权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

A hybrid Monte Carlo algorithm for simulating phase transitions in dense polymer systems

用于模拟致密聚合物系统相变的混合蒙特卡罗算法

基本信息

批准号：
EP/L026708/1
负责人：
Thomas Prellberg
金额：
$ 33.36万
依托单位：
Queen Mary University of London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2014
资助国家：
英国
起止时间：
2014 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FL026708%2F1
关键词：
hybrid Monte Carlo algorithm simulating

项目摘要

Lattice models of polymers such as the model of self-avoiding walks (SAW) on a regular lattice have been at the forefront of research in statistical mechanics for more than half a century; they have been of interest to chemists, physicists, and mathematicians alike. Indeed, the Encyclopædia Britannica gives SAW as one of two examples of classical combinatorial problems. Recent work on SAW includes a rigorous mathematical study by Fields medallist Stanislav Smirnov. Polymer models incorporating more realistic effects, such as internal structure and interactions, are considerably harder to analyse. Normally not even the existence of the thermodynamic limit is proven, and one focusses either on computer simulations or on the study of somewhat simplified models that allow explicit solutions for the partition function, while still generally showing very complicated structures. I propose to combine cutting-edge algorithms in the areas of Monte-Carlo simulations, thereby developing a novel hybrid algorithm suitable for the simulation of compact polymers in spatially restricted environments, with the aim of investigating behaviour of polymers in dense environments or at low temperatures. Prominent examples are given by polymer crystallisation or the folding of proteins. This project crosslinks many different disciplines, ranging across Mathematics, Chemistry, and Biology, and the techniques developed within the context of lattice polymers will have an impact reaching far beyond this setting: the proposed algorithm development will be of benefit for general rare-event simulations in the context of complexity theory.

半个多世纪以来，聚合物的晶格模型（如规则晶格上的自回避行走模型（SAW））一直处于统计力学研究的前沿;化学家、物理学家和数学家都对它们感兴趣。事实上，《大英百科全书》将SAW作为经典组合问题的两个例子之一。SAW最近的工作包括菲尔兹奖获得者Stanislav Smirnov的严格数学研究。聚合物模型包含更真实的效果，如内部结构和相互作用，要分析起来要困难得多。通常情况下，甚至没有热力学极限的存在被证明，并且人们专注于计算机模拟或研究稍微简化的模型，这些模型允许显式求解配分函数，同时通常仍然显示非常复杂的结构。我建议联合收割机尖端的算法在蒙特-卡罗模拟领域，从而开发一种新的混合算法，适合于在空间受限的环境中的紧凑的聚合物的模拟，其目的是调查在密集的环境中或在低温下的聚合物的行为。突出的例子是聚合物结晶或蛋白质折叠。该项目交叉了许多不同的学科，包括数学，化学和生物学，在晶格聚合物的背景下开发的技术将产生远远超出此设置的影响：所提出的算法开发将有利于复杂性理论背景下的一般稀有事件模拟。