Multiple fragmentation of critical continuum percolation clusters

Abstract

The scaling properties of multiple fragmentation were examined by Monte Carlo simulations in continuum percolation, in which inclusion particles, i.e., overlapping discs and spheres, were assumed to be connected if they overlapped. Each inclusion particle may be multiply connected to other particles, and a large cluster can be fragmented into many smaller clusters by removing a fragmenting particle, thereby enabling a study of multiple fragmentation. The scaling exponents for binary, ternary and quaternary fragmentation were calculated, and the probability distribution of the daughter clusters was also examined. The power laws and scaling relations known for lattice bond percolation equally held for the binary, ternary and quaternary fragmentation of critical continuum percolation clusters.