Kinetics of two-species aggregation-annihilation processes on globally coupled networks
全局耦合网络上的两种类集团的聚集-湮没反应动力学

Kinetics of diffusion-limited aggregation-annihilation process on globally coupled networks is investigated by the Monte Carlo simulation.In the system,when two clusters of the same species meet at the same node,they will aggregate and form a larger one; while if two clusters of different species meet at the same node,they will annihilate each other.The simulation results show that,（i） if the two species have equal initial concentrations,the concentration of clusters c（t） and the concentration of particles g（t） follow power laws at large time,c（t）～t-α and g（t）～t-β,with the exponentsαandβsatisfying a = 2/3 and a = 2/（2 + q）;meanwhile, the cluster size distribution can take the scaling form aκ（t） = k-τtωΦ（κ/tz）,where r≈-1.27q,ω≈（3 + 1.27q）/（2 + q） and z =α/2 = 1/（2 + q）;（ii） if the two species have different initial concentrations,the cluster concentration of the heavy species ca（t） follows the power law at large time,cA（t）～t-α,whereα= 1/（1 + q）,and the cluster size distribution of the heavy species can obey the scaling law at large time,aκ（t） = k-τt-ωΦ（k/tz）,with the scaling exponentsτ≈-1.27q,ω≈（2 + 1.27q）/（1 + q） and z =α= 1/（1 + q）.The simulation results accord well with the reported theoretic analyses.