Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface

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.

/pdf/cohesive-frictional-powders-contact-models-for-tension-1oj68hfvyc.pdf

Cohesive, frictional powders: contact models for tension

H E Stanley Oxford: University Press 1971 pp xx + 308 price ?5 In the past fifteen years or so there has been a lot of experimental and theoretical work on the nature of critical phenomena in the neighbourhood of second order phase transitions. It has not been easy to get a good overall view of this work without digging through the rather complex original literature, although there are some good review articles covering particular aspects of the work.

https://iopscience.iop.org/article/10.1088/0031-9112/23/4/018/pdf

Introduction to Phase Transitions and Critical Phenomena

Solitary waves in the granular chain

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstraint. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.

How Hertzian Solitary Waves Interact with Boundaries in a 1D Granular Medium

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains’ masses and the striker mass. Numerical calculations and experiments corroborate these findings.

Solitary wave trains in granular chains: experiments, theory and simulations

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease The characteristic time is mainly a function involving the grains' masses and the striker mass Numerical calculations and experiments corroborate these findings

Solitary wave trains in granular chains: Experiments, theory and simulations

It has been seen that inertial mismatches in 1D granular chains lead to remarkable energy absorption which increases with the number of spheres, $N$, and tapering, $q$. Short chains, however, are limited in that regard, and we therefore present one solution which greatly improves performance for any size chain. These strongly nonlinear and scalable systems feature surprisingly complicated dynamics and are inadequately represented by a hard-sphere approximation. Additionally, such systems have shock absorption capacities that vary as a function of position along the chain. In this Letter, we present results in the form of normalized kinetic energy diagrams to illustrate the impressive mitigation capability of both original and improved tapered chains.

Surajit Sen

Papers

Solitary waves in the granular chain

How Hertzian Solitary Waves Interact with Boundaries in a 1D Granular Medium

Solitary wave trains in granular chains: experiments, theory and simulations

Solitary wave trains in granular chains: Experiments, theory and simulations

Decorated, tapered, and highly nonlinear granular chain.