147 research outputs found
Linear response subordination to intermittent energy release in off-equilibrium aging dynamics
The interpretation of experimental and numerical data describing
off-equilibrium aging dynamics crucially depends on the connection between
spontaneous and induced fluctuations. The hypothesis that linear response
fluctuations are statistically subordinated to irreversible outbursts of
energy, so-called quakes, leads to predictions for averages and fluctuations
spectra of physical observables in reasonable agreement with experimental
results [see e.g. Sibani et al., Phys. Rev. B74:224407, 2006]. Using
simulational data from a simple but representative Ising model with plaquette
interactions, direct statistical evidence supporting the hypothesis is
presented and discussed in this work.
A strict temporal correlation between quakes and intermittent magnetization
fluctuations is demonstrated. The external magnetic field is shown to bias the
pre-existent intermittent tails of the magnetic fluctuation distribution, with
little or no effect on the Gaussian part of the latter. Its impact on energy
fluctuations is shown to be negligible.
Linear response is thus controlled by the quakes and inherits their temporal
statistics. These findings provide a theoretical basis for analyzing
intermittent linear response data from aging system in the same way as thermal
energy fluctuations, which are far more difficult to measure.Comment: 9 pages, 10 figures. Text improve
Evolution and extinction dynamics in rugged fitness landscapes
Macroevolution is considered as a problem of stochastic dynamics in a system
with many competing agents. Evolutionary events (speciations and extinctions)
are triggered by fitness records found by random exploration of the agents'
fitness landscapes. As a consequence, the average fitness in the system
increases logarithmically with time, while the rate of extinction steadily
decreases. This dynamics is studied by numerical simulations and, in a simpler
mean field version, analytically. We also study the effect of externally added
`mass' extinctions. The predictions for various quantities of paleontological
interest (life-time distributions, distribution of event sizes and behavior of
the rate of extinction) are robust and in good agreement with available data.
Brief version of parts of this work have been published as Letters. (PRL 75,
2055, (1995) and PRL, 79, 1413, (1997))Comment: 30 pages 9 figures LaTe
How a spin-glass remembers. Memory and rejuvenation from intermittency data: an analysis of temperature shifts
The memory and rejuvenation aspects of intermittent heat transport are
explored theoretically and by numerical simulation for Ising spin glasses with
short-ranged interactions. The theoretical part develops a picture of
non-equilibrium glassy dynamics recently introduced by the authors. Invoking
the concept of marginal stability, this theory links irreversible
`intermittent' events, or `quakes' to thermal fluctuations of record magnitude.
The pivotal idea is that the largest energy barrier surmounted prior
to by thermal fluctuations at temperature determines the rate of the intermittent events occurring near . The idea leads
to a rate of intermittent events after a negative temperature shift given by
, where the `effective age' has
an algebraic dependence on , whose exponent contains the temperatures
before and after the shift. The analytical expression is verified by numerical
simulations. Marginal stability suggests that a positive temperature shift could erase the memory of the barrier . The simulations show
that the barrier controls the intermittent dynamics,
whose rate is hence .
Additional `rejuvenation' effects are also identified in the intermittency
data for shifts of both signs.Comment: Revised introduction and discussion. Final version to appear in
Journal of Statistical Mechanics: Theory and Experimen
Aging and intermittency in a p-spin model of a glass
We numerically analyze the statistics of the heat flow between an aging
system and its thermal bath, following a method proposed and tested for a
spin-glass model in a recent Letter (P. Sibani and H.J. Jensen, Europhys.
Lett.69, 563 (2005)). The present system, which lacks quenched randomness,
consists of Ising spins located on a cubic lattice, with each plaquette
contributing to the total energy the product of the four spins located at its
corners. Similarly to our previous findings, energy leaves the system in rare
but large, so called intermittent, bursts which are embedded in reversible and
equilibrium-like fluctuations of zero average. The intermittent bursts, or
quakes, dissipate the excess energy trapped in the initial state at a rate
which falls off with the inverse of the age. This strongly heterogeneous
dynamical picture is explained using the idea that quakes are triggered by
energy fluctuations of record size, which occur independently within a number
of thermalized domains. From the temperature dependence of the width of the
reversible heat fluctuations we surmise that these domains have an exponential
density of states. Finally, we show that the heat flow consists of a
temperature independent term and a term with an Arrhenius temperature
dependence. Microscopic dynamical and structural information can thus be
extracted from numerical intermittency data. This type of analysis seems now
within the reach of time resolved micro-calorimetry techniques.Comment: 9 pages, 6 figures, europhysics letter style, to appear in Physical
Review
A soluble model of evolution and extinction dynamics in a rugged fitness landscape
We consider a continuum version of a previously introduced and numerically
studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve
by an optimization process in a rugged fitness landscape and die due to their
competitive interactions. We first formulate dynamical equations for the
fitness distribution and the survival probability. Secondly we analytically
derive the law which characterizes the life time distribution of
biological genera. Thirdly we discuss other dynamical properties of the model
such as the rate of extinction and conclude with a brief discussion.Comment: 6 pages LaTeX source with 2 figures. Submitted to PRL (Jan. 97
Properties of the energy landscape of network models for covalent glasses
We investigate the energy landscape of two dimensional network models for
covalent glasses by means of the lid algorithm. For three different particle
densities and for a range of network sizes, we exhaustively analyse many
configuration space regions enclosing deep-lying energy minima. We extract the
local densities of states and of minima, and the number of states and minima
accessible below a certain energy barrier, the 'lid'. These quantities show on
average a close to exponential growth as a function of their respective
arguments. We calculate the configurational entropy for these pockets of states
and find that the excess specific heat exhibits a peak at a critical
temperature associated with the exponential growth in the local density of
states, a feature of the specific heat also observed in real glasses at the
glass transition.Comment: RevTeX, 19 pages, 7 figure
Mean-field theory of temperature cycling experiments in spin-glasses
We study analytically the effect of temperature cyclings in mean-field
spin-glasses. In accordance with real experiments, we obtain a strong
reinitialization of the dynamics on decreasing the temperature combined with
memory effects when the original high temperature is restored. The same
calculation applied to mean-field models of structural glasses shows no such
reinitialization, again in accordance with experiments. In this context, we
derive some relations between experimentally accessible quantities and propose
new experimental protocols. Finally, we briefly discuss the effect of field
cyclings during isothermal aging.Comment: Some misprints corrected, references updated, final version to apper
in PR
Evolution on a Rugged Landscape:Pinning and Aging
Population dynamics on a rugged landscape is studied analytically and
numerically within a simple discrete model for evolution of N individuals in
one-dimensional fitness space. We reduce the set of master equations to a
single Fokker-Plank equation which allows us to describe the dynamics of the
population in terms of thermo-activated Langevin diffusion of a single particle
in a specific random potential. We found that the randomness in the mutation
rate leads to pinning of the population and on average to a logarithmic
slowdown of the evolution, resembling aging phenomenon in spin glass systems.
In contrast, the randomness in the replication rate turns out to be irrelevant
for evolution in the long-time limit as it is smoothed out by increasing
``evolution temperature''. The analytic results are in a good agreement with
numerical simulations.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
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