自回避行走模型中行走终止效应的研究  

Investigations of the walk termination effect in the self-avoiding walk model

作　　者：张晋鲁[1] 蒋建国[2] 张丽丽[1] 赵兴宇[1] 黄以能[1,2] 

机构地区：[1]伊犁师范学院物理与电子信息学院,凝聚态物理与材料设计研究所,新疆伊宁835000 [2]南京大学物理系,固体微结构实验室,南京210093

出　　处：《南京大学学报（自然科学版）》2010年第4期407-411,共5页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(10774064;30860076);新疆自治区教育厅重点基金(XJUEDU2007137);新疆自治区科技厅重点基金(200721104;200821184);伊犁师范学院重点基金

摘　　要：自回避行走(SAW)模型在线形高分子链的构象、高分子链的缠结效应和电子的局域化等研究领域中有着极为重要的应用.就模型本身的研究而言,主要有两个方面.其一是自回避行走的空间尺度的分布参量(如末端距等)与行走步数的标度规律研究.其二是对行走终止(WT)效应的研究.所谓WT效应指的是,在到达预期的行走步数N之前,由于自回避效应的存在导致行走无法继续下去的情况,而且行走终止步数n(n≤N)存在分布.本文中,首先定义了行走终止过程的分布几率qnN≡k/m,其中m为一个自回避行走系综中由于WT效应导致的没有到达预期的行走步数N的子系综中的自回避行走次数,k为在此子系综中行走终止步数为n的自回避行走次数.其次,对SAW模型的WT效应进行了计算机模拟,研究了qnN与N和n的变化规律.结果表明,对不同的N,qnN都可标度到一条与N无关的主曲线Qn≡CNqnN上,这里CN仅仅与N有关.再标度的行走终止过程的分布几率Qn随n的变大表现出先增加后减小的趋势,即存在一个与Qn最大值相对应的最可几的行走终止步数np.The well-known self-avoiding walk model has many important applications in fields of linear polymer configurations, polymer chain entanglement, and electron localization, etc. The self-avoiding walks means that the further walks cannot intersect with previous contrails. As to the study of the model itself, two aspects are mainly focused on. The primary one is the scaling characteristics of the spatial size of the walk contrail, such as the end-toend distanee, as a function of the set walk steps. And the secondary aspect is the walk termination effect of the model. The so called walk termination effect is that some walk processes are terminated before arriving at the set walk steps N due to the self-avoiding restriction, and it should be expected that the terminated walk steps n （n≤N） is a distributing quantity. In this paper, the walk termination probability P N, of the self-avoiding walks and the termination distribution probability of walk terminated 711 processes are first defined as PN≡ m/M and qN^n≡k/m respectively, where M is the total number of the self avoiding walk ensemble, rn is the number of the sub ensemble in which the walk steps cannot reach the set walk steps N, and k is the self-avoiding walk times with walk terminated steps being n in the sub-ensemble. Moreover, the walk termination effect is simulated by computer on a square lattice of two dimensions, and the variations of PN and qN^n versus both N and n are investigated. The simulated results indicate that there exists a critical walk steps Nc and Nc = 7 for the square lattice of two dimensions. And below Nc, PN is always equal to 0, but it increases monotonically to 1 with the increase of N above Nc, and specifically, PN. increases just a little for N〈10, but goes up rapidly between 20〈N〈100, and tends to 1 for N〉 200. And these behaviors present the definition of a characteristic termination steps of self-avoiding walks NT which corresponds to PN = 0.5, NT= 59 for the two dimensional square lattice. Furthermore and as ex

关 键 词：自回避行走 行走终止效应 行走终止分布几率 

分 类 号：O540[理学—物理]