Open AccessKinetics of two-species aggregation-annihilation processes on globally coupled networks
Author(s) -
Biao Zhu,
Pingping Li,
Jianhong Ke,
Lin Zhen-Quan
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.066802
Subject(s) - annihilation , scaling , physics , cluster (spacecraft) , power law , diffusion , kinetics , node (physics) , distribution (mathematics) , scaling law , cluster size , statistical physics , thermodynamics , combinatorics , molecular dynamics , quantum mechanics , statistics , mathematics , computer science , mathematical analysis , geometry , programming language
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- and g(t)t-, with the exponents and satisfying =2 and =2/(2 + q); meanwhile, the cluster size distribution can take the scaling form ak(t)=k-t-(k/tz), where -1.27q, (3 + 1.27q)/(2 + q) and z=/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-, where =1/(1 + q), and the cluster size distribution of the heavy species can obey the scaling law at large time, ak(t)=k-t-\varPhi (k/tz), with the scaling exponents -1.27q, (2 + 1.27q)/(1 + q) and z==1/(1 + q). The simulation results accord well with the reported theoretic analyses.