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Jones D.,Imperial College London | Jensen H.J.,Imperial College London | Sibani P.,Institute for Fysik Og Kemi
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

The fossil record has been interpreted as exhibiting a gradual decrease in the extinction rate. We use the individual based Tangled Nature model of evolutionary ecology to study the mechanisms behind this kind of nonstationary macrodynamics. We demonstrate that the long time aging in the system (manifested as a slowing down of the rate of large jumps, or quakes, that the system undergoes) is related to decreasing fluctuations in the offspring probability. The scenario is reminiscent of relaxation in a quenched spin glass but purely dynamical in nature since no energy barriers can be defined. © 2010 The American Physical Society. Source

Boettcher S.,Emory University | Sibani P.,Institute for Fysik Og Kemi
Journal of Physics Condensed Matter | Year: 2011

The far-from-equilibrium dynamics of glassy systems share important phenomenological traits. A transition is generally observed from a time-homogeneous dynamical regime to an ageing regime where physical changes occur intermittently and, on average, at a decreasing rate. It has been suggested that a global change of the independent time variable to its logarithm may render the ageing dynamics homogeneous: for colloids, this entails diffusion but on a logarithmic timescale. Our novel analysis of experimental colloid data confirms that the mean square displacement grows linearly in time at low densities and shows that it grows linearly in the logarithm of time at high densities. Correspondingly, pairs of particles initially in close contact survive as pairs with a probability which decays exponentially in either time or its logarithm. The form of the probability density function of the displacements shows that long-ranged spatial correlations are very long-lived in dense colloids. A phenomenological stochastic model is then introduced which relies on the growth and collapse of strongly correlated clusters ('dynamic heterogeneity'), and which reproduces the full spectrum of observed colloidal behaviors depending on the form assumed for the probability that a cluster collapses during a Monte Carlo update. In the limit where large clusters dominate, the collapse rate is 1/t, implying a homogeneous, log-Poissonian process that qualitatively reproduces the experimental results for dense colloids. Finally, an analytical toy-model is discussed to elucidate the strong dependence of the simulation results on the integrability (or lack thereof) of the cluster collapse probability function. © 2011 IOP Publishing Ltd. Source

Barettin D.,University of Southern Denmark | Sibani P.,Institute for Fysik Og Kemi
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

Monte Carlo algorithms such as the Wang-Landau algorithm and similar "entropic" methods are able to accurately sample the density of states of model systems and thereby give access to thermal equilibrium properties at any temperature. Thermal equilibrium is, however, unachievable at low temperatures in glassy systems. Such systems are characterized by a multitude of metastable configurations pictorially referred to as "valleys" of an energy landscape. Geometrical properties of the landscape, e.g., the local density of states describing the distribution in energy of the states belonging to a single valley, are key to understanding the dynamical properties of such systems. In this paper we combine the lid algorithm, a tool for landscape exploration previously applied to a range of models, with the Wang-Swendsen algorithm. To test this improved exploration tool, we consider a paradigmatic complex system, the Edwards-Anderson model in two and three spatial dimensions. We find a striking difference between the energy dependence of the local density of states in two dimensions and three dimensions-nearly linear in the first case, and nearly exponential in the second. The dynamical consequences of these findings are discussed. © 2011 American Physical Society. Source

Kenning G.G.,Indiana University of Pennsylvania | Bowen J.,University of California at Riverside | Sibani P.,Institute for Fysik Og Kemi | Rodriguez G.F.,University of California at Riverside
Physical Review B - Condensed Matter and Materials Physics | Year: 2010

Using a series of fast-cooling protocols we have probed aging effects in the spin-glass state as a function of temperature. Analyzing the logarithmic decay found at very long-time scales within a simple phenomenological barrier model leads to the extraction of an effective fluctuation time scale of the system at a particular temperature. This is the smallest dynamical time-scale defining a lower cutoff in a hierarchical description of the dynamics. We find that this fluctuation time scale, which is approximately equal to atomic spin-fluctuation time scales near the transition temperature, follows a generalized Arrhenius law. We discuss the hypothesis that, upon cooling to a measuring temperature within the spin-glass state, there is a range of dynamically inequivalent configurations in which the system can be trapped, and check within a numerical barrier model simulation, that this leads to subaging behavior in scaling aged thermoremanent magnetization decay curves, as recently discussed theoretically. © 2010 The American Physical Society. Source

Sibani P.,Institute for Fysik Og Kemi | Kenning G.G.,Indiana University of Pennsylvania
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2010

Linear response functions of aging systems are routinely interpreted using the scaling variable tobs / twμ, where tw is the time at which the field conjugated to the response is turned on or off, and where tobs is the "observation" time elapsed from the field change. The response curve obtained for different values of tw are usually collapsed using values of μ slightly below one, a scaling behavior generally known as subaging. Recent spin glass thermoremanent magnetization experiments have shown that the value of μ is strongly affected by the form of the initial cooling protocol, and even more importantly, that the tw dependence of the response curves vanishes altogether in the limit tobs tw. The latter result shows that tobs / twμ scaling of linear response data cannot be generally valid, thereby casting some doubt on the theoretical significance of the exponent μ. In this work, a common mechanism is proposed for the origin of both subaging and end of aging behavior in glassy dynamics. The mechanism combines real and configuration space properties of the state produced by the initial thermal quench which initiates the aging process. © 2010 The American Physical Society. Source

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