We propose an evolution model of cooperative agent and noncooperative agent aggregates to investigate the dynamic evolution behaviors of the system and the effects of the competing microscopic reactions on the dynamic...We propose an evolution model of cooperative agent and noncooperative agent aggregates to investigate the dynamic evolution behaviors of the system and the effects of the competing microscopic reactions on the dynamic evolution. In this model, each cooperative agent and noncooperative agent are endowed with integer values of cooperative spirits and nonco- operative spirits, respectively. The cooperative spirits of a cooperative agent aggregate and the noncooperative spirits of a noncooperative agent aggregate change via four competing microscopic reaction schemes： the win-win reaction between two cooperative agents, the lose-lose reaction between two noncooperative agents, the win-lose reaction between a coop- erative agent and a noncooperative agent （equivalent to the migration of spirits from cooperative agents to noncooperative agents）, and the cooperative agent catalyzed decline of noncooperative spirits. Based on the generalized Smoluchowski＇s rate equation approach, we investigate the dynamic evolution behaviors such as the total cooperative spirits of all coop- erative agents and the total noncooperative spirits of all noncooperative agents. The effects of the three main groups of competition on the dynamic evolution are revealed. These include： （i） the competition between the lose-lose reaction and the win-lose reaction, which gives rise to respectively the decrease and increase in the noncooperative agent spirits; （ii） the competition between the win-win reaction and the win-lose reaction, which gives rise to respectively the increase and decrease in the cooperative agent spirits; （iii） the competition between the win-lose reaction and the catalyzed-decline reaction, which gives rise to respectively the increase and decrease in the noncooperative agent spirits.展开更多
We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation ...We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K（i,j;l） l^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters v and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.展开更多
We propose a catalytically activated duplication model to mimic the coagulation and duplication of the DNA polymer system under the catalysis of the primer RNA. In the model, two aggregates of the same species can coa...We propose a catalytically activated duplication model to mimic the coagulation and duplication of the DNA polymer system under the catalysis of the primer RNA. In the model, two aggregates of the same species can coagulate themselves and a DNA aggregate of any size can yield a new monomer or double itself with the help of RNA aggregates. By employing the mean-field rate equation approach we analytically investigate the evolution behaviour of the system. For the system with catalysis-driven monomer duplications, the aggregate size distribution of DNA polymers αk（t） always follows a power law in size in the long-time limit, and it decreases with time or approaches a time-independent steady-state form in the case of the duplication rate independent of the size of the mother aggregates, while it increases with time increasing in the case of the duplication rate proportional to the size of the mother aggregates. For the system with complete catalysis-driven duplications, the aggregate size distribution αk（t） approaches a generalized or modified scaling form.展开更多
We propose a catalysis-select migration driven evolution model of two-species（A-and B-species） aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts ...We propose a catalysis-select migration driven evolution model of two-species（A-and B-species） aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts of species D the reaction will become one unit of species B migrating to species A.Meanwhile the catalyst aggregates of species C perform self-coagulation,as do the species D aggregates.We study this catalysis-select migration driven kinetic aggregation phenomena using the generalized Smoluchowski rate equation approach with C species catalysis-select migration rate kernel K（k;i,j） = Kkij and D species catalysis-select migration rate kernel J（k;i,j） = Jkij.The kinetic evolution behaviour is found to be dominated by the competition between the catalysis-select immigration and emigration,in which the competition is between JD0 and KC0（D0 and C0 are the initial numbers of the monomers of species D and C,respectively）.When JD0 KC0 〉 0,the aggregate size distribution of species A satisfies the conventional scaling form and that of species B satisfies a modified scaling form.And in the case of JD0 KC0 〈 0,species A and B exchange their aggregate size distributions as in the above JD0 KC0 〉 0 case.展开更多
We propose an irreversible binary coagulation model with a constant-reaction-number kernel, in which, among all the possible binary coagulation reactions, only p reactions are permitted to take place at every time. By...We propose an irreversible binary coagulation model with a constant-reaction-number kernel, in which, among all the possible binary coagulation reactions, only p reactions are permitted to take place at every time. By means of the generalized rate equation we investigate the kinetic behaviour of the system with the reaction rate kernel K（i;j） = （ij）^w （0 ≤w〈1/2）, at which an i-mer and a j-mer coagulate together to form a large one. It is found that for such a system there always exists a gelation transition at a finte time to, which is in contrast to the ordinary binary coagulation with the same rate kernel. Moreover, the pre-gelation behaviour of the cluster size distribution near the gelation point falls in a scaling regime and the typical cluster size grows as （to - t）-1/（1-2w）. On the other hand, our model can also provide some predictions for the evolution of the cluster distribution in multicomponent complex networks.展开更多
