共查询到20条相似文献,搜索用时 31 毫秒
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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 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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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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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 reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels
K(k;j)=K'(k;j)=λkjυ and the
constant aggregation rates
I1, I2 and fragmentation rates
J1, J2. Based on the mean-field theory, we investigate the evolution behavior of the aggregate size distributions in several
cases with different values of index υ. We find that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When J1=0 and J2 =0, the aggregate size distributions ak(t) and bk(t) obey the conventional scaling law, while when J1>0 and
J2>0, they obey the modified scaling law with an exponential scaling function. The total mass of either species remains conserved. 相似文献
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We propose a reversible model of the migration-driven aggregation-fragmentation process with the sym-metric migration rate kernels K(k;j) = K‘(k;j) = λkjv and the constant aggregation rates I1, I2 and fragmentationrates J1, J2. Based on the mean-field theory, we investigate the evolution behavior of the aggregate size distributions inseveral cases with different values of index v. We find that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When J1 = 0 and J2 = 0, the aggregate sizedistributions ak(t) and bk(t) obey the conventional scaling law, while when J1 > 0 and J2 > 0, they obey the modifiedscaling law with an exponential scaling function. The total mass of either species remains conserved. 相似文献
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M. Khorrami A. Aghamohammadi 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(3):223-227
A system of particles is studied in which the stochastic
processes are one-particle type-change (or one-particle diffusion)
and multi-particle annihilation. It is shown that, if the
annihilation rate tends to zero but the initial values of the
average number of the particles tend to infinity, so that the
annihilation rate times a certain power of the initial values of
the average number of the particles remain constant (the double
scaling) then if the initial state of the system is a
multi-Poisson distribution, the system always remains in a state
of multi-Poisson distribution, but with evolving parameters. The
large time behavior of the system is also investigated. The system
exhibits a dynamical phase transition. It is seen that for a
k-particle annihilation, if k is larger than a critical value
kc, which is determined by the type-change rates,
then annihilation does not enter the relaxation exponent of the
system; while for k < kc, it is the annihilation (in
fact k itself) which determines the relaxation exponent. 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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We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation
occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and
with the migration rates
KA(i;j)=K'A(i;j) ∝ijv1 and
KB(i;j)=K'B(i;j) ∝ijv2, we find that the evolution behavior of the system depends crucially on the
values of the indexes v1 and v2. The aggregate size
distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior
under the symmetrical conditions. 相似文献
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P. Abreu et al. 《The European Physical Journal C - Particles and Fields》2000,13(4):573-589
The fragmentation functions of quarks and gluons are measured in various three-jet topologies in Z decays from the full data
set collected with the Delphi detector at the Z resonance between 1992 and 1995. The results at different values of transverse momentum-like scales are
compared. A parameterization of the quark and gluon fragmentation functions at a fixed reference scale is given. The quark
and gluon fragmentation functions show the predicted pattern of scaling violations. The scaling violation for quark jets as
a function of a transverse momentum-like scale is in a good agreement with that observed in lower energy annihilation experiments. For gluon jets it appears to be significantly stronger. The scale dependences of the gluon and
quark fragmentation functions agree with the prediction of the DGLAP evolution equations from which the colour factor ratio
is measured to be:
Received: 5 November 1999 / Published online: 25 February 2000 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