19,718 research outputs found
Extension of Haff's cooling law in granular flows
The total energy E(t) in a fluid of inelastic particles is dissipated through
inelastic collisions. When such systems are prepared in a homogeneous initial
state and evolve undriven, E(t) decays initially as t^{-2} \aprox exp[ -
2\epsilon \tau] (known as Haff's law), where \tau is the average number of
collisions suffered by a particle within time t, and \epsilon=1-\alpha^2
measures the degree of inelasticity, with \alpha the coefficient of normal
restitution. This decay law is extended for large times to E(t) \aprox
\tau^{-d/2} in d-dimensions, far into the nonlinear clustering regime. The
theoretical predictions are quantitatively confirmed by computer simulations,
and holds for small to moderate inelasticities with 0.6< \alpha< 1.Comment: 7 pages, 4 PostScript figures. To be published in Europhysics Letter
Scaling Solutions of Inelastic Boltzmann Equations with Over-populated High Energy Tails
This paper deals with solutions of the nonlinear Boltzmann equation for
spatially uniform freely cooling inelastic Maxwell models for large times and
for large velocities, and the nonuniform convergence to these limits. We
demonstrate how the velocity distribution approaches in the scaling limit to a
similarity solution with a power law tail for general classes of initial
conditions and derive a transcendental equation from which the exponents in the
tails can be calculated. Moreover on the basis of the available analytic and
numerical results for inelastic hard spheres and inelastic Maxwell models we
formulate a conjecture on the approach of the velocity distribution function to
a scaling form.Comment: 15 pages, 4 figures. Accepted in J. Statistical Physic
Asymptotic solutions of the nonlinear Boltzmann equation for dissipative systems
Analytic solutions of the nonlinear Boltzmann equation in
-dimensions are studied for a new class of dissipative models, called
inelastic repulsive scatterers, interacting through pseudo-power law
repulsions, characterized by a strength parameter , and embedding
inelastic hard spheres () and inelastic Maxwell models (). The
systems are either freely cooling without energy input or driven by
thermostats, e.g. white noise, and approach stable nonequilibrium steady
states, or marginally stable homogeneous cooling states, where the data,
plotted versus , collapse on a scaling or
similarity solution , where is the r.m.s. velocity. The
dissipative interactions generate overpopulated high energy tails, described
generically by stretched Gaussians, with , where with in free cooling, and with when driven by white noise. Power law tails, , are
only found in marginal cases, where the exponent is the root of a
transcendental equation. The stability threshold depend on the type of
thermostat, and is for the case of free cooling located at . Moreover we
analyze an inelastic BGK-type kinetic equation with an energy dependent
collision frequency coupled to a thermostat, that captures all qualitative
properties of the velocity distribution function in Maxwell models, as
predicted by the full nonlinear Boltzmann equation, but fails for harder
interactions with .Comment: Submitted to: "Granular Gas Dynamics", T. Poeschel, N. Brilliantov
(eds.), Lecture Notes in Physics, Vol. LNP 624, Springer-Verlag,
Berlin-Heidelberg-New York, 200
Coherence freeze in an optical lattice investigated via pump-probe spectroscopy
Motivated by our observation of fast echo decay and a surprising coherence
freeze, we have developed a pump-probe spectroscopy technique for vibrational
states of ultracold Rb atoms in an optical lattice to gain information
about the memory dynamics of the system. We use pump-probe spectroscopy to
monitor the time-dependent changes of frequencies experienced by atoms and to
characterize the probability distribution of these frequency trajectories. We
show that the inferred distribution, unlike a naive microscopic model of the
lattice, correctly predicts the main features of the observed echo decay.Comment: 4 pages, 5 figure
Towards a Landau-Ginzburg-type Theory for Granular Fluids
In this paper we show how, under certain restrictions, the hydrodynamic
equations for the freely evolving granular fluid fit within the framework of
the time dependent Landau-Ginzburg (LG) models for critical and unstable fluids
(e.g. spinodal decomposition). The granular fluid, which is usually modeled as
a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the
spontaneous formation of vortices and of high density clusters. We suppress the
clustering instability by imposing constraints on the system sizes, in order to
illustrate how LG-equations can be derived for the order parameter, being the
rate of deformation or shear rate tensor, which controls the formation of
vortex patterns. From the shape of the energy functional we obtain the
stationary patterns in the flow field. Quantitative predictions of this theory
for the stationary states agree well with molecular dynamics simulations of a
fluid of inelastic hard disks.Comment: 19 pages, LaTeX, 8 figure
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Carphophis amoenus
Number of Pages: 7Integrative BiologyGeological Science
Microscopic approach to pion-nucleus dynamics
Elastic scattering of pions from finite nuclei is investigated utilizing a
contemporary, momentum--space first--order optical potential combined with
microscopic estimates of second--order corrections. The calculation of the
first--order potential includes:\ \ (1)~full Fermi--averaging integration
including both the delta propagation and the intrinsic nonlocalities in the
- amplitude, (2)~fully covariant kinematics, (3)~use of invariant
amplitudes which do not contain kinematic singularities, and (4)~a
finite--range off--shell pion--nucleon model which contains the nucleon pole
term. The effect of the delta--nucleus interaction is included via the mean
spectral--energy approximation. It is demonstrated that this produces a
convergent perturbation theory in which the Pauli corrections (here treated as
a second--order term) cancel remarkably against the pion true absorption terms.
Parameter--free results, including the delta--nucleus shell--model potential,
Pauli corrections, pion true absorption, and short--range correlations are
presented. (2 figures available from authors)Comment: 13 page
Power law tails of time correlations in a mesoscopic fluid model
In a quenched mesoscopic fluid, modelling transport processes at high
densities, we perform computer simulations of the single particle energy
autocorrelation function C_e(t), which is essentially a return probability.
This is done to test the predictions for power law tails, obtained from mode
coupling theory. We study both off and on-lattice systems in one- and
two-dimensions. The predicted long time tail ~ t^{-d/2} is in excellent
agreement with the results of computer simulations. We also account for finite
size effects, such that smaller systems are fully covered by the present theory
as well.Comment: 11 pages, 12 figure
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