The kinetic behavior of an aggregation-fragmentation-annihilation system with two distinct species is studied. We propose that the aggregation reaction occurs only between two clusters of the same species, and the irr...The kinetic behavior of an aggregation-fragmentation-annihilation system with two distinct species is studied. We propose that the aggregation reaction occurs only between two clusters of the same species, and the irreversible annihilation reaction occurs only between two clusters of different species, meanwhile there exists the fragmentation reaction of a cluster into two smaller clusters for either species. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distribution. In the case of the same initial concentrations of two species, the scaling descriptions for the cluster-mass distributions of the two species are found to break down completely. It is also observed that the kinetic behaviors of distinct species are quite complicated for the case of different initial concentrations of the two species. The clusters of larger initial concentration species (heavy species) possess peculiar scaling properties, while the cluster-mass distribution of light species has not scaling behavior. The exponents describing the scaling behavior for heavy species strongly depend on its fragmentation rate and initial monomer concentrations of two kinds of reactants.展开更多
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 b...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.展开更多
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 selfex...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.展开更多
We propose a catalysis-select migration driven evolution model of two-species（A-and B-species） aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts ...We propose a catalysis-select migration driven evolution model of two-species（A-and B-species） aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts of species D the reaction will become one unit of species B migrating to species A.Meanwhile the catalyst aggregates of species C perform self-coagulation,as do the species D aggregates.We study this catalysis-select migration driven kinetic aggregation phenomena using the generalized Smoluchowski rate equation approach with C species catalysis-select migration rate kernel K（k;i,j） = Kkij and D species catalysis-select migration rate kernel J（k;i,j） = Jkij.The kinetic evolution behaviour is found to be dominated by the competition between the catalysis-select immigration and emigration,in which the competition is between JD0 and KC0（D0 and C0 are the initial numbers of the monomers of species D and C,respectively）.When JD0 KC0 〉 0,the aggregate size distribution of species A satisfies the conventional scaling form and that of species B satisfies a modified scaling form.And in the case of JD0 KC0 〈 0,species A and B exchange their aggregate size distributions as in the above JD0 KC0 〉 0 case.展开更多
The coaggregating behavior of the cationic kinetic probe P16;with different types of surfactants are in complete agreement with predictions based on the newly proposed ESAg concept.
The kinetic behavior of an n-species (n?≥?3) aggregation–annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an ...The kinetic behavior of an n-species (n?≥?3) aggregation–annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible complete annihilation reaction occurs only between two species with adjacent number. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the cluster-mass distributions for the system. The results show that the kinetic behavior of the system not only depends crucially on the ratio of the aggregation rate I to the annihilation rate J, but also has relation with the initial concentration of each species and the species number's odevity. We find that the cluster-mass distribution of each species obeys always a scaling law. The scaling exponents may strongly depend on the reaction rates for most cases, however, for the case in which the ratio of the aggregation rate to the annihilation rate is equal to a certain value, the scaling exponents are only dependent on the initial concentrations of the reactants.展开更多
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 coa...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 αk（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 αk（t） approaches a generalized or modified scaling form.展开更多
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 ca...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.展开更多
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 ...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.展开更多
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 on...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.展开更多
We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously betw...We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates and , we find that the evolution behavior of the system depends crucially on the values of the indexes υ<SUB>1</SUB> and υ<SUB>2</SUB>. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.展开更多
Ductile transient liquid phase(TLP)bonding joints reinforced by multiple precipitates were produced using novel pre-sintered coatings and Au-Si fillers;therefore,the highest strength of NiTi/sapphire joints brazed at ...Ductile transient liquid phase(TLP)bonding joints reinforced by multiple precipitates were produced using novel pre-sintered coatings and Au-Si fillers;therefore,the highest strength of NiTi/sapphire joints brazed at 460℃ for 30 min reached 72 MPa.The pre-sintering process improved the surface-active of sapphire by forming metastable Ti_(3)O and non-stoichiometric Al_(2)O_(3).The typical brazing seam consisted of O-rich compounds,TiSi_(2),and Ti-Ni-Si,wherein the O-rich phase featured different crystallinity depending on the oxygen content.The sapphire/seam interface was either a nanoscale diffusion region or a Si-rich amorphous layer.The breakdown of the Stokes-Einstein relation(SER)occurred,and the deviation from SER increased with a higher cooling rate.The influence of coating thickness was reflected in(i)the supercooling related to the viscosity and fractional exponent of liquids and(ii)the microstructural change of the joint related to the driving force for crystal growth.This work presented a new strategy for joining ceramics to metals at lower temperatures but using the joint at higher temperatures;furthermore,gave an insight into the microstructure evolution and kinetics behaviors based on supercooling in a transient liquid phase bonding joint.展开更多
