163 research outputs found
Ripples in Tapped or Blown Powder
We observe ripples forming on the surface of a granular powder in a container
submitted from below to a series of brief and distinct shocks. After a few
taps, the pattern turns out to be stable against any further shock of the same
amplitude. We find experimentally that the characteristic wavelength of the
pattern is proportional to the amplitude of the shocks. Starting from
consideration involving Darcy's law for air flow through the porous granulate
and avalanche properties, we build up a semi-quantitative model which fits
satisfactorily the set of experimental observations as well as a couple of
additional experiments.Comment: 7 pages, four postscript figures, submitted PRL 11/19/9
Evolution on a Rugged Landscape:Pinning and Aging
Population dynamics on a rugged landscape is studied analytically and
numerically within a simple discrete model for evolution of N individuals in
one-dimensional fitness space. We reduce the set of master equations to a
single Fokker-Plank equation which allows us to describe the dynamics of the
population in terms of thermo-activated Langevin diffusion of a single particle
in a specific random potential. We found that the randomness in the mutation
rate leads to pinning of the population and on average to a logarithmic
slowdown of the evolution, resembling aging phenomenon in spin glass systems.
In contrast, the randomness in the replication rate turns out to be irrelevant
for evolution in the long-time limit as it is smoothed out by increasing
``evolution temperature''. The analytic results are in a good agreement with
numerical simulations.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
Coefficient of tangential restitution for the linear dashpot model
The linear dashpot model for the inelastic normal force between colliding
spheres leads to a constant coefficient of normal restitution,
const., which makes this model very popular for the investigation
of dilute and moderately dense granular systems. For two frequently used models
for the tangential interaction force we determine the coefficient of tangential
restitution , both analytically and by numerical integration of
Newton's equation. Although const. for the linear-dashpot model,
we obtain pronounced and characteristic dependencies of the tangential
coefficient on the impact velocity . The
results may be used for event-driven simulations of granular systems of
frictional particles.Comment: 12 pages, 12 figure
Evolution on a smooth landscape
We study in detail a recently proposed simple discrete model for evolution on
smooth landscapes. An asymptotic solution of this model for long times is
constructed. We find that the dynamics of the population are governed by
correlation functions that although being formally down by powers of (the
population size) nonetheless control the evolution process after a very short
transient. The long-time behavior can be found analytically since only one of
these higher-order correlators (the two-point function) is relevant. We compare
and contrast the exact findings derived herein with a previously proposed
phenomenological treatment employing mean field theory supplemented with a
cutoff at small population density. Finally, we relate our results to the
recently studied case of mutation on a totally flat landscape.Comment: Revtex, 15 pages, + 4 embedded PS figure
Dynamics of a bouncing dimer
We investigate the dynamics of a dimer bouncing on a vertically oscillated
plate. The dimer, composed of two spheres rigidly connected by a light rod,
exhibits several modes depending on initial and driving conditions. The first
excited mode has a novel horizontal drift in which one end of the dimer stays
on the plate during most of the cycle, while the other end bounces in phase
with the plate. The speed and direction of the drift depend on the aspect ratio
of the dimer. We employ event-driven simulations based on a detailed treatment
of frictional interactions between the dimer and the plate in order to
elucidate the nature of the transport mechanism in the drift mode.Comment: 4 pages, 5 figures, Movies:
http://physics.clarku.edu/~akudrolli/dime
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