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
Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The princi...Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λn(L, t) = Lγ/νf n(t L^(1/ν)), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ1, λ2 and λ6, we get the finite-size scaling form of the second moment correlation length ξ(L, t) = Lξ(tL^(1/ν)).It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.展开更多
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.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11121403 and 11504384
文摘Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λn(L, t) = Lγ/νf n(t L^(1/ν)), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ1, λ2 and λ6, we get the finite-size scaling form of the second moment correlation length ξ(L, t) = Lξ(tL^(1/ν)).It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.
