Sinusoidal shaking in event-driven simulations

Event-driven algorithms are a powerful and efficient simulation method that can be used to numerically study the behavior of particulate systems, such as granular materials or powders. Its superior efficiency originates from only considering analytically calculable points in time, where physically relevant events occur. This, however, is only possible for pairs of trajectories whose relative distance can be expressed as a polynomial of order less than or equal to four. For more complex trajectories, like a sinusoidal motion of a wall, the collision times have to be calculated numerically, which dramatically reduces the efficiency. In this paper we present a tabulation method implemented in an event-driven algorithm, which is able to efficiently handle the one-dimensional motion of a periodically moving wall. By demonstrating this for a sinusoidally moving wall, we enhance the comparability of simulations with (usually sinusoidally driven) experiments. Because granular materials or powders are systems which are easily accessible through both experiments and simulations, our work enhances the growing field of statistical physics far from equilibrium.