1,402 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
A Note on Edwards' Hypothesis for Zero-Temperature Ising Dynamics
We give a simple criterion for checking the so called Edwards' hypothesis in
certain zero-temperature, ferromagnetic spin-flip dynamics and use it to
invalidate the hypothesis in various examples in dimension one and higher.Comment: 11 pages, 4 figure
Shear localization in a model glass
Using molecular dynamics simulations, we show that a simple model of a glassy
material exhibits the shear localization phenomenon observed in many complex
fluids. At low shear rates, the system separates into a fluidized shear-band
and an unsheared part. The two bands are characterized by a very different
dynamics probed by a local intermediate scattering function. Furthermore, a
stick-slip motion is observed at very small shear rates. Our results, which
open the possibility of exploring complex rheological behavior using
simulations, are compared to recent experiments on various soft glasses.Comment: 4 pages, 4 figures (5 figure files
Gender homophily from spatial behavior in a primary school: a sociometric study
We investigate gender homophily in the spatial proximity of children (6 to 12
years old) in a French primary school, using time-resolved data on face-to-face
proximity recorded by means of wearable sensors. For strong ties, i.e., for
pairs of children who interact more than a defined threshold, we find
statistical evidence of gender preference that increases with grade. For weak
ties, conversely, gender homophily is negatively correlated with grade for
girls, and positively correlated with grade for boys. This different evolution
with grade of weak and strong ties exposes a contrasted picture of gender
homophily
Power injected in a granular gas
A granular gas may be modeled as a set of hard-spheres undergoing inelastic
collisions; its microscopic dynamics is thus strongly irreversible. As pointed
out in several experimental works bearing on turbulent flows or granular
materials, the power injected in a dissipative system to sustain a steady-state
over an asymptotically large time window is a central observable. We describe
an analytic approach allowing us to determine the full distribution of the
power injected in a granular gas within a steady-state resulting from
subjecting each particle independently either to a random force (stochastic
thermostat) or to a deterministic force proportional to its velocity (Gaussian
thermostat). We provide an analysis of our results in the light of the
relevance, for other types of systems, of the injected power to fluctuation
relations.Comment: 9 pages, 4 figures. Contribution to Proceedings of "Work,
Dissipation, and Fluctuations in Nonequilibrium Physics", Brussels, 200
Continuum limit of amorphous elastic bodies (III): Three dimensional systems
Extending recent numerical studies on two dimensional amorphous bodies, we
characterize the approach of elastic continuum limit in three dimensional
(weakly polydisperse) Lennard-Jones systems. While performing a systematic
finite-size analysis (for two different quench protocols) we investigate the
non-affine displacement field under external strain, the linear response to an
external delta force and the low-frequency harmonic eigenmodes and their
density distribution. Qualitatively similar behavior is found as in two
dimensions. We demonstrate that the classical elasticity description breaks
down below an intermediate length scale , which in our system is
approximately 23 molecular sizes. This length characterizes the correlations of
the non-affine displacement field, the self-averaging of external noise with
distance from the source and gives the lower wave length bound for the
applicability of the classical eigenfrequency calculations. We trace back the
"Boson-peak" of the density of eigenfrequencies (obtained from the velocity
auto-correlation function) to the inhomogeneities on wave lengths smaller than
.Comment: 27 pages, 11 figures, submitted to Phys. Rev.
Injected power and entropy flow in a heated granular gas
Our interest goes to the power injected in a heated granular gas and to the
possibility to interpret it in terms of entropy flow. We numerically determine
the distribution of the injected power by means of Monte-Carlo simulations.
Then, we provide a kinetic theory approach to the computation of such a
distribution function. Finally, after showing why the injected power does not
satisfy a Fluctuation Relation a la Gallavotti-Cohen, we put forward a new
quantity which does fulfill such a relation, and is not only applicable in a
variety of frameworks outside the granular world, but also experimentally
accessible.Comment: accepted in Europhys. Let
Fluctuations of power injection in randomly driven granular gases
We investigate the large deviation function pi(w) for the fluctuations of the
power W(t)=w t, integrated over a time t, injected by a homogeneous random
driving into a granular gas, in the infinite time limit. Starting from a
generalized Liouville equation we obtain an equation for the generating
function of the cumulants mu(lambda) which appears as a generalization of the
inelastic Boltzmann equation and has a clear physical interpretation.
Reasonable assumptions are used to obtain mu(lambda) in a closed analytical
form. A Legendre transform is sufficient to get the large deviation function
pi(w). Our main result, apart from an estimate of all the cumulants of W(t) at
large times t, is that pi(w) has no negative branch. This immediately results
in the failure of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in
previous studies had been suggested to be valid for injected power in driven
granular gases. We also present numerical results, in order to discuss the
finite time behavior of the fluctuations of W(t). We discover that their
probability density function converges extremely slowly to its asymptotic
scaling form: the third cumulant saturates after a characteristic time larger
than 50 mean free times and the higher order cumulants evolve even slower. The
asymptotic value is in good agreement with our theory. Remarkably, a numerical
check of the GCFR is feasible only at small times, since negative events
disappear at larger times. At such small times this check leads to the
misleading conclusion that GCFR is satisfied for pi(w). We offer an explanation
for this remarkable apparent verification. In the inelastic Maxwell model,
where a better statistics can be achieved, we are able to numerically observe
the failure of GCFR.Comment: 23 pages, 15 figure
First-order transition in small-world networks
The small-world transition is a first-order transition at zero density of
shortcuts, whereby the normalized shortest-path distance undergoes a
discontinuity in the thermodynamic limit. On finite systems the apparent
transition is shifted by . Equivalently a ``persistence
size'' can be defined in connection with finite-size
effects. Assuming , simple rescaling arguments imply that
. We confirm this result by extensive numerical simulation in one to
four dimensions, and argue that implies that this transition is
first-order.Comment: 4 pages, 3 figures, To appear in Europhysics Letter
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
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