Graphite, as a strategic mineral resource, the recycling from spent lithium-ion batteries(LIBs) has attracted considerable attention for meeting considerable economic value. However, closed-circuit recycling still suf...Graphite, as a strategic mineral resource, the recycling from spent lithium-ion batteries(LIBs) has attracted considerable attention for meeting considerable economic value. However, closed-circuit recycling still suffers from the lack of effective repair methods. Considering the existing defects, a series of Cchain length carbons have been successfully introduced to repair spent graphite. Obviously, with the evolution of carbon resources, the thickness and pores of the coating layer were tailored with the functional groups. Benefitting from the increased active sites and created fold structure, their coulombic efficiency is obviously restored from 14% to 86.89%, while the stable capacity is kept at approximately 384.9 mAh gafter 100 cycles. Moreover, their excellent rate properties are kept about approximately 200 mAh gat2 C, meeting the standard of commercial materials. Supported by the detailed kinetic behaviors, the enhanced rate is mainly dominated by pseudocapacitive behaviors, accompanied by deepening redox reactions. Meanwhile, the cost of the proposed approach for recycling spent graphite is 894.87 $ t^(-1),and the recycling profit for regenerating graphite is approximately 7000 $ t^(-1). Given this, this work is anticipated to shed light on the closed-circuit recycling of spent graphite and offer significant strategies to repair graphite.展开更多
We propose a three-species aggregation model with catalysis-driven decomposition. Based on the mean-field rate equations, we investigate the evoIution behavior of the system with the size-dependent catalysis-driven de...We propose a three-species aggregation model with catalysis-driven decomposition. Based on the mean-field rate equations, we investigate the evoIution behavior of the system with the size-dependent catalysis-driven decomposition rate J（i; j; k） = Jijk^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 at large times, while the total size of the decomposed species decreases exponentially with time and vanishes finally.展开更多
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 s...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 aconstant annihilation rate kernel, both species may scale according to the conventional scaling law in the symmetrical case and survive together at the end.展开更多
We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two...We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the seff-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.展开更多
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（...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.展开更多
We propose a sequential monomer reaction model for a two-species predator-prey system, in which the aggregates of either species can spontaneously produce or lose one monomer and meanwhile, a type-B aggregate can prey...We propose a sequential monomer reaction model for a two-species predator-prey system, in which the aggregates of either species can spontaneously produce or lose one monomer and meanwhile, a type-B aggregate can prey upon one monomer of a type-A aggregate when they meet. Using the mean-field rate equation approach, we analytically investigate the kinetic behavior of the system. The results show that the evolution of the system depends crucially on the details of the rate kernels. The aggregate size distribution of either species approaches the conventional or modified scaling form in most cases. Moreover, the total size of either species grows exponentially with time in some cases and asymptotically retains a constant quantity in other cases, while it decays with time and vanishes finally in the rest cases.展开更多
We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with...We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with a special rate kernel. For the system without monomer input, the concentration aj（t） of the Aj clusters （j 〉 1） asymptotically retains a nonzero quantity, while for the system with monomer input, it decays with time and vanishes finally. We also investigate the kinetics of an interesting model with fixed-rate monomer adsorption. For the ease without monomer source, the evolution of the system will halt at a finite time; while the system evolves infinitely in time in the case with monomer source. Finally, we also suggest a connection between the fixed-rate monomer adsorption systems and growing networks.展开更多
A new technology of treating molybdenum residues by simultaneous ultrafine milling and alkali leaching was put forward to recover molybdenum from metallurgical residues. The effects of residue size, milling time, soli...A new technology of treating molybdenum residues by simultaneous ultrafine milling and alkali leaching was put forward to recover molybdenum from metallurgical residues. The effects of residue size, milling time, solid content, n (Na 2CO 3)/ n (Mo) and slurry pH value on molybdenum leaching rate were investigated. The results indicate that a simpler process, lower slurry temperature, 50% shorter treating time, 60% decrease of Na 2CO 3 content and 15% increase of molybdenum leaching rate can be obtained by the new technology compared with the traditional process. The leaching kinetic equation was determined, and calculation of active energy ( E =56.2 kJ/mol) shows that the leaching process of molybdenum residues by simultaneous ultrafine milling and alkali leaching is controlled by chemical reaction. Potential exists for the new process to form the basis for an economically viable, environmentally friendly process to recover valuable elements from residues.展开更多
文摘The kinetic behavior of an aggregation-fragmentation-annihilation system with two distinct species is studied. We propose that the aggregation reaction occurs only between two clusters of the same species, and the irreversible annihilation reaction occurs only between two clusters of different species, meanwhile there exists the fragmentation reaction of a cluster into two smaller clusters for either species. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distribution. In the case of the same initial concentrations of two species, the scaling descriptions for the cluster-mass distributions of the two species are found to break down completely. It is also observed that the kinetic behaviors of distinct species are quite complicated for the case of different initial concentrations of the two species. The clusters of larger initial concentration species (heavy species) possess peculiar scaling properties, while the cluster-mass distribution of light species has not scaling behavior. The exponents describing the scaling behavior for heavy species strongly depend on its fragmentation rate and initial monomer concentrations of two kinds of reactants.
