139 research outputs found
Aging in Dense Colloids as Diffusion in the Logarithm of Time
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 aging 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 aging dynamics homogeneous: for colloids, this entails
diffusion but on a logarithmic time scale. 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.Comment: 6 pages, extensively revised, final version; for related work, see
http://www.physics.emory.edu/faculty/boettcher/ or
http://www.fysik.sdu.dk/staff/staff-vip/pas-personal.htm
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
Tempo and Mode of Evolution in the Tangled Nature Model
We study the Tangled Nature model of macro evolution and demonstrate that the
co-evolutionary dynamics produces an increasingly correlated core of well
occupied types. At the same time the entire configuration of types becomes
increasing de-correlated. This finding is related to ecosystem evolution. The
systems level dynamics of the model is subordinated to intermittent transitions
between meta-stable states. We improve on previous studies of the statistics of
the transition times and show that the fluctuations in the offspring
probability decreases with number of transitions. The longtime adaptation, as
seen by an increasing population size is demonstrated to be related to the
convexity of the offspring probability. We explain how the models behaviour is
a mathematical reflection of Darwin's concept of adaptation of profitable
variations.Comment: 6 pages, 5 figure
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
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
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
Record dynamics of evolving metastable systems: theory and applications
Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as âphysical agingâ, but from the vantage point of RD, the evolution of a class of systems of physical, biological, and cultural origin is rooted in a hierarchically structured configuration space and can, therefore, be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self-Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time-series, and connects it to the statistics of quakes in metastable hierarchical systems, arguing that the relaxation effects of quakes can generally be described by power laws unrelated to criticality. Several different applications of RD have been developed over the years. Some of these are described, showing the basic RD hypothesis and how the log-time homogeneity of quake dynamics, can be empirically verified in a given context. The discussion summarizes the paper and briefly mentions applications not discussed in detail. Finally, the outlook points to possible improvements and to new areas of research where RD could be of use
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
Records in a changing world
In the context of this paper, a record is an entry in a sequence of random
variables (RV's) that is larger or smaller than all previous entries. After a
brief review of the classic theory of records, which is largely restricted to
sequences of independent and identically distributed (i.i.d.) RV's, new results
for sequences of independent RV's with distributions that broaden or sharpen
with time are presented. In particular, we show that when the width of the
distribution grows as a power law in time , the mean number of records is
asymptotically of order for distributions with a power law tail (the
\textit{Fr\'echet class} of extremal value statistics), of order
for distributions of exponential type (\textit{Gumbel class}), and of order
for distributions of bounded support (\textit{Weibull class}),
where the exponent describes the behaviour of the distribution at the
upper (or lower) boundary. Simulations are presented which indicate that, in
contrast to the i.i.d. case, the sequence of record breaking events is
correlated in such a way that the variance of the number of records is
asymptotically smaller than the mean.Comment: 12 pages, 2 figure
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