THE NEAR-CRITICAL AND SUPER-CRITICAL ASYMPTOTIC BEHAVIOR IN THE THERMODYNAMIC LIMIT OF REVERSIBLE RANDOM POLYMERIZATION PROCESSES

作     者：韩东 Han Dong (Department of Mathematics, University of Xinjiang, Urumqi 830046, China)

作者机构：Department of Mathematics University of Xinjiang Urumqi 830046 China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2000年第20卷第3期

页      面：380-389页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：supported in part by National NaturalScience Foundation of China!196610O3 

主　　题：polymerization Markov process limit behavior stationary distribution 

摘      要：In this paper, the near-critical and super-critical asymptotic behavior of a reversible Markov process as a chemical model for polymerization was studied. The results of the present paper, together with an analysis of the sub-critical stage, establish the existence of three distinct stages (sub-critical, near-critical and super-critical stages) of polymerization (in the thermodynamic limit as N -- +infinity,),depending on the value of strength of the fragmentation reaction. These three stages correspond to the size of the largest length of polymers of size N to be itself of order log N, Nm/m+1 (m greater than or equal to 2, m not equal 4n, n greater than or equal to 1) and N, respectively.