基金National Natural Science Foundation of China under Grant Nos.10275048 and 10305009the Natural Science Foundation of Zhejiang Province of China under Grant No.102067
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10775104, 10275048, and 10305009the Zhejiang Provincial Natural Science Foundation of China under Grant No. 102067
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 10775104)
文摘We propose a catalysis-select migration driven evolution model of two-species（A-and B-species） aggregates,where one unit of species A migrates to species B under the catalysts of species C,while under the catalysts of species D the reaction will become one unit of species B migrating to species A.Meanwhile the catalyst aggregates of species C perform self-coagulation,as do the species D aggregates.We study this catalysis-select migration driven kinetic aggregation phenomena using the generalized Smoluchowski rate equation approach with C species catalysis-select migration rate kernel K（k;i,j） = Kkij and D species catalysis-select migration rate kernel J（k;i,j） = Jkij.The kinetic evolution behaviour is found to be dominated by the competition between the catalysis-select immigration and emigration,in which the competition is between JD0 and KC0（D0 and C0 are the initial numbers of the monomers of species D and C,respectively）.When JD0 KC0 〉 0,the aggregate size distribution of species A satisfies the conventional scaling form and that of species B satisfies a modified scaling form.And in the case of JD0 KC0 〈 0,species A and B exchange their aggregate size distributions as in the above JD0 KC0 〉 0 case.
文摘The coaggregating behavior of the cationic kinetic probe P16;with different types of surfactants are in complete agreement with predictions based on the newly proposed ESAg concept.
文摘The kinetic behavior of an n-species (n?≥?3) aggregation–annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible complete annihilation reaction occurs only between two species with adjacent number. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the cluster-mass distributions for the system. The results show that the kinetic behavior of the system not only depends crucially on the ratio of the aggregation rate I to the annihilation rate J, but also has relation with the initial concentration of each species and the species number's odevity. We find that the cluster-mass distribution of each species obeys always a scaling law. The scaling exponents may strongly depend on the reaction rates for most cases, however, for the case in which the ratio of the aggregation rate to the annihilation rate is equal to a certain value, the scaling exponents are only dependent on the initial concentrations of the reactants.
基金supported by the National Natural Science Foundation of China (Grant Nos 10275048,10305009 and 10875086)by the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067)
文摘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 αk（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 αk（t） approaches a generalized or modified scaling form.
基金The project supported by National Natural Science Foundation of China under Grant No.10305009the Natural Science Foundation of Zhejiang Province of China under Grant No.102067
文摘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.
基金Supported by National Natural Science Foundation of China under Grant Nos.10875086 and 10775104
文摘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.
基金National Natural Science Foundation of China under Grant Nos.10775104 and 10305009
文摘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.
文摘We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates and , we find that the evolution behavior of the system depends crucially on the values of the indexes υ<SUB>1</SUB> and υ<SUB>2</SUB>. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.
基金supported by the National MCF Energy R&D Program(No.2019YFE03100100)National Natural Science Foundation of China(NSFC,Nos.51975150,51974101,U21A20128,52175302,and 52105332)+2 种基金National Strategic International Science and Technology Innovation Cooperation Key Project(No.2020YFE0205304)Natural Science Foundation of Heilongjiang Province,China(Nos.JQ2020E003 and LH2020E037)Applied Basic Research Key Project of Yunnan(No.202002AB080001-1).
文摘Ductile transient liquid phase(TLP)bonding joints reinforced by multiple precipitates were produced using novel pre-sintered coatings and Au-Si fillers;therefore,the highest strength of NiTi/sapphire joints brazed at 460℃ for 30 min reached 72 MPa.The pre-sintering process improved the surface-active of sapphire by forming metastable Ti_(3)O and non-stoichiometric Al_(2)O_(3).The typical brazing seam consisted of O-rich compounds,TiSi_(2),and Ti-Ni-Si,wherein the O-rich phase featured different crystallinity depending on the oxygen content.The sapphire/seam interface was either a nanoscale diffusion region or a Si-rich amorphous layer.The breakdown of the Stokes-Einstein relation(SER)occurred,and the deviation from SER increased with a higher cooling rate.The influence of coating thickness was reflected in(i)the supercooling related to the viscosity and fractional exponent of liquids and(ii)the microstructural change of the joint related to the driving force for crystal growth.This work presented a new strategy for joining ceramics to metals at lower temperatures but using the joint at higher temperatures;furthermore,gave an insight into the microstructure evolution and kinetics behaviors based on supercooling in a transient liquid phase bonding joint.
