Competition between aggregation and migration processes of a multi-species system

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.     

Kinetics of catalytically activated duplication in aggregation growth

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 a_k(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 a_k(t) approaches a generalized or modified scaling form.     

Relativistic quantum and classical kinetic equations in the tomographic-probability representation

Using the Radon integral transform of the relativistic kinetic equation for a spin-zero particle, we obtain the classical and quantum evolution equations for the tomographic probability density (tomogram) describing the states of the particle in both the classical and quantum pictures. The Green functions (propagators) of the evolution equations of a free particle are constructed. The examples of the evolution of Gaussian tomogram is considered.     

Solvable Catalyzed Birth-Death-Exchange Competition Model of Three Speciese

A competition model of three species in exchange-driven aggregation growth is proposed. In the model, three distinct aggregates grow by exchange of monomers and in parallel, birth of species A is catalyzed by species B and death of species A is catalyzed by species C. The rates for both catalysis processes are proportional to kj^v and ky respectively, where ν（ω） is a parameter reflecting the dependence of the catalysis reaction rate of birth （death） on the catalyst aggregate＇s size. The kinetic evolution behaviors of the three species are investigated by the rate equation approach based on the mean-field theory： The form of the aggregate size distribution of A-species αk（t） is found to be dependent crucially on the two catalysis rate kernel parameters. The results show that （i） in case of ν ≤O, the form of ak （t） mainly depends on the competition between self-exchange of species A and species-C-catalyzed death of species A; （ii） in case of ν 〉 0, the form of αk（t） mainly depends on the competition between species-B-catalyzed birth of species A and species-C-catalyzed death of species A.     

Solvable Catalyzed Birth-Death-Exchange Competition Model of Three Species

A competition model of three species in exchange-driven aggregation growth is proposed. In the model, three distinct aggregates grow by exchange of monomers and in parallel, birth of species A is catalyzed by species B and death of species A is catalyzed by species C. The rates for both catalysis processes are proportional to kj^υ and kj^ω respectively, where υ(ω) is a parameter reflecting the dependence of the catalysis reaction rate of birth (death) on the catalyst aggregate's size. The kinetic evolution behaviors of the three species are investigated by the rate equation approach based on the mean-field theory. The form of the aggregate size distribution ofA-species a_k(t) is found to be dependent crucially on the two catalysis rate kernel parameters. The results show that (i) in case of υ ≤ 0, the form of a_k(t) mainly depends on the competition between self-exchange of species A andspecies-C-catalyzed death of species A; (ii) in case of υ>0, the form of a_k(t) mainly depends on the competition between species-B-catalyzed birth of species A and species-C-catalyzed death of species A.     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

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 ） = J1 k, population aggregate＇s self-birth rate kernel J2（ k ） = J2k and population-catalyzed fitness birth rate kernel I（k,j） = Ikj＇. The kinetic behavior of the fitness was found depending crucially on the parameter v, which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst （population） aggregate. （i） In the v ≤ 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 αk（t） does not have scale form. （ii） When v ≥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 αk （t） approaches a generalized scaling form.     

N体随机凝聚过程中集团分布的长时渐近行为

研究两种不同类型集团的N体不可逆的随机凝聚过程,这两种不同类型的集团分别是活性团和非活性团.用生成函数的方法直接求出凝聚速率为常数时,活性团和非活性团的密度分布,结果表明它们的长时渐近行为,具有普适性,同时给出它们的类标度形式及相应的标度指数. 关键词： 随机凝聚过程 凝聚速率 密度分布 生成函数     

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.     

冷却速率对Lennard-Jones体系凝固过程中结构与动力学性质的影响

用分子动力学模拟方法研究了五种不同冷却速率对Lennard-Jones体系凝固过程中结构与动力学性质的影响。采用两种不同的方法来确定玻璃转变温度Tg,并且对结晶温度Tc、径向分布函数g(r)、均方位移函数MSD与扩散系数D、平均配位数进行比较分析。结果表明：冷却速率影响Lennard-Jones体系凝固过程中的结构。当使用足够高的冷却速率冷却时,体系发生玻璃化转变,而且冷却速率越快,玻璃转变温度越高;当冷却速率较小时,体系形成晶体,而且冷却速率越慢,结晶温度越高,结晶程度也越高。同时发现,冷却速率对扩散系数和平均配位数也有很大影响,二者在体系发生玻璃转变时都有一个缓变的过程,表明了过冷液相区的存在。     

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.     