We propose two solvable cluster growth models, in which an irreversible aggregation spontaneously occurs between any two clusters of the same species; meanwhile, monomer birth or death of species A occurs with the hel...We propose two solvable cluster growth models, in which an irreversible aggregation spontaneously occurs between any two clusters of the same species; meanwhile, monomer birth or death of species A occurs with the help of species B. The system with the size-dependent monomer birth/death rate kernel K（i, j） = Jijv is then investigated by means of the mean-field rate equation. The results show that the kinetic scaling behaviour of species A depends crucially on the value of the index v. For the model with catalysis-driven monomer birth, the cluster-mass distribution of species A obeys the conventional scaling law in the v ≤ 0 case, while it satisfies a generalized scaling form in the v ≥ 0 case; moreover, the total mass of species A is a nonzero value in the v 〈 0 case while it grows continuously with time in the v ≥ 0 case. For the model with catalysis-driven monomer death, the cluster-mass distribution also approaches the conventional scaling form in the v 〈 0 case, while the conventional scaling description of the system breaks down in the v ≥ 0 case. Additionally, the total mass of species A retains a nonzero quantity in the v 〈 0 case, but it decreases to zero with time in the v ≥ 0 case.展开更多
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 specie...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.展开更多
We propose a catalytically activated replication-decline model of three species, in which two aggregates of the same species can coagulate themselves, an A aggregate of any size can replicate itself with the help of B...We propose a catalytically activated replication-decline model of three species, in which two aggregates of the same species can coagulate themselves, an A aggregate of any size can replicate itself with the help of B aggregates, and the decline of A aggregate occurs under the catalysis of C aggregates. By means of mean-field rate equations, we derive the asymptotic solutions of the aggregate size distribution ak（t） of species A, which is found to depend strongly on the competition among three mechanisms： the self-coagulation of species A, the replication of species A catalyzed by species B, and the decline of species A catalyzed by species C. When the self-coagulation of species A dominates the system, the aggregate size distribution a^（t） satisfies the conventional scaling form. When the catalyzed replication process dominates the system, ak（t） takes the generalized scaling form. When the catalyzed decline process dominates the system, ak（t） approaches the modified scaling form.展开更多
This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution b...This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I（k） = Ik and a fragmentation rate kernel L（i,j） = L, we find that the total number MoA（t） and the total mass of the pest aggregates MA （t） both increase exponentially with time if L ≠ 0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J1 （k） ---- J1 k, it is found that only when I 〈 J1 B0 （B0 is the concentration of catalyst aggregates） can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.展开更多
We propose a catalytically activated aggregation-fragmentation model of three species, in which two clusters of species A can coagulate into a larger one under the catalysis of B clusters; otherwise, one cluster of sp...We propose a catalytically activated aggregation-fragmentation model of three species, in which two clusters of species A can coagulate into a larger one under the catalysis of B clusters; otherwise, one cluster of species A will fragment into two smaller clusters under the catalysis of C clusters. By means of mean-field rate equations, we derive the asymptotic solutions of the cluster-mass distributions ak（t） of species A, which is found to depend strongly on the competition between the catalyzed aggregation process and the catalyzed fragmentation process. When the catalyzed aggregation process dominates the system, the cluster-mass distribution ak（t） satisfies the conventional scaling form. When the catalyzed fragmentation process dominates the system, the scaling description of ak （t） breaks down completely and the monodisperse initial condition of species A would not be changed in the long-time limit. In the marginal case when the effects of catalyzed aggregation and catalyzed fragmentation counteract each other, ak（t） takes the modified scaling form and the system can eventually evolve to a steady state.展开更多
