Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised.Comment: 6 pages, 6 figures (7 postscript files), submitted to EPJ

Phase space diffusion and low temperature aging

We study the dynamical evolution of a system with a phase space consisting of configurations with random energies. The dynamics we use is of Glauber type. It allows for some dynamical evolution ang aging even at very low temperatures, through the search of configurations with lower energies.Comment: 11 pages latex, 1 ps figure adde

Lack of energy equipartition in homogeneous heated binary granular mixtures

We consider the problem of determining the granular temperatures of the components of a homogeneous binary heated mixture of inelastic hard spheres, in the framework of Enskog kinetic theory. Equations are derived for the temperatures of each species and their ratio, which is different from unity, as may be expected since the system is out of equilibrium. We focus on the particular heating mechanism where the inelastic energy loss is compensated by an injection through a random external force (``stochastic thermostat''). The influence of various parameters and their possible experimental relevance is discussed.Comment: 8 pages, 9 eps figures, to be published in Granular Matte

On the properties of small-world network models

We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a ``small-world'' behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a ``small-world'' one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite.Comment: 19 pages including 15 figures, version accepted for publication in EPJ

Glass transition and random walks on complex energy landscapes

We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies focusing on particular examples of energy landscapes obtained by sampling energy minima and saddles of small systems. We point out how the relation between the energies of the minima and their number of neighbors should be studied in connection with the network's global topology, and show how the tools developed in complex network theory can be put to use in this context

On the definition of temperature in dense granular media

In this Letter we report the measurement of a pseudo-temperature for compacting granular media on the basis of the Fluctuation-Dissipation relations in the aging dynamics of a model system. From the violation of the Fluctuation-Dissipation Theorem an effective temperature emerges (a dynamical temperature T_{dyn}) whose ratio with the equilibrium temperature T_d^{eq} depends on the particle density. We compare the results for the Fluctuation-Dissipation Ratio (FDR) T_{dyn}/T_d^{eq} at several densities with the outcomes of Edwards' approach at the corresponding densities. It turns out that the FDR and the so-called Edwards' ratio coincide at several densities (very different ages of the system), opening in this way the door to experimental checks as well as theoretical constructions.Comment: RevTex4 4 pages, 4 eps figure

Basins of attraction of metastable states of the spherical pp-spin model

We study the basins of attraction of metastable states in the spherical $p$-spin spin glass model, starting the relaxation dynamics at a given distance from a thermalized condition. Weighting the initial condition with the Boltzmann distribution we find a finite size for the basins. On the contrary, a white weighting of the initial condition implies vanishing basins of attraction. We make the corresponding of our results with the ones of a recently constructed effective potential.Comment: LaTeX, 7 pages, 7 eps figure

The rich behavior of the Boltzmann equation for dissipative gases

Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing results for Maxwell molecules and hard spheres to large classes of particle interactions, from very hard spheres to softer than Maxwell molecules, as well as to more general forcing mechanisms, beyond free cooling and white noise driving. By combining this method with numerical solutions, obtained from the Direct Simulation Monte Carlo (DSMC) method, we study a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We establish a criterion connecting the stability of the non-equilibrium steady state to an exponentially bound form for the velocity distribution $F$, which varies depending on the forcing mechanism. Power laws arise in marginal stability cases, of which several new cases are reported. Our results provide a minimal framework for interpreting large classes of experiments on driven granular gases