5,904 research outputs found
Escaping from nonhyperbolic chaotic attractors
We study the noise-induced escape process from chaotic attractors in
nonhyperbolic systems. We provide a general mechanism of escape in the low
noise limit, employing the theory of large fluctuations. Specifically, this is
achieved by solving the variational equations of the auxiliary Hamiltonian
system and by incorporating the initial conditions on the chaotic attractor
unambiguously. Our results are exemplified with the H{\'e}non and the Ikeda map
and can be implemented straightforwardly to experimental data.Comment: replaced with published versio
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
Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs
We define 2-decompositions of ribbon graphs, which generalise 2-sums and
tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial
of such a 2-decomposition, and derive the classical Brylawski formula for the
Tutte polynomial of a tensor product as a (very) special case. This study was
initially motivated from knot theory, and we include an application of our
formulae to mutation in knot diagrams.Comment: Version 2 has minor changes. To appear in Annals of Combinatoric
Velocity correlations in dense granular gases
We report the statistical properties of spherical steel particles rolling on
an inclined surface being driven by an oscillating wall. Strong dissipation
occurs due to collisions between the particles and rolling and can be tuned by
changing the number density. The velocities of the particles are observed to be
correlated over large distances comparable to the system size. The distribution
of velocities deviates strongly from a Gaussian. The degree of the deviation,
as measured by the kurtosis of the distribution, is observed to be as much as
four times the value corresponding to a Gaussian, signaling a significant
breakdown of the assumption of negligible velocity correlations in a granular
system.Comment: 4 pages, 4 Figure
Propagating front in an excited granular layer
A partial monolayer of ~ 20000 uniform spherical steel beads, vibrated
vertically on a flat plate, shows remarkable ordering transitions and
cooperative behavior just below 1g maximum acceleration. We study the stability
of a quiescent disordered or ``amorphous'' state formed when the acceleration
is switched off in the excited ``gaseous'' state. The transition from the
amorphous state back to the gaseous state upon increasing the plate's
acceleration is generally subcritical: An external perturbation applied to one
bead initiates a propagating front that produces a rapid transition. We measure
the front velocity as a function of the applied acceleration. This phenomenon
is explained by a model based on a single vibrated particle with multiple
attractors that is perturbed by collisions. A simulation shows that a
sufficiently high rate of interparticle collisions can prevent trapping in the
attractor corresponding to the nonmoving ground state.Comment: 16 pages, 9 figures, revised version, to appear in Phys. Rev. E, May
199
Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions
We study velocity statistics of electrostatically driven granular gases. For
two different experiments: (i) non-magnetic particles in a viscous fluid and
(ii) magnetic particles in air, the velocity distribution is non-Maxwellian,
and its high-energy tail is exponential, P(v) ~ exp(-|v|). This behavior is
consistent with kinetic theory of driven dissipative particles. For particles
immersed in a fluid, viscous damping is responsible for the exponential tail,
while for magnetic particles, long-range interactions cause the exponential
tail. We conclude that velocity statistics of dissipative gases are sensitive
to the fluid environment and to the form of the particle interaction.Comment: 4 pages, 3 figure
Phase transition in inelastic disks
This letter investigates the molecular dynamics of inelastic disks without
external forcing. By introducing a new observation frame with a rescaled time,
we observe the virtual steady states converted from asymptotic energy
dissipation processes. System behavior in the thermodynamic limit is carefully
investigated. It is found that a phase transition with symmetry breaking occurs
when the magnitude of dissipation is greater than a critical value.Comment: 9 pages, 6 figure
Clustering and Non-Gaussian Behavior in Granular Matter
We investigate the properties of a model of granular matter consisting of
Brownian particles on a line subject to inelastic mutual collisions. This model
displays a genuine thermodynamic limit for the mean values of the energy and
the energy dissipation. When the typical relaxation time associated with
the Brownian process is small compared with the mean collision time
the spatial density is nearly homogeneous and the velocity probability
distribution is gaussian. In the opposite limit one has
strong spatial clustering, with a fractal distribution of particles, and the
velocity probability distribution strongly deviates from the gaussian one.Comment: 4 pages including 3 eps figures, LaTex, added references, corrected
typos, minimally changed contents and abstract, to published in
Phys.Rev.Lett. (tentatively on 28th of October, 1998
Inelastic Collapse of Three Particles
A system of three particles undergoing inelastic collisions in arbitrary
spatial dimensions is studied with the aim of establishing the domain of
``inelastic collapse''---an infinite number of collisions which take place in a
finite time. Analytic and simulation results show that for a sufficiently small
restitution coefficient, , collapse can
occur. In one dimension, such a collapse is stable against small perturbations
within this entire range. In higher dimensions, the collapse can be stable
against small variations of initial conditions, within a smaller range,
.Comment: 6 pages, figures on request, accepted by PR
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
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