基金financially supported by the National Key Research and Development Program(2019YFC1907801,2019YFC1907804)the National Natural Science Foundation of China(51904340)the Natural Science Foundation of Hunan(2020JJ4733,2021JJ20066)。
文摘Graphite, as a strategic mineral resource, the recycling from spent lithium-ion batteries(LIBs) has attracted considerable attention for meeting considerable economic value. However, closed-circuit recycling still suffers from the lack of effective repair methods. Considering the existing defects, a series of Cchain length carbons have been successfully introduced to repair spent graphite. Obviously, with the evolution of carbon resources, the thickness and pores of the coating layer were tailored with the functional groups. Benefitting from the increased active sites and created fold structure, their coulombic efficiency is obviously restored from 14% to 86.89%, while the stable capacity is kept at approximately 384.9 mAh gafter 100 cycles. Moreover, their excellent rate properties are kept about approximately 200 mAh gat2 C, meeting the standard of commercial materials. Supported by the detailed kinetic behaviors, the enhanced rate is mainly dominated by pseudocapacitive behaviors, accompanied by deepening redox reactions. Meanwhile, the cost of the proposed approach for recycling spent graphite is 894.87 $ t^(-1),and the recycling profit for regenerating graphite is approximately 7000 $ t^(-1). Given this, this work is anticipated to shed light on the closed-circuit recycling of spent graphite and offer significant strategies to repair graphite.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10775104,10875086,and 10305009by the Zhejiang Provincial Natural Science Foundation of China under Grant No.102067
文摘We propose a three-species aggregation model with catalysis-driven decomposition. Based on the mean-field rate equations, we investigate the evoIution behavior of the system with the size-dependent catalysis-driven decomposition rate J（i; j; k） = Jijk^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 at large times, while the total size of the decomposed species decreases exponentially with time and vanishes finally.
文摘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 aconstant annihilation rate kernel, both species may scale according to the conventional scaling law in the symmetrical case and survive together at the end.
基金The project supported by National Natural Science Foundation of China under Grant No. 10305009 and the Natural Science Foundation of Zhejiang Province of China under Grant No. 102067
文摘We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the seff-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.
基金supported by National Natural Science Foundation of China under Grant Nos. 10775104 and 10305009
文摘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.
基金supported by National Natural Science Foundation of China under Grant Nos.10775104 and 10305009Natural Science Foundation of Zhejiang Province of China under Grant No.102067
文摘We propose a sequential monomer reaction model for a two-species predator-prey system, in which the aggregates of either species can spontaneously produce or lose one monomer and meanwhile, a type-B aggregate can prey upon one monomer of a type-A aggregate when they meet. Using the mean-field rate equation approach, we analytically investigate the kinetic behavior of the system. The results show that the evolution of the system depends crucially on the details of the rate kernels. The aggregate size distribution of either species approaches the conventional or modified scaling form in most cases. Moreover, the total size of either species grows exponentially with time in some cases and asymptotically retains a constant quantity in other cases, while it decays with time and vanishes finally in the rest cases.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10775104 and 10305009
文摘We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with a special rate kernel. For the system without monomer input, the concentration aj（t） of the Aj clusters （j 〉 1） asymptotically retains a nonzero quantity, while for the system with monomer input, it decays with time and vanishes finally. We also investigate the kinetics of an interesting model with fixed-rate monomer adsorption. For the ease without monomer source, the evolution of the system will halt at a finite time; while the system evolves infinitely in time in the case with monomer source. Finally, we also suggest a connection between the fixed-rate monomer adsorption systems and growing networks.
文摘A new technology of treating molybdenum residues by simultaneous ultrafine milling and alkali leaching was put forward to recover molybdenum from metallurgical residues. The effects of residue size, milling time, solid content, n (Na 2CO 3)/ n (Mo) and slurry pH value on molybdenum leaching rate were investigated. The results indicate that a simpler process, lower slurry temperature, 50% shorter treating time, 60% decrease of Na 2CO 3 content and 15% increase of molybdenum leaching rate can be obtained by the new technology compared with the traditional process. The leaching kinetic equation was determined, and calculation of active energy ( E =56.2 kJ/mol) shows that the leaching process of molybdenum residues by simultaneous ultrafine milling and alkali leaching is controlled by chemical reaction. Potential exists for the new process to form the basis for an economically viable, environmentally friendly process to recover valuable elements from residues.
