Exchange-Driven Growth with Birth Rate Less Than Death

We further study the kinetic behavior of the exchange-drivengrowth with birth and death for the case of birth rate kernelbeing less than that of death based on the mean-field theory. Thesymmetric exchange rate kernel is K(k,j)=K'(k,j)=Ikj^υ,and the birth and death rates are proportional to the aggregate'ssize. The long time asymptotic behavior of the aggregate sizedistribution a_k(t) is found to obey a much unusual scaling lawwith an exponentially growing scaling function Φ(x)=exp(x).