Simulating Hard Rigid Bodies

TL;DR

This paper develops algorithms for simulating systems of convex hard rigid bodies, enabling more realistic modeling of complex particles in condensed matter, biology, and soft matter through event-driven molecular dynamics.

Contribution

It introduces new algorithms for calculating distances and contact times between convex rigid bodies, and an optimized collision detection method for elongated particles.

Findings

Algorithms successfully simulate convex rigid bodies.

Enhanced collision detection improves efficiency.

Applications span multiple scientific fields.

Abstract

Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in condensed matter. The next level of description is to consider particles as rigid objects of generic shape, which would enrich the possible phenomenology enormously. This kind of modeling will prove to be interesting in all those situations in which steric effects play a relevant role. These include biology, soft matter, granular materials and molecular systems. With a view to developing a general recipe for event-driven Molecular Dynamics simulations of hard rigid bodies, two algorithms for calculating the distance between two convex hard rigid bodies and the contact time of two colliding hard rigid bodies solving a non-linear set of equations will be described. Building on these two methods, an event-driven molecular dynamics algorithm for simulating systems of convex hard rigid bodies will be developed and illustrated in details. In order to optimize the collision detection between very elongated hard rigid bodies, a novel nearest-neighbor list method based on an oriented bounding box will be introduced and fully explained. Efficiency and performance of the new algorithm proposed will be extensively tested for uniaxial hard ellipsoids and superquadrics. Finally applications in various scientific fields will be reported and discussed.