Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: A study within combinatorial framework

For this work, we studied a finite system of discrete-size aggregating particles for two types kernels with arbitrary parameters, condensation (or branched-chain polymerization) kernel, K(i, j) = (A + i)(A j), and linear combination the constant additive kernels, A i j. They were solved under monodisperse initial conditions in combinatorial approach assumption that coagulation process takes place continuous time individual coalescences are instantaneous. Thus, no coalescence steps can occur at same each act is marked label. generating function method Lagrange inversion used derivations expressions an average number clusters given size its corresponding standard deviation. tested against numerical simulations. High precision theoretical predictions was observed wide range stages, except post-gel phase case kernel where results only approximate. specific values A, these allowed to obtain known constant, product kernels. Beside previously chains, (i−1 j−1)a, they substantially widen set arbitrary-parameter approach.