13,451 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 $F(v,t)$ of the nonlinear Boltzmann equation in
$d$-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 $\nu$, and embedding
inelastic hard spheres ($\nu=1$) and inelastic Maxwell models ($\nu=0$). 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,
$v^d_0(t) F(v,t)$ plotted versus $c=v/v_0(t)$, collapse on a scaling or
similarity solution $f(c)$, where $v_0(t)$ is the r.m.s. velocity. The
dissipative interactions generate overpopulated high energy tails, described
generically by stretched Gaussians, $f(c) \sim \exp[-\beta c^b]$ with $0 < b <
2$, where $b=\nu$ with $\nu>0$ in free cooling, and $b=1+{1/2} \nu$ with $\nu
\geq 0$ when driven by white noise. Power law tails, $f(c) \sim 1/c^{a+d}$, are
only found in marginal cases, where the exponent $a$ 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 $\nu=0$. 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 $\nu>0$.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

### Hydrogenated grain boundaries in graphene

We have investigated by means of first principles calculations the structural
and electronic properties of hydrogenated graphene structures with distinct
grain boundary defects. Our total energy results reveal that the adsorption of
a single H is more stable at grain boundary defect. The electronic structure of
the grains boundaries upon hydrogen adsorption have been examined. Further
total energy calculations indicate that the adsorption of two H on two neighbor
carbons, forming a basic unit of graphane, is more stable at the defect region.
Therefore, we expect that these extended defects would work as a nucleation
region for the formation of a narrow graphane strip embedded in graphene
region

### Reverse logistics - a framework

In this paper we define and compare Reverse Logistics definitions. We start by giving an understanding framework of Reverse Logistics: the why-what-how. By this means, we put in context the driving forces for Reverse Logistics, a typology of return reasons, a classification of products, processes and actors. In addition we provide a decision framework for Reverse Logistics and we present it according to long, medium and short term decisions, i.e. strategic-tactic-operational decisions.Framework;Decision-making;Reverse logistics;Theory building

### 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

### Self-Diffusion in Simple Models: Systems with Long-Range Jumps

We review some exact results for the motion of a tagged particle in simple
models. Then, we study the density dependence of the self diffusion
coefficient, $D_N(\rho)$, in lattice systems with simple symmetric exclusion in
which the particles can jump, with equal rates, to a set of $N$ neighboring
sites. We obtain positive upper and lower bounds on
$F_N(\rho)=N((1-\r)-[D_N(\rho)/D_N(0)])/(\rho(1-\rho))$ for $\rho\in [0,1]$.
Computer simulations for the square, triangular and one dimensional lattice
suggest that $F_N$ becomes effectively independent of $N$ for $N\ge 20$.Comment: 24 pages, in TeX, 1 figure, e-mail addresses: [email protected],
[email protected], [email protected]

### A Framework for Reverse Logistics

Reverse Logistics has been stretching out worldwide, involving all the layers of supply chains in various industry sectors. While some actors in the chain have been forced to take products back, others have pro-actively done so, attracted by the value in used products One way or the other, Reverse Logistics has become a key competence in modern supply chains. In this paper, we present a content analysis of reverse logistics issues. To do so, we propose a content framework focusing on the following questions with respect to reverse logistics: why? what? how?; and, who?, i.e. driving forces and return reasons, what type of products are streaming back, how are they being recovered, and who is executing and managing the various operations. These four basic characteristics are interrelated and their combination determines to a large extent the type of issues arising from the resulting reverse logistics system.supply chain management;reverse logistics;content analysis;theory;framework

- …