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

Minimum Perimeter Rectangles That Enclose Congruent Non-Overlapping Circles

We use computational experiments to find the rectangles of minimum perimeter into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings found, the circles form the usual regular square-grid or hexagonal patterns or their hybrids. However, for most values of n in the tested range n =< 5000, e.g., for n = 7, 13, 17, 21, 22, 26, 31, 37, 38, 41, 43...,4997, 4998, 4999, 5000, we prove that the optimum cannot possibly be achieved by such regular arrangements. Usually, the irregularities in the best packings found for such n are small, localized modifications to regular patterns; those irregularities are usually easy to predict. Yet for some such irregular n, the best packings found show substantial, extended irregularities which we did not anticipate. In the range we explored carefully, the optimal packings were substantially irregular only for n of the form n = k(k+1)+1, k = 3, 4, 5, 6, 7, i.e., for n = 13, 21, 31, 43, and 57. Also, we prove that the height-to-width ratio of rectangles of minimum perimeter containing packings of n congruent circles tends to 1 as n tends to infinity.Comment: existence of irregular minimum perimeter packings for n not of the form (10) is conjectured; smallest such n is n=66; existence of irregular minimum area packings is conjectured, e.g. for n=453; locally optimal packings for the two minimization criteria are conjecturally the same (p.22, line 5); 27 pages, 12 figure