New results on a parity-dependent model of aggregation kinetics

Publisher Website
Google Scholar
Abstract
A reaction kernel, K(j,k) = K(k,j), is studied, for which the Smoluchowski equations of aggregation ċj = (1/2)∑k,l = 1∞K(k,l)ckcl[δk + l,j-δk,j -δl,j] can be solved. It takes only three values: K(j,k) = K if j and k are both odd, K(j,k) = L if j and k are both even and K(j,k) = M if j and k have different parities. A considerable simplification over previous treatments is presented for the general case (K, L and M are three arbitrary positive numbers), and the time evolution of the concentrations is exhibited in completely explicit form for the (new) special case L = 4M. In another special case, K = M, the equation for the generating function of the concentrations can be reduced to quadratures; the analysis of this case, and of the general case, is postponed to a future paper.

This publication has 12 references indexed in Scilit: