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Population and Asset Distributions in Economically Competitive Activities： a Rate-Equation Approach

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Chinese Physics Letters 2004年第7期21卷 1216-1219页

作者： kejian-hong CAIXiao-Ou LINZhen-Quan SchoolofPhysicsandElectronicInformation WenzhouNormalCollegeWenzhou325027

We introduce a simple asset migration model for the wealth redistribution in economical activities, in which a unit of asset migrates from one individual to another whenever they interact. By means of the mean-field rate equation, we have analysed the dynamic behaviour of the system. In the random migration case, the asset distribution of individuals takes the standard Gaussian form and consistently decreases to zero at the end. As for the system in which only the richer can gain assets from the poorer, it is found that the individual asset distribution is discontinuous at a critical point and only the individuals with asset absolute value less than a cutoff value have a uniform and non-zero distribution. Moreover, the result shows that for the system with migration bias the assets of the individuals may have a cutoff value at each given time, which is different from the system without migration bias.

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Kinetics of an n—Species Aggregation Chain Model with Complete Annihilation

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Communications in Theoretical Physics 2003年第1期39卷 115-120页

作者： kejian－hong LINZhen－Quan DpeartmentofPhysicsandElectronicInformationScience WenzhouNormalCollegeWenzhou325027China DpeartmentofPhysicsandElectronicInformationScience WenzhouNormalCollegeWenzhou325027Chi

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 mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the cluster-mass 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.

关键词： kinetic behavior aggregation-annihilation process scaling law rate equations

Kinetic Behavior of Aggregation—Fragmentation Process with Annihilation

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Communications in Theoretical Physics 2002年第3期37卷 297-302页

作者： kejian－hong LINZhen－Quan DepartmentofPhysicsandElectronicInformationScience WenzhouNormalCollegeWenzhou325027ZhejiangProvinceChina DepartmentofPhysicsandElectronicInformationScience WenzhouNormalCollegeWenzhou325027Zheji

The kinetic behavior of an aggregation-fragmentation-annihilation system with two distinct species is studied. We propose that the aggregation reaction occurs only between two clusters of the same species, and the irreversible annihilation reaction occurs only between two clusters of different species, meanwhile there exists the fragmentation reaction of a cluster into two smaller clusters for either species. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distribution. In the case of the same initial concentrations of two species, the scaling descriptions for the cluster-mass distributions of the two species are found to break down completely. It is also observed that the kinetic behaviors of distinct species are quite complicated for the case of different initial concentrations of the two species. The clusters of larger initial concentration species (heavy species) possess peculiar scaling properties, while the cluster-mass distribution of light species has not scaling behavior. The exponents describing the scaling behavior for heavy species strongly depend on its fragmentation rate and initial monomer concentrations of two kinds of reactants.

关键词： kinetic behavior aggregation-fragmentation-annihilation process scaling description rate equation

Scaling Behavior of an Aggregation-Migration Model

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Communications in Theoretical Physics 2004年第5期41卷 781-786页

作者： kejian-hong LINZhen-Quan ZHUANGYou-Yi SchoolofPhysicsandElectronicInformation WenzhouNormalCollegeWenzhou325027China

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 and , we find that the evolution behavior of the system depends crucially on the values of the indexes υ1 and υ2. 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.

关键词： kinetic behavior aggregation-migration process scaling law

Exchange-Driven Growth with Birth Rate Less Than Death

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Communications in Theoretical Physics 2005年第5期43卷 837-840页

作者： LINZhen-Quan kejian-hong YEGao-Xiang DepartmentofPhysics ZhejiangUniversityHangzhou310027China／／DepartmentofPhysicsWenzhouNormalCollegeWenzhou325027China DepartmentofPhysics WenzhouNormalCollegeWenzhou325027China DepartmentofPhysics ZhejiangUniversityHangzhou310027China

We further study the kinetic behavior of the exchange-driven growth withbirth and death for the case of birth rate kernel being less than that of death based on themean-Geld theory. The symmetric exchange rate kernel is K(k,j) = K′(k,j) = Ikj~v, and the birth anddeath rates are proportional to the aggregate's size. The long time asymptotic behavior of theaggregate size distribution a_k(t) is found to obey a much unusual scaling law with an exponentiallygrowing scaling function Φ(x) = exp(x).

