目     录
摘     要 3
Abstract 4
第一章     物理理论基础 6
第一节  引言 6
第二节   Monte Carlo方法的基本思想 6
第三节  统计理论基础 7
第四节   高分子统计物理基础 8
一、 高分子链方格子模型 8
二、 高分子链的抽样方法 9
第五节    标度理论基础 10
第六节  Fokker-Planck方程 10
第七节    Arrhenius方程 11
第二章 模型与算法 13
第一节  四位置模型及键涨落算法 13
一、引言 13
二、算法概述 13
三、  对四位置模型的改进及具体算法 14
第二节  受限高分子穿越纳米通道模型及键涨落算法的应用 17
一、引言 17
二、模型描述 17
三、  具体算法 18
第三节   算法的并行化处理 21
一、引言 21
二、并行键涨落算法 21
第三章  模拟结果与讨论 23
第一节   逃逸时间τ随纳米管长度L的变化 23
第二节   逃逸时间τ随链单元数N的变化 28
第三节  结论 31
第四章     与解析理论的比较 33
第一节   相同条件下理想高斯链的解析结果 33
第二节  模拟与解析结果的比较 34
参考文献 35

摘     要
人类文明经过几千年的演化发展，在自然科学的诸多领域都取得了辉煌的成就，但是涉及到人类自身奥秘的学科——生物学，却有许多未解之谜，因此它也成为当今最有活力的学科之一，其中最引人注目的一个问题就是DNA，RNA等分子在细胞中的动力学行为。
这一问题的研究可以带来如下成果进展：首先，受限高分子的性质在许多生物过程中是非常重要的，可以作为细胞中复杂的传输机理研究的一部分，对生命至关重要；其次，几何限制如何影响高分子的动力学行为是一个很有趣的统计力学问题；最后，人们可以利用逐渐成熟的纳米结构及纳米流体结构理论随意操纵人造受限环境，从而直接观察高分子在其中的动力学行为，这样的研究有助于我们更深入得理解高分子的静态及动态性质。同时，当受限空间的尺度与高分子的回转半径相当时，由于所能取得的构象受到制约，高分子将会表现出与在溶液状态下完全不同的动力学行为。
基于上述原因，人们已经从实验及解析理论方面对受限高分子的动力学行为进行了研究，然而由于实验技术的限制及排除体积的影响，详细而准确的信息却无从得到。而计算机模拟可以同时弥补解析理论与实验中的不足，因此我们将在本文中重点强调。
本文分四个部分：首先讨论了研究单链高分子在受限空间中的动力学问题的物理理论基础；第二部分给出了计算机模拟所用的键长涨落算法(bond fluctuation algorithm)及其相应的改进；第三部利用Metropolis Monte Carlo动力学方法结合上面改进的算法，模拟了二维条件下的单链高分子穿越纳米管道，从一方形空间进入另一方形空间的动力学过程，得到了穿越过程中的各个阶段所需时间以及总的穿越时间与纳米管长度以及高分子链长的关系；最后与相同条件下的高斯链穿越过程的理论解析结果进行了比较。
本文充分体现了物理学，计算机等科学在分子生物学和高分子物理研究中的意义，显示了交*学科旺盛的生命力。

Abstract
Human beings have acquired illustrious accomplishments in many fields of natural science through millennia evolution of human civilization, but there has been many ill-defined enigmas in biology, a vital subject involved the secrets of human beings selves, in which one of the most interesting questions is that how the polymer as DNA and RNA moves in confined environments.
Some of the motivations of this interest are as follows. First, the properties of polymers in confined environments are very important in many biological processes. It is of vital importance to life, as being part of complicated transport machinery in the cell. Secondly, how the geometrical constraints affect the dynamics of polymers is an interesting problem of statistical mechanics. Thirdly, with the advance in nanofabrication and nanometer-scale fluidic structures, one can manufacture various artificial confined environments to observe the dynamical behaviors of polymers at single-chain level directly. Such direct observations have provided us with a deeper understanding of the static and dynamic properties of single polymer chain. When the typical length scales of the confinement are of the order with the dimension of an enclosed polymer, it is expected to introduce new behavior due to the prohibition of conformations that would otherwise be available to a molecule free in solution.
So, the single-chain polymer dynamical properties in confined environments have been studied by using experimental perspectives and theoretical approaches, though, from which detailed and precise results cannot be obtained because of the limit of experimental technology and the influence of excluded volume. However, computer simulation could offset these deficiencies, with which we emphasize on studying such a dynamical process in this paper.
This paper contains four parts: First, we discuss the physical basis of confined polymer dynamics; Secondly, we obtain the bond fluctuation algorithm and its amelioration; Thirdly, combined  Metropolis Monte Carlo dynamical method with bond fluctuation algorithm, the dynamical translocation process of a single chain with excluded volume through a nanometer-scale pore from a square to the other in two dimensions is simulated. Explicit relations are derived for the dependence of the mean translocation time on pore length and chain length; Finally, compared with the analytical theory of Gaussian chain under the same condition.
The significance of physics and computer in molecular biology and polymer is represented in this paper, which reveals the bloomy vitality of cross subjects.

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