1,307 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
Simulation of Entangled Polymer Solutions
We present a computer simulation of entangled polymer solutions at
equilibrium. The chains repel each other via a soft Gaussian potential,
appropriate for semi-dilute solutions at the scale of a correlation blob. The
key innovation to suppress chain crossings is to use a pseudo-continuous model
of a backbone which effectively leaves no gaps between consecutive points on
the chain, unlike the usual bead-and-spring model. Our algorithm is
sufficiently fast to observe the entangled regime using a standard desktop
computer. The simulated structural and mechanical correlations are in fair
agreement with the expected predictions for a semi-dilute solution of entangled
chains
Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule
A spatial scale-free network is introduced and studied whose motivation has
been originated in the growing Internet as well as the Airport networks. We
argue that in these real-world networks a new node necessarily selects one of
its neighbouring local nodes for connection and is not controlled by the
preferential attachment as in the Barab\'asi-Albert (BA) model. This
observation has been mimicked in our model where the nodes pop-up at randomly
located positions in the Euclidean space and are connected to one end of the
nearest link. In spite of this crucial difference it is observed that the
leading behaviour of our network is like the BA model. Defining link weight as
an algebraic power of its Euclidean length, the weight distribution and the
non-linear dependence of the nodal strength on the degree are analytically
calculated. It is claimed that a power law decay of the link weights with time
ensures such a non-linear behavior. Switching off the Euclidean space from the
same model yields a much simpler definition of the Barab\'asi-Albert model
where numerical effort grows linearly with .Comment: 6 pages, 6 figure
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
Metastable configurations of spin models on random graphs
One-flip stable configurations of an Ising-model on a random graph with
fluctuating connectivity are examined. In order to perform the quenched average
of the number of stable configurations we introduce a global order-parameter
function with two arguments. The analytical results are compared with numerical
simulations.Comment: 11 pages Revtex, minor changes, to appear in Phys. Rev.
Melting-freezing cycles in a relatively sheared pair of crystalline monolayers
The nonequilibrium dynamical behaviour that arises when two ordered
two-dimensional monolayers of particles are sheared over each other is studied
in Brownian dynamics simulations. A curious sequence of nonequilibrium states
is observed as the driving rate is increased, the most striking of which is a
sliding state with irregular alternation between disordered and ordered states.
We comment on possible mechanisms underlying these cycles, and experiments that
could observe them.Comment: 7 pages, 8 figures, minor changes in text and figures, references
adde
Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks
I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted Barabási-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the contact process. I compare simulation results with spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects due to network inhomogeneities. Finite-size study of the QMF shows the expected disappearance of the epidemic threshold λc in the thermodynamic limit and an inverse participation ratio ∼0.25, meaning localization in case of disassortative weight scheme. Contrarily, for the multiplicative weights and the unweighted trees, this value vanishes in the thermodynamic limit, suggesting only weak rare-region effects in agreement with the dynamical simulations. Strong corrections to the mean-field behavior in case of disassortative weights explains the concave shape of the order parameter ρ(λ) at the transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths phases as the consequence of quenched topological heterogeneities
The International Trade Network
Bilateral trade relationships in the international level between pairs of
countries in the world give rise to the notion of the International Trade
Network (ITN). This network has attracted the attention of network researchers
as it serves as an excellent example of the weighted networks, the link weight
being defined as a measure of the volume of trade between two countries. In
this paper we analyzed the international trade data for 53 years and studied in
detail the variations of different network related quantities associated with
the ITN. Our observation is that the ITN has also a scale invariant structure
like many other real-world networks.Comment: 9 pages, 7 figure
Non-equilibrium mean-field theories on scale-free networks
Many non-equilibrium processes on scale-free networks present anomalous
critical behavior that is not explained by standard mean-field theories. We
propose a systematic method to derive stochastic equations for mean-field order
parameters that implicitly account for the degree heterogeneity. The method is
used to correctly predict the dynamical critical behavior of some binary spin
models and reaction-diffusion processes. The validity of our non-equilibrium
theory is furtherly supported by showing its relation with the generalized
Landau theory of equilibrium critical phenomena on networks.Comment: 4 pages, no figures, major changes in the structure of the pape
Long-Range Navigation on Complex Networks using L\'evy Random Walks
We introduce a strategy of navigation in undirected networks, including
regular, random, and complex networks, that is inspired by L\'evy random walks,
generalizing previous navigation rules. We obtained exact expressions for the
stationary probability distribution, the occupation probability, the mean first
passage time, and the average time to reach a node on the network. We found
that the long-range navigation using the L\'evy random walk strategy, compared
with the normal random walk strategy, is more efficient at reducing the time to
cover the network. The dynamical effect of using the L\'evy walk strategy is to
transform a large-world network into a small world. Our exact results provide a
general framework that connects two important fields: L\'evy navigation
strategies and dynamics on complex networks.Comment: 6 pages, 3 figure
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