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 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 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.     

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.     

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 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.     

Scaling in Rate-Changeable Birth and Death Processes with Random Removals

We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.     

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.     

Competition Between Self-birth and Catalyzed Death in Aggregation Growth with Catalysis Injection

We propose two irreversible aggregation growth models of aggregates of two distinct species （.4 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 and B-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 effective rate KAo play important roles in the cases of I 〉 JBo and I = JBo. The evolution behaviors of the total mass M1^A（t） and the total aggregate number MA（t） are obtained, and the aggregate size distribution ak（t） of species A is found to approach a generalized scaling form in the case of I ≥ JBo and a special modified scaling form in the case of I 〈 JB0. The periodical evolution of the B-monomers concentration plays an exponential form of the periodic modulation.     

Competition Between Self-birth and Catalyzed Death in Aggregation Growth with Catalysis Injection

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 I_A(K)=Ik, catalyzed death rate kernel J_AB(k)=Jk and self exchange rate kernel K_A(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 M^A(t)₁ and the total aggregate number M^A(t)₀ are obtained, and the aggregate size distribution a_k(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.     

The entanglement of two moving atoms interacting with a single-mode field via a three-photon process

In this paper, the entanglement of two moving atoms induced by a single-mode field via a three-photon process is investigated. It is shown that the entanglement is dependent on the category of the field, the average photon number N, the number p of half-wave lengths of the field mode and the atomic initial state. Also, the sudden death and the sudden birth of the entanglement are detected in this model and the results show that the existence of the sudden death and the sudden birth depends on the parameter and the category of the mode field. In addition, the three-photon process is a higher order nonlinear process.     

非线性聚集生长理论的研究及其应用

首先介绍了非线性聚集生长计算机模型与生长规则和非线性聚集生长的实验原理与装置,然后阐述了计算凝聚物分形维数的计算机模拟方法和实验方法,最后论述了非线性聚集生长理论在大气颗粒物、薄膜生长方面的应用。     

Weibel Instability Growth Rate in Magnetized Plasmas with Quasi-Relativistic Distribution Function

The mechanism of the Weibel instability is investigated for dense magnetized plasmas. As we know, due to the electron velocity distribution, the Coulomb collision effect of electron-ion and the relativistic properties play an important role in such study. In this study an analytical expression for the growth rate and the condition of restricting the Weibel instability are derived for low-frequency limit. These calculations are done for the oscillation frequency dependence on the electron cyclotron frequency. It is shown that, the relativistic properties of the particle lead to increasing the growth rate of the instability. On the other hand the collision effects and background magnetic field try to decrease the growth rate by decreasing the temperature anisotropy and restricting the particles movement.     

Phase Transitions for the Growth Rate of Linear Stochastic Evolutions

We consider a discrete-time stochastic growth model on d-dimensional lattice. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process and the voter model. We study the phase transition for the growth rate of the “total number of particles” in this framework. The main results are roughly as follows: If d≥3 and the system is “not too random”, then, with positive probability, the growth rate of the total number of particles is of the same order as its expectation. If on the other hand, d=1,2, or the system is “random enough”, then the growth rate is slower than its expectation. We also discuss the above phase transition for the dual processes and its connection to the structure of invariant measures for the model with proper normalization. Supported in part by JSPS Grant-in-Aid for Scientific Research, Kiban (C) 17540112.     

Growth Rate of Spherulites in Thin Films: Direct Evidence of Failure of Traditional Growth Theory

Growth rates of PPS and PVDF spherulites in very thin films were measured. The growth rates change by about four orders of magnitude within the crystallization temperature ranges examined in this work. Film thickness at the position of the spherulite for which growth rates were determined was measured; the film thickness was deduced from retardation in the spherulite. In the light of the criterion we proposed, film thicknesses more than several tens of microns are required for the growth rate to change by four orders of magnitude. However, the thickness of the thinnest film examined experimentally was less than 1 μm. This discrepancy between theory and experiment is large and violates the framework of the traditional growth model unrecoverably.     

Mathematical Models of Death Signaling Networks

This review provides an overview of the progress made by computational and systems biologists in characterizing different cell death regulatory mechanisms that constitute the cell death network. We define the cell death network as a comprehensive decision-making mechanism that controls multiple death execution molecular circuits. This network involves multiple feedback and feed-forward loops and crosstalk among different cell death-regulating pathways. While substantial progress has been made in characterizing individual cell death execution pathways, the cell death decision network is poorly defined and understood. Certainly, understanding the dynamic behavior of such complex regulatory mechanisms can be only achieved by applying mathematical modeling and system-oriented approaches. Here, we provide an overview of mathematical models that have been developed to characterize different cell death mechanisms and intend to identify future research directions in this field.     

Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators

In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.     

不同气流环境下氟化氘激光对45#钢靶的辐照效应

通过表面形貌观察、温度场分析,研究了切向空气气流、切向氮气气流、自然对流3种环境下氟化氘（DF）激光对45#钢靶的辐照效应,结果表明：切向空气气流环境下,钢靶烧蚀效果最显著,靶板后表面中心温升最高;切向氮气气流环境下,钢靶有一定的烧蚀,但温升最低;自然对流环境下,烧蚀效果最差。实验结果表明：切向气流可移除部分熔化物,特别在切向空气气流环境下剧烈的氧化反应可促进钢靶温度升高,显著增强激光对钢靶的烧蚀,停止激光辐照后切向气流的冷却效应起主要作用。根据实际物理问题建立了相应的数值计算模型,模拟了不同气流环境下激光对钢靶的辐照效应,其中,利用生死单元的方法,模拟了切向空气气流环境下激光对钢靶的烧蚀,并考虑了氧化放热的影响。模拟结果与实验结果基本相符,解释了气流在激光辐照效应中的作用。     

量子垒生长速率对InGaN基绿光LED性能的影响

利用MOCVD技术在图形化Si(111)衬底上生长了InGaN/GaN绿光LED外延材料。在GaN量子垒的生长过程中,保持NH₃流量不变,通过调节三乙基镓(TEGa)源的流量来改变垒生长速率,研究了量子垒生长速率对LED性能的影响。使用二次离子质谱仪(SIMS)和荧光显微镜(FLM)分别对量子阱的阱垒界面及晶体质量进行了表征,使用电致发光测试系统对LED光电性能进行了表征。实验结果表明,垒慢速生长,在整个测试电流密度范围内,外量子效率(EQE)明显提升。我们认为,小电流密度下,EQE的提升归结为量子阱晶体质量的改善;而大电流密度下,EQE的提升则归结为阱垒界面陡峭程度的提升。