July 27, 2001
We present a molecular dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short distance correlations in the non-equilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e. factorization of the two-particle distribution function, $f^{(2)}(x_1,x_2) \simeq \chi f^(1)(x_1) f^{(1)}(x_2)$ in a product of single particle ones, where $x_i = \{{\bf r}_i, {\bf v}_i \}$ with $i=1,2$ and $\chi$ represents the position correlation. We have found that molecular chaos is only violated in a small region of the two-particle phase space $\{x_1,x_2\}$, where there is a predominance of grazing collisions. The size of this singular region grows with increasing inelasticity. The existence of particle- and noise-induced recollisions magnifies the departure from mean field behavior. The implications of this breakdown in several physical quantities are explored.
Similar papers 1
August 26, 2002
The velocity distribution of inelastic granular gas is examined numerically on two dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after a several inelastic collisions per particle, the system falls in the state that the Boltzmann equation predicts with the stationary form of velocity distribution. It turns out, however, that due...
October 20, 1998
The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long range correlations, which behave as $\sim 1/r$ in three and $\sim \ln(L/r)$ in two dimensions. We calculate the corresponding structure factors over the whole range of wave numbers, and find good agreement with two-dimensional molecular dynamics simulations. It is also shown by means of a mode coupling calculation, how the mean field values for the steady st...
October 6, 1998
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the result of the balance between the dissipation and the random forces which inject energies. These models exhibit a genuine thermodynamic limit, i.e. at fixed density the mean values of kinetic energy and dissipated energy per particle are indep...
November 7, 2000
A statistical mechanical study of fluidized granular media is presented. Using a special energy injection mechanism, homogeneous fluidized stationary states are obtained. Molecular dynamics simulations and theoretical analysis of the inelastic hard-disk model show that there is a large asymmetry in the two-particle distribution function between pairs that approach and separate. Large velocity correlations appear in the postcollisional states, due to the dissipative character ...
May 27, 2002
We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the ``stochastic thermostat'' model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high velocity stre...
May 19, 2005
We study the appearance of large-scale dynamical heterogeneities in a simplified model of a driven, dissipative granular system. Simulations of steady-state gravity-driven flows of inelastically colliding hard disks show the formation of large-scale linear structures of particles with a high collision frequency. These chains can be shown to carry much of the collisional stress in the system due to a dynamical correlation that develops between the momentum transfer and time be...
December 13, 2002
We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking techniques. We identify all particles in the system and link their positions to form trajectories over long times. Thus, we identify particle collisions to measure the effective coefficient of restitution and find a broad distribution of values ...
October 20, 2023
The statistical-physical study of granular matter is essential to understand, from a fundamental point of view, the many different phenomena emerging in these classical many-body systems. Under rapid-flow conditions, granular materials exhibit a gas-like behavior, which can be described from the kinetic theory of gases. However, unlike molecular gases, a granular gas dissipates energy upon particle collisions, thus being completely out of equilibrium. Then, whereas the simple...
May 23, 2013
The homogeneous state of a granular flow of smooth inelastic hard spheres or disks described by the Enskog-Boltzmann kinetic equation is analyzed. The granular gas is fluidized by the presence of a random force and a drag force. The combined action of both forces, that act homogeneously on the granular gas, tries to mimic the interaction of the set of particles with a surrounding fluid. The first stochastic force thermalizes the system, providing for the necessary energy reco...
April 7, 2018
The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of the velocity distribution of a driven granular gas is a stretched exponential that, counterintuitively, decays slower than that of the corresponding elastic gas in equilibrium. However, a derivation of this result starting from a microscopic ...