Physical Knots

这位研究人员和他的同事们研究“物理结”，弥合了结和链的纯拓扑属性与物理现实系统之间的差距，在物理现实系统中，厚度、曲率、排斥力和随机性等属性是显而易见的。重点领域包括：理解不同类型系统中随机缠结如何随纤维长度增加；确定打结的最佳构象的存在、唯一性和几何性质；模拟打结的DNA环；理解打结的“对称能量”如何模拟物理行为，如分子对酶的可及性和发射的细丝的自我照射；确定各种打结能量之间的关系；理解打结，如折叠蛋白质，如何在有自由端的细丝中形成打结。这个项目有助于理解物质的基本行为方式之一：固体占据空间；一张材料将空间的一部分与另一部分分开；一根弦与自身或其他弦缠绕在一起。越来越多的科学意识到打结和纠缠是发生的，并且在任何大小的物理上都是重要的，从DNA和其他聚合物之类的分子到太阳中的磁力线。但还有许多基本问题尚未得到解答：在不同的环境中，结和缠结是如何产生或销毁的？当一个人拉紧一个结时会发生什么？为什么数学上不同种类的结在物理情况下的表现方式不同？我们如何在计算机上模拟结，以及计算机模拟在多大程度上反映了实际行为？这一现象的重要性，加上大量悬而未决的问题，使这一领域令人着迷，具有研究价值。特别是，该项目寻求为国家利益领域做出贡献，包括增加对DNA分子行为的了解，并帮助阐明蛋白质折叠的过程。

The investigator and his colleagues study "Physical Knots," bridging the gap between purely topological properties of knots and links, and physically realistic systems in which properties such as thickness, curvature, repelling forces, and randomness are evident. Focus areas include: understanding how random tangling increases with filament length in different kinds of systems; determining existence, uniqueness, and geometric properties of optimal conformations of knots; modeling gel electrophoresis of knotted DNA loops; understanding how the "symmetric energy" of knots models physical behavior such as accessibility of molecules to enzymes and self-irradiation of filaments that emit; determining relationships between various knot energies; understanding how knots, such as folding proteins, form in filaments with free ends.This project contributes to the understanding of one of the fundamental ways that matter behaves: a solid object occupies space; a sheet of material separates one part of space from another; and a string tangles with itself or other strings. There is growing scientific awareness that knotting and tangling happen, and are physically important, at every scale of size, from molecules such as DNA and other polymers, to magnetic field lines in the sun. But there are many basic questions that are not yet answered: How are knots and tangles created, or destroyed, in various settings? What happens when one pulls a knot tight? Why do mathematically different kinds of knots behave the way they do in physical situations? How can we model knots on the computer, and how well do the computer simulations reflect actual behavior? The combination of importance of the phenomenon, together with substantial open questions, makes this area fascinating and valuable for research. In particular, the project seeks to contribute to areas of national interest, including increasing understanding of the behavior of DNA molecules, and helping to elucidate the process of protein folding.