An exactly solvable model for externally controlled coagulation
F. Leyvraz, Hans Rudolf Tschudi · Journal of Physics A Mathematical and General · 1980
The authors consider a system of coagulating monomers together with an external source of monomer with arbitrary production rate p(t). The moments M k (t)= Sigma n=1 n k nu n (t), where nu n (t) is the concentration of n-mer at time t (and therefore also the weight and z average of the system), are obtained exactly as a function of p(t). The special case where the external source is the conversion of a substrate molecule to a monomer is discussed in more detail. If p(t) is an exponential, the concentrations nu n (t) can actually be evaluated by a simple contour integral.