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

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)=Ikj^u. 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 a_k(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 a_k(t) approaches a generalized scaling form.     

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

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 Amk and Amj of the same species with the rate kernels Km (k,j)=Kmkj (m=1, 2,..., n, n≥2), and aggregates of An species catalyze a monomer-birth of Al species (l=1,2,..., n-1) with the catalysis rate kernel Jl(k,j)=Jlkjυ. The kinetic behaviors are investigated by means of the mean-field theory. We find that the evolution behavior of aggregate-size distribution alk(t) of Al species depends crucially on the value of the catalysis rate parameter v: (i) alk(t) obeys the conventional scaling law in the case of υ≤0, (ii) alk (t) satisfies a modified scaling form in the case of υ＞0. In the second model,the mechanism of monomer-birth of An-species catalyzed by Al species is added on the basis of the first model, that is,the aggregates of Al and An species catalyze each other to cause monomer-birth. The kinetic behaviors of Al and Anspecies are found to fall into two categories for the different υ: (i) growth obeying conventional scaling form with υ≤0,(ii) gelling at finite time withυ＞0.     

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

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.     

Kinetic Behaviors of Catalysis-Driven Growth of Three-Species Aggregates on Base of Exchange-Driven Aggregations

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.     

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

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.     

Aggregation Behaviors of a Two-Species System with Lose-Lose Interactions

We propose an aggregation evolution model of two-species （A- and B-species） aggregates to study the prevalent aggregation phenomena in social and economic systems. In this model, A- and B-species aggregates perform self-exchange-driven growths with the exchange rate kernels K（k, l） = Kkl and L（k, l） = Lkl, respectively, and the two species aggregates perform self-birth processes with the rate kernels J1（k） = J1 k and J2（ k ） = J2k, and meanwhile the interaction between the aggregates of different species A and B causes a lose-lose scheme with the rate kernel H（k,l） = Hkl. Based on the mean-field theory, we investigated the evolution behaviors of the two species aggregates to study the competitions among above three aggregate evolution schemes on the distinct initial monomer concentrations A0 and B0 of the two species. The results show that the evolution behaviors of A- and B-species are crucially dominated by the competition between the two self-birth processes, and the initial monomer concentrations Ao and Bo play important roles, while the lose-lose scheme play important roles in some special cases.     

Kinetic evolutionary behavior of catalysis-select migration

We propose a catalysis-select migration driven evolution model of two-species(A-and B-species) aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts of species D the reaction will become one unit of species B migrating to species A.Meanwhile the catalyst aggregates of species C perform self-coagulation,as do the species D aggregates.We study this catalysis-select migration driven kinetic aggregation phenomena using the generalized Smoluchowski rate equation approach with C species catalysis-select migration rate kernel K(k;i,j) = Kkij and D species catalysis-select migration rate kernel J(k;i,j) = Jkij.The kinetic evolution behaviour is found to be dominated by the competition between the catalysis-select immigration and emigration,in which the competition is between JD0 and KC0(D0 and C0 are the initial numbers of the monomers of species D and C,respectively).When JD0 KC0 > 0,the aggregate size distribution of species A satisfies the conventional scaling form and that of species B satisfies a modified scaling form.And in the case of JD0 KC0 < 0,species A and B exchange their aggregate size distributions as in the above JD0 KC0 > 0 case.     

Cluster Growth Through Monomer Adsorption Processes

We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with a special rate kernel. For the system without monomer input, the concentration aj（t） of the Aj clusters （j 〉 1） asymptotically retains a nonzero quantity, while for the system with monomer input, it decays with time and vanishes finally. We also investigate the kinetics of an interesting model with fixed-rate monomer adsorption. For the ease without monomer source, the evolution of the system will halt at a finite time; while the system evolves infinitely in time in the case with monomer source. Finally, we also suggest a connection between the fixed-rate monomer adsorption systems and growing networks.     

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

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.     

Stock mechanics: Predicting recession in S&P500, DJIA and NASDAQ

Proposed in this paper is an original method assuming potential and kinetic energies for prices and for the conservation of their sum that has been developed for forecasting exchanges. Connections with a power law are shown. Semiempirical applications on the S&P500, DJIA, and NASDAQ predict a forthcoming recession in them. An emerging market, the Istanbul Stock Exchange index ISE-100 is found harboring a potential to continue to rise.     

