The maximum volume hard subset model for Poisson processes: simulation aspects

Abstract

We introduce a process of non-intersecting convex particles by thinning a primary particle process such that the remaining particles are mutually non-intersecting and have maximum total volume among all such subsystems. This approach is based on the idea to construct hardcore processes by suitable dependent thinnings proposed by Matérn but generates packings with higher volume fractions than the known thinning models. Due to the enormous complexity of the computations involved, we develop a two-phase heuristic algorithm whose first phase turns out to yield a structure of Matérn III type. We focus mainly on the generation of packings with high volume fractions and present some simulation results for Poisson primary particle processes of equally sized balls in ℝ² and ℝ³. The results are compared with the well-known random sequential adsorption model and Matérn type models.

Keywords:

• Poisson process
• dense packing
• random packing
• random sequential adsorption
• Matérn hardcore process

AMS Subject Classifications :

• 60D05
• 60G55
• 62M30