A Universal Method for Modeling and Characterizing Non-Circular Packing Systems Based on n-Point Correlation Functions

A universal method for modeling and characterizing non-circular particles is developed. The n-point correlation functions (n = 1, 2 and 3) are efficiently computed with a GPU parallel computing procedure. An algorithm for dynamic packing of impenetrable non-circular particles is developed based on the fast estimation of overlap information using a one-point correlation function. The packing algorithm is independent of particle shape and proved to be reliable by examples of polygons and super-ellipses. In addition, penetrable packings are generated in an efficient and precise way. Using a two-point correlation function, these non-circular packs are accurately characterized and compared in terms of features such as penetrable and impenetrable, packing fraction and particle shape. In addition, three-point correlation functions are also illustrated and discussed.