Studies On Dynamic Models Of Migration-driven Aggregate Growth And Their Numerical Simulations

Migration-driven growth of aggregation is an importantphenomenon in the nature, social and economic system. We mainly studydynamic behaviors of the entire, partial and monomer migrationprocesses, and also discuss the effect of fitness on the dynamic evolutionbehaviors.In this system, when two clusters meet, one or several, even all ofparticles may migrate from one group to another. When choosing thetarget node, one can decide the preference based on its size or its fitness.Kinetics of migration-driven aggregate growth processes is investigatedby Monte-Carlo simulations. Then the cluster concentration C (t), thecluster size distribution a s(t)and the cumulative cluster concentration P(s) are discussed. The main research contents of this thesis are shown below.Firstly, the dynamic models of entire, partial and monomermigration process and then analyze the dynamics of these migrationmodels are introduced. The influence of the network topology on thesystem dynamics is also investigated. The results are listed as follows.(1)For the entire, partial and monomer migration system on the globalcoupling network，the cluster concentration always takes the power-lawform,C (t)~t, and the cluster size distribution obeys the traditionalscaling law: a()~w ttsf(s/tzs). Moreover, for entire migration, thepower-law exponent and the diffusion exponent q have the relationas follows:1/q. The power-law exponent of the partial migrationsystem decreases with the increase of migration exponent, while thepower-law exponent of the monomer migration is the smallest, which isclose to that of the partial migration system with3.(2) For entire,partial and monomer migration process on regular and BA scale-freenetworks, the cluster concentration has no longer the power-low form,and after long-time evolution, the cluster concentration will decrease to asteady value, due to the fact that each non-empty site is surrounded byempty neighboring sites and migration cannot occur any more.Secondly, the influence of fitness on the evolution behaviors ofmigration systems is discussed. When initial fitness distribution isGaussian distribution, the cluster concentration for the migration system on the global coupling network satisfies the power-law form, and theclusters size distribution obeys the scaling law. But for migration oncomplex network, the cluster concentration is no longer of the scaling law.Especially, for the migration system on the BA scale-free network, thecluster concentration as a function of cluster size takes approximately thepower-law forma~s swith3.3. When the initial fitness distributionsatisfies the uniform distribution, for the migration system on the globalcoupling network, the cluster concentration satisfies the power law onlyin the case of the migration barrier c00, and it no longer follows thepower-law relationship with the increase ofc0.In the end, the brief summary and outlook of our investigations aregiven.