Event-Driven Dynamics of Rigid Bodies Interacting via Discretized Potentials

A framework for performing event-driven, adaptive time step simulations of systems of rigid bodies interacting under stepped or terraced potentials in which the potential energy is only allowed to have discrete values is outlined. The scheme is based on a discretization of an underlying continuous potential that effectively determines the times at which interaction energies change. As in most event-driven approaches, the method consists of specifying a means of computing the free motion, evaluating the times at which interactions occur, and determining the consequences of interactions on subsequent motion for the terraced-potential. The latter two aspects are shown to be simply expressible in terms of the underlying smooth potential. Within this context, algorithms for computing the times of interaction events and carrying out efficient event-driven simulations are discussed. The method is illustrated on system composed of rigid rods in which the constituents interact via a terraced potential that depends on the relative orientations of the rods.