1,081 research outputs found
On the definition of temperature in dense granular media
In this Letter we report the measurement of a pseudo-temperature for
compacting granular media on the basis of the Fluctuation-Dissipation relations
in the aging dynamics of a model system. From the violation of the
Fluctuation-Dissipation Theorem an effective temperature emerges (a dynamical
temperature T_{dyn}) whose ratio with the equilibrium temperature T_d^{eq}
depends on the particle density. We compare the results for the
Fluctuation-Dissipation Ratio (FDR) T_{dyn}/T_d^{eq} at several densities with
the outcomes of Edwards' approach at the corresponding densities. It turns out
that the FDR and the so-called Edwards' ratio coincide at several densities
(very different ages of the system), opening in this way the door to
experimental checks as well as theoretical constructions.Comment: RevTex4 4 pages, 4 eps figure
Vulnerability of weighted networks
In real networks complex topological features are often associated with a
diversity of interactions as measured by the weights of the links. Moreover,
spatial constraints may as well play an important role, resulting in a complex
interplay between topology, weight, and geography. In order to study the
vulnerability of such networks to intentional attacks, these attributes must be
therefore considered along with the topological quantities. In order to tackle
this issue, we consider the case of the world-wide airport network, which is a
weighted heterogeneous network whose evolution and structure are influenced by
traffic and geographical constraints. We first characterize relevant
topological and weighted centrality measures and then use these quantities as
selection criteria for the removal of vertices. We consider different attack
strategies and different measures of the damage achieved in the network. The
analysis of weighted properties shows that centrality driven attacks are
capable to shatter the network's communication or transport properties even at
very low level of damage in the connectivity pattern. The inclusion of weight
and traffic therefore provides evidence for the extreme vulnerability of
complex networks to any targeted strategy and need to be considered as key
features in the finding and development of defensive strategies
Tapping Spin Glasses
We consider a tapping dynamics, analogous to that in experiments on granular
media, on spin glasses and ferromagnets on random thin graphs. Between taps,
zero temperature single spin flip dynamics takes the system to a metastable
state. Tapping, corresponds to flipping simultaneously any spin with
probability . This dynamics leads to a stationary regime with a steady state
energy . We analytically solve this dynamics for the one dimensional
ferromagnet and spin glass. Numerical simulations for spin glasses and
ferromagnets of higher connectivity are carried out, in particular we find a
novel first order transition for the ferromagnetic systems.Comment: 5 pages, 3 figures, RevTe
Heterogeneous aging in spin glasses
We introduce a set of theoretical ideas that form the basis for an analytical
framework capable of describing nonequilibrium dynamics in glassy systems. We
test the resulting scenario by comparing its predictions with numerical
simulations of short-range spin glasses. Local fluctuations and responses are
shown to be connected by a generalized local out-of-equilibrium
fluctuation-dissipation relation. Scaling relationships are uncovered for the
slow evolution of heterogeneities at all time scales.Comment: Substantially reorganized to improve clarity of exposition. Accepted
for publication in Physical Review Letters. 5 pages, 4 figure
Effective temperatures of a heated Brownian particle
We investigate various possible definitions of an effective temperature for a
particularly simple nonequilibrium stationary system, namely a heated Brownian
particle suspended in a fluid. The effective temperature based on the
fluctuation dissipation ratio depends on the time scale under consideration, so
that a simple Langevin description of the heated particle is impossible. The
short and long time limits of this effective temperature are shown to be
consistent with the temperatures estimated from the kinetic energy and Einstein
relation, respectively. The fluctuation theorem provides still another
definition of the temperature, which is shown to coincide with the short time
value of the fluctuation dissipation ratio
Local structure of liquid carbon controls diamond nucleation
Diamonds melt at temperatures above 4000 K. There are no measurements of the
steady-state rate of the reverse process: diamond nucleation from the melt,
because experiments are difficult at these extreme temperatures and pressures.
