449 research outputs found
Continuum simulations of shocks and patterns in vertically oscillated granular layers
We study interactions between shocks and standing-wave patterns in vertically
oscillated layers of granular media using three-dimensional, time-dependent
numerical solutions of continuum equations to Navier-Stokes order. We simulate
a layer of grains atop a plate that oscillates sinusoidally in the direction of
gravity. Standing waves form stripe patterns when the accelerational amplitude
of the plate's oscillation exceeds a critical value. Shocks also form with each
collision between the layer and the plate; we show that pressure gradients
formed by these shocks cause the flow to reverse direction within the layer.
This reversal leads to an oscillatory state of the pattern that is subharmonic
with respect to the plate's oscillation. Finally, we study the relationship
between shocks and patterns in layers oscillated at various frequencies and
show that the pattern wavelength increases monotonically as the shock strength
increases.Comment: 12 pages, 9 figure
Onset of Patterns in an Ocillated Granular Layer: Continuum and Molecular Dynamics Simulations
We study the onset of patterns in vertically oscillated layers of
frictionless dissipative particles. Using both numerical solutions of continuum
equations to Navier-Stokes order and molecular dynamics (MD) simulations, we
find that standing waves form stripe patterns above a critical acceleration of
the cell. Changing the frequency of oscillation of the cell changes the
wavelength of the resulting pattern; MD and continuum simulations both yield
wavelengths in accord with previous experimental results. The value of the
critical acceleration for ordered standing waves is approximately 10% higher in
molecular dynamics simulations than in the continuum simulations, and the
amplitude of the waves differs significantly between the models. The delay in
the onset of order in molecular dynamics simulations and the amplitude of noise
below this onset are consistent with the presence of fluctuations which are
absent in the continuum theory. The strength of the noise obtained by fit to
Swift-Hohenberg theory is orders of magnitude larger than the thermal noise in
fluid convection experiments, and is comparable to the noise found in
experiments with oscillated granular layers and in recent fluid experiments on
fluids near the critical point. Good agreement is found between the mean field
value of onset from the Swift-Hohenberg fit and the onset in continuum
simulations. Patterns are compared in cells oscillated at two different
frequencies in MD; the layer with larger wavelength patterns has less noise
than the layer with smaller wavelength patterns.Comment: Published in Physical Review
Dynamics of drag and force distributions for projectile impact in a granular medium
Our experiments and molecular dynamics simulations on a projectile
penetrating a two-dimensional granular medium reveal that the mean deceleration
of the projectile is constant and proportional to the impact velocity. Thus,
the time taken for a projectile to decelerate to a stop is independent of its
impact velocity. The simulations show that the probability distribution
function of forces on grains is time-independent during a projectile's
penetration of the medium. At all times the force distribution function
decreases exponentially for large forces.Comment: 4 page
Rhombic Patterns: Broken Hexagonal Symmetry
Landau-Ginzburg equations derived to conserve two-dimensional spatial symmetries lead to the prediction that rhombic arrays with characteristic angles slightly differ from 60 degrees should form in many systems. Beyond the bifurcation from the uniform state to patterns, rhombic patterns are linearly stable for a band of angles near the 60 degrees angle of regular hexagons. Experiments conducted on a reaction-diffusion system involving a chlorite-iodide-malonic acid reaction yield rhombic patterns in good accord with the theory.Energy Laboratory of the University of HoustonOffice of Naval ResearchU.S. Department of Energy Office of Basic Energy SciencesRobert A. Welch FoundationCenter for Nonlinear Dynamic
From time series to superstatistics
Complex nonequilibrium systems are often effectively described by a
`statistics of a statistics', in short, a `superstatistics'. We describe how to
proceed from a given experimental time series to a superstatistical
description. We argue that many experimental data fall into three different
universality classes: chi^2-superstatistics (Tsallis statistics), inverse
chi^2-superstatistics, and log-normal superstatistics. We discuss how to
extract the two relevant well separated superstatistical time scales tau and T,
the probability density of the superstatistical parameter beta, and the
correlation function for beta from the experimental data. We illustrate our
approach by applying it to velocity time series measured in turbulent
Taylor-Couette flow, which is well described by log-normal superstatistics and
exhibits clear time scale separation.Comment: 7 pages, 9 figure
Phase transition in a static granular system
We find that a column of glass beads exhibits a well-defined transition
between two phases that differ in their resistance to shear. Pulses of
fluidization are used to prepare static states with well-defined particle
volume fractions in the range 0.57-0.63. The resistance to shear is
determined by slowly inserting a rod into the column of beads. The transition
occurs at for a range of speeds of the rod.Comment: 4 pages, 4 figures. The paper is significantly extended, including
new dat
The Bouncing Jet: A Newtonian Liquid Rebounding off a Free Surface
We find that a liquid jet can bounce off a bath of the same liquid if the
bath is moving horizontally with respect to the jet. Previous observations of
jets rebounding off a bath (e.g. Kaye effect) have been reported only for
non-Newtonian fluids, while we observe bouncing jets in a variety of Newtonian
fluids, including mineral oil poured by hand. A thin layer of air separates the
bouncing jet from the bath, and the relative motion replenishes the film of
air. Jets with one or two bounces are stable for a range of viscosity, jet flow
rate and velocity, and bath velocity. The bouncing phenomenon exhibits
hysteresis and multiple steady states.Comment: 9 pages, 7 figures. submitted to Physical Review
- …