Poissonian and non Poissonian Voronoi Diagrams with application to the aggregation of molecules

TL;DR

This paper explores various distributions governing Poissonian and non-Poissonian Voronoi diagrams, deriving new distribution models and applying them to simulate molecular aggregation processes.

Contribution

It introduces new distribution models for Voronoi diagrams and presents an algorithm for simulating molecular aggregation of methanol and water.

Findings

Derived distributions from gamma variates for Voronoi diagrams.

Presented algorithms for simulating molecular aggregation.

Analyzed non-Poissonian seed distributions in Voronoi diagrams.

Abstract

The distributions that regulate the spatial domains of the Poissonian Voronoi Diagrams are discussed adopting the sum of gamma variate of argument two. The distributions that arise from the product and quotient of two gamma variates of argument two are also derived. Three examples of non Poissonian seeds for the Voronoi Diagrams are discussed. The developed algorithm allows the simulation of an aggregation of methanol and water.