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

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

The average shape of a fluctuation: universality in excursions of stochastic processes

We study the average shape of a fluctuation of a time series x(t), that is the average value _T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law of the form _T = T^\alpha f(t/T) is obeyed. The scaling function f(s) is to a large extent independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.Comment: 5 pages, 5 figures, accepted for publication in Phys. Rev. Let

On the out of equilibrium order parameters in long-range spin-glases

We show that the dynamical order parameters can be reexpressed in terms of the distribution of the staggered auto-correlation and response functions. We calculate these distributions for the out of equilibrium dynamics of the Sherrington-Kirpatrick model at long times. The results suggest that the landscape this model visits at different long times in an out of equilibrium relaxation process is, in a sense, self-similar. Furthermore, there is a similarity between the landscape seen out of equilibrium at long times and the equilibrium landscape. The calculation is greatly simplified by making use of the superspace notation in the dynamical approach. This notation also highlights the rather mysterious formal connection between the dynamical and replica approaches.Comment: 25 pages, Univ. di Roma I preprint #1049 (we replaced the file by the RevTex file, figures available upon request

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

Average trajectory of returning walks

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For uncorrelated random walks the average shape is semicircular, independently from the single increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations induces non trivial asymmetric shapes, which are studied numerically.Comment: 16 pages, 16 figures; accepted for publication in Phys. Rev.

Variant esp gene as a marker of a distinct genetic lineage of vancomycin-resistant Enterococcus faecium

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Brownian forces in sheared granular matter

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilised, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.Comment: 4 pages, 5 figures and 1 tabl

Analytical results for generalized persistence properties of smooth processes

We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the diffusion equation evolving from random initial conditions, one of the simplest coarsening systems. Exact results are obtained in certain limits, and rely on a new method to deal with constrained multiplicative processes. An excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found.Comment: 21 pages, 4 figures, to appear in Journal of Physics