Using numerical simulations, we estimate the diamond nucleation rate and find
that it increases by many orders of magnitude when the pressure is increased at
constant supersaturation. The reason is that an increase in pressure changes
the local coordination of carbon atoms from three-fold to four-fold. It turns
out to be much easier to nucleate diamond in a four-fold coordinated liquid
than in a liquid with three-fold coordination, because in the latter case the
free-energy cost to create a diamond-liquid interface is higher. We speculate
that this mechanism for nucleation control is relevant for crystallization in
many network-forming liquids. On the basis of our calculations, we conclude
that homogeneous diamond nucleation is likely in carbon-rich stars and unlikely
in gaseous planets
How glasses explore configuration space
We review a statistical picture of the glassy state derived from the analysis
of the off-equilibrium fluctuation-dissipation relations. We define an
ultra-long time limit where ``one time quantities'' are close to equilibrium
while response and correlation can still display aging.
In this limit it is possible to relate the fluctuation-response relation to
static breaking of ergodicity. The resulting picture suggests that even far
from that limit, the fluctuation-dissipation ratio relates to the rate of
growth of the configurational entropy with free-energy density.Comment: To appear in the proceedings of the "3rd workshop on non-equilibrium
phenomena in supercooled fluids, glasses and amorphous materials" Pisa 22-27
September 200
Observing the evaporation transition in vibro-fluidized granular matter
By shaking a sand box the grains on the top start to jump giving the picture
of evaporating a sand bulk, and a gaseous transition starts at the surface
granular matter (GM) bed. Moreover the mixture of the grains in the whole bed
starts to move in a cooperative way which is far away from a Brownian
description. In a previous work we have shown that the key element to describe
the statistics of this behavior is the exclusion of volume principle, whereby
the system obeys a Fermi configurational approach. Even though the experiment
involves an archetypal non-equilibrium system, we succeeded in defining a
global temperature, as the quantity associated to the Lagrange parameter in a
maximum entropic statistical description. In fact in order to close our
approach we had to generalize the equipartition theorem for dissipative
systems. Therefore we postulated, found and measured a fundamental dissipative
parameter, written in terms of pumping and gravitational energies, linking the
configurational entropy to the collective response for the expansion of the
centre of mass (c.m.) of the granular bed. Here we present a kinetic approach
to describe the experimental velocity distribution function (VDF) of this
non-Maxwellian gas of macroscopic Fermi-like particles (mFp). The evaporation
transition occurs mainly by jumping balls governed by the excluded volume
principle. Surprisingly in the whole range of low temperatures that we measured
this description reveals a lattice-gas, leading to a packing factor, which is
independent of the external parameters. In addition we measure the mean free
path, as a function of the driving frequency, and corroborate our prediction
from the present kinetic theory.Comment: 6 pages, 4 figures, submitted for publication September 1st, 200
Monte-Carlo simulations of the violation of the fluctuation-dissipation theorem in domain growth processes
Numerical simulations of various domain growth systems are reported, in order
to compute the parameter describing the violation of fluctuation dissipation
theorem (FDT) in aging phenomena. We compute two-times correlation and response
functions and find that, as expected from the exact solution of a certain
mean-field model (equivalent to the O(N) model in three dimensions, in the
limit of N going to infinity), this parameter is equal to one (no violation of
FDT) in the quasi-equilibrium regime (short separation of times), and zero in
the aging regime.Comment: 5 pages, 5 eps figure
Exactly solvable analogy of small-world networks
We present an exact description of a crossover between two different regimes
of simple analogies of small-world networks. Each of the sites chosen with a
probability from sites of an ordered system defined on a circle is
connected to all other sites selected in such a way. Every link is of a unit
length. Thus, while changes from 0 to 1, an averaged shortest distance
between a pair of sites changes from to .
We find the distribution of the shortest distances and obtain a
scaling form of . In spite of the simplicity of the models
under consideration, the results appear to be surprisingly close to those
obtained numerically for usual small-world networks.Comment: 4 pages with 3 postscript figure
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