Interplay of Topology and Geometry in Polymeric Critical Phenomena

该项目旨在对DNA等复杂聚合物中的关键拓扑驱动行为产生新的理解。长链聚合物丰富的几何行为以及它们如何随着环境的变化而改变形状的数学模型为我们理解这些无处不在的分子提供了一个框架。环状聚合物和DNA等复杂聚合物表现出打结和连接等拓扑性质。最近扭曲DNA的实验显示了由拓扑和几何性质相互作用而产生的新现象。利用先进的数学和计算技术，该项目旨在解释拓扑约束和变化如何干扰关键的聚合物行为。

This project aims to develop new understanding of key topologically driven behaviour in complex polymers such as DNA. The mathematical modelling of the rich geometric behaviour of long-chain polymers and how they change their shape in response to the environment has provided a framework for our understanding of these ubiquitous molecules. Complex polymers such as ring polymers and DNA display topological properties such as knotting and linking. Recent experiments twisting DNA demonstrate novel phenomena precipitated by the interplay of topological and geometric properties. Using advanced mathematical and computational techniques, the project aims to explain how topological constraints and changes disturb key polymer behaviour.