Scaling in Rate-Changeable Birth and Death Processes with Random Removals

• 来源期刊: 理论物理通讯(英文版)
• 年，卷（期）: 2009,（1）
• 页码范围: 165-169
• 页数: 5页
• 语种: 英文

摘要

We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I(t)k or lose one monomer at a rate J(t)k, and with a probability P(t) an aggregate of any size is randomly removed. We then analytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I(t)-J(t) as well as the birth rate I(t). The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I(t) - J(t) ≥ P(t) or [J(t) + P(t) - I(t)]t (≌) 0 at t > 1; otherwise, it will become extinct.