We propose a reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels K (k; j) = K′(k; j) =λkj^v and the constant aggregation rates I1, I2 and fragmentati...We propose a reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels K (k; j) = K′(k; j) =λkj^v and the constant aggregation rates I1, I2 and fragmentation rates Jl, J2. 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 find that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When Jl = 0 and J2 = O, the aggregate size distributions αk(t) and bk(t) obey the conventional scaling law, while when Jl > 0 and J2 > O, they obey the modified scaling law with an exponential scaling function. The total mass of either species remains conserved.展开更多
We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously betw...We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates and , we find that the evolution behavior of the system depends crucially on the values of the indexes υ<SUB>1</SUB> and υ<SUB>2</SUB>. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.展开更多
文摘We propose a reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels K (k; j) = K′(k; j) =λkj^v and the constant aggregation rates I1, I2 and fragmentation rates Jl, J2. 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 find that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When Jl = 0 and J2 = O, the aggregate size distributions αk(t) and bk(t) obey the conventional scaling law, while when Jl > 0 and J2 > O, they obey the modified scaling law with an exponential scaling function. The total mass of either species remains conserved.
文摘We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates and , we find that the evolution behavior of the system depends crucially on the values of the indexes υ<SUB>1</SUB> and υ<SUB>2</SUB>. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.
