Dynamics of aggregation－annihilation process with cluster removals

We have studied the kinetic behaviours of irreversible aggregation－annihilation models with cluster removals. In the models, an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible annihilation reaction occurs simultaneously between two different species; meanwhile, the clusters of large size are gradually removed from the system. In a mean-field limit, we obtain the general solutions of the cluster-mass distributions for the cases with an arbitrary removal probability. We found that the cluster-mass distribution of either species satisfies a generalized or modified scaling form. The results also indicate that the evolution behaviours of the systems depend strongly on the details of the reaction events.     

Competition Between Self-birth and Catalyzed Death in Aggregation Growth with Catalysis Injection

We propose two irreversible aggregation growth models of aggregates of two distinct species （.4 and B） to study the interactions between virus aggregates and medicine efficacy aggregates in the virus-medicine cooperative evolution system. The A-species aggregates evolve driven by self monomer birth and B-species aggregate-catalyzed monomer death in model I and by self birth, catalyzed death, and self monomer exchange reactions in model II, while the catalyst B-species aggregates are assumed to be injected into the system sustainedly or at a periodic time-dependent rate. The kinetic behaviors of the A-species aggregates are investigated by the rate equation approach based on the mean-field theory with the self birth rate kernel IA（k） = Ik, catalyzed death rate kernel JAB（k） = Jk and self exchange rate kernel KA （k, l） = Kkl. The kinetic behaviors of the A-species aggregates are mainly dominated by the competition between the two effects of the self birth （with the effective rate I） and the catalyzed death （with the effective rate JB0）, while the effects of the self exchanges of the A-species aggregates which appear in an effective rate KAo play important roles in the cases of I 〉 JBo and I = JBo. The evolution behaviors of the total mass M1^A（t） and the total aggregate number MA（t） are obtained, and the aggregate size distribution ak（t） of species A is found to approach a generalized scaling form in the case of I ≥ JBo and a special modified scaling form in the case of I 〈 JB0. The periodical evolution of the B-monomers concentration plays an exponential form of the periodic modulation.     

Kinetics of Catalysis-Driven Aggregation Processes with Sequential Input of Catalyst

We investigate the kinetic behavior of a two-species catalysis-driven aggregation model, in which coagulation of species A occurs only with the help of species B. We suppose the monomers of species B are stable and cannot selfcoagulate in reaction processes. Meanwhile, the monomers are continuously injected into the system. The model with a constant rate kernel is investigated by means of the mean-field rate equation. We show that the Mneties of the system depends crucially on the details of the input term. The injection rate of species B is assumed to take the given time- dependent form K（t） -t^λ, and the sealing solution of the duster size distribution is then investigated analytically. It is found that the cluster size distribution can satisfy the conventional or modified scaling form in most cases.     

Solvable Catalyzed Birth-Death-Exchange Competition Model of Three Speciese

A competition model of three species in exchange-driven aggregation growth is proposed. In the model, three distinct aggregates grow by exchange of monomers and in parallel, birth of species A is catalyzed by species B and death of species A is catalyzed by species C. The rates for both catalysis processes are proportional to kj^v and ky respectively, where ν（ω） is a parameter reflecting the dependence of the catalysis reaction rate of birth （death） on the catalyst aggregate＇s size. The kinetic evolution behaviors of the three species are investigated by the rate equation approach based on the mean-field theory： The form of the aggregate size distribution of A-species αk（t） is found to be dependent crucially on the two catalysis rate kernel parameters. The results show that （i） in case of ν ≤O, the form of ak （t） mainly depends on the competition between self-exchange of species A and species-C-catalyzed death of species A; （ii） in case of ν 〉 0, the form of αk（t） mainly depends on the competition between species-B-catalyzed birth of species A and species-C-catalyzed death of species A.     

Aggregation Behaviors of a Two-Species System with Lose-Lose Interactions

We propose an aggregation evolution model of two-species （A- and B-species） aggregates to study the prevalent aggregation phenomena in social and economic systems. In this model, A- and B-species aggregates perform self-exchange-driven growths with the exchange rate kernels K（k, l） = Kkl and L（k, l） = Lkl, respectively, and the two species aggregates perform self-birth processes with the rate kernels J1（k） = J1 k and J2（ k ） = J2k, and meanwhile the interaction between the aggregates of different species A and B causes a lose-lose scheme with the rate kernel H（k,l） = Hkl. Based on the mean-field theory, we investigated the evolution behaviors of the two species aggregates to study the competitions among above three aggregate evolution schemes on the distinct initial monomer concentrations A0 and B0 of the two species. The results show that the evolution behaviors of A- and B-species are crucially dominated by the competition between the two self-birth processes, and the initial monomer concentrations Ao and Bo play important roles, while the lose-lose scheme play important roles in some special cases.     

Kinetics of an n-Species Aggregation Chain Model with Complete Annihilation

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 rnean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the clustermass 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.     

Solvable Aggregation-Migration-Annihilation Processes of a Multispecies System

An aggregation-migration-annihilation model is proposed for a two-species-group system. In the system, aggregation reactions occur between any two aggregates of the same species and migration reactions between two different species in the same group and joint annihilation reactions between two species from different groups. The kinetics of the system is then investigated in the framework of the mean-field theory. It is found that the scaling solutions of the aggregate size distributions depend crucially on the ratios of the equivalent aggregation rates of species groups to the annihilation rates. Each species always scales according to a conventional or modified scaling form; moreover, the governing scaling exponents are nonuniversal and dependent on the reaction details for most cases.     

Solvable Aggregation-Migration-Annihilation Processes of a Multispecies System

An aggregation-migration-annihilation model is proposed for a two-species-group system. In the system,aggregation reactions occur between any two aggregates of the same species and migration reactions between two different species in the same group and joint annihilation reactions between two species from different groups. The kinetics of the system is then investigated in the framework of the mean-field theory. It is found that the scaling solutions of the aggregate size distributions depend crucially on the ratios of the equivalent aggregation rates of species groups to the annihilation rates. Each species always scales according to a conventional or modified scaling form; moreover, the governing scaling exponents are nonuniversal and dependent on the reaction details for most cases.     

Competition between aggregation and migration processes of a multi-species system

We propose a solvable multi-species aggregation--migration model, in which irreversible aggregations occur between any two aggregates of the same species and reversible migrations occur between any two different species. The kinetic behaviour of an aggregation--migration system is then studied by means of the mean-field rate equation. The results show that the kinetics of the system depends crucially on the details of reaction events such as initial concentration distributions and ratios of aggregation rates to migration rate. In general, the aggregate mass distribution of each species always obeys a conventional or a generalized scaling law, and for most cases at least one species is scaled according to a conventional form with universal constants. Moreover, there is at least one species that can survive finally.