An aggregation growth model of three species A, B and C with the competition between catalyzed birth and catalyzed death is proposed. Irreversible aggregation occurs between any two aggregates of the like species with...An aggregation growth model of three species A, B and C with the competition between catalyzed birth and catalyzed death is proposed. Irreversible aggregation occurs between any two aggregates of the like species with theconstant rate kernels In（n = 1,2, 3）. Meanwhile, a monomer birth of an A species aggregate of size k occurs under the catalysis of a B species aggregate of size j with the catalyzed birth rate kernel K（k, j） = Kkj^v, and a monomer death of an A species aggregate of size k occurs under the catalysis of a C species aggregate of size j with the catalyzed death rate kernel L（k, j） = Lkj^v, whcre v is a parameter reflecting the dependence of the catalysis reaction rates of birth and death on the size of catalyst aggregate. The kinetic evolution behaviours 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 ak （t） is found to be dependent crucially on the competition between the catalyzed birth and death of A species, as well as the irreversible aggregation processes of the three species： （i） In the v 〈 0 case, the irreversible aggregation dominates the process, and ak（t） satisfies the conventional scaling form; （2） In the v ≥ 0 casc, the competition between the catalyzed birth and death dominates the process. When the catalyzed birth controls the process, ak（t） takes the conventional or generalized scaling form. While the catalyzed death controls the process, the scaling description of the aggregate size distribution breaks down completely.展开更多
We propose an adsorption-desorption model for a deposit growth system, in which the adsorption and desorption of particles coexist. By means of the generalized rate equation we investigate the cluster （island） size ...We propose an adsorption-desorption model for a deposit growth system, in which the adsorption and desorption of particles coexist. By means of the generalized rate equation we investigate the cluster （island） size distribution in the dynamic equilibrium state. The results show that the evolution behaviour of the system depends crucially on the details of the rate kernels. The cluster size distribution can take the scale-free power-law form in some cases, while it grows exponentially with size in other cases.展开更多
We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the uncondit...We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the unconditional imitation rule; moreover, each＇agent can change his type to adopt another updating rule once the number he sequentially loses the game at is beyond his upper limit of tolerance. The cooperative behaviors of such heterogeneous systems are then investigated by Monte Carlo simulations. The numerical results show the equilibrium cooperation frequency and composition as functions of the cost-to-benefit ratio r are both of plateau structures with discontinuous steplike jumps, and the number of plateaux varies non-monotonically with the upper limit of tolerance VT as well as the initial composition of agents faO. Besides, the quantities of the cooperation frequency and composition are dependent crucially on the system parameters including VT, faO, and r. One intriguing observation is that when the upper limit of tolerance is small, the cooperation frequency will be abnormally enhanced with the increase of the cost-to-benefit ratio in the range of 0 〈 r 〈 1/4. We then probe into the relative cooperation frequencies of either type of agents, which are also of plateau structures dependent on the system parameters. Our results may be helpful to understand the cooperative behaviors of heterogenous agent systems.展开更多
This paper proposes a controlled particle deposition model for cluster growth on the substrate surface and then presents exact results for the cluster （island） size distribution. In the system, at every time step a ...This paper proposes a controlled particle deposition model for cluster growth on the substrate surface and then presents exact results for the cluster （island） size distribution. In the system, at every time step a fixed number of particles are injected into the system and immediately deposited onto the substrate surface. It investigates the cluster size distribution by employing the generalized rate equation approach. The results exhibit that the evolution behaviour of the system depends crucially on the details of the adsorption rate kernel. The cluster size distribution can take the Poisson distribution or the conventional scaling form in some cases, while it is of a quite complex form in other cases.展开更多
The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the Gaussian.distribution constants b and bw is constructed by generalizing that on tra...The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the Gaussian.distribution constants b and bw is constructed by generalizing that on translationally invariant square lattice.The critical behaviours are studied by the renormalization-group approach and spin rescaling method.They are found to be quite different from that on translationally invariant square lattice.There are two critical points at(K^(*)=b,K^(*)_(w)=0)and(K^(*)=0,K^(*)_(w)=bw),and the correlation length critical exponents are calculated.展开更多
We introduce a two-species symbiosis-driven growth model, in which two species can mutually benefit for their monomer birth and the self-death of each species simultaneously occurs. By means of the generalized rate eq...We introduce a two-species symbiosis-driven growth model, in which two species can mutually benefit for their monomer birth and the self-death of each species simultaneously occurs. By means of the generalized rate equation, we investigate the dynamic evolution of the system under the monodisperse initial condition. It is found that the kinetic behaviour of the system depends crucially on the details of the rate kernels as well as the initial concentration distributions. The cluster size distribution of either species cannot be scaled in most cases; while in some special cases, they both consistently take the universal scaling form. Moreover, in some cases the system may undergo a gelation transition and the pre-gelation behaviour of the cluster size distributions satisfies the scaling form in the vicinity of the gelation point. On the other hand, the two species always live and die together.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 11175131)
