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.     

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.     

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 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.     

Kinetics of a Migration－Driven Aggregation－Fragmentation Process

We propose a reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels K(k;j)=K'(k;j)=λkj^υ 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 a_k(t) and b_k(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.     

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.     

A Kind of Atomic Coherent State as a Two-Mode Squeezed State

We find that a kind of atomic coherent state, formed as exp [ξ J₊- ξ^*J_-] |00>, when the SU(2) generators J_± are taken as Fan's form, J₊=(1/2)(a₁-a₂†)(a₁†-a₂), J_=(1/2) (a₁†+a₂)(a₁+a₂†), and J₀=(1/2) (a₁†a₂†-a₁a₂), is simultaneously a two-mode squeezed state. We analyse this squeezed state's physical properites, such as the cross-correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.     

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.     

硼酸盐玻璃中Eu掺杂对Ag纳米颗粒的析出机制及其发光性质研究

采用高温熔融法制备了Eu-Ag共掺的硼酸盐玻璃,利用吸收光谱和发射光谱等研究了玻璃中网络形成体B₂O₃含量变化和Eu离子共掺对于Ag在基质中赋存状态的影响。在Eu-Ag共掺玻璃的吸收光谱中发现,随着B₂O₃含量的增加,Ag纳米颗粒在4 10 nm附近的宽带吸收强度逐渐下降;玻璃在340 nm光源激发下,位于350～600 nm的蓝绿光区出现一个Ag分子团簇的宽带发光,且其发光强度随B₂O₃含量的增加逐渐增强。在Eu或Ag单掺的玻璃中可分别观测到微弱的Eu3+或Ag分子团簇的本征发射,而Eu-Ag共掺样品中Eu3+和Ag分子团簇的发光都得到了显著的增强。并且Eu离子浓度的增加促进了Ag纳米颗粒在410 nm附近的宽带吸收。对Eu离子的添加促进Ag纳米颗粒析出的机理进行了讨论。同时,由于Eu3+的5D₀→7F_J的电子跃迁发射为橙红光,Ag纳米团簇可发射蓝绿光甚至黄光,因此通过玻璃结构的调控和Eu离子掺杂浓度的调节可以实现玻璃的白光发射,这有望成为潜在的白光LED用玻璃照明材料。     

杂多酸环戊二烯钒衍生物的合成、谱学性质及抗肿瘤活性

合成了杂多酸环戊二烯钒衍生物[Bu₄N]₄[(CpV)PW₁₁O₃₉](1),[Bu₄N]₄H[(CpV)SiW₁₁O₃₉](2)和[Bu₄N]₄[A-β-(η5-CpV)SiW₉V₃O₄₀](3),并通过元素分析、IR、51V和183W NMR谱进行了结构表征。结果表明配合物(1)和(2)为结合型有机金属配合物,(3)为支撑型杂多酸有机金属配合物。体外抗肿瘤活性研究表明化合物(1)对HL-60和B₁₆均具有一定的抑制作用。     

New Convenient Way for Disentangling Exponential Operator Composed of Angular Momentum Operators

In the preceding paper (Commun. Theor. Phys. 51 (2009) 321) we have recommended a convenient method for disentangling exponential operators. In this work we use this method for disentangling exponential operators composed of angular momentum operators. We mainly disentangle the form of exp [ 2hJ_z+gJ₊+kJ_-] as the ordering exp(... J₊) exp (...J_z)exp(...J_-), we employ the Schwinger Bose realization J_-=b⁺a, J₊=a⁺b, J_z=( a⁺a-b⁺b)/2 to fulfil this task, without appealing to Lie algebra method. Note that this operator's disentangling is different from its decomposition in normal ordering.     

