8,154 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 Modeling of Droplet Evaporation on Superhydrophobic Surfaces
When a drop of water is placed on a rough surface, there are two possible
extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets
trapped underneath the droplet and the one characterized by the homogeneous
wetting of the surface, called the Wenzel (W) state. A way to investigate the
transition between these two states is by means of evaporation experiments, in
which the droplet starts in a CB state and, as its volume decreases, penetrates
the surface's grooves, reaching a W state. Here we present a theoretical model
based on the global interfacial energies for CB and W states that allows us to
predict the thermodynamic wetting state of the droplet for a given volume and
surface texture. We first analyze the influence of the surface geometric
parameters on the droplet's final wetting state with constant volume, and show
that it depends strongly on the surface texture. We then vary the volume of the
droplet keeping fixed the geometric surface parameters to mimic evaporation and
show that the drop experiences a transition from the CB to the W state when its
volume reduces, as observed in experiments. To investigate the dependency of
the wetting state on the initial state of the droplet, we implement a cellular
Potts model in three dimensions. Simulations show a very good agreement with
theory when the initial state is W, but it disagrees when the droplet is
initialized in a CB state, in accordance with previous observations which show
that the CB state is metastable in many cases. Both simulations and theoretical
model can be modified to study other types of surface.Comment: 23 pages, 7 figure
Non-Markovian incoherent quantum dynamics of a two-state system
We present a detailed study of the non-Markovian two-state system dynamics
for the regime of incoherent quantum tunneling. Using perturbation theory in
the system tunneling amplitude , and in the limit of strong system-bath
coupling, we determine the short time evolution of the reduced density matrix
and thereby find a general equation of motion for the non-Markovian evolution
at longer times. We relate the nonlocality in time due to the non-Markovian
effects with the environment characteristic response time. In addition, we
study the incoherent evolution of a system with a double-well potential, where
each well consists several quantized energy levels. We determine the crossover
temperature to a regime where many energy levels in the wells participate in
the tunneling process, and observe that the required temperature can be much
smaller than the one associated with the system plasma frequency. We also
discuss experimental implications of our theoretical analysis.Comment: 10 pages, published versio
Lattice gases in slab geometries
Non-mean-field-type excess correlations at short times are present in three-dimensional (3D) computer simulations of the velocity autocorrelation function, but absent in 1D, 2D, and 4D. They are caused by ring collisions in a quasi-3D slab of size 2 x L x L x L in a face-centered-hypercubic lattice with periodic boundary conditions, which is the only available lattice-gas cellular automaton with 3D isotropic fluid flow. We evaluate this excess correlation. The simulation data agree very well with our exact result
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