Chains of Viscoelastic Spheres

Given a chain of viscoelastic spheres with fixed masses of the first and last particles. We raise the question: How to chose the masses of the other particles of the chain to assure maximal energy transfer? The results are compared with a chain of particles for which a constant coefficient of restitution is assumed. Our simple example shows that the assumption of viscoelastic particle properties has not only important consequences for very large systems (see [1]) but leads also to qualitative changes in small systems as compared with particles interacting via a constant restitution coefficient.Comment: 11 pages, 6 figure

Third and fourth degree collisional moments for inelastic Maxwell models

The third and fourth degree collisional moments for $d$-dimensional inelastic Maxwell models are exactly evaluated in terms of the velocity moments, with explicit expressions for the associated eigenvalues and cross coefficients as functions of the coefficient of normal restitution. The results are applied to the analysis of the time evolution of the moments (scaled with the thermal speed) in the free cooling problem. It is observed that the characteristic relaxation time toward the homogeneous cooling state decreases as the anisotropy of the corresponding moment increases. In particular, in contrast to what happens in the one-dimensional case, all the anisotropic moments of degree equal to or less than four vanish in the homogeneous cooling state for $d\geq 2$.Comment: 15 pages, 3 figures; v2: addition of two new reference

Thermal collapse of a granular gas under gravity

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.Comment: 4 pages, 12 eps figures, to appear in PR

A model of ballistic aggregation and fragmentation

A simple model of ballistic aggregation and fragmentation is proposed. The model is characterized by two energy thresholds, Eagg and Efrag, which demarcate different types of impacts: If the kinetic energy of the relative motion of a colliding pair is smaller than Eagg or larger than Efrag, particles respectively merge or break; otherwise they rebound. We assume that particles are formed from monomers which cannot split any further and that in a collision-induced fragmentation the larger particle splits into two fragments. We start from the Boltzmann equation for the mass-velocity distribution function and derive Smoluchowski-like equations for concentrations of particles of different mass. We analyze these equations analytically, solve them numerically and perform Monte Carlo simulations. When aggregation and fragmentation energy thresholds do not depend on the masses of the colliding particles, the model becomes analytically tractable. In this case we show the emergence of the two types of behavior: the regime of unlimited cluster growth arises when fragmentation is (relatively) weak and the relaxation towards a steady state occurs when fragmentation prevails. In a model with mass-dependent Eagg and Efrag the evolution with a cross-over from one of the regimes to another has been detected

Coefficient of tangential restitution for the linear dashpot model

The linear dashpot model for the inelastic normal force between colliding spheres leads to a constant coefficient of normal restitution, $\epsilon_n=$const., which makes this model very popular for the investigation of dilute and moderately dense granular systems. For two frequently used models for the tangential interaction force we determine the coefficient of tangential restitution $\epsilon_t$, both analytically and by numerical integration of Newton's equation. Although $\epsilon_n=$const. for the linear-dashpot model, we obtain pronounced and characteristic dependencies of the tangential coefficient on the impact velocity $\epsilon_t=\epsilon_t(\vec{g})$. The results may be used for event-driven simulations of granular systems of frictional particles.Comment: 12 pages, 12 figure

Granular gases under extreme driving

We study inelastic gases in two dimensions using event-driven molecular dynamics simulations. Our focus is the nature of the stationary state attained by rare injection of large amounts of energy to balance the dissipation due to collisions. We find that under such extreme driving, with the injection rate much smaller than the collision rate, the velocity distribution has a power-law high energy tail. The numerically measured exponent characterizing this tail is in excellent agreement with predictions of kinetic theory over a wide range of system parameters. We conclude that driving by rare but powerful energy injection leads to a well-mixed gas and constitutes an alternative mechanism for agitating granular matter. In this distinct nonequilibrium steady-state, energy cascades from large to small scales. Our simulations also show that when the injection rate is comparable with the collision rate, the velocity distribution has a stretched exponential tail.Comment: 6 pages, 7 figures; new version contains 2 new figures and text describing cascade

Active particles with chirality: Application to pedestrian flows

We analyse pattern formation in systems of active particles with right/left asymmetry of the interaction forces in the context of pedestrian dynamics. To describe the inter-particle interactions we use the standard social force model and supplement it with the new type of force, reflecting the chirality of pedestrians. We perform numerical simulations of two pedestrian flows moving in opposite directions in a long corridor. We observe phase transition from disordered motion to multi-lane motion and quantify it in terms of the order parameter. Also we observe a phase transition from the multi-lane to two-lane motion, which occurs with varying number density of pedestrians and strength of the chirality force. We perform a qualitative analysis to predict the critical density of this transition and its dependence on the chirality. The results of our analysis agree fairly well with the simulation data. Our findings may find applications in urbanistic and transport problems

Long-Range Ordering of Vibrated Polar Disks

Vibrated polar disks have been used experimentally to investigate collective motion of driven particles, where fully-ordered asymptotic regimes could not be reached. Here we present a model reproducing quantitatively the single, binary and collective properties of this granular system. Using system sizes not accessible in the laboratory, we show in silico that true long-range order is possible in the experimental system. Exploring the model's parameter space, we find a phase diagram qualitatively different from that of dilute or point-like particle systems.Comment: 5 pages, 4 figure

Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order

We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{\alpha-1}$. We reveal a relation between pattern formation kinetics and structural properties of arising patterns. We propose a mean-field theory which provides a fair description for sufficiently small $\alpha$. When $\alpha \to \infty$, highly ordered structures locally identical to the Apollonian packing are formed. We introduce a quantitative criterion of the regularity of the pattern formation process. When $\alpha \gg 1$, a sharp transition from irregular to regular pattern formation regime is found to occur near the jamming coverage of standard random sequential adsorption with monodisperse size distribution.Comment: 8 pages, LaTeX, 5 figures, to appear in Phys.Rev.

Fractal formation and ordering in random sequential adsorption

We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered as $\alpha$ increases, and that the Apollonian packing is obtained at $\alpha \to \infty$ limit. We introduce the entropy production rate as a quantitative criteria of regularity and observe a transition from an irregular regime of the pattern formation to a regular one. We develop a scaling theory that relates kinetic and structural properties of the system.Comment: 4 pages, RevTex, 4 postscript figures. To appear in Phys.Rev.Let