Event-Driven Molecular Dynamics in Parallel

Although event-driven algorithms have been shown to be far more efficient than time-driven methods such as conventional molecular dynamics, they have not become as popular. The main obstacle seems to be the difficulty of parallelizing event-driven molecular dynamics. Several basic ideas have been discussed in recent years, but to our knowledge no complete implementation has been published yet. In this paper we present a parallel event-driven algorithm including dynamic load-balancing, which can be easily implemented on any computer architecture. To simplify matters our explanations refer to a basic multi-particle system of hard spheres, but can be extended easily to a wide variety of possible models.Comment: 10 pages, 9 figure

Mean Field theory for a driven granular gas of frictional particles

We propose a mean field (MF) theory for a homogeneously driven granular gas of inelastic particles with Coulomb friction. The model contains three parameters, a normal restitution coefficient $r_n$, a maximum tangential restitution coefficient $r_t^m$, and a Coulomb friction coefficient $\mu$. The parameters can be tuned to explore a wide range of physical situations. In particular, the model contains the frequently used $\mu \to \infty$ limit as a special case. The MF theory is compared with the numerical simulations of a randomly driven monolayer of spheres for a wide range of parameter values. If the system is far away from the clustering instability ($r_n \approx 1$), we obtain a good agreement between mean field and simulations for $\mu=0.5$ and $r_t^m=0.4$, but for much smaller values of $r_n$ the agreement is less good. We discuss the reasons of this discrepancy and possible refinements of our computational scheme.Comment: 6 pages, 3 figures (10 *.eps files), elsart style (macro included), in Proceedings of the International Conference "Statistical Mechanics and Strongly Correlated Systems", University of Rome "La Sapienza" (Italy), 27-29 September 199

Towards dense, realistic granular media in 2D

The development of an applicable theory for granular matter - with both qualitative and quantitative value - is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.\ud \ud In most systems, low density co-exists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional nonlinear phenomena and material properties are important in realistic granular media, involving, e.g.:\ud \ud (i) multi-particle interactions and elasticity\ud (ii) strong dissipation,\ud (iii) friction,\ud (iv) long-range forces and wet contacts,\ud (v) wide particle size distributions and\ud (vi) various particle shapes.\ud \ud \ud Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some cannot.\ud \ud This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions and corrections given are qualitatively true also in 3D.\ud \ud Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier–Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws - one by one - in order to account for the realistic physical effects and properties listed above

The effect of friction on wide shear bands

Frictional and frictionless granular materials in a split-bottom ring shear cell geometry show wide shear bands under slow, quasi-static deformation. Here, the differences between frictional and frictionless materials are elaborated using discrete element simulations (DEM). Several continuum fields like the density, the velocity field, the deformation gradient, and the stress are used here for comparison.\ud \ud Interestingly, the shear stress intensity, i.e., the shear stress divided by the pressure, is approximately constant throughout the wide shear band, as long as the strain rate is large enough—indicating a Mohr-Coulomb type yield stress fluid. The “viscosity,” i.e., the shear stress divided by the strain rate, is proportional to the pressure, which is increasing with the contact number density. Furthermore, the viscosity is inversely proportional to the nondimensional strain rate, indicating shear softening behavior inside the wide shear bands

Clustering Instabilities, Arching, and Anomalous Interaction Probabilities as Examples for Cooperative Phenomena in Dry Granular Media

In a freely cooling granular material fluctuations in density and temperature cause position dependent energy loss. Due to strong local dissipation, pressure and energy drop rapidly and material moves from `hot' to `cold' regions, leading to even stronger dissipation and thus causing the density instability. The assumption of `molecular chaos' is valid only in the homogeneous cooling regime. As soon as the density instability occurs, the impact parameter is not longer uniformly distributed. The pair-correlation and the structure functions show that the molecular chaos assumption --- together with reasonable excluded volume modeling --- is important for short distances and irrelevant on large length scales. In this study, the probability distribution of the collision frequency is examined for pipe flow and for freely cooling granular materials as well. Uncorrelated events lead to a Poisson distribution for the collision frequencies. In contrast, the fingerprint of the cooperative phenomena discussed here is a power-law decay of the probability for many collisions per unit time. Keywords: discrete element method, event driven simulations, clustering instability, arching, shock waves, power-law distribution, cooperative phenomena.Comment: 27 pages 14 figs (2 color

Cohesive, frictional powders: contact models for tension

The contacts between cohesive, frictional particles with sizes in the range 0.1–10 μm are the subject of this study. Discrete element model (DEM) simulations rely on realistic contact force models—however, too much details make both implementation and interpretation prohibitively difficult. A rather simple, objective contact model is presented, involving the physical properties of elastic–plastic repulsion, dissipation, adhesion, friction as well as rolling- and torsion-resistance. This contact model allows to model bulk properties like friction, cohesion and yield-surfaces. Very loose packings and even fractal agglomerates have been reported in earlier work. The same model also allows for pressure-sintering and tensile strength tests as presented in this study