Analytical Description of the Hole Overlapping Process on the Nuclear-Track Membrane Surface

摘要

The classical problem of overlapping circular holes of equal diameters on one surface of a nuclear track membrane was considered. Using the Monte Carlo method, the probabilities of overlapping W_k(P) of nuclear pores with a multiplicity of k < 32 at a porosity of P < 0.30 were determined and analytical expressions for their approximation were derived. The results were analyzed in terms of an approach based on a kinetic equation for a discrete Markov process. It was shown that the W_k(P) values obtained for multiple pores with a multiplicity of k < 7 are consistent with the theory if two-step processes are taken into account.