Bimolecular chemical reactions on weighted complex networks.
We investigate the kinetics of bimolecular chemical reactions A+A→0 and A+B→0 on weighted scale-free networks (WSFNs) with degree distribution P(k)∼k^{-γ} . On WSFNs, a weight w{ij} is assigned to the link between node i and j . We consider the symmetric weight given as w{ij}=(k{i}k{j})^{μ} , where k{i} and k{j} are the degree of node i and j . The hopping probability T{ij} of a particle from node i to j is then given as T{ij}∝(k{i}k{j})^{μ} . From a mean-field analysis, we analytically show in the thermodynamic limit that the kinetics of A+A→0 and A+B→0 are identical and there exist two crossover μ values, μ{1c}=γ-2 and μ{2c}=(γ-3)/2 . The density of particles ρ(t) algebraically decays in time t as t^{-α} with α=1 for μ<μ{2c} and α=(μ+1)/(γ-μ-2) for μ{2c}≤μ<μ{1c} . For μ≥μ{1c} , ρ decays exponentially. With the mean-field rate equation for ρ(t) , we also analytically show that the kinetics on the WSFNs is mapped onto that on unweighted SFNs with P(k)∼k^{-γ^{'}} with γ^{'}=(μ+γ)/(μ+1) .
Kwon
Sungchul
S
Department of Physics and Research Institute of Basic Sciences, Kyung Hee University, Seoul, Korea.
Choi
Woosik
W
Kim
Yup
Y
D001704:Biopolymers / Q000737:chemistry* / Q000378:metabolism*; D003198:Computer Simulation; D007700:Kinetics; D008954:Models, Biological; D008956:Models, Chemical; D015398:Signal Transduction / Q000502:physiology*
D001704:Biopolymers