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Kinetic Behaviors of a Competitive Population and Fitness System in Exchange-Driven Growth

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Communications in Theoretical Physics 2008年第7期50卷 105-110页

作者： LU Ke lin zhen-quan SUN Yun-Fei Department of Physics Wenzhou University Wenzhou 325027 China

We proposed an aggregation model of two species aggregates of fitness and population to study the interaction between the two species in their exchange-driven processes of the same species by introducing the monomer birth of fitness catalyzed by the population, where the fitness aggregates perform self-death process and the population aggregates perform self-birth process. The kinetic behaviors of the aggregate size distributions of the fitness and population were analyzed by the rate equation approach with their exchange rate kernel K1（k,j） = K1kj and K2（k,j） = K2kj, the fitness aggregate＇s self-death rate kernel J1 （ k ） = J1 k, population aggregate＇s self-birth rate kernel J2（ k ） = J2k and population-catalyzed fitness birth rate kernel I（k,j） = Ikj＇. The kinetic behavior of the fitness was found depending crucially on the parameter v, which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst （population） aggregate. （i） In the v ≤ 0 case, the effect of catalyzed-birth of fitness is rather weak and the exchange-driven aggregation and self-death of the fitness dominate the process, and the fitness aggregate size distribution αk（t） does not have scale form. （ii） When v ≥0, the effect of the population-catalyzed birth of fitness gets strong enough, and the catalyzed-birth and self-death of the fitness aggregates, together with the self-birth of the population aggregates dominate the evolution process of the fitness aggregates. The aggregate size distribution αk （t） approaches a generalized scaling form.

关键词： kinetic behavior aggregate growths catalyzed-birth rate equations

Critical Behaviour of the Gaussian Model on Sierpinski Carpets

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Chinese Physics Letters 2001年第7期18卷 882-884页

作者： lin zhen-quan KONG Xiang-Mu Department of Physics Wenzhou Normal CollegeWenzhou 325027 Department of Physics Qufu Normal UniversityQufu 273165

The Gaussian model on Sierpinski carpets with two types of nearest neighbour interactions K and Kw and two corresponding types of the *** constants b and bw is constructed by generalizing that on translationally invariant square *** critical behaviours are studied by the renormalization-group approach and spin rescaling *** are found to be quite different from that on translationally invariant square *** are two critical points at(K^(*)=b,K^(*)_(w)=0)and(K^(*)=0,K^(*)_(w)=bw),and the correlation length critical exponents are calculated.

关键词： method critical invariant

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

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Communications in Theoretical Physics 2008年第1期49卷 235-238页

作者： CHEN Yu KE Jian-Hong lin zhen-quan School of Physics and Electronic Information Wenzhou University Wenzhou 325027 China

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.

关键词： kinetic behavior catalysis aggregation scaling law

Novel Biased Aggregation-Annihilation Model

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Communications in Theoretical Physics 2007年第2期47卷 355-360页

作者： KE Jian-Hong lin zhen-quan CHEN Xiao-Shuang School of Physics and Electronic Information Wenzhou University Wenzhou 325027 China State Laboratory of Infrared Physics Shanghai Institute of Technical Physics the Chinese Academy of Sciences Shanghai 200083 China

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.

关键词： kinetic behavior aggregation-annihilation scaling law rate equation

Kinetic Behavior of Exchange-Driven Growth with Catalyzed-Birth Processes

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Communications in Theoretical Physics 2006年第6X期46卷 1113-1120页

作者： WANG Hai-Feng lin zhen-quan KONG Xiang-Mu Department of Physics Wenzhou University Wenzhou 325027 China Department of Physics Qufu Normal University Qufu 273165 China

