Kinetics of a migration-driven aggregation-fragmentation process

We propose a reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels K(k; j) = K'(k; j) = lambdakj(upsilon) and the constant aggregation rates I-1, I-2 and fragmentation rates J(1), J(2). Based on the mean-field theory, we investigate the evolution behavior of the aggregate size distributions in several cases with different values of index v. We End that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When J(1) = 0 and J(2) = 0, the aggregate size distributions a(k)(t) and b(k)(t) obey the conventional scaling law, while when J(1) > 0 and J(2) > 0, they obey the modified scaling law with an exponential scaling function. The total mass of either species remains conserved.