A heap-based algorithm for the study of one-dimensional particle systems

This paper discusses the implementation of a fast heap-based event-driven scheme for integrating numerically 1D systems of N interacting particles, provided the dynamics can be integrated between two successive collisions. The collision times are ordered on a heap, reducing the complexity to O(log N) operations per collision. As a consequence, for large values of N, the present algorithm is faster than earlier algorithms in the literature, which are O(N). This opens up the perspective of studying the statistical mechanics of such systems for large numbers of particles and long periods of times. Classical (Newtonian) self-gravitating systems are presented as one possible application of the present algorithm. Nevertheless, the algorithm is more general and, for example, can also be applied to models of the motion of matter in an expanding universe.