Kinetics of a migration-driven aggregation process with birth and death.
We propose an irreversible aggregation model driven by migration and birth-death processes with the symmetric migration rate kernel K(k;j)=K'(k;j)=Ikj(upsilon), and the birth rate J(1)k and death rate J(2)k proportional to the aggregate's size k. Based on the mean-field theory, we investigate the evolution behavior of the system through developing the scaling theory. The total mass M1 is reserved in the J(1)=J(2) case and increases exponentially with time in the J1>J2 case. In these cases, the long-time asymptotic behavior of the aggregate size distribution a(k)(t) always obeys the scaling law for the upsilon<or=2 case. This model may provide a more natural description for diverse aggregation processes such as the evolution of the distribution of city population and individual wealth.
Lin
Zhenquan
Z
Department of Physics, Wenzhou Normal College, Wenzhou 325027, China. linzhenquan@yahoo.com.cn
Ke
Jianhong
J