文摘We propose an evolution model of cooperative agent and noncooperative agent aggregates to investigate the dynamic evolution behaviors of the system and the effects of the competing microscopic reactions on the dynamic evolution. In this model, each cooperative agent and noncooperative agent are endowed with integer values of cooperative spirits and nonco- operative spirits, respectively. The cooperative spirits of a cooperative agent aggregate and the noncooperative spirits of a noncooperative agent aggregate change via four competing microscopic reaction schemes： the win-win reaction between two cooperative agents, the lose-lose reaction between two noncooperative agents, the win-lose reaction between a coop- erative agent and a noncooperative agent （equivalent to the migration of spirits from cooperative agents to noncooperative agents）, and the cooperative agent catalyzed decline of noncooperative spirits. Based on the generalized Smoluchowski＇s rate equation approach, we investigate the dynamic evolution behaviors such as the total cooperative spirits of all coop- erative agents and the total noncooperative spirits of all noncooperative agents. The effects of the three main groups of competition on the dynamic evolution are revealed. These include： （i） the competition between the lose-lose reaction and the win-lose reaction, which gives rise to respectively the decrease and increase in the noncooperative agent spirits; （ii） the competition between the win-win reaction and the win-lose reaction, which gives rise to respectively the increase and decrease in the cooperative agent spirits; （iii） the competition between the win-lose reaction and the catalyzed-decline reaction, which gives rise to respectively the increase and decrease in the noncooperative agent spirits.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104)
文摘We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation, while the catalyst aggregates of the same species B or C perform self-coagulation processes. By means of the generalized Smoluchowski rate equation based on the mean-field assumption, we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K（i,j;l） l^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate. The relation between the values of parameters v and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A. It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.
基金supported by the National Natural Science Foundation of China (Grant Nos 10275048,10305009 and 10875086)by the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067)
文摘We propose a catalytically activated duplication model to mimic the coagulation and duplication of the DNA polymer system under the catalysis of the primer RNA. In the model, two aggregates of the same species can coagulate themselves and a DNA aggregate of any size can yield a new monomer or double itself with the help of RNA aggregates. By employing the mean-field rate equation approach we analytically investigate the evolution behaviour of the system. For the system with catalysis-driven monomer duplications, the aggregate size distribution of DNA polymers αk（t） always follows a power law in size in the long-time limit, and it decreases with time or approaches a time-independent steady-state form in the case of the duplication rate independent of the size of the mother aggregates, while it increases with time increasing in the case of the duplication rate proportional to the size of the mother aggregates. For the system with complete catalysis-driven duplications, the aggregate size distribution αk（t） approaches a generalized or modified scaling form.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104)
文摘We propose a catalysis-select migration driven evolution model of two-species（A-and B-species） aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts of species D the reaction will become one unit of species B migrating to species A.Meanwhile the catalyst aggregates of species C perform self-coagulation,as do the species D aggregates.We study this catalysis-select migration driven kinetic aggregation phenomena using the generalized Smoluchowski rate equation approach with C species catalysis-select migration rate kernel K（k;i,j） = Kkij and D species catalysis-select migration rate kernel J（k;i,j） = Jkij.The kinetic evolution behaviour is found to be dominated by the competition between the catalysis-select immigration and emigration,in which the competition is between JD0 and KC0（D0 and C0 are the initial numbers of the monomers of species D and C,respectively）.When JD0 KC0 〉 0,the aggregate size distribution of species A satisfies the conventional scaling form and that of species B satisfies a modified scaling form.And in the case of JD0 KC0 〈 0,species A and B exchange their aggregate size distributions as in the above JD0 KC0 〉 0 case.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10305009 and 10275048, and the Zhejiang Provincial Natural Science Foundation of China under Grant No 102067.
