Driven low density granular mixtures

We study the steady state properties of a 2D granular mixture in the presence of energy driving by employing simple analytical estimates and Direct Simulation Monte Carlo. We adopt two different driving mechanisms: a) a homogeneous heat bath with friction and b) a vibrating boundary (thermal or harmonic) in the presence of gravity. The main findings are: the appearance of two different granular temperatures, one for each species; the existence of overpopulated tails in the velocity distribution functions and of non trivial spatial correlations indicating the spontaneous formation of cluster aggregates. In the case of a fluid subject to gravity and to a vibrating boundary, both densities and temperatures display non uniform profiles along the direction normal to the wall, in particular the temperature profiles are different for the two species while the temperature ratio is almost constant with the height. Finally, we obtained the velocity distributions at different heights and verified the non gaussianity of the resulting distributions.Comment: 19 pages, 12 figures, submitted for publicatio

Which is the temperature of granular systems? A mean field model of free cooling inelastic mixtures

We consider a mean field model describing the free cooling process of a two component granular mixture, a generalization of so called Maxwell model. The cooling is viewed as an ordering process and the scaling behavior is attributed to the presence of an attractive fixed point at $v=0$ for the dynamics. By means of asymptotic analysis of the Boltzmann equation and of numerical simulations we get the following results: 1)we establish the existence of two different partial granular temperatures, one for each component, which violates the Zeroth Law of Thermodynamics; 2) we obtain the scaling form of the two distribution functions; 3) we prove the existence of a continuous spectrum of exponents characterizing the inverse-power law decay of the tails of the velocity, which generalizes the previously reported value 4 for the pure model; 4) we find that the exponents depend on the composition, masses and restitution coefficients of the mixture; 5) we also remark that the reported distributions represent a dynamical realization of those predicted by the Non Extensive Statistical Mechanics, in spite of the fact that ours stem from a purely dynamical approach.Comment: 23 pages, 9 figures. submitted for publicatio

Multiple time-scale approach for a system of Brownian particles in a non-uniform temperature field

The Smoluchowsky equation for a system of interacting Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented by a mean-field description. We present numerical results that compare well with the theoretical prediction together with an extensive discussion on the prescription of the Langevin equation in overdamped systems.Comment: 8 pages, 2 figure

Steady state properties of a mean field model of driven inelastic mixtures

We investigate a Maxwell model of inelastic granular mixture under the influence of a stochastic driving and obtain its steady state properties in the context of classical kinetic theory. The model is studied analytically by computing the moments up to the eighth order and approximating the distributions by means of a Sonine polynomial expansion method. The main findings concern the existence of two different granular temperatures, one for each species, and the characterization of the distribution functions, whose tails are in general more populated than those of an elastic system. These analytical results are tested against Monte Carlo numerical simulations of the model and are in general in good agreement. The simulations, however, reveal the presence of pronounced non-gaussian tails in the case of an infinite temperature bath, which are not well reproduced by the Sonine method.Comment: 23 pages, 10 figures, submitted for publicatio

Effective equilibrium states in the colored-noise model for active matter II. A unified framework for phase equilibria, structure and mechanical properties

Active particles driven by colored noise can be approximately mapped onto a system that obeys detailed balance. The effective interactions which can be derived for such a system allow the description of the structure and phase behavior of the active fluid by means of an effective free energy. In this paper we explain why the related thermodynamic results for pressure and interfacial tension do not represent the results one would measure mechanically. We derive a dynamical density functional theory, which in the steady state simultaneously validates the use of effective interactions and provides access to mechanical quantities. Our calculations suggest that in the colored-noise model the mechanical pressure in the coexisting phases might be unequal and the interfacial tension can become negative

Phase separation in systems with absorbing states

We study the problem of phase separation in systems with a positive definite order parameter, and in particular, in systems with absorbing states. Owing to the presence of a single minimum in the free energy driving the relaxation kinetics, there are some basic properties differing from standard phase separation. We study analytically and numerically this class of systems; in particular we determine the phase diagram, the growth laws in one and two dimensions and the presence of scale invariance. Some applications are also discussed.Comment: Submitted to Europhysics Let

Non equilibrium inertial dynamics of colloidal systems

We consider the properties of a one dimensional fluid of brownian inertial hard-core particles, whose microscopic dynamics is partially damped by a heat-bath. Direct interactions among the particles are represented as binary, instantaneous elastic collisions. Collisions with the heath bath are accounted for by a Fokker-Planck collision operator, whereas direct collisions among the particles are treated by a well known method of kinetic theory, the Revised Enskog Theory. By means of a time multiple time-scale method we derive the evolution equation for the average density. Remarkably, for large values of the friction parameter and/or of the mass of the particles we obtain the same equation as the one derived within the dynamic density functional theory (DDF). In addition, at moderate values of the friction constant, the present method allows to study the inertial effects not accounted for by DDF method. Finally, a numerical test of these corrections is provided.Comment: 13 pages+ 3 Postscript figure

Phase-space approach to dynamical density functional theory

We consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. We show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, we obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtelties of kinetic theory in the derivation of dynamical density functional theory

Mean-field dynamical density functional theory

We examine the out-of-equilibrium dynamical evolution of density profiles of ultrasoft particles under time-varying external confining potentials in three spatial dimensions. The theoretical formalism employed is the dynamical density functional theory (DDFT) of Marini Bettolo Marconi and Tarazona [J. Chem. Phys. {\bf 110}, 8032 (1999)], supplied by an equilibrium excess free energy functional that is essentially exact. We complement our theoretical analysis by carrying out extensive Brownian Dynamics simulations. We find excellent agreement between theory and simulations for the whole time evolution of density profiles, demonstrating thereby the validity of the DDFT when an accurate equilibrium free energy functional is employed.Comment: 8 pagers, 4 figure

Thermally induced directed currents in hard rod systems

We study the non equilibrium statistical properties of a one dimensional hard-rod fluid undergoing collisions and subject to a spatially non uniform Gaussian heat-bath and periodic potential. The system is able to sustain finite currents when the spatially inhomogeneous heat-bath and the periodic potential profile display an appropriate relative phase shift, $\phi$. By comparison with the collisionless limit, we determine the conditions for the most efficient transport among inelastic, elastic and non interacting rods. We show that the situation is complex as, depending on shape of the temperature profile, the current of one system may outperform the others.Comment: 5 pages, 2 figure