Physical Knots

物理结

基本信息

  • 批准号:
    0107747
  • 负责人:
  • 金额:
    $ 12.4万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2001
  • 资助国家:
    美国
  • 起止时间:
    2001-10-01 至 2004-09-30
  • 项目状态:
    已结题

项目摘要

Knots are self-entangled filaments. In mathematics, they have been most commonly studied as purely topological objects. But physical knots are knots made of real physical stuff, from rope to DNA or other large flexible molecules; or purely mathematical knots endowed with physical-like properties such as energy or thickness. The goals of physical knot theory are to mathematically model and help understand real physical systems, and to use physically inspired measures of knot complexity to develop novel methods for knot recognition/classification and gain deeper understanding of configuration spaces of knots. The investigator also casts a wider net, looking for connections between physical knot theory and polymer theory, as well as analogies between physical knot theory and other important optimization and configuration problems such as protein folding.Modern laboratory technology lets scientists see the tiniest structures of life. Modern computers let researchers visualize and simulate how the structures interact. This combined technology has helped make geometry and topology an essential tool in medicine, polymers, and other areas of chemistry, physics, and biology. Knotting, or other tangling of filaments, is one of the fundamental ways that matter behaves, and is a key phenomenon in this scientific interaction. Knotting and tangling happen at every scale studied by science, from microscopic DNA loops to everyday rope to tangled magnetic field loops in the solar corona. The investigator, collaborators, and students study fundamental problems that arise in all these physical systems: How are knots and tangles created? What properties of the various systems cause essentially different kinds of knots and tangles? Can the structure be simplified or completely untangled? If so, how? How do the mathematical properties of different kinds of knots or tangles influence physical behavior? The project contributes to the effort of finding good data structures and good manipulation and visualization tools for topological and geometric objects -- essential tools for work in the realm of the very small. These efforts are at the interface of information technology, nanotechnology, and biotechnology. In materials and manufacturing, as well as in biotechnology, the work could have considerable impact by providing effective models of the topological and geometric behavior of polymers in general, and DNA in the specific.
结是自缠绕的细丝。在数学中,它们通常被当作纯粹的拓扑学对象来研究。但物理结是由真实的物理物质组成的结,从绳子到DNA或其他大的柔性分子;或者纯粹的数学结,被赋予类似物理的属性,如能量或厚度。物理节点理论的目标是对真实的物理系统进行数学建模和帮助理解,并使用物理启发的节点复杂性度量来开发新的节点识别/分类方法,从而加深对节点构形空间的理解。研究人员还撒下了更大的网,寻找物理结理论和聚合物理论之间的联系,以及物理结理论和其他重要的优化和构型问题(如蛋白质折叠)之间的类比。现代实验室技术让科学家们看到了生命的最微小结构。现代计算机可以让研究人员可视化并模拟这些结构是如何相互作用的。这种结合的技术使几何和拓扑学成为医学、聚合物以及其他化学、物理和生物学领域的基本工具。打结或细丝的其他缠绕是物质行为的基本方式之一,也是这种科学相互作用中的一个关键现象。打结和纠缠发生在科学研究的每一个尺度上,从微小的DNA环到日常生活中的绳索,再到太阳日冕中纠结的磁场环。研究人员、合作者和学生研究所有这些物理系统中出现的基本问题:结和缠结是如何产生的?不同系统的什么特性导致了本质上不同种类的结和缠结?这个结构能被简化或完全解开吗?如果是这样的话,是如何做到的呢?不同类型的结或缠结的数学特性如何影响物理行为?该项目有助于为拓扑和几何对象寻找良好的数据结构和良好的操纵和可视化工具--这是在非常小的领域工作的基本工具。这些努力是在信息技术、纳米技术和生物技术的界面上进行的。在材料和制造领域,以及在生物技术领域,这项工作通过提供聚合物一般的拓扑和几何行为的有效模型,特别是DNA的拓扑和几何行为,可以产生相当大的影响。

项目成果

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Gregory Buck其他文献

TEMPTED: time-informed dimensionality reduction for longitudinal microbiome studies
  • DOI:
    10.1186/s13059-024-03453-x
  • 发表时间:
    2024-12-19
  • 期刊:
  • 影响因子:
    9.400
  • 作者:
    Pixu Shi;Cameron Martino;Rungang Han;Stefan Janssen;Gregory Buck;Myrna Serrano;Kouros Owzar;Rob Knight;Liat Shenhav;Anru R. Zhang
  • 通讯作者:
    Anru R. Zhang
The collinear central configuration of n equal masses

