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 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.     

Simple Schemes of CQED for Realizing Swap, Entangling and CNOT Quantum Gates

We consider two cavities which are spatially separated and connected by an optical fibre. There are multi two-level atoms in each of the cavities. The atoms resonantly interact with the cavity fields but there is no direct interaction between the atoms. We show that perfect swap and entangling quantum gates can be realised between the two atoms clusters if modes of the electromagnetic field in the cavities and fibre are initially not excited. Compared with the single atom scheme, we find that the multi-atom scheme can speed up the quantum gates by a factor √N where N is number of the atoms in each of the cavities. We also consider the case where two two-level atoms in distant cavities that are coupled by an optical fibre. We find if both of the atoms interact resonantly with the fields, a highly reliable CNOT gate can be achieved within much less operation time than that of the non- resonant case. The sensibility of these gates to various parameters contained in the models under consideration is also investigated.     

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.     

Kinetics of Catalysis-Driven Aggregation Processes with Sequential Input of Catalyst

We investigate the kinetic behavior of a two-species catalysis-driven aggregation model, in which coagulation of species A occurs only with the help of species B. We suppose the monomers of species B are stable and cannot selfcoagulate in reaction processes. Meanwhile, the monomers are continuously injected into the system. The model with a constant rate kernel is investigated by means of the mean-field rate equation. We show that the Mneties of the system depends crucially on the details of the input term. The injection rate of species B is assumed to take the given time- dependent form K（t） -t^λ, and the sealing solution of the duster size distribution is then investigated analytically. It is found that the cluster size distribution can satisfy the conventional or modified scaling form in most cases.     

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.     

Comparing Two Definitions of Work for a Biological Quantum Heat Engine

Systems of photosynthetic reaction centres have been modelled as heat engines, while it has also been reported that the efficiency and power of such heat engines can be enhanced by quantum interference — a trait that has attracted much interest. We compare two definitions of the work of such a photosynthetic heat engine, i.e. definition A used by Weimer et al. and B by Dorfman et al. We also introduce a coherent interaction between donor and acceptor(CIDA) to demonstrate a reversible energy transport. We show that these two definitions of work can impart contradictory results, that is, CIDA enhances the power and efficiency of the photosynthetic heat engine with definition B but not with A. Additionally, we find that both reversible and irreversible excitation-energy transport can be described with definition A, but definition B can only model irreversible transport. As a result, we conclude that definition A is more suitable for photosynthetic systems than definition B.     

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.     

An extended master-equation approach applied to aggregation in freeway traffic

We restudy the master-equation approach applied to aggregation in a one-dimensional freeway, where the decay transition probabilities for the jump processes are reconstructed based on a car-following model. According to the reconstructed transition probabilities, the clustering behaviours and the stochastic properties of the master equation in a one-lane freeway traffic model are investigated in detail The numerical results show that the size of the clusters initially below the critical size of the unstable cluster and initially above that of the unstable cluster all enter the same stable state, which also accords with the nucleation theory and is known from the result in earlier work. Moreover, we have obtained more reasonable parameters of the master equation based on some results of cellular automata models.     

Calculation of Covariance Matrix for Multi-mode Gaussian States in Decoherence Processes

We investigate the dynamics of n single-mode continuous variable systems in a generic Gaussian state under the influence of the independent and correlated noises making use of the characteristic function method. In two models the bath is assumed to be a squeezed thermal one. We derive an explicit input-output expression between the initial and final covariance matrices. As an example, we study the evolution of entanglement of three-mode Gaussian state embedded in two noisy models.     

Phase separation and abnormal transport behaviours in La0.7-xGdxSr0.3MnO3 system

The magnetic and transport behaviours of the La_{0.7-x}Gd_xSr_{0.3}MnO_3 (0≤x≤0.70) system are investigated. The experimental results indicate that with increasing Gd doping content, the magnetism of the system changes from the long-range ferromagnetic order state to the cluster-spin glass state, then to the antiferromagnetic (AFM) state. It is interesting that the phase separation appears at x=0.30 and 0.40 and disappears for x≥0.50 where the AFM state occurs. At high doping content, the transport behaviours exhibit abnormality, e.g. there are two temperature ranges in which the ρ－T curves can be well fitted by a variable-range hopping (VRH) model. We suggest that the VRH does not come from the hopping of carriers between clusters, but from the different magnetic backgrounds in the clusters.     

Ab initio calculations for the absorption spectra and polarizabilities of small sulfur clusters

Absorption spectra for Sn clusters （n=2...8） are calculated using an adiabatic time-dependent density functional formalism within the local density approximation （LDA）. We compare the calculated spectra with those computed using a simple LDA approach. The time-dependent LDA （TDLDA） spectra display a significant blue shift with respect to the LDA spectra. The calculated spectra present a variety of features that can be used for comparison with future experimental investigations. We also obtain a significant threshold absorption, which can distinguish between different ground states of the sulfur clusters. In addition, the polarizabilities of the clusters are calculated by using the higherorder finite-difference pseudopotential density functional method in real space. We find that the polarizabilities of the clusters considered are higher than the value estimated from the ＇hard sphere＇ model using the bulk static dielectric constant. The computed polarizabilities per atom tend to decrease with increasing cluster size. The polarizabilities are closely related to the HOMO-LUMO gaps and the geometrical configurations.     

Aggregation Behaviors of Cr Atoms Sputtering Deposited on Flat and Curved Liquid Surfaces

We report on the aggregation behaviors of Cr atoms deposited on flat and curved silicone oil substrates by the sputtering technique. It is found that the Cr atoms are prone to form quasi-circular clusters first and then these clusters connect with each other to form ramified or network-shaped aggregates. In the case of a fiat liquid surface, large quasi-circular clusters are frequently observed and their sizes increase with the deposition time. In the case of a curved surface with a larger curvature, the Cr atoms and dusters tend to move toward to the oil drop edge, and ramified aggregates with small widths are shaped. In the case of a curved surface with smaller curvature, large quasi-circular clusters and ramified aggregations can coexist. Based on the motion features of the Cr atoms and clusters on different liquid surfaces, various distinct film morphologies are discussed in detail.     

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.