23 research outputs found
Reflection of traveling waves near the onset of binary-fluid convection
The reflection coefficient of linear traveling waves in binary-fluid convection is calculated for the experimental situation of rigid, impermeable boundaries. Results for a range of parameters of interest to experiments in ethanol-water mixtures are displayed and compared with experiment
Thermal convection in fluidized granular systems
Thermal convection is observed in molecular dynamic simulation of a fluidized
granular system of nearly elastic hard disks moving under gravity, inside a
rectangular box. Boundaries introduce no shearing or time dependence, but the
energy injection comes from a slip (shear-free) thermalizing base. The top wall
is perfectly elastic and lateral boundaries are either elastic or periodic. The
observed convection comes from the effect of gravity and the spontaneous
granular temperature gradient that the system dynamically develops.Comment: 4 pages, 5 figure
Hydrodynamic Description of Granular Convection
We present a hydrodynamic model that captures the essence of granular
dynamics in a vibrating bed. We carry out the linear stability analysis and
uncover the instability mechanism that leads to the appearance of the
convective rolls via a supercritical bifurcation of a bouncing solution. We
also explicitly determine the onset of convection as a function of control
parameters and confirm our picture by numerical simulations of the continuum
equations.Comment: 14 pages, RevTex 11pages + 3 pages figures (Type csh
A Continuum Description of Vibrated Sand
The motion of a thin layer of granular material on a plate undergoing
sinusoidal vibrations is considered. We develop equations of motion for the
local thickness and the horizontal velocity of the layer. The driving comes
from the violent impact of the grains on the plate. A linear stability theory
reveals that the waves are excited non-resonantly, in contrast to the usual
Faraday waves in liquids. Together with the experimentally observed continuum
scaling, the model suggests a close connection between the neutral curve and
the dispersion relation of the waves, which agrees quite well with experiments.
For strong hysteresis we find localized oscillon solutions.Comment: paper has been considerably extended (11 instead of 6 pages; 6
instead of 4 figures) much better agreement with experiment. obtain now
oscillons in 1 dimensio
Traffic Equations and Granular Convection
We investigate both numerically and analytically the convective instability
of granular materials by two dimensional traffic equations. In the absence of
vibrations the traffic equations assume two distinctive classes of fixed bed
solutions with either a spatially uniform or nonuniform density profile. The
former one exists only when the function V(\rho) that monitors the relaxation
of grains assumes a cut off at the closed packed density, \rho_c, with
V(\rho_c)=0, while the latter one exists for any form of V. Since there is
little difference between the uniform and nonuniform solution deep inside the
bed, the convective instability of the bulk may be studied by focusing on the
stability of the uniform solution. In the presence of vibrations, we find that
the uniform solution bifurcates into a bouncing solution, which then undergoes
a supercritical bifurcation to the convective instability. We determine the
onset of convection as a function of control parameters and confirm this
picture by solving the traffic equations numerically, which reveals bouncing
solutions, two convective rolls, and four convective rolls. Further, convective
patterns change as the aspect ratio changes: in a vertically long container,
the rolls move toward the surface, and in a horizontally long container, the
rolls move toward the walls. We compare these results with those reported
previously with a different continuum model by Hayakawa, Yue and Hong[Phys.
Rev. Lett. 75,2328, 1995]. Finally, we also present a derivation of the traffic
equations from Enskoq equation.Comment: 34 pages, 10 figure
A nonlinear hydrodynamical approach to granular materials
We propose a nonlinear hydrodynamical model of granular materials. We show
how this model describes the formation of a sand pile from a homogeneous
distribution of material under gravity, and then discuss a simulation of a
rotating sandpile which shows, in qualitative agreement with experiment, a
static and dynamic angle of repose.Comment: 17 pages, 14 figures, RevTeX4; minor changes to wording and some
additional discussion. Accepted by Phys. Rev.