Existence theory of the linear equations appearing in the Chapman-Enskog solutions to two kinetic equations for liquids

The linear operators appearing in the Chapman-Enskog solutions to Kirkwood's Fokker-Planck kinetic equation and to Rice and Allnatt's kinetic equation are studied in this article. Existence proofs are given for the linearized Chapman-Enskog equations involving either the Fokker-Planck or the Rice-Allnatt operators. It is shown that the Fokker-Planck and Rice-Allnatt operators, defined in the domain appropriate to kinetic theory, are essentially self-adjoint. It is also shown that the spectrum of either of these operators coincides with the spectrum of the self-adjoint extension of the corresponding operator.Sloan Foundation Fellow 1968–70. Guggenheim Fellow 1969–70.     

A kinetic theory of spectral line shapes

The methods of kinetic theory are used to describe the radiation from an atom immersed in a gas of perturbing particles. It is shown that the line shape can be expressed in terms of a one-particle distribution function. The appropriate BBGKY hierarchy of equations is derived. This hierarchy is then truncated by assuming that only two-body collisions are important. The resulting equations are solved to obtain a non-Markovian kinetic equation which describes the combined effects of Doppler and pressure broadening. When the Markovian assumption is applied, a generalized linear Boltzmann equation is obtained which describes the line shape in the region where the impact limit is valid and which also describes the phenomenon of collisional narrowing.This research was supported in part by the Advanced Research Projects Agency of the Department of Defense, monitored by Army Research Office-Durham under Contract No. DA-31-124-ARO-D-139.     

差分法求解时空分布的激光动力学模型

利用速率方程理论和差分法数值计算,建立了描述激光器内部粒子数密度和光子数密度的时间演化和空间分布的动力学模型.该方法完善了普通的激光速率方程理论,为了解激光能量的时间演化和空间分布提供了较好的理论模型. 关键词： 速率方程 差分法 动力学模型 铜激光     

Bursting behaviours in cascaded stimulated Brillouin scattering

Stimulated Brillouin scattering is studied by numerically solving the Vlasov-Maxwell system.A cascade of stimulated Brillouin scattering can occur when a linearly polarized laser pulse propagates in a plasma.It is found that a stimulated Brillouin scattering cascade can reduce the scattering and increase the transmission of light,as well as introduce a bursting behaviour in the evolution of the laser-plasma interaction.The bursting time in the reflectivity is found to be less than half the ion acoustic period.The ion temperature can affect the stimulated Brillouin scattering cascade,which can repeat several times at low ion temperatures and can be completely eliminated at high ion temperatures.For stimulated Brillouin scattering saturation,higher-harmonic generation and wave-wave interaction of the excited ion acoustic waves can restrict the amplitude of the latter.In addition,stimulated Brillouin scattering cascade can restrict the amplitude of the scattered light.     

单体迁移驱使的聚集体生长

本文提出了一个可解的聚集体生长模型。在系统中，在质量为l的B聚集体的作用下，一个单体从质量为i的A聚集体迁移到质量为j的A聚集体，这个迁移反应速率核为K(i;j;l) i^μ j^ν l^varpi（ω≥0）。利用平均场速率方程方法，本文得到了几种不同情况下的聚集体质量分布的解析解。对μ=ν的系统，在μ<3/2的情况下系统的聚集体质量分布a_k(t)具有一种普适的标度形式。对于μ≠ν的系统，只有在μ<ν和μ+ν<2的情况下a_k(t)才满足标度形式。同时，在μ+ν>2（μ≠ν）或者μ>3/2（μ=ν）的情况下，系统将发生类凝胶相变。此外，本文也研究了反应核为K(i;j;l)μ(i^μ j^ν+ i^νj^μ )lω的系统的动力学标度行为。结果表明，聚集体质量分布只有在μ+ν<3的情况下才遵循标度律，而在其他情况下系统将在足够长的时间后发生类凝胶相变。