1,557 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
Basins of attraction of metastable states of the spherical -spin model
We study the basins of attraction of metastable states in the spherical
-spin spin glass model, starting the relaxation dynamics at a given distance
from a thermalized condition. Weighting the initial condition with the
Boltzmann distribution we find a finite size for the basins. On the contrary, a
white weighting of the initial condition implies vanishing basins of
attraction. We make the corresponding of our results with the ones of a
recently constructed effective potential.Comment: LaTeX, 7 pages, 7 eps figure
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.
Boundary Condition of Polyelectrolyte Adsorption
The modification of the boundary condition for polyelectrolyte adsorption on
charged surface with short-ranged interaction is investigated under two
regimes. For weakly charged Gaussian polymer in which the short-ranged
attraction dominates, the boundary condition is the same as that of the neutral
polymer adsorption. For highly charged polymer (compressed state) in which the
electrostatic interaction dominates, the linear relationship (electrostatic
boundary condition) between the surface monomer density and the surface charge
density needs to be modified.Comment: 4 page
Rank-based model for weighted network with hierarchical organization and disassortative mixing
Motivated by a recently introduced network growth mechanism that rely on the
ranking of node prestige measures [S. Fortunato \emph{et al}., Phys. Rev. Lett.
\textbf{96}, 218701 (2006)], a rank-based model for weighted network evolution
is studied. The evolution rule of the network is based on the ranking of node
strength, which couples the topological growth and the weight dynamics. Both
analytical solutions and numerical simulations show that the generated networks
possess scale-free distributions of degree, strength, and weight in the whole
region of the growth dynamics parameter (). We also characterize the
clustering and correlation properties of this class of networks. It is showed
that at a structural phase transition occurs, and for the
generated network simultaneously exhibits hierarchical organization and
disassortative degree correlation, which is consistent with a wide range of
biological networks.Comment: 4 pages, 5 figure
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.
Thermalization of an anisotropic granular particle
We investigate the dynamics of a needle in a two-dimensional bath composed of
thermalized point particles. Collisions between the needle and points are
inelastic and characterized by a normal restitution coefficient . By
using the Enskog-Boltzmann equation, we obtain analytical expressions for the
translational and rotational granular temperatures of the needle and show that
these are, in general, different from the bath temperature. The translational
temperature always exceeds the rotational one, though the difference decreases
with increasing moment of inertia. The predictions of the theory are in very
good agreement with numerical simulations of the model.Comment: 7 pages, 6 Figures, submitted to PRE. Revised version (Fig1, Fig5 and
Fig6 corrected + minor typos
Compaction dynamics of a granular media under vertical tapping
We report new experimental results on granular compaction under consecutive
vertical taps. The evolution of the mean volume fraction and of the mean
potential energy of a granular packing presents a slow densification until a
final steady-state, and is reminiscent to usual relaxation in glasses via a
stretched exponential law. The intensity of the taps seems to rule the
characteristic time of the relaxation according to an Arrhenius's type relation
>. Finally, the analysis of the vertical volume fraction profile reveals an
almost homogeneous densification in the packing.Comment: 7 pages, 4 figures, to appear in Europhysics Letter
Exact calculations of first-passage quantities on recursive networks
We present general methods to exactly calculate mean-first passage quantities
on self-similar networks defined recursively. In particular, we calculate the
mean first-passage time and the splitting probabilities associated to a source
and one or several targets; averaged quantities over a given set of sources
(e.g., same-connectivity nodes) are also derived. The exact estimate of such
quantities highlights the dependency of first-passage processes with respect to
the source-target distance, which has recently revealed to be a key parameter
to characterize transport in complex media. We explicitly perform calculations
for different classes of recursive networks (finitely ramified fractals,
scale-free (trans)fractals, non-fractals, mixtures between fractals and
non-fractals, non-decimable hierarchical graphs) of arbitrary size. Our
approach unifies and significantly extends the available results in the field.Comment: 16 pages, 10 figure
Voter model with non-Poissonian interevent intervals
Recent analysis of social communications among humans has revealed that the
interval between interactions for a pair of individuals and for an individual
often follows a long-tail distribution. We investigate the effect of such a
non-Poissonian nature of human behavior on dynamics of opinion formation. We
use a variant of the voter model and numerically compare the time to consensus
of all the voters with different distributions of interevent intervals and
different networks. Compared with the exponential distribution of interevent
intervals (i.e., the standard voter model), the power-law distribution of
interevent intervals slows down consensus on the ring. This is because of the
memory effect; in the power-law case, the expected time until the next update
event on a link is large if the link has not had an update event for a long
time. On the complete graph, the consensus time in the power-law case is close
to that in the exponential case. Regular graphs bridge these two results such
that the slowing down of the consensus in the power-law case as compared to the
exponential case is less pronounced as the degree increases.Comment: 18 pages, 8 figure
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