76 research outputs found
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 -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
-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
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