17,034 research outputs found
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
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
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
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
On the dependence of the avalanche angle on the granular layer thickness
A layer of sand of thickness h flows down a rough surface if the inclination
is larger than some threshold value theta which decreases with h. A tentative
microscopic model for the dependence of theta with h is proposed for rigid
frictional grains, based on the following hypothesis: (i) a horizontal layer of
sand has some coordination z larger than a critical value z_c where mechanical
stability is lost (ii) as the tilt angle is increased, the configurations
visited present a growing proportion $_s of sliding contacts. Instability with
respect to flow occurs when z-z_s=z_c. This criterion leads to a prediction for
theta(h) in good agreement with empirical observations.Comment: 6 pages, 2 figure
Dynamical instabilities in density-dependent hadronic relativistic models
Unstable modes in asymmetric nuclear matter (ANM) at subsaturation densities
are studied in the framework of relativistic mean-field density-dependent
hadron models. The size of the instabilities that drive the system are
calculated and a comparison with results obtained within the non-linear Walecka
model is presented. The distillation and anti-distillation effects are
discussed.Comment: 8 pages, 8 Postscript figures. Submitted for publication in Phys.
Rev.
Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP
In this paper we focus on the Hamilton-Jacobi method to determine the entropy
of a self-dual black hole by using linear and quadratic GUPs(generalized
uncertainty principles). We have obtained the Bekenstein-Hawking entropy of
self-dual black holes and its quantum corrections that are logarithm and also
of several other types.Comment: Latex, 7 pages, no figure. Version to appear in PLB. arXiv admin
note: substantial text overlap with arXiv:1502.0017
Symmetry-preserving contact interaction model for heavy-light mesons
We use a symmetry-preserving regularization method of ultraviolet divergences
in a vector-vector contact interac- tion model for low-energy QCD. The contact
interaction is a representation of nonperturbative kernels used Dyson-Schwinger
and Bethe-Salpeter equations. The regularization method is based on a
subtraction scheme that avoids standard steps in the evaluation of divergent
integrals that invariably lead to symmetry violation. Aiming at the study of
heavy-light mesons, we have implemented the method to the pseudoscalar pion and
Kaon mesons. We have solved the Dyson-Schwinger equation for the u, d and s
quark propagators, and obtained the bound-state Bethe-Salpeter amplitudes in a
way that the Ward-Green-Takahashi identities reflecting global symmetries of
the model are satisfied for arbitrary routing of the momenta running in loop
integrals
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