Exchange-Driven Growth with Birth Rate Less Than Death

We further study the kinetic behavior of the exchange-driven growth withbirth and death for the case of birth rate kernel being less than that of death based on themean-Geld theory. The symmetric exchange rate kernel is K(k,j) = K′(k,j) = Ikj~v, and the birth anddeath rates are proportional to the aggregate's size. The long time asymptotic behavior of theaggregate size distribution a_k(t) is found to obey a much unusual scaling law with an exponentiallygrowing scaling function Φ(x) = exp(x).