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