光纤化学传感同步吸收-荧光法的建立

建立一种光纤化学传感同步测定吸收光谱和荧光光谱的新方法。自制同步吸收-荧光比色皿,结合光纤化学传感技术,建立同步吸收-荧光光谱法检测仪器,分别测定罗丹明B,维生素B₂,维生素B₆等溶液的同步吸收-荧光光谱,且与传统的紫外-可见吸光光度法和荧光法进行对比。同步吸收-荧光光谱法测得罗丹明B,维生素B₂,维生素B₆与传统吸光光度法和荧光光谱法检测的吸收光谱图和荧光光谱的图谱大体一致。最大荧光强度波长与传统的荧光方法比较准确度高,但最大吸收波长略有偏差。同步吸收-荧光光谱法等同于同步测定荧光物质的吸收光谱和荧光光谱,实现二光谱合二为一,测定最大发射波长时准确度高,但最大吸收波长略有偏差,值得深一步研究。     

有机硼酸盐插层Zn/Al-LDH的红外和拉曼光谱特征

研究了碳酸根和硼酸根的二元锌铝水滑石的X射线衍射,拉曼和红外光谱特征。采用一步水热共沉淀法,分别制得结晶良好的层间为碳酸根和硼酸根的二元锌铝水滑石。X射线衍射分析显示,硼酸根插层后水滑石（003）特征衍射峰向小角度移动,峰型尖锐,水滑石通道高度从0.28 nm增加至0.42 nm;红外光谱和拉曼光谱特征表明,硼酸根插层后,碳酸根的红外和拉曼特征峰消失。层间硼酸根以B₃O₃(OH)-₄,B₄O₅(OH)2-₄和B(OH)-₄三种形式存在。随层间离子的不同,与羟基相关的红外光谱和拉曼光谱峰位均有所改变。研究结果表明以硼酸三正丁酯为插层剂,可获得单一相、纯度较高的硼酸根型锌铝水滑石,拉曼光谱可准确探测水滑石层间阴离子变化对其结构和性能的影响。     

Statistical Properties of Multispecies Competition Ecosystems Subjected to Dichotomous Noises

We investigate statistical properties of multispecies competition ecosystems subjected to both symmetric and asymmetric dichotomous noises. The expression of the stationary probability distribution function (SPDF) is analytically derived by means of mean-field approximation, and verified bystochastic simulations. The results indicate that: (i) A noiseamplitude (a₀), a noise autocorrelation time (τ₀) and a noise symmetry parameter (k) all can affect the SPDF; (ii) There is an optimal τ₀, which makes the mean value of population density be maximal, near which a transition takes place, i.e., the stationary mean value of species density (_st) suddenly falls to a lower constant; (iii) As k decreases, the maximum of< x>_st and the optimal τ₀ increase. The parameter planes of τ₀-a₀² and τ₀-k for the transition are plotted.     

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.     

Aggregation Processes with Catalysis-Driven Decomposition

We propose a three-species aggregation model with catalysis-drivendecomposition. Based on the mean-field rate equations, weinvestigate the evolution behavior of the system with thesize-dependent catalysis-driven decomposition rate J(i;j;k)=J ijk^v and the constant aggregation rates. The results show that the cluster size distribution of the species without decomposition can always obey the conventional scaling law in the case of 0≤ v ≤1, while the kinetic evolution of the decomposed species depends crucially on the index v. Moreover, the total size of the species without decomposition can keep a nonzero value atlarge times, while the total size of the decomposed speciesdecreases exponentially with time and vanishes finally.     

Kinetics of a Migration-Driven Aggregation-Fragmentation Process

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.     

Monomer Migration and Annihilation Processes

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.     

取代基对双酞菁铥LB膜及光谱特性的影响

采用紫外-可见吸收光谱的方法研究了三种稀土夹心双酞菁铥化合物在溶液和LB膜中的聚集性和光谱特性。实验结果表明三种稀土双酞菁化合物在氯仿溶液中形成了H-聚集体,但当浓度比较低时,溶液中表现出单体的吸收。取代基OC₈H₁₇的加入使氯仿溶液中双酞菁铥化合物的聚集性减弱,而且使得吸收峰发生红移,对吸收峰的强度也有较大的影响,造成了Soret吸收带的分裂。另外,取代基OC₈H₁₇对LB膜中双酞菁分子的存在状态有较大的影响,在LB膜中,TmPc₂和TmPcPc*分子以H-聚集体的形式存在,而TmPc*₂分子以T-聚集体的形式存在。形成LB膜后,由于双酞菁分子之间排列紧密,相互作用加强,使得薄膜中分子聚集体的吸收峰相对于溶液中聚集体的吸收峰发生了一定的红移,薄膜中分子排列方向的不同对吸收光谱也有一定的影响。