Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E ...Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E 74 （2006） 036101] and here we focus on its evolutionary process of phase transition. In order to show how the weighted transport influences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-free networks. We find that there is a hierarchical relaxation dynamics in the evolution and there is a scaling relation between the relaxation time and the jumping exponent. The relaxation dynamics can be illustrated by a mean-field equation. The theoretical predictions are confirmed by our numerical simulations.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos.10475027 and 10635040the Pujiang Project of Shanghai under Grant No.05PJ14036+1 种基金the Shuguang Project of Shanghai under Grant No.05SG27the New Century Excellent Talent Project of the Ministry of Education of China under Grant No.-05-0424
文摘Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E 74 （2006） 036101] and here we focus on its evolutionary process of phase transition. In order to show how the weighted transport influences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-free networks. We find that there is a hierarchical relaxation dynamics in the evolution and there is a scaling relation between the relaxation time and the jumping exponent. The relaxation dynamics can be illustrated by a mean-field equation. The theoretical predictions are confirmed by our numerical simulations.
