1,398 research outputs found
On the validity of the Boltzmann equation to describe low density granular systems
The departure of a granular gas in the instable region of parameters from the
initial homogeneous cooling state is studied. Results from Molecular Dynamics
and from Direct Monte Carlo simulation of the Boltzmann equation are compared.
It is shown that the Boltzmann equation accurately predicts the low density
limit of the system. The relevant role played by the parallelization of the
velocities as time proceeds and the dependence of this effect on the density is
analyzed in detail
Transversal inhomogeneities in dilute vibrofluidized granular fluids
The spontaneous symmetry breaking taking place in the direction perpendicular
to the energy flux in a dilute vibrofluidized granular system is investigated,
using both a hydrodynamic description and simulation methods. The latter
include molecular dynamics and direct Monte Carlo simulation of the Boltzmann
equation. A marginal stability analysis of the hydrodynamic equations, carried
out in the WKB approximation, is shown to be in good agreement with the
simulation results. The shape of the hydrodynamic profiles beyond the
bifurcation is discussed
Electronic States of Graphene Nanoribbons
We study the electronic states of narrow graphene ribbons (``nanoribbons'')
with zigzag and armchair edges. The finite width of these systems breaks the
spectrum into an infinite set of bands, which we demonstrate can be
quantitatively understood using the Dirac equation with appropriate boundary
conditions. For the zigzag nanoribbon we demonstrate that the boundary
condition allows a particle- and a hole-like band with evanescent wavefunctions
confined to the surfaces, which continuously turn into the well-known zero
energy surface states as the width gets large. For armchair edges, we show that
the boundary condition leads to admixing of valley states, and the band
structure is metallic when the width of the sample in lattice constant units is
divisible by 3, and insulating otherwise. A comparison of the wavefunctions and
energies from tight-binding calculations and solutions of the Dirac equations
yields quantitative agreement for all but the narrowest ribbons.Comment: 5 pages, 6 figure
Diffusion in a Granular Fluid - Simulation
The linear response description for impurity diffusion in a granular fluid
undergoing homogeneous cooling is developed in the preceeding paper. The
formally exact Einstein and Green-Kubo expressions for the self-diffusion
coefficient are evaluated there from an approximation to the velocity
autocorrelation function. These results are compared here to those from
molecular dynamics simulations over a wide range of density and inelasticity,
for the particular case of self-diffusion. It is found that the approximate
theory is in good agreement with simulation data up to moderate densities and
degrees of inelasticity. At higher density, the effects of inelasticity are
stronger, leading to a significant enhancement of the diffusion coefficient
over its value for elastic collisions. Possible explanations associated with an
unstable long wavelength shear mode are explored, including the effects of
strong fluctuations and mode coupling
Adsorption of a binary mixture of monomers with nearest-neighbour cooperative effects
A model for the adsorption of a binary mixture on a one-dimensional infinite
lattice with nearest neighbour cooperative effects is considered. The particles
of the two species are both monomers but differ in the repulsive interaction
experienced by them when trying to adsorb. An exact expression for the coverage
of the lattice is derived. In the jamming limit, it is a monotonic function of
the ratio between the attempt frequencies of the two species, varying between
the values corresponding to each of the two single species. This is in contrast
with the results obtained in other models for the adsorption of particles of
different sizes. The structure of the jamming state is also investigated.Comment: v2: Errors in the figures fixed; same text; 23 pages, 5 figures.
Accepted for publication in Journal of Physics A: Mathematical and Genera
Linear Response for Granular Fluids
The linear response of an isolated, homogeneous granular fluid to small
spatial perturbations is studied by methods of non-equilibrium statistical
mechanics. The long wavelength linear hydrodynamic equations are obtained, with
formally exact expressions for the susceptibilities and transport coefficients.
The latter are given in equivalent Einstein-Helfand and Green-Kubo forms. The
context of these results and their contrast with corresponding results for
normal fluids are discussed.Comment: Submitted to PR
Symmetry breaking and clustering in a vibrated granular gas with several macroscopically connected compartments
The spontaneous symmetry breaking in a vibro-fluidized low-density granular
gas in three connected compartments is investigated. When the total number of
particles in the system becomes large enough, particles distribute themselves
unequally among the three compartments. Particles tend to concentrate in one of
the compartments, the other two having the (relatively small) same average
number of particles. A hydrodynamical model that accurately predicts the
bifurcation diagram of the system is presented. The theory can be easily
extended to the case of an arbitrary number of connected compartments
Piezoelectric mechanism of orientation of stripe structures in two-dimensional electron systems
A piezoelectric mechanism of orientation of stripes in two-dimensional
quantum Hall systems in GaAs heterostructures is considered. The anisotropy of
the elastic moduli and the boundary of the sample are taken into account. It is
found that in the average the stripes line up with the [110] axis. In double
layer systems the wave vector of the stripe structure rotates from the [110] to
[100] axis if the period of density modulation becomes large than the
interlayer distance. From the experimental point of view it means that in
double layer systems anisotropic part of resistivity changes its sign under
variation of the external magnetic field.Comment: 8 page
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