60 research outputs found
Extremal noise events, intermittency and Log-Poisson statistics in non-equilibrium aging of complex systems
We review the close link between intermittent events ('quakes') and extremal
noise fluctuations which has been advocated in recent numerical and theoretical
work. From the idea that record-breaking noise fluctuations trigger the quakes,
an approximate analytical description of non-equilibrium aging as a Poisson
process with logarithmic time arguments can be derived. Theoretical predictions
for measurable statistical properties of mesoscopic fluctuations are
emphasized, and supporting numerical evidence is included from simulations of
short-ranged Ising spin-glass models, of the ROM model of vortex dynamics in
type II superconductors, and of the Tangled Nature model of biological
evolution.Comment: 12 pages, 9 figures, to appear in the Proceedings of the third SPIE
International Symposium on Fluctuations and Noise, 23-26 May 2005, Austin,
Texa
Coarse-graining complex dynamics: Continuous Time Random Walks vs. Record Dynamics
Continuous Time Random Walks (CTRW) are widely used to coarse-grain the
evolution of systems jumping from a metastable sub-set of their configuration
space, or trap, to another via rare intermittent events. The multi-scaled
behavior typical of complex dynamics is provided by a fat-tailed distribution
of the waiting time between consecutive jumps. We first argue that CTRW are
inadequate to describe macroscopic relaxation processes for three reasons:
macroscopic variables are not self-averaging, memory effects require an
all-knowing observer,and different mechanisms whereby the jumps affect
macroscopic variables all produce identical long time relaxation behaviors.
Hence, CTRW shed no light on the link between microscopic and macroscopic
dynamics. We then highlight how a more recent approach, Record Dynamics (RD)
provides a viable alternative, based on a very different set of physical ideas:
while CTRW make use of a renewal process involving identical traps of infinite
size, RD embodies a dynamical entrenchment into a hierarchy of traps which are
finite in size and possess different degrees of meta-stability. We show in
particular how RD produces the stretched exponential, power-law and logarithmic
relaxation behaviors ubiquitous in complex dynamics, together with the
sub-diffusive time dependence of the Mean Square Displacement characteristic of
single particles moving in a complex environment.Comment: 6 pages. To appear in EP
Optimization by Record Dynamics
Large dynamical changes in thermalizing glassy systems are triggered by
trajectories crossing record sized barriers, a behavior revealing the presence
of a hierarchical structure in configuration space. The observation is here
turned into a novel local search optimization algorithm dubbed Record Dynamics
Optimization, or RDO. RDO uses the Metropolis rule to accept or reject
candidate solutions depending on the value of a parameter akin to the
temperature, and minimizes the cost function of the problem at hand through
cycles where its `temperature' is raised and subsequently decreased in order to
expediently generate record high (and low) values of the cost function. Below,
RDO is introduced and then tested by searching the ground state of the
Edwards-Anderson spin-glass model, in two and three spatial dimensions. A
popular and highly efficient optimization algorithm, Parallel Tempering (PT) is
applied to the same problem as a benchmark. RDO and PT turn out to produce
solution of similar quality for similar numerical effort, but RDO is simpler to
program and additionally yields geometrical information on the system's
configuration space which is of interest in many applications. In particular,
the effectiveness of RDO strongly indicates the presence of the above mentioned
hierarchically organized configuration space, with metastable regions indexed
by the cost (or energy) of the transition states connecting them.Comment: 14 pages, 12 figure
Log-Poisson statistics and full aging in glassy systems
We argue that Poisson statistics in logarithmic time provides an idealized
description of non-equilibrium configurational rearrangements in aging glassy
systems. The description puts stringent requirements on the geometry of the
metastable attractors visited at age . Analytical implications for the
residence time distributions as a function of and the correlation
functions are derived. These are verified by extensive numerical studies of
short range Ising spin glasses.Comment: v3 (final): 8 pages, 4 figures. Minor change
Mesoscopic real space structures in aging spin-glasses: the Edwards-Anderson model
Isothermal simulational data for the 3D Edwards-Anderson spin glass are
collected at several temperatures below and, in analogy with a
recent model of dense colloidal suspensions,interpreted in terms of clusters of
contiguous spins overturned by quakes, non-equilibrium events linked to record
sized energy fluctuations. We show numerically that, to a good approximation,
these quakes are statistically independent and constitute a Poisson process
whose average grows logarithmically in time. The overturned clusters are local
projections on one of the two ground states of the model, and grow likewise
logarithmically in time. Data collected at different temperatures can be
collapsed by scaling them with , a hitherto unnoticed feature of the
E-A model, which we relate on the one hand to the geometry of configuration
space and on the other to experimental memory and rejuvenation effects. The
rate at which a cluster flips is shown to decrease exponentially with the size
of the cluster, as recently assumed in a coarse grained model of dense
colloidal dynamics. The evolving structure of clusters in real space is finally
sssociated to the decay of the thermo-remanent magnetization.
Our analysis provides an unconventional coarse-grained description of spin
glass aging as statistically subordinated to a Poisson quaking process and
highlights record dynamics as a viable common theoretical framework for aging
in different systems.Comment: 13 pages, 6 figs. Revised text and notation, several typos correcte
Evolution and non-equilibrium physics. A study of the Tangled Nature Model
We argue that the stochastic dynamics of interacting agents which replicate,
mutate and die constitutes a non-equilibrium physical process akin to aging in
complex materials. Specifically, our study uses extensive computer simulations
of the Tangled Nature Model (TNM) of biological evolution to show that
punctuated equilibria successively generated by the model's dynamics have
increasing entropy and are separated by increasing entropic barriers. We
further show that these states are organized in a hierarchy and that limiting
the values of possible interactions to a finite interval leads to stationary
fluctuations within a component of the latter. A coarse-grained description
based on the temporal statistics of quakes, the events leading from one
component of the hierarchy to the next, accounts for the logarithmic growth of
the population and the decaying rate of change of macroscopic variables.
Finally, we question the role of fitness in large scale evolution models and
speculate on the possible evolutionary role of rejuvenation and memory effects.Comment: 6 pages, 6 figure
- …