关键词： aggregation exchange-driven growth birth and death

Monomer Migration and Annihilation Processes

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Communications in Theoretical Physics 2005年第5期43卷 953-956页

作者： kejian-hong LINZhen-Quan ZHUANGYou-Yi SchoolofPhysicsandElectronicInformation WenzhouNormalCollegeWenzhou325027China

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 aconstant annihilation rate kernel, both species may scale according to the conventional scaling law in the symmetrical case and survive together at the end.

关键词： kinetic behavior migration annihilation scaling law

Nonuniversality and Breakdown of Scaling in Aggregation Process with Removal Term

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Communications in Theoretical Physics 2003年第1X期40卷 123-126页

作者： kejian-hong LINZhen-Quan CHENYun-Su DepartmentofPhysicsandElectronicInformationScience WenzhouNormalCollegeWenzhou325027China

We study the kinetics of an irreversible aggregation model with removal term. We solve the mean-field rate equation to obtain the general solution of the cluster-mass distribution for the case with arbitrary time-dependent remora/probability P(t). In particular, we analyze the scaling properties of the cluster distribution in the case with P(t)=u(t+t0)^v and find that the cluster-mass distribution always obeys a scaling law. We also investigate the kinetic behavior of another simple system, in which the removal probability of a cluster is proportional to its mass, and the results indicate that for this system the scaring description of the cluster-mass distribution breaks down completely.

关键词：缩放行为聚集过程速率方程动力学分析移动项

Probability Properties of Multi-contact in Protein Molecules

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Chemical Research in Chinese Universities 2003年第3期19卷 370-375页

作者： WANGXiang-hong kejian-hong HUMin-xiao ZHANGLin-xi DepartmentofPhysics WenzhouNormalCollegeWenzhou325000P.R.China DepartmentofPhysics ZhejiangUniversityHangzhou310028P.R.China

The compact conformations of polymers are important because the native conformations of all bio-polymers with certain function are highly compact. The properties of mutil-contact bio-polymer chains were studied by Gaussian statistics of the random-flight chain. The theoretical expressions(were given, also), the calculations of probability distributions and correlation functions for different topologic cases were derived and made respectively. Comparison between single, double and triple contacts was also made. By means of setting the parameters, the results of the current calculations of the multiple contacts are just the same as those calculated by single, double or tripe contacts separately. It is a useful method to investigate native conformations of biopolymers. The probabilities of multi contacts and correlation functions between chain 's contacts were calculated for the Gaussian chains. Because the bond probability distributions are Gaussian 's distributions, the probability distributions of the separations of various points along the chains are always consecutive. All the contacts may break up into several groups, and each group consists of many contacts. Here we investigated the probability distribution from one group to three groups of contacts.

关键词： Random-flight model Protein molecule Correlation function

Kinetic behaviour of two—species—group aggregation process with complete annihilation

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Chinese Physics B 2003年第4期12卷 443-451页

作者： kejian-hong LinZhen-Quan WangXiang-hong DepartmentofPhysicsandElectronicInformationScience WenzhouNormalCollegeWenzhou325027China

We propose a two-species-group aggregation-annihilation model in which an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible joint annihilation reaction occurs between two distinct species groups. Based on the mean-field theory, we have investigated the rate equations of the process with constant reaction rates to obtain the asymptotic descriptions of the cluster-mass distributions. The results indicate that for the symmetrical initial cases the kinetic behaviour of the system depends crucially on the ratio of the equivalent aggregation rate to the annihilation rate. The cluster-mass distribution of each species always obeys a conventional or modified scaling law in each individual case. Moreover, all the species cannot finally survive except for the cases in which at least one equivalent aggregation rate is less than twice the annihilation rate.

关键词： kinetic behaviour aggregation-annihilation scaling law