459 research outputs found
Experimental study of the compaction dynamics for 2D anisotropic granular materials
We present an experimental study of the compaction dynamics for
two-dimensional anisotropic granular systems. Compaction dynamics is measured
at three different scales : (i) the macroscopic scale through the packing
fraction , (ii) the mesoscopic scale through both fractions of aligned
grains and ideally ordered grains , and (iii) the
microscopic scale through both rotational and translational grain mobilities
. The effect of the grain rotations on the compaction dynamics has
been measured. At the macroscopic scale, we have observed a discontinuity in
the late stages of the compaction curve. At the mesoscopic scale, we have
observed the formation and the growth of domains made of aligned grains. From a
microscopic point of view, measurements reveal that the beginning of the
compaction process is essentially related to translational motion of the
grains. The grains rotations drive mainly the process during the latest stages
of compaction.Comment: 8pages, 11 figure
Glass transition in granular media
In the framework of schematic hard spheres lattice models for granular media
we investigate the phenomenon of the ``jamming transition''. In particular,
using Edwards' approach, by analytical calculations at a mean field level, we
derive the system phase diagram and show that ``jamming'' corresponds to a
phase transition from a ``fluid'' to a ``glassy'' phase, observed when
crystallization is avoided. Interestingly, the nature of such a ``glassy''
phase turns out to be the same found in mean field models for glass formers.Comment: 7 pages, 4 figure
Site Percolation and Phase Transitions in Two Dimensions
The properties of the pure-site clusters of spin models, i.e. the clusters
which are obtained by joining nearest-neighbour spins of the same sign, are
here investigated. In the Ising model in two dimensions it is known that such
clusters undergo a percolation transition exactly at the critical point. We
show that this result is valid for a wide class of bidimensional systems
undergoing a continuous magnetization transition. We provide numerical evidence
for discrete as well as for continuous spin models, including SU(N) lattice
gauge theories. The critical percolation exponents do not coincide with the
ones of the thermal transition, but they are the same for models belonging to
the same universality class.Comment: 8 pages, 6 figures, 2 tables. Numerical part developed; figures,
references and comments adde
Relaxation properties in a lattice gas model with asymmetrical particles
We study the relaxation process in a two-dimensional lattice gas model, where
the interactions come from the excluded volume. In this model particles have
three arms with an asymmetrical shape, which results in geometrical frustration
that inhibits full packing. A dynamical crossover is found at the arm
percolation of the particles, from a dynamical behavior characterized by a
single step relaxation above the transition, to a two-step decay below it.
Relaxation functions of the self-part of density fluctuations are well fitted
by a stretched exponential form, with a exponent decreasing when the
temperature is lowered until the percolation transition is reached, and
constant below it. The structural arrest of the model seems to happen only at
the maximum density of the model, where both the inverse diffusivity and the
relaxation time of density fluctuations diverge with a power law. The dynamical
non linear susceptibility, defined as the fluctuations of the self-overlap
autocorrelation, exhibits a peak at some characteristic time, which seems to
diverge at the maximum density as well.Comment: 7 pages and 9 figure
The jamming transition of Granular Media
We briefly review the basics ideas and results of a recently proposed
statistical mechanical approach to granular materials. Using lattice models
from standard Statistical Mechanics and results from a mean field replica
approach and Monte Carlo simulations we find a jamming transition in granular
media closely related to the glass transition in super-cooled liquids. These
models reproduce the logarithmic relaxation in granular compaction and
reversible-irreversible lines, in agreement with experimental data. The models
also exhibit aging effects and breakdown of the usual fluctuation dissipation
relation. It is shown that the glass transition may be responsible for the
logarithmic relaxation and may be related to the cooperative effects underlying
many phenomena of granular materials such as the Reynolds transition.Comment: 18 pages with 6 postscript figures. to appear in J.Phys: Cond. Ma
Percolation and cluster Monte Carlo dynamics for spin models
A general scheme for devising efficient cluster dynamics proposed in a
previous letter [Phys.Rev.Lett. 72, 1541 (1994)] is extensively discussed. In
particular the strong connection among equilibrium properties of clusters and
dynamic properties as the correlation time for magnetization is emphasized. The
general scheme is applied to a number of frustrated spin model and the results
discussed.Comment: 17 pages LaTeX + 16 figures; will appear in Phys. Rev.
Heterogeneous slow dynamics in a two dimensional doped classical antiferromagnet
We introduce a lattice model for a classical doped two dimensional
antiferromagnet which has no quenched disorder, yet displays slow dynamics
similar to those observed in supercooled liquids. We calculate two-time spatial
and spin correlations via Monte Carlo simulations and find that for
sufficiently low temperatures, there is anomalous diffusion and
stretched-exponential relaxation of spin correlations. The relaxation times
associated with spin correlations and diffusion both diverge at low
temperatures in a sub-Arrhenius fashion if the fit is done over a large
temperature-window or an Arrhenius fashion if only low temperatures are
considered. We find evidence of spatially heterogeneous dynamics, in which
vacancies created by changes in occupation facilitate spin flips on
neighbouring sites. We find violations of the Stokes-Einstein relation and
Debye-Stokes-Einstein relation and show that the probability distributions of
local spatial correlations indicate fast and slow populations of sites, and
local spin correlations indicate a wide distribution of relaxation times,
similar to observ ations in other glassy systems with and without quenched
disorder.Comment: 12 pages, 17 figures, corrected erroneous figure, and improved
quality of manuscript, updated reference
Shaking a Box of Sand
We present a simple model of a vibrated box of sand, and discuss its dynamics
in terms of two parameters reflecting static and dynamic disorder respectively.
The fluidised, intermediate and frozen (`glassy') dynamical regimes are
extensively probed by analysing the response of the packing fraction to steady,
as well as cyclic, shaking, and indicators of the onset of a `glass transition'
are analysed. In the `glassy' regime, our model is exactly solvable, and allows
for the qualitative description of ageing phenomena in terms of two
characteristic lengths; predictions are also made about the influence of grain
shape anisotropy on ageing behaviour.Comment: Revised version. To appear in Europhysics Letter
Thermodynamic versus Topological Phase Transitions: Cusp in the Kert\'esz Line
We present a study of phase transitions of the Curie--Weiss Potts model at
(inverse) temperature , in presence of an external field . Both
thermodynamic and topological aspects of these transitions are considered. For
the first aspect we complement previous results and give an explicit equation
of the thermodynamic transition line in the -- plane as well as the
magnitude of the jump of the magnetization (for . The signature
of the latter aspect is characterized here by the presence or not of a giant
component in the clusters of a Fortuin--Kasteleyn type representation of the
model. We give the equation of the Kert\'esz line separating (in the
-- plane) the two behaviours. As a result, we get that this line
exhibits, as soon as , a very interesting cusp where it
separates from the thermodynamic transition line
Scaling properties in off equilibrium dynamical processes
In the present paper, we analyze the consequences of scaling hypotheses on
dynamic functions, as two times correlations . We show, under general
conditions, that must obey the following scaling behavior , where the scaling variable is
and , two
undetermined functions. The presence of a non constant exponent
signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure
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