Optimal Geometry: Theory and Computation
最佳几何形状:理论与计算
基本信息
- 批准号:0071520
- 负责人:
- 金额:$ 9.75万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2000
- 资助国家:美国
- 起止时间:2000-09-15 至 2004-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Sullivan0071520 The investigator, with his collaborators, studies geometric optimization problems like finding minimum-energy shapes for surfaces and knots in space. They extend their recent classification of embedded constant-mean-curvature surfaces with three ends to the more general case of surfaces with any number of coplanar ends, and also investigate in detail surfaces with truncated ends. In addition, the investigator computes these surfaces numerically, in order, for instance, to create interactive computer graphics. This project uses Willmore's elastic bending energy, and its gradient flow, to discover new minimal surfaces in euclidean and spherical space. The Willmore flow has been recently shown to have short-time solutions, but the investigator considers whether it can fail to have long-time solutions. This project also studies configurations for knots which minimize ropelength, giving new lower bounds for the ropelength of small knots, and new asymptotic bounds on the growth of ropelength with crossing number. Finally, the investigator uses his experience with numerical modeling of curves and surfaces to give new understanding of geometrically natural discretizations for quantities related to curvature. Many real-world problems can be cast in the form of optimizing some feature of a shape; mathematically, these become variational problems for geometric energies. For instance, thin films, like those in foams, usually minimize their area and thus are constant-mean curvature surfaces. Cell membranes are more complicated bilayer surfaces which minimize an elastic bending energy known mathematically as the Willmore energy. Knotted curves achieve an optimal shape when a rope is pulled tight, or if a charged knotted wire repels itself electrostatically; understanding such configurations helps explain the behavior of biological molecules like DNA. This project explores such phsically natural problems, which remain challenging from both theoretical and computational standpoints.
研究人员Sullivan0071520和他的合作者研究几何优化问题,比如为空间中的表面和节点寻找最小能量形状。他们将其最近的三端嵌入常平均曲率曲面的分类扩展到具有任意数目的共面端的曲面的更一般情况,并且还研究了具有截断端的曲面的细节。此外,调查者还对这些表面进行数值计算,以便例如创建交互式计算机图形。该项目利用Willmore的弹性弯曲能及其梯度流,在欧几里得和球面空间中发现新的极小曲面。威尔莫尔流最近被证明有短期解决方案,但调查人员考虑它是否会没有长期解决方案。这个项目还研究了最小化长度的纽结的构型,给出了小结的长度的新的下界,以及关于长度随交叉数增长的新的渐近界。最后,研究人员利用他在曲线和曲面的数值建模方面的经验,对与曲率相关的量的几何自然离散化给予了新的理解。许多现实世界的问题可以转化为形状的某些特征的优化形式;从数学上讲,这些问题变成了几何能量的变分问题。例如,薄膜,如泡沫中的薄膜,通常使其面积最小,因此是恒定平均曲率曲面。细胞膜是更复杂的双层表面,它最大限度地减少了弹性弯曲能量,在数学上称为威尔莫尔能量。当绳索被拉紧时,或者如果带电的打结的电线自我静电排斥,打结的曲线就会达到最佳形状;了解这种配置有助于解释DNA等生物分子的行为。这个项目探索了这样的物理自然问题,从理论和计算的角度来看,这些问题仍然具有挑战性。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
John Sullivan其他文献
Control of posture during tasks representing common work-related postures – a reliability study
代表常见工作相关姿势的任务期间的姿势控制——可靠性研究
- DOI:
10.1080/00140139.2014.994566 - 发表时间:
2015 - 期刊:
- 影响因子:2.4
- 作者:
R. Mani;S. Milosavljevic;John Sullivan - 通讯作者:
John Sullivan
Design of Vibrotactile Feedback and Stimulation for Music Performance
音乐表演的振动触觉反馈和刺激设计
- DOI:
10.1007/978-3-319-58316-7_10 - 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
Marcello Giordano;John Sullivan;M. Wanderley - 通讯作者:
M. Wanderley
MP56-19 COMPARING PLAQUE MORPHOLOGY BETWEEN MEN DEVELOPING PEYRONIE'S DISEASE (PD) AFTER RADICAL PROSTATECTOMY (RP) TO THAT OF DE NOVO PEYRONIE'S DISEASE PATIENTS
- DOI:
10.1016/j.juro.2017.02.1772 - 发表时间:
2017-04-01 - 期刊:
- 影响因子:
- 作者:
John Sullivan;Yanira Ortega;Kelly Chiles;Lawrence Jenkins;John Mulhall - 通讯作者:
John Mulhall
SPERM MOTILITY ON TESTICULAR SPERM EXTRACTION (TESE) SAMPLES DEFINES SPECTRUM OF NORMALCY IN POST-VASECTOMY PATIENTS
- DOI:
10.1016/j.fertnstert.2021.07.909 - 发表时间:
2021-09-01 - 期刊:
- 影响因子:
- 作者:
Amelia Aynaz Khoei;John Sullivan;Oscar Santiago Velazquez-Castro;Peter Ignatius Kenny;Kevin Campbell;Larry I. Lipshultz - 通讯作者:
Larry I. Lipshultz
