KE Jian-Hong1,2, LIN Zhen-Quan1, CHEN Xiao-Shuang2
¹School of Physics and Electronic Information, Wenzhou University, Wenzhou 325027
²National Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083
A Solvable Symbiosis-Driven Growth Model
KE Jian-Hong1,2;LIN Zhen-Quan1;CHEN Xiao-Shuang2
¹School of Physics and Electronic Information, Wenzhou University, Wenzhou 325027
²National Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083
Abstract： We introduce a two-species symbiosis-driven growth model, in which two species can mutually benefit for their monomer birth and the self-death of each species simultaneously occurs. By means of the generalized rate equation, we investigate the dynamic evolution of the system under the monodisperse initial condition. It is found that the kinetic behaviour of the system depends crucially on the details of the rate kernels as well as the initial concentration distributions. The cluster size distribution of either species cannot be scaled in most cases; while in some special cases, they both consistently take the universal scaling form. Moreover, in some cases the system may undergo a gelation transition and the pre-gelation behaviour of the cluster size distributions satisfies the scaling form in the vicinity of the gelation point. On the other hand, the two species always live and die together.
2006, Vol. 23 
