We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two...We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the seff-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.展开更多
The kinetic behavior of an n-species (n?≥?3) aggregation–annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an ...The kinetic behavior of an n-species (n?≥?3) aggregation–annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible complete annihilation reaction occurs only between two species with adjacent number. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the cluster-mass distributions for the system. The results show that the kinetic behavior of the system not only depends crucially on the ratio of the aggregation rate I to the annihilation rate J, but also has relation with the initial concentration of each species and the species number's odevity. We find that the cluster-mass distribution of each species obeys always a scaling law. The scaling exponents may strongly depend on the reaction rates for most cases, however, for the case in which the ratio of the aggregation rate to the annihilation rate is equal to a certain value, the scaling exponents are only dependent on the initial concentrations of the reactants.展开更多
The kinetic behavior of an aggregation-annihilation system with two species groups is studied in this paper.We propose that an aggregation reaction occurs only between the same species and an irreversible joint annihi...The kinetic behavior of an aggregation-annihilation system with two species groups is studied in this paper.We propose that an aggregation reaction occurs only between the same species and an irreversible joint annihilation reaction occurs only between the two species belonging to distinct groups. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distributions for the symmetrical cases. We find that the cluster-mass distribution of each species obeys a standard scaling description in certain cases. Meanwhile, breakdown of the standard scaling description is also found for the distribution in some special cases and the cluster-mass distribution comes in a peculiar scaling regime. The evolutionbehaviour of the system depends crucially on the reaction rates and the ratio of initial concentrations between the two groups. Moreover, the species numbers of the two groups also play important roles in the properties of the cluster distributions.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10305009 and the Natural Science Foundation of Zhejiang Province of China under Grant No. 102067
文摘We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the seff-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.
文摘The kinetic behavior of an n-species (n?≥?3) aggregation–annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible complete annihilation reaction occurs only between two species with adjacent number. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the cluster-mass distributions for the system. The results show that the kinetic behavior of the system not only depends crucially on the ratio of the aggregation rate I to the annihilation rate J, but also has relation with the initial concentration of each species and the species number's odevity. We find that the cluster-mass distribution of each species obeys always a scaling law. The scaling exponents may strongly depend on the reaction rates for most cases, however, for the case in which the ratio of the aggregation rate to the annihilation rate is equal to a certain value, the scaling exponents are only dependent on the initial concentrations of the reactants.
文摘The kinetic behavior of an aggregation-annihilation system with two species groups is studied in this paper.We propose that an aggregation reaction occurs only between the same species and an irreversible joint annihilation reaction occurs only between the two species belonging to distinct groups. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distributions for the symmetrical cases. We find that the cluster-mass distribution of each species obeys a standard scaling description in certain cases. Meanwhile, breakdown of the standard scaling description is also found for the distribution in some special cases and the cluster-mass distribution comes in a peculiar scaling regime. The evolutionbehaviour of the system depends crucially on the reaction rates and the ratio of initial concentrations between the two groups. Moreover, the species numbers of the two groups also play important roles in the properties of the cluster distributions.
