2,457 research outputs found
Free cooling and inelastic collapse of granular gases in high dimensions
The connection between granular gases and sticky gases has recently been
considered, leading to the conjecture that inelastic collapse is avoided for
space dimensions higher than 4. We report Molecular Dynamics simulations of
hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular
medium is monitored throughout the cooling process. The behaviour is found to
be very similar to that of a two-dimensional system, with a shearing-like
instability of the velocity field and inelastic collapse when collisions are
inelastic enough, showing that the connection with sticky gases needs to be
revised.Comment: 6 pages, 6 figures (7 postscript files), submitted to EPJ
Phase space diffusion and low temperature aging
We study the dynamical evolution of a system with a phase space consisting of
configurations with random energies. The dynamics we use is of Glauber type. It
allows for some dynamical evolution ang aging even at very low temperatures,
through the search of configurations with lower energies.Comment: 11 pages latex, 1 ps figure adde
On the properties of small-world network models
We study the small-world networks recently introduced by Watts and Strogatz
[Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We
characterize the geometrical properties resulting from the coexistence of a
local structure and random long-range connections, and we examine their
evolution with size and disorder strength. We show that any finite value of the
disorder is able to trigger a ``small-world'' behaviour as soon as the initial
lattice is big enough, and study the crossover between a regular lattice and a
``small-world'' one. These results are corroborated by the investigation of an
Ising model defined on the network, showing for every finite disorder fraction
a crossover from a high-temperature region dominated by the underlying
one-dimensional structure to a mean-field like low-temperature region. In
particular there exists a finite-temperature ferromagnetic phase transition as
soon as the disorder strength is finite.Comment: 19 pages including 15 figures, version accepted for publication in
EPJ
Glass transition and random walks on complex energy landscapes
We present a simple mathematical model of glassy dynamics seen as a random
walk in a directed, weighted network of minima taken as a representation of the
energy landscape. Our approach gives a broader perspective to previous studies
focusing on particular examples of energy landscapes obtained by sampling
energy minima and saddles of small systems. We point out how the relation
between the energies of the minima and their number of neighbors should be
studied in connection with the network's global topology, and show how the
tools developed in complex network theory can be put to use in this context
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
Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
Combining analytical and numerical methods, we study within the framework of
the homogeneous non-linear Boltzmann equation, a broad class of models relevant
for the dynamics of dissipative fluids, including granular gases. We use the
new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and
extend our results to a different heating mechanism, namely a deterministic
non-linear friction force. We derive analytically the high energy tail of the
velocity distribution and compare the theoretical predictions with high
precision numerical simulations. Stretched exponential forms are obtained when
the non-equilibrium steady state is stable. We derive sub-leading corrections
and emphasize their relevance. In marginal stability cases, power-law behaviors
arise, with exponents obtained as the roots of transcendental equations. We
also consider some simple BGK (Bhatnagar, Gross, Krook) models, driven by
similar heating devices, to test the robustness of our predictions
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