Two catalyzed-birth models of n-species （n ≥ 2） aggregates with exchange-driven growth processes are proposed and compared. In the first one, the exchange reaction occurs between any two aggregates Ak^m and Af^m of the same species with the rate kernels Km（k,j）= Kmkj （m = 1, 2,... ,n, n ≥ 2）, and aggregates of A^n species catalyze a monomer-birth of A^l species （l = 1, 2 , n - 1） with the catalysis rate kernel Jl（k,j） -Jlkj^v. The kinetic behaviors are investigated by means of the mean-field theory. We find that the evolution behavior of aggregate-size distribution ak^l（t） of A^l species depends crucially on the value of the catalysis rate parameter v：（i） ak^l（t） obeys the conventional scaling law in the case of v ≤ 0, （ii） ak^l（t） satisfies a modified scaling form in the case of v 〉 0. In the second model, the mechanism of monomer-birth of An-species catalyzed by A^l species is added on the basis of the first model, that is, the aggregates of A^l and A^n species catalyze each other to cause monomer-birth. The kinetic behaviors of A^l and A^n species are found to fall into two categories for the different v：（i） growth obeying conventional scaling form with v ≤ 0, （ii） gelling at finite time with v 〉 0.

关键词： behavior exchange-driven growth catalyzed-birth scaling law rate equations

Solvable Aggregation-Migration-Annihilation Processes of a Multispecies System

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Communications in Theoretical Physics 2006年第1X期46卷 161-166页

作者： KE Jian-Hong lin zhen-quan CHEN Xiao-Shuang School of Physics and Electronic Information Wenzhou University Wenzhou 325027 China National Laboratory of Infrared Physics Shanghai Institute of Technical Physics the Chinese Academy of Sciences Shanghai 200083 China

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.

关键词： aggregation migration annihilation scaling law

Analytical Results of a Two-Species Predator-Prey Model

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Communications in Theoretical Physics 2008年第3期49卷 791-796页

We propose a sequential monomer reaction model for a two-species predator-prey system, in which the aggregates of either species can spontaneously produce or lose one monomer and meanwhile, a type-B aggregate can prey upon one monomer of a type-A aggregate when they meet. Using the mean-field rate equation approach, we analytically investigate the kinetic behavior of the system. The results show that the evolution of the system depends crucially on the details of the rate kernels. The aggregate size distribution of either species approaches the conventional or modified scaling form in most cases. Moreover, the total size of either species grows exponentially with time in some cases and asymptotically retains a constant quantity in other cases, while it decays with time and vanishes finally in the rest cases.

关键词： kinetic behavior monomer reaction scaling law

Kinetic Behavior of Aggregation-Exchange Growth Process with Catalyzed-Birth

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Communications in Theoretical Physics 2007年第3期47卷 479-486页

作者： HAN An-Jia CHEN Yu lin zhen-quan KE Jian-Hong Department of Physics Wenzhou University Wenzhou 325027 China

We propose an aggregation model of a two-species system to mimic the growth of cities＇ population and assets, in which irreversible coagulation reactions and exchange reactions occur between any two aggregates of the same species, and the monomer-birth reactions of one species occur by the catalysis Of the other species. In the case with population-catalyzed birth of assets, the rate kernel of an asset aggregate Bκ of size k grows to become an aggregate Bκ＋1 through a monomer-birth catalyzed by a population aggregate Aj of size j is J（κ,j） = Jkjλ. And in mutually catalyzed birth model, the birth rate kernels of population and assets are H（k,j）=Hkjη and J（k,j） = Jkjλ, respectively. The kinetics of the system is investigated based on the mean-field theory. In the model of population-catalyzed birth of aseets, the long-time asymptotic behavior of the assets aggregate size distribution obeys the conventional or modified scaling form. In mutually catalyzed birth system, the asymptotic behaviors of population and assets obey the conventional scaling form in the case of η=λ =0, and they obey the modified scaling form in the case of η=0, λ=1. In the case of η = λ= 1, the total mass of population aggregates and that of asset aggregates both grow much faster than those in population-catalyzed birth of assets model, and they approaches to infinite values in finite time.

关键词： kinetic behvavior aggregation-exchange growth catalyzed-birth scaling law rate equations

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

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Communications in Theoretical Physics 2009年第10期52卷 735-742页

作者： WANG Hai-Feng lin zhen-quan GAO Yan ZHANG Heng Department of Physics Teacthers College Shihezi University Shihezi 832003 China Department of Physics Wenzhou University Wenzhou 325027 China

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.

关键词： aggregation exchange-driven growth catalysis kinetic behaviour