文摘We propose an irreversible binary coagulation model with a constant-reaction-number kernel, in which, among all the possible binary coagulation reactions, only p reactions are permitted to take place at every time. By means of the generalized rate equation we investigate the kinetic behaviour of the system with the reaction rate kernel K（i;j） = （ij）^w （0 ≤w〈1/2）, at which an i-mer and a j-mer coagulate together to form a large one. It is found that for such a system there always exists a gelation transition at a finte time to, which is in contrast to the ordinary binary coagulation with the same rate kernel. Moreover, the pre-gelation behaviour of the cluster size distribution near the gelation point falls in a scaling regime and the typical cluster size grows as （to - t）-1/（1-2w）. On the other hand, our model can also provide some predictions for the evolution of the cluster distribution in multicomponent complex networks.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10305009 and 10275048） and the Zhejiang Provincial Natural Science Foundation, China （Grant No 102067）.
文摘We propose two solvable cluster growth models, in which an irreversible aggregation spontaneously occurs between any two clusters of the same species; meanwhile, monomer birth or death of species A occurs with the help of species B. The system with the size-dependent monomer birth/death rate kernel K（i, j） = Jijv is then investigated by means of the mean-field rate equation. The results show that the kinetic scaling behaviour of species A depends crucially on the value of the index v. For the model with catalysis-driven monomer birth, the cluster-mass distribution of species A obeys the conventional scaling law in the v ≤ 0 case, while it satisfies a generalized scaling form in the v ≥ 0 case; moreover, the total mass of species A is a nonzero value in the v 〈 0 case while it grows continuously with time in the v ≥ 0 case. For the model with catalysis-driven monomer death, the cluster-mass distribution also approaches the conventional scaling form in the v 〈 0 case, while the conventional scaling description of the system breaks down in the v ≥ 0 case. Additionally, the total mass of species A retains a nonzero quantity in the v 〈 0 case, but it decreases to zero with time in the v ≥ 0 case.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10305009 and 10275048） and the Zhejiang Provincial Natural Science Foundation of China （Grant No 102067）.
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 11145004)
文摘We propose a catalytically activated replication-decline model of three species, in which two aggregates of the same species can coagulate themselves, an A aggregate of any size can replicate itself with the help of B aggregates, and the decline of A aggregate occurs under the catalysis of C aggregates. By means of mean-field rate equations, we derive the asymptotic solutions of the aggregate size distribution ak（t） of species A, which is found to depend strongly on the competition among three mechanisms： the self-coagulation of species A, the replication of species A catalyzed by species B, and the decline of species A catalyzed by species C. When the self-coagulation of species A dominates the system, the aggregate size distribution a^（t） satisfies the conventional scaling form. When the catalyzed replication process dominates the system, ak（t） takes the generalized scaling form. When the catalyzed decline process dominates the system, ak（t） approaches the modified scaling form.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104)
文摘This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I（k） = Ik and a fragmentation rate kernel L（i,j） = L, we find that the total number MoA（t） and the total mass of the pest aggregates MA （t） both increase exponentially with time if L ≠ 0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J1 （k） ---- J1 k, it is found that only when I 〈 J1 B0 （B0 is the concentration of catalyst aggregates） can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10275048 and 10875086)by the Science Foundation of Shihezi University (Grant No.RCZX200745)
文摘We propose a catalytically activated aggregation-fragmentation model of three species, in which two clusters of species A can coagulate into a larger one under the catalysis of B clusters; otherwise, one cluster of species A will fragment into two smaller clusters under the catalysis of C clusters. By means of mean-field rate equations, we derive the asymptotic solutions of the cluster-mass distributions ak（t） of species A, which is found to depend strongly on the competition between the catalyzed aggregation process and the catalyzed fragmentation process. When the catalyzed aggregation process dominates the system, the cluster-mass distribution ak（t） satisfies the conventional scaling form. When the catalyzed fragmentation process dominates the system, the scaling description of ak （t） breaks down completely and the monodisperse initial condition of species A would not be changed in the long-time limit. In the marginal case when the effects of catalyzed aggregation and catalyzed fragmentation counteract each other, ak（t） takes the modified scaling form and the system can eventually evolve to a steady state.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10275048 and 10305009)the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067)
文摘An aggregation growth model of three species A, B and C with the competition between catalyzed birth and catalyzed death is proposed. Irreversible aggregation occurs between any two aggregates of the like species with theconstant rate kernels In（n = 1,2, 3）. Meanwhile, a monomer birth of an A species aggregate of size k occurs under the catalysis of a B species aggregate of size j with the catalyzed birth rate kernel K（k, j） = Kkj^v, and a monomer death of an A species aggregate of size k occurs under the catalysis of a C species aggregate of size j with the catalyzed death rate kernel L（k, j） = Lkj^v, whcre v is a parameter reflecting the dependence of the catalysis reaction rates of birth and death on the size of catalyst aggregate. The kinetic evolution behaviours 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 ak （t） is found to be dependent crucially on the competition between the catalyzed birth and death of A species, as well as the irreversible aggregation processes of the three species： （i） In the v 〈 0 case, the irreversible aggregation dominates the process, and ak（t） satisfies the conventional scaling form; （2） In the v ≥ 0 casc, the competition between the catalyzed birth and death dominates the process. When the catalyzed birth controls the process, ak（t） takes the conventional or generalized scaling form. While the catalyzed death controls the process, the scaling description of the aggregate size distribution breaks down completely.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10775104 and 10305009.
