46 research outputs found
Analytic study of the urn model for separation of sand
We present an analytic study of the urn model for separation of sand recently
introduced by Lipowski and Droz (Phys. Rev. E 65, 031307 (2002)). We solve
analytically the master equation and the first-passage problem. The analytic
results confirm the numerical results obtained by Lipowski and Droz. We find
that the stationary probability distribution and the shortest one among the
characteristic times are governed by the same free energy. We also analytically
derive the form of the critical probability distribution on the critical line,
which supports their results obtained by numerically calculating Binder
cumulants (cond-mat/0201472).Comment: 6 pages including 3 figures, RevTe
Transversal inhomogeneities in dilute vibrofluidized granular fluids
The spontaneous symmetry breaking taking place in the direction perpendicular
to the energy flux in a dilute vibrofluidized granular system is investigated,
using both a hydrodynamic description and simulation methods. The latter
include molecular dynamics and direct Monte Carlo simulation of the Boltzmann
equation. A marginal stability analysis of the hydrodynamic equations, carried
out in the WKB approximation, is shown to be in good agreement with the
simulation results. The shape of the hydrodynamic profiles beyond the
bifurcation is discussed
Dynamics of vibrofluidized granular gases in periodic structures
The behavior of a driven granular gas in a container consisting of
connected compartments is studied employing a microscopic kinetic model. After
obtaining the governing equations for the occupation numbers and the granular
temperatures of each compartment we consider the various dynamical regimes. The
system displays interesting analogies with the ordering processes of phase
separating mixtures quenched below the their critical point. In particular, we
show that below a certain value of the driving intensity the populations of the
various compartments become unequal and the system clusterizes. Such a
phenomenon is not instantaneous, but is characterized by a time scale, ,
which follows a Vogel-Vulcher exponential behavior. On the other hand, the
reverse phenomenon which involves the ``evaporation'' of a cluster due to the
driving force is also characterized by a second time scale which diverges at
the limit of stability of the cluster.Comment: 11 pages, 17 figure