Physical Knots

研究者和他的同事们研究“物理结”，弥合了纯粹拓扑性质的结和链接与物理现实系统之间的差距，在物理现实系统中，厚度、曲率、排斥力和随机性等特性是显而易见的。重点领域包括：了解在不同种类的系统中，随机缠结是如何随着纤维长度的增加而增加的；确定结点最优构象的存在性、唯一性和几何性质DNA结环凝胶电泳模型；了解结的“对称能量”如何模拟物理行为，如分子对酶的可及性和发出的细丝的自辐照；确定各种结能之间的关系；了解结，如折叠蛋白质，是如何在末端自由的细丝中形成的。该项目有助于理解物质行为的基本方式之一：固体物体占据空间；一张材料将空间的一部分与另一部分隔开；一根弦与自己或其他弦纠缠在一起。越来越多的科学家意识到，打结和缠结在任何尺度上都会发生，并且在物理上都很重要，从DNA和其他聚合物这样的分子到太阳的磁力线。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破坏的？当一个人把绳结拉紧时会发生什么？为什么数学上不同种类的结在物理情况下的行为方式不同？我们如何在计算机上模拟绳结，计算机模拟在多大程度上反映了实际行为？这一现象的重要性与大量悬而未决的问题相结合，使这一领域具有吸引力和研究价值。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分子行为的理解，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.