Heat flux of a granular gas with homogeneous temperature

A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved two--dimensional silo. At a macroscopic level, the state is identified with one solution to the inelastic Navier--Stokes equations, due to the coupling between the heat flux induced by the density gradient and the external force. On the contrary, at the mesoscopic level, by exactly solving a BGK model or the inelastic Boltzmann equation in an approximate way, a one--parametric family of solutions is found. Molecular dynamics simulations of the system in the quasi--elastic limit are in agreement with the theoretical results

Mass transport of driven inelastic Maxwell mixtures

Mass transport of a driven granular binary mixture is analyzed from the inelastic Boltzmann kinetic equation for inelastic Maxwell models (IMM). The mixture is driven by a thermostat constituted by two terms: a stochastic force and a drag force proportional to the particle velocity. The combined action of both forces attempts to mimic the interaction of solid particles with the interstitial surrounding gas. As with ordinary gases, the use of IMM allows us to exactly evaluate the velocity moments of the Boltzmann collision operator and so, it opens up the possibility of obtaining the exact forms of the Navier--Stokes transport coefficients of the granular mixture. In this work, the diffusion coefficients associated with the mass flux are explicitly determined in terms of the parameters of the mixture. As a first step, the steady homogeneous state reached by the system when the energy lost by collisions is compensated for by the energy injected by the thermostat is addressed. In this steady state, the ratio of kinetic temperatures are determined and compared against molecular dynamics simulations for inelastic hard spheres (IHS). The comparison shows an excellent agreement, even for strong inelasticity and/or disparity in masses and diameters. As a second step, the set of kinetic equations for the mixture is solved by means of the Chapman-Enskog method for states near homogeneous steady states. In the first-order approximation, the mass flux is obtained and the corresponding diffusion transport coefficients identified. The results show that the predictions for IMM obtained in this work coincide with those previously derived for IHS in the first-Sonine approximation when the non-Gaussian corrections to the zeroth-order approximation are neglected.Comment: 10 pages, 2 figures; paper submitted for its publication in AIP Conference Proceedings (RGD31

The noisy voter model under the influence of contrarians

The influence of contrarians on the noisy voter model is studied at the mean-field level. The noisy voter model is a variant of the voter model where agents can adopt two opinions, optimistic or pessimistic, and can change them by means of an imitation (herding) and an intrinsic (noise) mechanisms. An ensemble of noisy voters undergoes a finite-size phase transition, upon increasing the relative importance of the noise to the herding, form a bimodal phase where most of the agents shear the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states. By the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents (anti-herding). We first consider the case of only contrarians and show that the only possible steady state is the unimodal one. More generally, when voters and contrarians are present, we show that the bimodal-unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four, and their characteristic rates are small enough. For the number of contrarians bigger or equal to four, the voters and the contrarians can be seen only in the unimodal phase. Moreover, if the number of voters and contrarians, as well as the noise and herding rates, are of the same order, then the probability functions of the steady state are very well approximated by the Gaussian distribution

Mesoscopic description of the adiabatic piston: kinetic equations and H\mathcal H-theorem

The adiabatic piston problem is solved at the mesoscale using a Kinetic Theory approach. The problem is to determine the evolution towards equilibrium of two gases separated by a wall with only one degree of freedom (the adiabatic piston). A closed system of equations for the distribution functions of the gases conditioned to a position of the piston and the distribution function of the piston is derived from the Liouville equation, under the assumption of a generalized molecular chaos. It is shown that the resulting kinetic description has the canonical equilibrium as a steady-state solution. Moreover, the Boltzmann entropy, which includes the motion of the piston, verifies the $\mathcal H$-theorem. The results are generalized to any short-ranged repulsive potentials among particles and include the ideal gas as a limiting case.Comment: 25 pages, 2 figure

Anomalous transport of impurities in inelastic Maxwell gases

A mixture of dissipative hard grains generically exhibits a breakdown of kinetic energy equipartition. The undriven and thus freely cooling binary problem, in the tracer limit where the density of one species becomes minute, may exhibit an extreme form of this breakdown, with the minority species carrying a finite fraction of the total kinetic energy of the system. We investigate the fingerprint of this non-equilibrium phase transition, akin to an ordering process, on transport properties. The analysis, performed by solving the Boltzmann kinetic equation from a combination of analytical and Monte Carlo techniques, hints at the possible failure of hydrodynamics in the ordered region. As a relevant byproduct of the study, the behaviour of the second and fourth-degree velocity moments is also worked out.Comment: The title has been changed. The paper has been enlarged with respect to our first version. 13 pages, 9 figures. To be published in EPJ