Preoperative Urine Culture Does Not Reliably Correlate with Intraoperative Stone Culture in Patients Undergoing Endoscopic or Percutaneous Management for Urolithiasis
- DOI:
10.1016/j.jamcollsurg.2019.08.701 - 发表时间:
2019-10-01 - 期刊:
- 影响因子:
- 作者:
John Barlog;John Sullivan;William N. Harris;Jyoti Chouhan;Andrew Winer;John Shields - 通讯作者:
John Shields
John Sullivan的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('John Sullivan', 18)}}的其他基金
Doctoral Dissertation Research in Political Science: Testing Group-Level Differences in Political Decision-Making
政治学博士论文研究:测试政治决策中的群体差异
- 批准号:
0819591 - 财政年份:2008
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Doctoral Dissertation Research in Political Science: The Impact of Expectations of Legislative Processes on Legitimacy Perceptions
政治学博士论文研究:立法过程的期望对合法性认知的影响
- 批准号:
9911620 - 财政年份:2000
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Doctoral Dissertation Research in Political Science: Policy Uncertainly and Attitude Strength in Candidate Evaluations
政治学博士论文研究:政策不确定性和候选人评估中的态度强度
- 批准号:
9905317 - 财政年份:1999
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Theory and Computation of Optimal Geometries
最佳几何理论与计算
- 批准号:
9727859 - 财政年份:1997
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Electronic Networks: Enhancing Civic Life or Diverting Scarce Resources
电子网络:改善公民生活或转移稀缺资源
- 批准号:
9619147 - 财政年份:1997
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Doctoral Dissertation Research: Free Speech or Hate Speech? Democracy, Racism and the Law in France and the United States
博士论文研究:言论自由还是仇恨言论?
- 批准号:
9510522 - 财政年份:1995
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
RUI: Fate of Xenografts in Biomphalaria glabrata (Mollusca: Pulmonata)
RUI:光滑双脐动物(软体动物:肺动物)异种移植物的命运
- 批准号:
9017264 - 财政年份:1991
- 资助金额:
$ 9.75万 - 项目类别:
Continuing Grant
Orleans Physics Resource Teacher In-Classroom Support
奥尔良物理资源教师课堂支持
- 批准号:
8955126 - 财政年份:1990
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Research Initiation: Numerical Solution of Hazardous Waste Containment and Consolidation via Artificial Ground Freezing
研究启动:危险废物人工冻结固结数值解
- 批准号:
8808477 - 财政年份:1988
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Doctoral Dissertation Research in Political Science
政治学博士论文研究
- 批准号:
8712207 - 财政年份:1987
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
相似国自然基金
2019年度国际理论物理中心-ICTP School on Geometry and Gravity (smr 3311)
- 批准号:11981240404
- 批准年份:2019
- 资助金额:1.5 万元
- 项目类别:国际(地区)合作与交流项目
新型IIIB、IVB 族元素手性CGC金属有机化合物(Constrained-Geometry Complexes)的合成及反应性研究
- 批准号:20602003
- 批准年份:2006
- 资助金额:26.0 万元
- 项目类别:青年科学基金项目
相似海外基金
Spheres of Influence: Arithmetic Geometry and Chromatic Homotopy Theory
影响范围:算术几何和色同伦理论
- 批准号:
2401472 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Continuing Grant
Conference: Representation Theory and Related Geometry
会议:表示论及相关几何
- 批准号:
2401049 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
A1-Homotopy Theory and Applications to Enumerative Geometry and Number Theory
A1-同伦理论及其在枚举几何和数论中的应用
- 批准号:
2405191 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
CAREER: Mixing and Equidistribution in Number Theory and Geometry
职业:数论和几何中的混合和均匀分布
- 批准号:
2337911 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Continuing Grant
Exploring Large-Scale Geometry via Local and Nonlocal Potential Theory
通过局部和非局部势理论探索大尺度几何
- 批准号:
2348748 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Stable Homotopy Theory in Algebra, Topology, and Geometry
代数、拓扑和几何中的稳定同伦理论
- 批准号:
2414922 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Representation Theory and Symplectic Geometry Inspired by Topological Field Theory
拓扑场论启发的表示论和辛几何
- 批准号:
2401178 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Representation Theory and Geometry in Monoidal Categories
幺半群范畴中的表示论和几何
- 批准号:
2401184 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Continuing Grant
Conference: Tensor Invariants in Geometry and Complexity Theory
会议:几何和复杂性理论中的张量不变量
- 批准号:
2344680 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Standard Grant
Number theory and geometry behind quantum interaction models
量子相互作用模型背后的数论和几何
- 批准号:
24K16941 - 财政年份:2024
- 资助金额:
$ 9.75万 - 项目类别:
Grant-in-Aid for Early-Career Scientists