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Population and Asset Distributions in Economically Competitive Activities： a rate-Equation Approach

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Chinese Physics Letters 2004年第7期21卷 1216-1219页

作者： KEJian-Hong CAIXiao-Ou LINZhen-Quan SchoolofPhysicsandElectronicInformation WenzhouNormalCollegeWenzhou325027

We introduce a simple asset migration model for the wealth redistribution in economical activities, in which a unit of asset migrates from one individual to another whenever they interact. By means of the mean-field rate equation, we have analysed the dynamic behaviour of the system. In the random migration case, the asset distribution of individuals takes the standard Gaussian form and consistently decreases to zero at the end. As for the system in which only the richer can gain assets from the poorer, it is found that the individual asset distribution is discontinuous at a critical point and only the individuals with asset absolute value less than a cutoff value have a uniform and non-zero distribution. Moreover, the result shows that for the system with migration bias the assets of the individuals may have a cutoff value at each given time, which is different from the system without migration bias.

关键词： rate equations Statistical Biases system behavior bias(electronics) Cutoffs critical point Bias Immigration Discontinuous

Theoretical study and optimization of a high power mid-infrared erbium-doped ZBLAN fibre laser

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Chinese Physics B 2011年第3期20卷 239-246页

作者：李剑峰 Stuart D.Jackson School of Optoelectronic Information University of Electronic Science and Technology of China Institute of Photonics and Optical Science School of PhysicsUniversity of Sydney

Based on the rate equations describing the erbium-doped fluoride glass （ZBLAN） fibre lasers with different pumping configurations being taken into account, this paper presents theoretical calculations related to the dynamic population density and the operation performance of a high power mid-infrared all-fibre erbium-doped ZBLAN fibre laser. It shows that the ground-state absorption, excited-state absorption and energy-transfer-upconversion processes co-exist and produce a population balance, causing the laser to operate stably at a continuous wave state. A good agreement between the theoretical results and recent experimental measurement is obtained. Furthermore, the laser structure parameters including fibre length, reflectance of output fibre Bragg grating and pumping configurations are quantitatively optimised to achieve the best performance. The results show, as expected, that the slope efficiency of the fibre laser can be improved significantly through optimisation, which then provides an important guide for the design of high-performance mid-infrared erbium-doped ZBLAN fibre lasers.

关键词： Lerbium-doped fibre laser mid-infrared fibre laser ZBLAN fibre rate equations

Kinetics of celestite conversion to acidic strontium oxalate hydrate in aqueous solution of oxalic acid

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Transactions of Nonferrous Metals Society of China 2019年第6期29卷 1332-1345页

作者： Mert ZORAGA Cem KAHRUMAN Ibrahim YUSUFOGLU Istanbul University-Cerrahpasa Engineering FacultyMetallurgical and Materials Engineering Department

Conversion of SrSO4 to acidic strontium oxalate hydrate(H[Sr(C2O4)1.5(H2O)]) in aqueous H2C2O4 solutions proceeds as a consecutive reaction. In the first step of the consecutive reaction, SrSO4 reacts with H2C2O4 and pseudomorphic conversion to SrC2 O4·H2O occurs. In the second step, SrC2 O4·H2O reacts with H2C2O4 to form H[Sr(C2 O4)1.5(H2O)]. Sr(HC2 O4)(C2 O4)0.5·H2 O crystallizes during cooling of the reaction mixture to room temperature if the solution reaches the saturation concentration of (H[Sr(C2O4)1.5(H2O)]. The aims of this study are the derivation of reaction rate equations and the determination of the kinetic parameters such as pre-exponential factor, apparent activation energy and order of H2C2O4 concentration for each reaction *** conversions of SrSO4 were calculated using the quantitative amounts of dissolved S and Sr. It was determined that the reaction rate increased at the initial time of reaction by increasing the temperature using solutions with approximately same H2C2O4 concentrations. The reaction extends very slowly after a certain time in solutions with low H2C2O4 concentration and ends by the formation of a protective layer of SrC2O4-H2O around the surfaces of solid particles. Fractional conversion of SrSO4 is increased by increasing concentration of H2C2O4 at constant temperature. Kinetic model equations were derived using shrinking core model for each step.

关键词： celestite concentrate pseudomorphic conversion rate equations kinetic parameters conversion reaction

Kinetics of oxidative coupling of methane:Bridging the gap between comprehension and description

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Journal of Natural Gas Chemistry 2009年第3期18卷 273-287页

作者： Mikhail Sinev Zukhra Fattakhova Vladimir Lomonosov Yurii Gordienko Semenov Institute of Chemical Physics ZAO "SCHAG" Company

The development of notions about the mechanism of the oxidative coupling of methane （OCM） over oxide catalysts and corresponding progress in its kinetic description are reviewed and discussed. The latter becomes essential at the stage of scaling up and optimization of the process in pilot and industrial reactors. It is demonstrated that the main achievements in the development of kinetic models can be reached by combining the approaches conventionally used in homogeneous gas-phase kinetics and in heterogeneous catalysis. In particular, some important features of the OCM process can be described if several elementary reactions of free radical species （formation and transformation） with surface active sites are included into the detailed scheme of methane oxidation in gas. However, some important features, such as a non-additive character of the reciprocal influence of methane and ethane in the case of their simultaneous presence in the reaction mixture, cannot yet be described and comprehended in the framework of schemes developed so far. Possible ways towards an advanced kinetic model, accounting the main principles of catalyst functioning （redox nature of active sites） and pathways of product formation （via free radicals） are traced.

