Slowdown in the Annihilation of Two Species Diffusion-Limited Reaction on Fractal Scale-Free Networks

In the diffusion-limited reaction process A + B → ∅ on random scale-free networks, particle density decays as ρ(t) ~t − α when ρ A (0) = ρ B (0), where α> 1 for the degree exponent 2 < γ< 3 and α= 1 for γ ≤ 3. We investigate the reaction on fractal scale-free networks numerically, finding ρ(t) decays slowly with the exponent α ≈ d s / 4 < 1, where d s is the spectral dimension of the network.

[1]  L. Gallos,et al.  Influence of a complex network substrate on reaction–diffusion processes , 2007 .

[2]  J S Kim,et al.  Fractality in complex networks: critical and supercritical skeletons. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  L. Gallos,et al.  Absence of kinetic effects in reaction-diffusion processes in scale-free networks. , 2004, Physical review letters.

[4]  Blumen,et al.  Scaling properties of diffusion-limited reactions: Simulation results. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[5]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[6]  Hildegard Meyer-Ortmanns,et al.  Self-similar scale-free networks and disassortativity. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Redner,et al.  Fluctuation-dominated kinetics in diffusion-controlled reactions. , 1985, Physical review. A, General physics.

[8]  S. Havlin,et al.  Self-similarity of complex networks , 2005, Nature.

[9]  R. Pastor-Satorras,et al.  Diffusion-annihilation processes in complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Scaling properties of diffusion-limited reactions on fractal and euclidean geometries , 1991 .

[11]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[12]  Sergei Maslov,et al.  Modularity and extreme edges of the internet. , 2003, Physical review letters.

[13]  Shlomo Havlin,et al.  Origins of fractality in the growth of complex networks , 2005, cond-mat/0507216.

[14]  S. Havlin,et al.  Scaling theory of transport in complex biological networks , 2007, Proceedings of the National Academy of Sciences.

[15]  B. Kahng,et al.  Annihilation of two-species reaction–diffusion processes on fractal scale-free networks , 2008, 0811.2293.

[16]  H. Stanley,et al.  Novel dimension-independent behaviour for diffusive annihilation on percolation fractals , 1984 .

[17]  Soon-Hyung Yook,et al.  Diffusive capture processes for information search , 2007 .

[18]  K-I Goh,et al.  Skeleton and fractal scaling in complex networks. , 2006, Physical review letters.

[19]  Leyvraz,et al.  Spatial structure in diffusion-limited two-species annihilation. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[20]  Z. Burda,et al.  Statistical ensemble of scale-free random graphs. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Markus Porto,et al.  Multicomponent reaction-diffusion processes on complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Shlomo Havlin,et al.  Fractal and transfractal recursive scale-free nets , 2007 .