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Kinetics of Migration-Driven Aggregation Process on Complex Networks

Author: ZhuBiao
Tutor: KeJianHong
School: Wenzhou University
Course: Condensed Matter Physics
Keywords: complex networks migration-driven Monte Carlo simulation kinetic behavior scaling law
CLC: O157.5
Type: Master's thesis
Year: 2011
Downloads: 41
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Abstract


The phenomenon of migration-driven aggregation processes underlies in nature and social science, which has become a hot topic of nonequilibrium statistical physics in the last few decades. In this paper, we investigated the kinetics of migration-driven aggregation processes on complex networks. By studying the kinetic behaviors of migration-driven aggregation processes on regular network, small-world network, scale-free network and globally coupled network, respectively, we discussed the effect of the topological characteristics of the network on reaction kinetics. The paper is organized as follows:In Chapter 1, we introduced several typical complex network models and their static characteristics. At the same time, we introduced the history of several migration-driven aggregate models and some recent research progress. In Chapter 2, we devoted to studying whole migration processes of aggregates on regular network, small-world network, scale-free network and globally-coupled network, respectively. Simulation results show that: (i) For whole migration processes on regular network, the concentration of clusters c(t) follows power laws at large times, moreover, the exponent is found to satisfyα=d/(2+qd) for d≤2 andα=1/(1+q) for d>2.Therefore, irreversible whole migration processes are of a critical dimension dc(dc=2); (ii)For whole migration processes on small-world networks, the concentration of clusters c(t) follows power laws at large times if the value of p (a parameter that quantifies the number of shortcuts) is large or small enough; while, if p is of medium value, the concentration of clusters doesn’t follow power laws exactly; (iii)For whole migration processes on scale-free network and globally coupled network, simulation results show that the concentration of clusters always takes power-law form. Moreover, the aggregate-size distribution ak(t) in whole migration systems on the above-mentioned networks obeys the scaling law. In Chapter 3, we devoted to studying irreversible monomer migration processes on globally coupled network and analyzed monomer neighbor-migration on complex networks qualitatively. For monomer migration-driven aggregation on global coupled networks, simulation results show that for the system with the initial monodisperse distribution and biased migration, the concentration of clusters c(t) takes power laws form and the aggregate-size distribution ak(t) obeys the scaling law ifξ≥η. For complex network neighbors dynamic behavior of single migration process,the concentration of clusters decreases with time but don’t follow power laws, and become a dynamic equilibrium finally. For the same network, the greater theη,the less concentration of clusters in the system; For the sameη, the concentration of clusters fall some more in the scale-free network. In the last chapter, we summarize the results of the paper.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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