Rigorous Derivation and Analysis of Coupling of Kinetic Equations and Their Hydrodynamic Limits for a Simplified Boltzmann Model

In this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model. We prove the global convergence of the Chapman–Enskog expansion for this model. We then study the existence theory and asymptotic behaviour of the coupled systems. To solve the coupled problems we propose to use the transmission time marching algorithm. We then develop a convergence theory for the resulting algorithms.     

Competing role of catalysis-coagulation and catalysis-fragmentation in kinetic aggregation behaviours

We propose a kinetic aggregation model where species A aggregates evolve by the catalysis-coagulation and the catalysis-fragmentation,while the catalyst aggregates of the same species B or C perform self-coagulation processes.By means of the generalized Smoluchowski rate equation based on the mean-field assumption,we study the kinetic behaviours of the system with the catalysis-coagulation rate kernel K(i,j;l) ∝ l ν and the catalysis-fragmentation rate kernel F(i,j;l) ∝ l μ,where l is the size of the catalyst aggregate,and ν and μ are two parameters reflecting the dependence of the catalysis reaction on the size of the catalyst aggregate.The relation between the values of parameters ν and μ reflects the competing roles between the two catalysis processes in the kinetic evolution of species A.It is found that the competing roles of the catalysis-coagulation and catalysis-fragmentation in the kinetic aggregation behaviours are not determined simply by the relation between the two parameters ν and μ,but also depend on the values of these two parameters.When ν μ and ν≥ 0,the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution a k(t) obeys the conventional or generalized scaling law;when ν μ and ν≥ 0 or ν 0 but μ≥ 0,the catalysis-fragmentation process may play a dominating role and a k(t) approaches the scale-free form;and in other cases,a balance is established between the two competing processes at large times and a k(t) obeys a modified scaling law.     

Kinetic theory of vibrational relaxation in a radiation field: The optic-acoustic effect

A microscopic derivation is presented of the rate equations governing vibrational relaxation occurring in the optic-acoustic effect. Detailed expressions applicable to the spectrophone experiment are given both for an excitation source consisting of a broadband radiation field and for laserdriven systems. It is clear from the present treatment that no real advantage accrues from the use of laser excitation sources in the standard spectrophone experiment, due to the resultant strong dependence of the driving force itself on the mechanical chopper frequency. For broadband radiation field the dependence on the chopper frequency is removed and the standard result containing the Einstein coefficient of induced absorption is recovered. The spectrophone response for the simplest case of a two-level system is given explicitly and its similarity to phenomenologically derived expressions is pointed out.The work of F.R.M. was supported in part by a grant from the National Research Council of Canada. The work of A.T. was supported by the Foundation for Fundamental Research on Matter, which is sponsored by the Netherlands Organization for the Advancement of Pure Research.     

The Evolution of a Gas in a Radiation Field from a Kinetic Point of View

An existence theorem is derived for a system of kinetic equations describing the evolution of a gas in a radiation field from a kinetic point of view. The geometrical setting is the slab and given indata. The photons ingoing distribution functions are Dirac measures.     

槽道流POD重构及湍流动能耗散率分析

采用二维粒子图像测速仪（2DPIV）对槽道内涡波流场进行实验研究,用POD技术对2DPIV瞬态速度矢量场进行主导模态重构,得到槽道内的平均流速和湍流动能分布;采用大涡PIV方法对湍流动能耗散率分布进行计算.结果表明：重构流场表征了原始流场的主导结构,剔除了噪声等干扰信息;大涡PIV方法能有效地估算动能耗散率的分布;湍流动能在壁面附近较小,在接近槽道中心区域湍流动能越来越大,呈现出射流的特征;动能耗散率的峰值出现在壁面附近和槽道中心区域,动能耗散率随着远离壁面程度的增加先降低后逐渐增加直至达到峰值.     

Kinetics of Infection-Driven Growth Model with Birth and Death

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 J1 k 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.     

Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.