【作者】 王伟；

【导师】 张长海；

【作者基本信息】 吉林大学 ， 计算机软件与理论， 2006， 硕士

【摘要】 Monte Carlo方法作为一种独立的计算方法渗透到各个科学领域,它并非是一种简单的数值计算方法,而是对实际问题的直接模拟,即根据实际问题的概率法则,用计算机进行抽样实验。在物理,化学等领域中Monte Carlo方法常被称为“计算机模拟”或“计算机实验”,它已经成为自然科学的第三分支,与理论科学和实验科学鼎立。Monte Carlo方法在上世纪50年代应用于高分子科学的研究中,随着计算机技术的发展和性能的提高,如今它的应用几乎涉及高分子科学的各个领域,并继续发挥着重要作用。本文选择Monte Carlo方法在高分子聚集态结构统计科学中的应用为研究方向。全文共七章,第一章是前言,第二章介绍Monte Carlo方法的基础和随机抽样方法,第三章讨论了高分子凝聚模型,介绍了格子模型,并给出了这些模型在计算机上的实现方法,并通过模型计算出聚集速率、粒度分布、回转半径等物理统计量,第四章讨论了分子凝胶模型中重要任务:环识别算法。更多还原

【Abstract】 The major problem of predicting and designing new materials by computer science is theagility of simulation methods. So-called simulation methods are the mathematical modelswhich are devised for complicated and real systems by computer implement. When therelated characters and boundary situation are given, computers can run various operations,simulate experiments, and then research the evolution of system. Computer simulation as animportant technology has been applied in many academic fields, and received a huge amountof fruits, especially when the experiments fail to give out the result concerning the singleatom or molecule motion. Moreover, when the theory is hard to be associated with the naturephenomenon, when the simple approximate method fails to give out the correct result,computer simulation brings the convenience. Monte Carlo method had been applied into the research of polymer as early as 1950s.Currently, Monte Carlo method almost has been applied in every field of polymer researchdue to the development of computer. Unlike the general methods, Monte Carlo method is not a complicated one. It couldtrack the system evaluation without the influence of any condition. Therefore, sometimes itis called experiment of computer simulation. Although Monte Carlo method has beenapplied broadly, it is still hard to give out the comprehensive summary about how toassociate theory with polymer. In this paper, we systemically research the Monte Carlomethod in the polymer aggregation simulation. An important difference between MonteCarlo method and other analysis methods is that there is no analysis method suitable for allsituations, but the programming skill is various. When Monte Carlo method is used to simulate a certain process, it needs all kinds ofpossibility contributions. The most distinguish characteristic of Monte Carlo method is theuse of random number, which is distributed evenly between 0 and 1. In this paper, weimplement a high-quality random number algorithm and a new means to check the quality ofrandom number. In the theory of polymer solution, the impregnant is recognized as the continuousmedium in the space. Then, the space is turned into the discreteness to optimize the ability ofcomputer simulation. The idea of lattice model is that macromolecule unit only could takesome set points in the space. Although the copolymer in the lattice model are different fromthe real ones, some statistics characteristics are not depend on the details of copolymer . Inthis paper, we integrate the DLCA model and Lattice model, and propose a new lattice modelby implementing the simulation method of copolymer. We have to sample the copolymer distribution for getting copolymer statisticparameters through Monte Carlo method. We can get distributing samples those satisfydifferent conditions through sampling. When the sample capacity is big enough, We cancompute the samples to get the average copolymer statistic parameters In this paper, we use Monte Carlo method to simulate the growing process ofcopolymer. When the sample is big enough, the aggregation state of copolymer and thestatistic average value which show various parameters of this state are given by computingover the sample. During the simulation process, those statistic parameters includes: (1)Thecopolymer aggregation rate, the physic mass distribution and area dimension in the growingprocess of copolymer;(2) gyration radius and fractal dimension.Chemical structure could manifest the characteristic of the whole molecular bysumming its main structure characteristics, and also has been the base of chemicaldescription. With the high development of computer, many chemists have turned tocomputer for help. Many chemical structure system based on database managementtechnology(CAS On-line,DARC, GREMAS .etc) have been established. In these systems,all chemical structures have been seen as graphs, atoms as vertex, and chemical hood asmargin. Therefore, the graph concept becomes a useful tool for chemical structure computersystem.One of basic problems of chemical structure computer system is the reorganizationand analysis for ring structure. The statistics of chemical ring is very important formacromolecule copolymer ’s chemical rings. In this paper, we apply the graph concept intothe chemical structure and propose an efficient algorithm for the ring perception.更多还原