共查询到20条相似文献,搜索用时 31 毫秒
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We propose a three-species aggregation model with catalysis-drivendecomposition. Based on the mean-field rate equations, weinvestigate the evolution behavior of the system with thesize-dependent catalysis-driven decomposition rate J(i;j;k)=J ijkv and the constant aggregation rates. The results show that the cluster size distribution of the species without decomposition can always obey the conventional scaling law in the case of 0≤ v ≤1, while the kinetic evolution of the decomposed species depends crucially on the index v. Moreover, the total size of the species without decomposition can keep a nonzero value atlarge times, while the total size of the decomposed speciesdecreases exponentially with time and vanishes finally. 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
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KEJian-Hong LINZhen-Quan 《理论物理通讯》2002,37(3):297-302
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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 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. 相似文献
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CHEN Yu KE Jian-Hong LIN Zhen-Quan 《理论物理通讯》2008,49(1):235-238
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. 相似文献
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SUN Yun-Fei CHEN Dan LIN Zhen-Quan KE Jian-Hong 《理论物理通讯》2009,51(6):1042-1054
We propose a solvable aggregation model to mimic the evolution of population A, asset B, and the quantifiable resource C in a society. In this system, the population and asset aggregates themselves grow through selfexchanges with the rate kernels Kl(k,j) = K1kj and K2(h,j) = K2kj, respectively. The actions of the population and asset aggregations on the aggregation evolution of resource aggregates are described by the population-catalyzed monomer death of resource aggregates and asset-catalyzed monomer birth of resource aggregates with the rate kerne/s J1(k,j)=J1k and J2(k,j) = J2k, respectively. Meanwhile, the asset and resource aggregates conjunctly catalyze the monomer birth of population aggregates with the rate kernel I1 (k,i,j) = I1ki^μjη, and population and resource aggregates conjunctly catalyze the monomer birth of asset aggregates with the rate kernel /2(k, i, j) = I2ki^νj^η. The kinetic behaviors of species A, B, and C are investigated by means of the mean-field rate equation approach. The effects of the population-catalyzed death and asset-catalyzed birth on the evolution of resource aggregates based on the self-exchanges of population and asset appear in effective forms. The coefficients of the effective population-catalyzed death and the asset-catalyzed birth are expressed as J1e = J1/K1 and J2e= J2/K2, respectively. The aggregate size distribution of C species is found to be crucially dominated by the competition between the effective death and the effective birth. It satisfies the conventional scaling form, generalized scaling form, and modified scaling form in the cases of J1e〈J2e, J1e=J2e, and J1e〉J2e, respectively. Meanwhile, we also find the aggregate size distributions of populations and assets both fall into two distinct categories for different parameters μ,ν, and η: (i) When μ=ν=η=0 and μ=ν=η=1, the population and asset aggregates obey the generalized scaling forms; and (ii) When μ=ν=1,η=0, and μ=ν=η=1, the population and asset aggregates experience gelation transitions at finite times and the scaling forms break down. 相似文献
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We propose a two-species monomer migration-annihilation model, in
which monomer migration reactions occur between any two aggregates
of the same species and monomer annihilation reactions occur
between two different species. Based on the mean-field rate
equations, we investigate the evolution behaviors of the
processes. For the case with an annihilation rate kernel
proportional to the sizes of the reactants, the aggregation size
distribution of either species approaches the modified scaling
form in the symmetrical initial case, while for the asymmetrical
initial case the heavy species with a large initial data scales
according to the conventional form and the light one does not
scale. Moreover, at most one species can survive finally. For the
case with a constant annihilation rate kernel, both species may
scale according to the conventional scaling law in the symmetrical
case and survive together at the end. 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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We study the kinetic behaviour of the growth of aggregates driven by reversible migration between any two aggregates. For a simple model with the migration rate K(i;j)=K′(i;j)∝i^uj^v at which the monomers migrate from the aggregates of size i to those of size j, we find that the aggregate size distribution in the system with u+v≤3 and u<2 approaches a conventional scaling form, which reduces to the Smoluchovski form in the u=1 case. On the other hand, for the system with u<2, the average aggregate size S(t) grows exponentially in the u+v=3 case and as (tlnt)^{1/(5-2u)} in another special case of v=u-2. Moreover, this typical size S(t) grows as t^{1/(3-u-v)} in the general u-2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