93 research outputs found
Model of coarsening and vortex formation in vibrated granular rods
Neicu and Kudrolli observed experimentally spontaneous formation of the
long-range orientational order and large-scale vortices in a system of vibrated
macroscopic rods. We propose a phenomenological theory of this phenomenon,
based on a coupled system of equations for local rods density and tilt. The
density evolution is described by modified Cahn-Hilliard equation, while the
tilt is described by the Ginzburg-Landau type equation. Our analysis shows
that, in accordance to the Cahn-Hilliard dynamics, the islands of the ordered
phase appear spontaneously and grow due to coarsening. The generic vortex
solutions of the Ginzburg-Landau equation for the tilt correspond to the
vortical motion of the rods around the cores which are located near the centers
of the islands.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let
Coarsening of granular clusters: two types of scaling behaviors
We report on an experimental study of small cluster dynamics during the
coarsening process in driven granular submonolayers of 120mkm bronze particles.
The techniques of electrostatic and vertical mechanical vibration were employed
to excite the granular gas. We measure the scaling exponent for the evaporation
of small clusters during coarsening. It was found that the surface area of
small clusters S vs time t behaves as S ~ (t_0-t)^(2/3) for lower frequencies
and S ~ (t_0-t) for higher frequencies. We argue that the change in the scaling
exponent is related to the transition from three dimensional to two dimensional
character of motion in the granular gas.Comment: 4 pages,5 figures, submitted to Phys.Rev.
Onset of Collective Oscillation in Chemical Turbulence under Global Feedback
Preceding the complete suppression of chemical turbulence by means of global
feedback, a different universal type of transition, which is characterized by
the emergence of small-amplitude collective oscillation with strong turbulent
background, is shown to occur at much weaker feedback intensity. We illustrate
this fact numerically in combination with a phenomenological argument based on
the complex Ginzburg-Landau equation with global feedback.Comment: 6 pages, 8 figures; to appear in Phys. Rev.
Velocity Fluctuations in Electrostatically Driven Granular Media
We study experimentally the particle velocity fluctuations in an
electrostatically driven dilute granular gas. The experimentally obtained
velocity distribution functions have strong deviations from Maxwellian form in
a wide range of parameters. We have found that the tails of the distribution
functions are consistent with a stretched exponential law with typical
exponents of the order 3/2. Molecular dynamic simulations shows qualitative
agreement with experimental data. Our results suggest that this non-Gaussian
behavior is typical for most inelastic gases with both short and long range
interactions.Comment: 4 pages, 4 figure
Partially fluidized shear granular flows: Continuum theory and MD simulations
The continuum theory of partially fluidized shear granular flows is tested
and calibrated using two dimensional soft particle molecular dynamics
simulations. The theory is based on the relaxational dynamics of the order
parameter that describes the transition between static and flowing regimes of
granular material. We define the order parameter as a fraction of static
contacts among all contacts between particles. We also propose and verify by
direct simulations the constitutive relation based on the splitting of the
shear stress tensor into a``fluid part'' proportional to the strain rate
tensor, and a remaining ``solid part''. The ratio of these two parts is a
function of the order parameter. The rheology of the fluid component agrees
well with the kinetic theory of granular fluids even in the dense regime. Based
on the hysteretic bifurcation diagram for a thin shear granular layer obtained
in simulations, we construct the ``free energy'' for the order parameter. The
theory calibrated using numerical experiments with the thin granular layer is
applied to the surface-driven stationary two dimensional granular flows in a
thick granular layer under gravity.Comment: 20 pages, 19 figures, submitted to Phys. Rev.
Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
Scroll waves are three-dimensional analogs of spiral waves. The linear
stability spectrum of untwisted and twisted scroll waves is computed for a
two-variable reaction-diffusion model of an excitable medium. Different bands
of modes are seen to be unstable in different regions of parameter space. The
corresponding bifurcations and bifurcated states are characterized by
performing direct numerical simulations. In addition, computations of the
adjoint linear stability operator eigenmodes are also performed and serve to
obtain a number of matrix elements characterizing the long-wavelength
deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.
Dynamics of electrostatically-driven granular media. Effects of Humidity
We performed experimental studies of the effect of humidity on the dynamics
of electrostatically-driven granular materials. Both conducting and dielectric
particles undergo a phase transition from an immobile state (granular solid) to
a fluidized state (granular gas) with increasing applied field. Spontaneous
precipitation of solid clusters from the gas phase occurs as the external
driving is decreased. The clustering dynamics in conducting particles is
primarily controlled by screening of the electric field but is aided by
cohesion due to humidity. It is shown that humidity effects dominate the
clustering process with dielectric particles.Comment: 4 pages, 4 fig
Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation
We look for singlevalued solutions of the squared modulus M of the traveling
wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using
Clunie's lemma, we first prove that any meromorphic solution M is necessarily
elliptic or degenerate elliptic. We then give the two canonical decompositions
of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica
Nonequilibrium Dynamics in the Complex Ginzburg-Landau Equation
We present results from a comprehensive analytical and numerical study of
nonequilibrium dynamics in the 2-dimensional complex Ginzburg-Landau (CGL)
equation. In particular, we use spiral defects to characterize the domain
growth law and the evolution morphology. An asymptotic analysis of the
single-spiral correlation function shows a sequence of singularities --
analogous to those seen for time-dependent Ginzburg-Landau (TDGL) models with
O(n) symmetry, where is even.Comment: 11 pages, 5 figure
Clustering transitions in vibro-fluidized magnetized granular materials
We study the effects of long range interactions on the phases observed in
cohesive granular materials. At high vibration amplitudes, a gas of magnetized
particles is observed with velocity distributions similar to non-magnetized
particles. Below a transition temperature compact clusters are observed to form
and coexist with single particles. The cluster growth rate is consistent with a
classical nucleation process. However, the temperature of the particles in the
clusters is significantly lower than the surrounding gas, indicating a
breakdown of equipartition. If the system is quenched to low temperatures, a
meta-stable network of connected chains self-assemble due to the anisotropic
nature of magnetic interactions between particles.Comment: 4 pages, 5 figure
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