290 research outputs found

### Viewing the efficiency of chaos control

This paper aims to cast some new light on controlling chaos using the OGY-
and the Zero-Spectral-Radius methods. In deriving those methods we use a
generalized procedure differing from the usual ones. This procedure allows us
to conveniently treat maps to be controlled bringing the orbit to both various
saddles and to sources with both real and complex eigenvalues. We demonstrate
the procedure and the subsequent control on a variety of maps. We evaluate the
control by examining the basins of attraction of the relevant controlled
systems graphically and in some cases analytically

### Bursts in the Chaotic Trajectory Lifetimes Preceding the Controlled Periodic Motion

The average lifetime ($\tau(H)$) it takes for a randomly started trajectory
to land in a small region ($H$) on a chaotic attractor is studied. $\tau(H)$ is
an important issue for controlling chaos. We point out that if the region $H$
is visited by a short periodic orbit, the lifetime $\tau(H)$ strongly deviates
from the inverse of the naturally invariant measure contained within that
region ($\mu_N(H)^{-1}$). We introduce the formula that relates
$\tau(H)/\mu_N(H)^{-1}$ to the expanding eigenvalue of the short periodic orbit
visiting $H$.Comment: Accepted for publication in Phys. Rev. E, 3 PS figure

### Why do Particle Clouds Generate Electric Charges?

Grains in desert sandstorms spontaneously generate strong electrical charges;
likewise volcanic dust plumes produce spectacular lightning displays. Charged
particle clouds also cause devastating explosions in food, drug and coal
processing industries. Despite the wide-ranging importance of granular charging
in both nature and industry, even the simplest aspects of its causes remain
elusive, because it is difficult to understand how inert grains in contact with
little more than other inert grains can generate the large charges observed.
Here, we present a simple yet predictive explanation for the charging of
granular materials in collisional flows. We argue from very basic
considerations that charge transfer can be expected in collisions of identical
dielectric grains in the presence of an electric field, and we confirm the
model's predictions using discrete-element simulations and a tabletop granular
experiment

### Subdiffusive axial transport of granular materials in a long drum mixer

Granular mixtures rapidly segregate radially by size when tumbled in a
partially filled horizontal drum. The smaller component moves toward the axis
of rotation and forms a buried core, which then splits into axial bands. Models
have generally assumed that the axial segregation is opposed by diffusion.
Using narrow pulses of the smaller component as initial conditions, we have
characterized axial transport in the core. We find that the axial advance of
the segregated core is well described by a self-similar concentration profile
whose width scales as $t^\alpha$, with $\alpha \sim 0.3 < 1/2$. Thus, the
process is subdiffusive rather than diffusive as previously assumed. We find
that $\alpha$ is nearly independent of the grain type and drum rotation rate
within the smoothly streaming regime. We compare our results to two
one-dimensional PDE models which contain self-similarity and subdiffusion; a
linear fractional diffusion model and the nonlinear porous medium equation.Comment: 4 pages, 4 figures, 1 table. Submitted to Phys Rev Lett. For more
info, see http://www.physics.utoronto.ca/nonlinear

### 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

### Creep motion in a granular pile exhibiting steady surface flow

We investigate experimentally granular piles exhibiting steady surface flow.
Below the surface flow, it has been believed exisitence of a `frozen' bulk
region, but our results show absence of such a frozen bulk. We report here that
even the particles in deep layers in the bulk exhibit very slow flow and that
such motion can be detected at an arbitrary depth. The mean velocity of the
creep motion decays exponentially with depth, and the characteristic decay
length is approximately equal to the particle-size and independent of the flow
rate. It is expected that the creep motion we have seeen is observable in all
sheared granular systems.Comment: 3 pages, 4 figure

### Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to
inelastic mutual collisions, when it is stirred by a bidimensional smooth
chaotic flow. A simple dynamical model is introduced where four different time
scales are explicitly considered: i) the Stokes time, accounting for the
inertia of the particles, ii) the mean collision time among the grains, iii)
the typical time scale of the flow, and iv) the inverse of the Lyapunov
exponent of the chaotic flow, which gives a typical time for the separation of
two initially close parcels of fluid. Depending on the relative values of these
different times a complex scenario appears for the long-time steady spatial
distribution of particles, where clusters of particles may or not appear.Comment: 4 pages, 3 figure

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