Gregory Buck的其他文献

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{{ truncateString('Gregory Buck', 18)}}的其他基金

RAPID: Modeling the Host-Microbiome-Virome Interactions and their Impact on COVID-19 Severity.
RAPID:对宿主-微生物组-病毒组相互作用及其对 COVID-19 严重程度的影响进行建模。
  • 批准号:
    2034995
  • 财政年份:
    2020
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Standard Grant
Assembling the Tree of Life: Phylum Euglenozoa
组装生命之树:眼虫门
  • 批准号:
    0830056
  • 财政年份:
    2008
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Continuing Grant
BBSI:The Bioinformatics and Bioengineering Summer Institute at VCU
BBSI:弗吉尼亚联邦大学生物信息学和生物工程暑期学院
  • 批准号:
    0609038
  • 财政年份:
    2006
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Continuing Grant
NIH-NSF BBSI: Virginia Commonwealth University
NIH-NSF BBSI:弗吉尼亚联邦大学
  • 批准号:
    0234101
  • 财政年份:
    2003
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Continuing Grant
NSF Minority Postdoctoral Research Fellowship for FY-1999
1999 财年 NSF 少数族裔博士后研究奖学金
  • 批准号:
    9904152
  • 财政年份:
    1999
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Fellowship Award
Research at Undergraduate Institutions, Collaborative Research: Physical Knot Theory
本科院校研究、合作研究:物理结理论
  • 批准号:
    9706865
  • 财政年份:
    1997
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Standard Grant
Research at Undergraduate Institutions Collaborative Research, Energy Functions for Knots
本科院校合作研究,结的能量函数
  • 批准号:
    9420088
  • 财政年份:
    1994
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Standard Grant
Acquisition of Radioanalytic Imager
收购放射分析成像仪
  • 批准号:
    9016233
  • 财政年份:
    1991
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Standard Grant

相似海外基金

Geodesic arcs and surfaces for hyperbolic knots and 3-manifolds
双曲结和 3 流形的测地线弧和曲面
  • 批准号:
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  • 财政年份:
    2024
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Conference: Richmond Geometry Meeting: Knots, Moduli, and Strings
会议:里士满几何会议:结、模数和弦
  • 批准号:
    2240741
  • 财政年份:
    2023
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    $ 12.4万
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Studies in knots and 3-manifolds
结和 3 流形的研究
  • 批准号:
    RGPIN-2020-05491
  • 财政年份:
    2022
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Discovery Grants Program - Individual
Connections between Algebra and Topology: Using algebraic number theory and TQFTs to study knots
代数与拓扑之间的联系:使用代数数论和 TQFT 研究纽结
  • 批准号:
    559329-2021
  • 财政年份:
    2022
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Knots, Disks, and Exotic Phenomena in Dimension 4
第 4 维中的结、圆盘和奇异现象
  • 批准号:
    2204349
  • 财政年份:
    2022
  • 资助金额:
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MPS-Ascend: Bi-Orderability, Fibered Knots, and Cyclic Branched Covers
MPS-Ascend:双向可排序性、纤维结和循环分支覆盖层
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    2213213
  • 财政年份:
    2022
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Fellowship Award
A study of homological invariants of knots and 3-manifolds
结和3-流形的同调不变量的研究
  • 批准号:
    22K03318
  • 财政年份:
    2022
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Classification of cosmetic surgeries on knots in rational homology spheres
有理同调域中结的整容手术分类
  • 批准号:
    22K03301
  • 财政年份:
    2022
  • 资助金额:
    $ 12.4万
  • 项目类别:
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A new look into various arithmetic and topological invariants through the eyes of modular knots
从模结的角度重新审视各种算术和拓扑不变量
  • 批准号:
    21K18141
  • 财政年份:
    2021
  • 资助金额:
    $ 12.4万
  • 项目类别:
    Grant-in-Aid for Challenging Research (Pioneering)
Collaborative Research: From Quantum Droplets & Spinor Solitons to Vortex Knots & Topological States: Beyond the Standard Mean-Field in Atomic BECs
合作研究:来自量子液滴
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    2110030
  • 财政年份:
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