文摘We propose an adsorption-desorption model for a deposit growth system, in which the adsorption and desorption of particles coexist. By means of the generalized rate equation we investigate the cluster （island） size distribution in the dynamic equilibrium state. The results show that the evolution behaviour of the system depends crucially on the details of the rate kernels. The cluster size distribution can take the scale-free power-law form in some cases, while it grows exponentially with size in other cases.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175131 and 10875086)
文摘We propose an evolutionary snowdrift game model for heterogeneous systems with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the unconditional imitation rule; moreover, each＇agent can change his type to adopt another updating rule once the number he sequentially loses the game at is beyond his upper limit of tolerance. The cooperative behaviors of such heterogeneous systems are then investigated by Monte Carlo simulations. The numerical results show the equilibrium cooperation frequency and composition as functions of the cost-to-benefit ratio r are both of plateau structures with discontinuous steplike jumps, and the number of plateaux varies non-monotonically with the upper limit of tolerance VT as well as the initial composition of agents faO. Besides, the quantities of the cooperation frequency and composition are dependent crucially on the system parameters including VT, faO, and r. One intriguing observation is that when the upper limit of tolerance is small, the cooperation frequency will be abnormally enhanced with the increase of the cost-to-benefit ratio in the range of 0 〈 r 〈 1/4. We then probe into the relative cooperation frequencies of either type of agents, which are also of plateau structures dependent on the system parameters. Our results may be helpful to understand the cooperative behaviors of heterogenous agent systems.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10775104, 10875086 and 10305009)
文摘This paper proposes a controlled particle deposition model for cluster growth on the substrate surface and then presents exact results for the cluster （island） size distribution. In the system, at every time step a fixed number of particles are injected into the system and immediately deposited onto the substrate surface. It investigates the cluster size distribution by employing the generalized rate equation approach. The results exhibit that the evolution behaviour of the system depends crucially on the details of the adsorption rate kernel. The cluster size distribution can take the Poisson distribution or the conventional scaling form in some cases, while it is of a quite complex form in other cases.
基金Supported by the Foundation of“151 Talent Engineering”of Zhejiang Province,and the Foundation of“551 Talent Engineering”of Wenzhou City of China.
文摘The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the Gaussian.distribution constants b and bw is constructed by generalizing that on translationally invariant square lattice.The critical behaviours are studied by the renormalization-group approach and spin rescaling method.They are found to be quite different from that on translationally invariant square lattice.There are two critical points at(K^(*)=b,K^(*)_(w)=0)and(K^(*)=0,K^(*)_(w)=bw),and the correlation length critical exponents are calculated.
基金Supported by the National Natural Science Foundation of China under Grant No 10305009, and the Zhejiang Provincial Natural Science Foundation of China under Grant No 102067.
文摘We introduce a two-species symbiosis-driven growth model, in which two species can mutually benefit for their monomer birth and the self-death of each species simultaneously occurs. By means of the generalized rate equation, we investigate the dynamic evolution of the system under the monodisperse initial condition. It is found that the kinetic behaviour of the system depends crucially on the details of the rate kernels as well as the initial concentration distributions. The cluster size distribution of either species cannot be scaled in most cases; while in some special cases, they both consistently take the universal scaling form. Moreover, in some cases the system may undergo a gelation transition and the pre-gelation behaviour of the cluster size distributions satisfies the scaling form in the vicinity of the gelation point. On the other hand, the two species always live and die together.
