starting from the deterministic meanfield rate equations, for large classes of systems the space of coexistence fixed points at which biodiversity is maximal. For systems with a single coexistence fixed point we derive complex GinzburgLandau equations that allow to describe spacetime pattern realized in two space dimensions. For selected cases we compare the theoretical predictions with the pattern observed in numerical simulations. 
Article: Surface phase diagram of the threedimensional kinetic Ising model in an oscillating magnetic field
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ABSTRACT: We study the surface phase diagram of the threedimensional kinetic Ising model below the equilibrium critical point subjected to a periodically oscillating magnetic field. Changing the surface interaction strength as well as the period of the external field, we obtain a nonequilibrium surface phase diagram that in parts strongly resembles the corresponding equilibrium phase diagram, with an ordinary transition, an extraordinary transition and a surface transition. These three lines meet at a special transition point. For weak surface couplings, however, the surface does not order. These results are found to remain qualitatively unchanged when using different singlespin flip dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the nonconserved dynamics of the Ising model on the twodimensional square lattice, where each spin is influenced preferentially by its East and North neighbours. The singlespin flip rates are such that the stationary state is Gibbsian with respect to the usual ferromagnetic Ising Hamiltonian. We show the existence, in the paramagnetic phase, of a dynamical transition between two regimes of violation of the fluctuationdissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuationdissipation ratio is finite, when the asymmetry parameter is less than a threshold value, and a regime of strong violation where this ratio vanishes asymptotically above the threshold. The present study suggests that this novel kind of dynamical transition in nonequilibrium stationary states, already found for the directed Ising chain and the spherical model with asymmetric dynamics, might be quite general. In contrast with the later models, the equaltime correlation function for the twodimensional directed Ising model depends on the asymmetry.  [Show abstract] [Hide abstract]
ABSTRACT: Systems with a bulk firstorder transition can display diverging correlation lengths close to a surface. This surface induced disordering yields a special type of surface criticality. Using extensive numerical simulations we study surface quantities in the twodimensional Potts model with a large number of states $q$ which undergoes a discontinuous bulk transition. The surface critical exponents are thereby found to depend on the value of $q$, which is in contrast to prior claims that these exponents should be universal and independent of $q$. It follows that surface induced disordering at firstorder transitions is characterized by exponents that depend on the details of the model.  [Show abstract] [Hide abstract]
ABSTRACT: When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system both in the well mixed case as well as on different types of lattices. The different routes to extinction are revealed by the probability distribution of the domination time, i.e. the time needed for one team to fully occupy the system. If swapping is allowed between neutral partners, then the probability distribution is dominated by very longlived states where a few very large domains persist, each domain being occupied by a mix of individuals from species that form one of the teams. Many aspects of the possible extinction scenarios are lost when only considering averaged quantities as for example the mean domination time. 
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ABSTRACT: In order to better understand the interplay of partnership and competition in population dynamics, we study a family of generalized MayLeonard models with N species. These models have a very rich structure, characterized by different types of spacetime patterns. Interesting partnership formations emerge following the maxim that “the enemy of my enemy is my friend”. In specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation. We classify the different types of dynamics through the analysis of the square of the adjacency matrix. The dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a Fourier analysis. Finally, after having identified collaborating teams, we study interface fluctuations where we initially populate different parts of the system with different teams. 
Article: Dynamic phase transition in the threedimensional kinetic Ising model in an oscillating field
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ABSTRACT: Using numerical simulations we investigate the properties of the dynamic phase transition that is encountered in the threedimensional Ising model subjected to a periodically oscillating magnetic field. The values of the critical exponents are determined through finitesize scaling. Our results show that the studied nonequilibrium phase transition belongs to the universality class of the equilibrium threedimensional Ising model.  [Show abstract] [Hide abstract]
ABSTRACT: Using extensive Monte Carlo simulations we study the properties of the nonequilibrium phase transition encountered in driven threedimensional Potts systems with magnetic friction. Our system consists of two threedimensional blocks, coupled through boundary spins, that move along their boundaries with a constant relative velocity. Changing the number of states in the system from two (Ising case) to nine states, we find different scenarios for the surface behavior depending on whether the bulk transition is continuous or discontinuous. In order to fully assess the properties of this nonequilibrium phase transition, we vary systematically the strength of the coupling between the two blocks as well as the value of the relative velocity. For strong couplings between the blocks the phase transition is found to be strongly anisotropic.  [Show abstract] [Hide abstract]
ABSTRACT: From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we explore a simple modification of the venerable Ising model in hopes of shedding some light on these issues. In both one and two dimensions, systems attached to two distinct heat reservoirs exhibit many of the hallmarks of phase transition. When such systems settle into a nonequilibrium steadystate they exhibit numerous interesting phenomena, including an unexpected ``freezing by heating.'' There are striking and surprising similarities between the behavior of these systems in one and two dimensions, but also intriguing differences. These phenomena will be explored and possible approaches to understanding the behavior will be suggested.
Publication Stats
1k  Citations  
224.88  Total Impact Points  
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Institutions

20072015

Virginia Polytechnic Institute and State University
 Department of Physics
Блэксбург, Virginia, United States


2014

University of Oxford
Oxford, England, United Kingdom


20002007

FriedrichAlexander Universität ErlangenNürnberg
 Institute of Theoretical Physics
Erlangen, Bavaria, Germany


2006

University of Florence
Florens, Tuscany, Italy


19971998

RWTH Aachen University
 Institut für Theorie der statistischen Physik A
Aachen, North RhineWestphalia, Germany 
Universität des Saarlandes
 Physikalische und Theoretische Chemie
Saarbrücken, Saarland, Germany
