Kinetics of migration-driven aggregation processes

Ke, Jianhong; Zhang, Lin

doi:10.1103/physreve.66.050102

Cited by 48 publications

(62 citation statements)

References 15 publications

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“…Normally, we study the interaction among individual objects, but the aggregation process enables us to look at the interaction among groups (Moussaid et al, 2010) or individual object's behavior under group interaction (Ke and Lin, 2002). With the development of knowledge in network (Ke et al, 2006a(Ke et al, , 2006b, we are capable of connecting aggregation process with social sciences (Bellaiche, 2010;Gonzalez-Avella et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…This scheme shows that for each individual monomer, it moves from smaller aggregates to bigger ones. However, a more general reversible reaction process exists as well where each monomer moves from bigger aggregates to smaller ones and vice versa (Ke and Lin, 2002). It is well known that in job markets, migration is reversible as jobs move from small cities to big ones and vice versa.…”

Section: Introductionmentioning

confidence: 99%

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Kinetics of jobs in multi-link cities with migration-driven aggregation process

Sun

2013

Economic Modelling

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kinetics of jobs in multi-link cities with migration-driven aggregation process

Sun

2013

Economic Modelling

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“…(9) or (10), which allow expressing ξ 1 and M µ as the functions of M 0 or M 1 only, see Eqs. (18), (26), and (34) below.…”

mentioning

confidence: 99%

“…In order to describe kinetics of step (iii), the approach proposed by Smoluchowski [14,15], a standard and widely-used tool for description of various coagulation phenomena, is reintroduced [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In the present case, concentrations of P (c π ), A (c α ), and B i , (ξ i ), i ∈ N, are the state variables.…”

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confidence: 99%

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Exact solutions of kinetic equations in an autocatalytic growth model

Jędrak

2013

Phys. Rev. E

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Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, ξ k = s k (ξ1) ∝ ξ k 1 /k was obtained, while in the latter, the functional form of s k (ξ1) is more complicated. In both cases, ξ1(t) = hµ(Mµ(t)) is a function of the moments of the mass distribution. Both functions, s k (ξ1) and hµ(Mµ), depend on the assumed mechanism of autocatalytic growth and monomer production, and not on other chemical reactions present in a system. PACS numbers: Keywords:Nucleation and growth phenomena, resulting in occurrence of a new phase from a homogeneous host phase, are ubiquitous in nature [1,2]. In many cases, apart from processes of coagulation and fragmentation, chemical reactions are also present in a system. Frequently, the chemical reactions account for phenomena studied by polymer and colloidal science.Nucleation and subsequent growth of metal nanoclusters in aqueous solution is a topic of considerable current interest, since solution route synthesis is one of the most convenient methods of producing transition-metal nanoparticles [3]. However, applicability of this method depends on the ability to control size and shape of the produced nanoparticles, which determine their unique optical, electronic and catalytic properties. For that reason, theoretical models capable of predicting the cluster size distribution, as well as its dependence on the experimentally controllable parameters of the system, are required.A mechanism of transition-metal colloidal nanoparticle formation has been proposed by Watzky and Finke [4], cf. [5][6][7][8]. The WF mechanism consists of (i) slow monomer, i.e., the zerovalent transition-metal atom (B 1 ) production due to reduction reaction A → B 1 of a metal precursor (A), usually a transition-metal complex coordination compound, (ii) fast autocatalytic reduction reaction A+B i → B i+1 taking place on the surface of growing metal nanoparticles, consisting of i atoms (B i ), and (iii) process of coagulation B i + B j ⇄ B i+j , reversible or otherwise. In the original WF scheme [4], step (iii) had not been considered. Irreversible coagulation was first introduced in [5].For the transition metals in which higher oxidation states are present, e.g. Au, at least one additional preliminary step of the form (iv) P → A is needed [9][10][11][12][13].As an excess of the reducing agent is usually used in the reactions (i), (ii), (iv), its concentration is fairly timeindependent, and all chemical reactions may be treated as irreversible. Furthermore, (i) and (iv) may be treated as reactions of pseudo-first order, while (ii) as a reaction of pseudo-second order.The WF mechani...

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Change of scaling and appearance of scale-free size distribution in aggregation kinetics by additive rules

Gordienko

2014

Physica A: Statistical Mechanics and its Applications

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The idealized general model of aggregate growth is considered on the basis of the simple additive rules that correspond to one-step aggregation process. The two idealized cases were analytically investigated and simulated by Monte Carlo method in the Desktop Grid distributed computing environment to analyze "pile-up" and "wall" cluster distributions in different aggregation scenarios. Several aspects of aggregation kinetics (change of scaling, change of size distribution type, and appearance of scale-free size distribution) driven by "zero cluster size" boundary condition were determined by analysis of evolving cumulative distribution functions. The "pile-up" case with a minimum active surface (singularity) could imitate piling up aggregations of dislocations, and the case with a maximum active surface could imitate arrangements of dislocations in walls. The change of scaling law (for pile-ups and walls) and availability of scale-free distributions (for walls) were analytically shown and confirmed by scaling, fitting, moment, and bootstrapping analyses of simulated probability density and cumulative distribution functions. The initial "singular" symmetric distribution of pile-ups evolves by the "infinite" diffusive scaling law and later it is replaced by the other "semi-infinite" diffusive scaling law with asymmetric distribution of pile-ups. In contrast, the initial "singular" symmetric distributions of walls initially evolve by the diffusive scaling law and later it is replaced by the other ballistic (linear) scaling law with scale-free exponential distributions without distinctive peaks. The conclusion was made as to possible applications of such approach for scaling, fitting, moment, and bootstrapping analyses of distributions in simulated and experimental data.

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Kinetics of migration-driven aggregation processes

Cited by 48 publications

References 15 publications

Kinetics of jobs in multi-link cities with migration-driven aggregation process

Kinetics of jobs in multi-link cities with migration-driven aggregation process

Exact solutions of kinetic equations in an autocatalytic growth model

Change of scaling and appearance of scale-free size distribution in aggregation kinetics by additive rules

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