650 research outputs found

### Violation of the Einstein relation in Granular Fluids: the role of correlations

We study the linear response in different models of driven granular gases. In
some situations, even if the the velocity statistics can be strongly
non-Gaussian, we do not observe appreciable violations of the Einstein formula
for diffusion versus mobility. The situation changes when strong correlations
between velocities and density are present: in this case, although a form of
fluctuation-dissipation relation holds, the differential velocity response of a
particle and its velocity self-correlation are no more proportional. This
happens at high densities and strong inelasticities, but still in the
fluid-like (and ergodic) regime.Comment: 18 pages, 6 figures, submitted for publicatio

### Influence of correlations on the velocity statistics of scalar granular gases

The free evolution of inelastic particles in one dimension is studied by
means of Molecular Dynamics (MD), of an inelastic pseudo-Maxwell model and of a
lattice model, with emphasis on the role of spatial correlations. We present an
exact solution of the 1d granular pseudo-Maxwell model for the scaling
distribution of velocities and discuss how this model fails to describe
correctly the homogeneous cooling stage of the 1d granular gas. Embedding the
pseudo-Maxwell gas on a lattice (hence allowing for the onset of spatial
correlations), we find a much better agreement with the MD simulations even in
the inhomogeneous regime. This is seen by comparing the velocity distributions,
the velocity profiles and the structure factors of the velocity field.Comment: Latex file: 6 pages, 5 figures (.eps). See also
http://axtnt3.phys.uniroma1.it/Maxwel

### Etching of random solids: hardening dynamics and self-organized fractality

When a finite volume of an etching solution comes in contact with a
disordered solid, a complex dynamics of the solid-solution interface develops.
Since only the weak parts are corroded, the solid surface hardens
progressively. If the etchant is consumed in the chemical reaction, the
corrosion dynamics slows down and stops spontaneously leaving a fractal solid
surface, which reveals the latent percolation criticality hidden in any random
system. Here we introduce and study, both analytically and numerically, a
simple model for this phenomenon. In this way we obtain a detailed description
of the process in terms of percolation theory. In particular we explain the
mechanism of hardening of the surface and connect it to Gradient Percolation.Comment: Latex, aipproc, 6 pages, 3 figures, Proceedings of 6th Granada
Seminar on Computational Physic

### Cooling of a lattice granular fluid as an ordering process

We present a new microscopic model of granular medium to study the role of
dynamical correlations and the onset of spatial order induced by the
inelasticity of the interactions. In spite of its simplicity, it features
several different aspects of the rich phenomenology observed in granular
materials and allows to make contact with other topics of statistical mechanics
such as diffusion processes, domain growth, persistence, aging phenomena.
Interestingly, while local observables being controlled by the largest
wavelength fluctuations seem to suggest a purely diffusive behavior, the
formation of spatially extended structures and topological defects, such as
vortices and shocks, reveals a more complex scenario.Comment: 4 pages, 4 figure

### Driven granular gases with gravity

We study fluidized granular gases in a stationary state determined by the
balance between an external driving and the bulk dissipation. The two
considered situations are inspired by recent experiments, where the gravity
plays a major role as a driving mechanism: in the first case gravity acts only
in one direction and the bottom wall is vibrated, in the second case gravity
acts in both directions and no vibrating walls are present. Simulations
performed under the molecular chaos assumption show averaged profiles of
density, velocity and granular temperature which are in good agreement with the
experiments. Moreover we measure the velocity distributions which show strong
non-Gaussian behavior, as experiments pointed out, but also density
correlations accounting for clustering, at odds with the experimental results.
The hydrodynamics of the first model is discussed and an exact solution is
found for the density and granular temperature as functions of the distance
from the vibrating wall. The limitations of such a solution, in particular in a
broad layer near the wall injecting energy, are discussed.Comment: Revised version accepted for publication. New results added and
discussions considering tangential forces. 27 pages (19 figures included), to
appear in Phys.Rev.

### What is the temperature of a granular medium?

In this paper we discuss whether thermodynamical concepts and in particular
the notion of temperature could be relevant for the dynamics of granular
systems. We briefly review how a temperature-like quantity can be defined and
measured in granular media in very different regimes, namely the glassy-like,
the liquid-like and the granular gas. The common denominator will be given by
the Fluctuation-Dissipation Theorem, whose validity is explored by means of
both numerical and experimental techniques. It turns out that, although a
definition of a temperature is possible in all cases, its interpretation is far
from being obvious. We discuss the possible perspectives both from the
theoretical and, more importantly, from the experimental point of view

### Velocity Tails for Inelastic Maxwell Models

We study the velocity distribution function for inelastic Maxwell models,
characterized by a Boltzmann equation with constant collision rate, independent
of the energy of the colliding particles. By means of a nonlinear analysis of
the Boltzmann equation, we find that the velocity distribution function decays
algebraically for large velocities, with exponents that are analytically
calculated.Comment: 4 pages, 2 figure

### Chemical fracture and distribution of extreme values

When a corrosive solution reaches the limits of a solid sample, a chemical
fracture occurs. An analytical theory for the probability of this chemical
fracture is proposed and confirmed by extensive numerical experiments on a two
dimensional model. This theory follows from the general probability theory of
extreme events given by Gumbel. The analytic law differs from the Weibull law
commonly used to describe mechanical failures for brittle materials. However a
three parameters fit with the Weibull law gives good results, confirming the
empirical value of this kind of analysis.Comment: 7 pages, 5 figures, to appear in Europhysics Letter

### Hydrodynamics of granular particles on a line

We investigate a lattice model representing a granular gas in a thin channel.
We deduce the hydrodynamic description for the model from the microscopic
dynamics in the large system limit, including the lowest finite-size
corrections. The main prediction from hydrodynamics, when finite-size
corrections are neglected, is the existence of a steady "uniform longitudinal
flow" (ULF), with the granular temperature and the velocity gradient both
uniform and directly related. Extensive numerical simulations of the system
show that such a state can be observed in the bulk of a finite-size system by
attaching two thermostats with the same temperature at its boundaries. The
relation between the ULF state and the shocks appearing in the late stage of a
cooling gas of inelastic hard rods is discussed.Comment: 12 pages, 6 figures, to be published on Physical Review E (in press

### Velocity fluctuations in a one dimensional Inelastic Maxwell model

We consider the velocity fluctuations of a system of particles described by
the Inelastic Maxwell Model. The present work extends the methods, previously
employed to obtain the one-particle velocity distribution function, to the
study of the two particle correlations. Results regarding both the homogeneous
cooling process and the steady state driven regime are presented. In particular
we obtain the form of the pair correlation function in the scaling region of
the homogeneous cooling process and show that some of its moments diverge. This
fact has repercussions on the behavior of the energy fluctuations of the model.Comment: 16 pages, 1 figure, to be published on Journal of Statistical
Mechanics: Theory and Experiment

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