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KE Jian-Hong LIN Zhen-Quan CHEN Xiao-Shuang 《理论物理通讯》2006,46(1):161-166
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. 相似文献
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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. 相似文献
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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. 相似文献
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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 1through a monomer-birth catalyzed by a population aggregate Aj of size j is J(k,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 assets,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 ofη =λ= 0,and they obey the modified scalingform 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. 相似文献
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We propose two irreversible aggregation growth models of aggregates of two distinct species (A 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 andB-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 effectiverate KA0 play important roles in the cases of I>JB0 and I=JB0. The evolution behaviors of the total mass MA(t)1 and the total aggregate number MA(t)0 are obtained, and the aggregate size distribution ak(t) of species A is found toapproach a generalized scaling form in the case of I ≧ JB0 and a special modified scaling form in the case of I0. The periodical evolution of the B-monomers concentration plays an exponential form of the periodic modulation. 相似文献
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We propose a two-species infection model, in which an infected aggregate can gain one monomer from a healthy one due to infection when they meet together. Moreover, both the healthy and infected aggregates may lose one monomer because of self-death, but a
healthy aggregate can spontaneously yield a new monomer. Consider
a simple system in which the birth/death rates are directly
proportional to the aggregate size, namely, the birth and death
rates of the healthy aggregate of size k are J1k and
J2k while the self-death rate of the infected aggregate of size k is J3k. We then investigate the kinetics of such a system by means of rate equation approach. For the
J1>>J2 case, the aggregate
size distribution of either species approaches the generalized
scaling form and the typical size of either species increases
wavily at large times. For the
J1=J2 case, the size distribution of healthy aggregates approaches the generalized
scaling form while that of infected aggregates satisfies the
modified scaling form. For the
J1<>J2 case, the size distribution of healthy aggregates satisfies the modified scaling form, but that of infected aggregates does not scale. 相似文献
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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 self-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 t,he 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. 相似文献
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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. 相似文献
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KEJian-Hong LINZhen-Quan 《理论物理通讯》2002,37(3):297-302
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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)=J1k, population aggregate's self-birth rate
kernel J2(k)=J2k and population-catalyzed fitness birth rate kernel
I(k,j)=Ikju. The kinetic behavior of the fitness was found depending crucially on the parameter u,
which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst (population) aggregate. (i)
In the u ≤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 ak(t) does not have scale form. (ii) When u>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 ak(t)
approaches a generalized scaling form. 相似文献
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WANG Hai-Feng LIN Zhen-Quan KONG Xiang-Mu 《理论物理通讯》2006,46(6):1113-1120
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. 相似文献
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KE Jian-Hong LIN Zhen-Quan CHEN Xiao-Shuang 《理论物理通讯》2009,51(1):165-169
We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I(t)k or lose one monomer at a rate J(t)k, and with a probability P(t) an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I(t) - J(t) as well as the birth rate I(t). The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I(t) - J(t) ≥ P(t) or [J(t) + P(t) - I(t)]t ≈ 0 at t ≥ 1; otherwise, it will become extinct. 相似文献
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KE Jian-Hong LIN Zhen-Quan CHEN Xiao-Shuang 《理论物理通讯》2008,49(3):791-796
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. 相似文献
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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 ak(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 ak(t) approaches a generalized or
modified scaling form. 相似文献