230 research outputs found

### Velocity correlations in granular materials

A system of inelastic hard disks in a thin pipe capped by hot walls is
studied with the aim of investigating velocity correlations between particles.
Two effects lead to such correlations: inelastic collisions help to build
localized correlations, while momentum conservation and diffusion produce long
ranged correlations. In the quasi-elastic limit, the velocity correlation is
weak, but it is still important since it is of the same order as the deviation
from uniformity. For system with stronger inelasticity, the pipe contains a
clump of particles in highly correlated motion. A theory with empirical
parameters is developed. This theory is composed of equations similar to the
usual hydrodynamic laws of conservation of particles, energy, and momentum.
Numerical results show that the theory describes the dynamics satisfactorily in
the quasi-elastic limit, however only qualitatively for stronger inelasticity.Comment: 12 pages (REVTeX), 15 figures (Postscript). submitted to Phys. Rev.

### Spectral estimates of the p-Laplace Neumann operator and Brennan's conjecture

In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂R2 . This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings

### Spectral estimates of the p-Laplace Neumann operator and Brennan's conjecture

In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂R2 . This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α -regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings

### 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

### 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

### Scaling and universality of critical fluctuations in granular gases

The global energy fluctuations of a low density gas granular gas in the
homogeneous cooling state near its clustering instability are studied by means
of molecular dynamics simulations. The relative dispersion of the fluctuations
is shown to exhibit a power-law divergent behavior. Moreover, the probability
distribution of the fluctuations presents data collapse as the system
approaches the instability, for different values of the inelasticity. The
function describing the collapse turns out to be the same as the one found in
several molecular equilibrium and non-equilibrium systems, except for the
change in the sign of the fluctuations

### Nontrivial Velocity Distributions in Inelastic Gases

We study freely evolving and forced inelastic gases using the Boltzmann
equation. We consider uniform collision rates and obtain analytical results
valid for arbitrary spatial dimension d and arbitrary dissipation coefficient
epsilon. In the freely evolving case, we find that the velocity distribution
decays algebraically, P(v,t) ~ v^{-sigma} for sufficiently large velocities. We
derive the exponent sigma(d,epsilon), which exhibits nontrivial dependence on
both d and epsilon, exactly. In the forced case, the velocity distribution
approaches a steady-state with a Gaussian large velocity tail.Comment: 4 pages, 1 figur

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