关键词： natural gas methane oxidative coupling of methane ethane ethylene kinetics mechanism rate equations

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

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Chinese Physics B 2010年第12期19卷 559-570页

作者：李晓东林振权宋美霞柯见洪 Department of Physics Wenzhou University

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^v and the catalysis-fragmentation rate kernel F（i,j; l） l^μ, where l is the size of the catalyst aggregate, and v 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 v 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 v and μ, but also depend on the values of these two parameters. When v 〉 μ and v ≥0, the kinetic evolution of species A is dominated by the catalysis-coagulation and its aggregate size distribution αk（t） obeys the conventional or generalized scaling law; when v 〈 μ and v ≥ 0 or v 〈 0 but μ≥ 0, the catalysis-fragmentation process may play a dominating role and ak（t） approaches the scale-free form; and in other cases, a balance is established between the two competing processes at large times and ακ（t） obeys a modified scaling law.

关键词： kinetic aggregation behaviour catalysis-coagulation catalysis-fragmentation rate equations

Study on the green upconversion saturation in Er^(3+) doped oxyfluoride tellurite glass

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Journal of Rare Earths 2009年第2期27卷 334-337页

作者：董力强黄世华温红宇康凯段晓霞 Key Laboratory of Luminescence and Optical Information (Ministry of Education) Institute of OptoelectronicTechnologyBeijing Jiaotong UniversityBeijing 100044China Research Institute of Chemical Defense Beijing 102205 China

The upconversion emission spectra of Er^3＋ doped oxyfluoride tellurite glasses excited by 808 nm laser diode （LD） were measured. The dependence of 550 nm upconversion emission on the excitation intensity was analyzed. Quadratic intensity dependence was only observed at weak excitation intensity. With increasing the excitation intensity, saturation was turned out. The experimental results were fitted to a model based on the rate equations.

关键词： upconversion saturation rate equations rare earths

Sexually Transmitted Diseases on Bipartite Graph

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Chinese Physics Letters 2009年第1期26卷 364-367页

作者：温罗生钟将杨小帆 School of Mathematics and Physics Chongqing University Chongqing 400044 School of Computer Science Chongqing University Chongqing 400044

We study the susceptible infected-susceptible （SIS） epidemic model on bipartite graph. According to the difference of sex conception in western and oriental nations, we construct the Barabasi Albert Barabasi Albert （BA-BA） model and Barabasi-Albert Homogeneity （BA-HO） model for sexually transmitted diseases （STDs）. Applying the rate equation approach, the positive equilibria of both models are given analytically. We find that the ratio between infected females and infected males is distinctly different in both models and the infected density in the BA-HO model is much less than that in the BA-BA model. These results explain that the countries with small ratio have less infected density than those with large ratio. Our numerical simulations verify these theoretical results.

关键词： SCALE-FREE NETWORKS COMPLEX NETWORKS CONTACTS Sexually Transmitted Diseases rate equations Bipartite graph complex networks Countries (nations)

227-W output all-fiberized Tm-doped fiber laser at 1908 nm

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Chinese Physics B 2014年第10期23卷 147-150页

作者：胡震岳闫平肖起榕柳强巩马理 Center for Photonics and Electronics State Key Laboratory of Tribology Department of Precision Instruments Tsinghua University

In this paper, we report that a diode-pumped thulium-doped double clad silica fiber laser can provide powers of up to 227 W at 1908 nm, corresponding to a slope efficiency of 54.3%, and an optical-to-optical efficiency of 51.2%. The output power, to the best of our knowledge, is the highest output at 1908 nm. The beam quality M2 factor is about 1.56. Also discussed in this paper is the dependence of the laser performance on fiber length.

关键词： thulium-doped fiber laser rate equations 1908 nm

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

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Communications in Theoretical Physics 2007年第3期47卷 479-486页

作者： HAN An-Jia CHEN Yu LIN Zhen-Quan KE Jian-Hong Department of Physics Wenzhou University Wenzhou 325027 China

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＋1 through a monomer-birth catalyzed by a population aggregate Aj of size j is J（κ,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 aseets, 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 of η=λ =0, and they obey the modified scaling form 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.

关键词： kinetic behvavior aggregation-exchange growth catalyzed-birth scaling law rate equations