17 research outputs found
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
Controlled Dynamics of Interfaces in a Vibrated Granular Layer
We present experimental study of a topological excitation, {\it interface},
in a vertically vibrated layer of granular material. We show that these
interfaces, separating regions of granular material oscillation with opposite
phases, can be shifted and controlled by a very small amount of an additional
subharmonic signal, mixed with the harmonic driving signal. The speed and the
direction of interface motion depends sensitively on the phase and the
amplitude of the subharmonic driving.Comment: 4 pages, 6 figures, RevTe
Nonequilibrium steady states in a vibrated-rod monolayer: tetratic, nematic and smectic correlations
We study experimentally the nonequilibrium phase behaviour of a horizontal
monolayer of macroscopic rods. The motion of the rods in two dimensions is
driven by vibrations in the vertical direction. Aside from the control
variables of packing fraction and aspect ratio that are typically explored in
molecular liquid crystalline systems, due to the macroscopic size of the
particles we are also able to investigate the effect of the precise shape of
the particle on the steady states of this driven system. We find that the shape
plays an important role in determining the nature of the orientational ordering
at high packing fraction. Cylindrical particles show substantial tetratic
correlations over a range of aspect ratios where spherocylinders have
previously been shown by Bates et al (JCP 112, 10034 (2000)) to undergo
transitions between isotropic and nematic phases. Particles that are thinner at
the ends (rolling pins or bails) show nematic ordering over the same range of
aspect ratios, with a well-established nematic phase at large aspect ratio and
a defect-ridden nematic state with large-scale swirling motion at small aspect
ratios. Finally, long-grain, basmati rice, whose geometry is intermediate
between the two shapes above, shows phases with strong indications of smectic
order.Comment: 18 pages and 13 eps figures, references adde
Dynamics of axial separation in long rotating drums
We propose a continuum description for the axial separation of granular
materials in a long rotating drum. The model, operating with two local
variables, concentration difference and the dynamic angle of repose, describes
both initial transient traveling wave dynamics and long-term segregation of the
binary mixture. Segregation proceeds through ultra-slow logarithmic coarsening.Comment: 4 pages, 3 Postscript figures; submitted to PR
Continuum theory of partially fluidized granular flows
A continuum theory of partially fluidized granular flows is developed. The
theory is based on a combination of the equations for the flow velocity and
shear stresses coupled with the order parameter equation which describes the
transition between flowing and static components of the granular system. We
apply this theory to several important granular problems: avalanche flow in
deep and shallow inclined layers, rotating drums and shear granular flows
between two plates. We carry out quantitative comparisons between the theory
and experiment.Comment: 28 pages, 23 figures, submitted to Phys. Rev.
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.
Competing Patterns of Signaling Activity in Dictyostelium discoideum
Quantitative experiments are described on spatio-temporal patterns of
coherent chemical signaling activity in populations of {\it Dictyostelium
discoideum} amoebae. We observe competition between spontaneously firing
centers and rotating spiral waves that depends strongly on the overall cell
density. At low densities, no complete spirals appear and chemotactic
aggregation is driven by periodic concentric waves, whereas at high densities
the firing centers seen at early times nucleate and are apparently entrained by
spiral waves whose cores ultimately serve as aggregation centers. Possible
mechanisms for these observations are discussed.Comment: 10 pages, RevTeX, 4 ps figures, accepted in PR