173 research outputs found
The Simplest Piston Problem II: Inelastic Collisions
We study the dynamics of three particles in a finite interval, in which two
light particles are separated by a heavy ``piston'', with elastic collisions
between particles but inelastic collisions between the light particles and the
interval ends. A symmetry breaking occurs in which the piston migrates near one
end of the interval and performs small-amplitude periodic oscillations on a
logarithmic time scale. The properties of this dissipative limit cycle can be
understood simply in terms of an effective restitution coefficient picture.
Many dynamical features of the three-particle system closely resemble those of
the many-body inelastic piston problem.Comment: 8 pages, 7 figures, 2-column revtex4 forma
The energy flux into a fluidized granular medium at a vibrating wall
We study the power input of a vibrating wall into a fluidized granular
medium, using event driven simulations of a model granular system. The system
consists of inelastic hard disks contained between a stationary and a vibrating
elastic wall, in the absence of gravity. Two scaling relations for the power
input are found, both involving the pressure. The transition between the two
occurs when waves generated at the moving wall can propagate across the system.
Choosing an appropriate waveform for the vibrating wall removes one of these
scalings and renders the second very simple.Comment: 5 pages, revtex, 7 postscript 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
Spatial Correlations in Compressible Granular Flows
For a freely evolving granular fluid, the buildup of spatial correlations in
density and flow field is described using fluctuating hydrodynamics. The theory
for incompressible flows is extended to the general, compressible case,
including longitudinal velocity and density fluctuations, and yields
qualitatively different results for long range correlations. The structure
factor of density fluctuations shows a maximum at finite wavenumber, shifting
in time to smaller wavenumbers and corresponding to a growing correlation
length. It agrees well with two-dimensional molecular dynamics simulations.Comment: 12 pages, Latex, 3 figure
Dynamics of Freely Cooling Granular Gases
We study dynamics of freely cooling granular gases in two-dimensions using
large-scale molecular dynamics simulations. We find that for dilute systems the
typical kinetic energy decays algebraically with time, E(t) ~ t^{-1}, in the
long time limit. Asymptotically, velocity statistics are characterized by a
universal Gaussian distribution, in contrast with the exponential high-energy
tails characterizing the early homogeneous regime. We show that in the late
clustering regime particles move coherently as typical local velocity
fluctuations, Delta v, are small compared with the typical velocity, Delta v/v
~ t^{-1/4}. Furthermore, locally averaged shear modes dominate over acoustic
modes. The small thermal velocity fluctuations suggest that the system can be
heuristically described by Burgers-like equations.Comment: 4 pages, 5 figure
Granular clustering in a hydrodynamic simulation
We present a numerical simulation of a granular material using hydrodynamic
equations. We show that, in the absence of external forces, such a system
phase-separates into high density and low density regions. We show that this
separation is dependent on the inelasticity of collisions, and comment on the
mechanism for this clustering behavior. Our results are compatible with the
granular clustering seen in experiments and molecular dynamic simulations of
inelastic hard disks.Comment: 4 pages, 5 figure
A dc voltage step-up transformer based on a bi-layer \nu=1 quantum Hall system
A bilayer electron system in a strong magnetic field at low temperatures,
with total Landau level filling factor nu =1, can enter a strongly coupled
phase, known as the (111) phase or the quantum Hall pseudospin-ferromagnet. In
this phase there is a large quantized Hall drag resistivity between the layers.
We consider here structures where regions of (111) phase are separated by
regions in which one of the layers is depleted by means of a gate, and various
of the regions are connected together by wired contacts. We note that with
suitable designs, one can create a DC step-up transformer where the output
voltage is larger than the input, and we show how to analyze the current flows
and voltages in such devices
Energy flows in vibrated granular media
We study vibrated granular media, investigating each of the three components
of the energy flow: particle-particle dissipation, energy input at the
vibrating wall, and particle-wall dissipation. Energy dissipated by
interparticle collisions is well estimated by existing theories when the
granular material is dilute, and these theories are extended to include
rotational kinetic energy. When the granular material is dense, the observed
particle-particle dissipation rate decreases to as little as 2/5 of the
theoretical prediction. We observe that the rate of energy input is the weight
of the granular material times an average vibration velocity times a function
of the ratio of particle to vibration velocity. `Particle-wall' dissipation has
been neglected in all theories up to now, but can play an important role when
the granular material is dilute. The ratio between gravitational potential
energy and kinetic energy can vary by as much as a factor of 3. Previous
simulations and experiments have shown that E ~ V^delta, with delta=2 for
dilute granular material, and delta ~ 1.5 for dense granular material. We
relate this change in exponent to the departure of particle-particle
dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR
Phase Changes in an Inelastic Hard Disk System with a Heat Bath under Weak Gravity for Granular Fluidization
We performed numerical simulations on a two-dimensional inelastic hard disk
system under gravity with a heat bath to study the dynamics of granular
fluidization. Upon increasing the temperature of the heat bath, we found that
three phases, namely, the condensed phase, locally fluidized phase, and
granular turbulent phase, can be distinguished using the maximum packing
fraction and the excitation ratio, or the ratio of the kinetic energy to the
potential energy.It is shown that the system behavior in each phase is very
different from that of an ordinary vibrating bed.Comment: 4 pages, including 5 figure
Shock-Like Dynamics of Inelastic Gases
We provide a simple physical picture which suggests that the asymptotic
dynamics of inelastic gases in one dimension is independent of the degree of
inelasticity. Statistical characteristics, including velocity fluctuations and
the velocity distribution are identical to those of a perfectly inelastic
sticky gas, which in turn is described by the inviscid Burgers equation.
Asymptotic predictions of this continuum theory, including the t^{-2/3}
temperature decay and the development of discontinuities in the velocity
profile, are verified numerically for inelastic gases.Comment: 4 pages, 5 figures, revte
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