Percolation of clusters with a residence time in the bond definition: Integral equation theory

We consider the clustering and percolation of continuum systems whose particles interact via the Lennard-Jones pair potential. A cluster definition is used according to which two particles are considered directly connected (bonded) at time t if they remain within a distance d, the connectivity distance, during at least a time of duration tau, the residence time. An integral equation for the corresponding pair connectedness function, recently proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved using the orthogonal polynomial approach developed by another of the authors [Phys. Rev. E 55, 426 (1997)]. We compare our results with those obtained by molecular dynamics simulations.