Estimates on eigenvalues and eigenfunctions in convex settings

凸设置中特征值和特征函数的估计

基本信息

  • 批准号:
    1954304
  • 负责人:
  • 金额:
    $ 10.72万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2020
  • 资助国家:
    美国
  • 起止时间:
    2020-06-01 至 2020-09-30
  • 项目状态:
    已结题

项目摘要

Elliptic differential equations are used to describe a wide variety of physical phenomena. A main goal of this project is to study a particular class of these equations that can be used to model the behavior of vibrations of a drum or an inhomogeneous material, the temperature distribution of a thermal conductor, or the distribution of the random motion of particles moving in a region of fluid. Other than in a few simple model cases, this behavior is still far from understood. By reformulating these problems in terms of partial differential equations, this project will study this behavior. One particular question of interest is how does the shape of a drum influence which part of the drum its vibrations are typically localized to. Another aim is to study free boundary problems. A free boundary is the region separating two different materials, such as the interface between water and the air in the ocean or between an insulating material and the air. The free boundary can be modeled via solving differential equations, and understanding its shape and the scale at which it appears smooth has applications to optimal shape design, electromagnetism, and fluid flow. This project contributes to the development of the US workforce through mentoring of undergraduate students.In this project, the PI will study eigenvalues and eigenfunctions on convex domains in Euclidean space and the sphere. A main goal of the project is to further the understanding of the level sets of the eigenfunction. The starting point is a quantitative property, namely the convexity of the level sets, and the aim is to use and develop techniques from elliptic and differential geometry theory to establish quantitative properties involving their shape and location with the domain. This would lead to understanding the region of the domain where the eigenfunctions localize in cases where no explicit formulae are available. Another part of the project involves variants of the classical Friedland-Hayman inequality concerning eigenvalues on the sphere. This will involve developing tools from convex geometry, isoperimetric inequality theory, and Brenier's optimal transportation mappings. This will be applied to prove regularity properties of minimizers of associated free boundary problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
椭圆微分方程被用来描述各种各样的物理现象。该项目的主要目标是研究这些方程中的一个特定类别,这些方程可用于模拟鼓或非均匀材料的振动行为,热导体的温度分布,或在流体区域中移动的颗粒的随机运动分布。除了在一些简单的模型案例中,这种行为仍然远未被理解。通过将这些问题重新表述为偏微分方程,本项目将研究这种行为。一个特别感兴趣的问题是鼓的形状如何影响其振动通常局限于鼓的哪个部分。另一个目的是研究自由边界问题。自由边界是分隔两种不同材料的区域,例如海洋中水和空气之间的界面或绝缘材料和空气之间的界面。自由边界可以通过求解微分方程来建模,并且了解其形状和其看起来光滑的尺度可以应用于最佳形状设计,电磁学和流体流动。该项目通过对本科生的指导,为美国劳动力的发展做出贡献。在该项目中,PI将研究欧几里德空间和球面中凸域上的特征值和特征函数。该项目的一个主要目标是进一步理解本征函数的水平集。起点是一个定量属性,即水平集的凸性,目的是使用和发展椭圆和微分几何理论的技术,以建立涉及其形状和位置的定量属性。这将导致理解在没有显式公式可用的情况下本征函数局部化的域的区域。该项目的另一部分涉及经典的Friedland-Hayman不等式的变体,涉及球面上的特征值。这将涉及开发工具,从凸几何,等周不等式理论,和Brenier的最佳运输映射。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。

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 }}

Thomas Beck其他文献

Duchon–Robert solutions for the Rayleigh–Taylor and Muskat problems
Rayleigh-Taylor 和 Muskat 问题的 Duchon-Robert 解
  • DOI:
    10.1016/j.jde.2013.09.001
  • 发表时间:
    2012
  • 期刊:
  • 影响因子:
    2.4
  • 作者:
    Thomas Beck;Philippe Sosoe;Percy Wong
  • 通讯作者:
    Percy Wong
Level Set Shape For Ground State Eigenfunctions On Convex Domains
凸域上基态本征函数的水平集形状
  • DOI:
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Thomas Beck
  • 通讯作者:
    Thomas Beck
Left Ventricular End-Diastolic Dimension for the Assessment of the Pulmonary to Systemic Flow Ratio in Congenital Heart Diseases
左心室舒张末期尺寸用于评估先天性心脏病的肺血流与体循环血流比率
  • DOI:
    10.1253/circj.cj-21-0896
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    3.3
  • 作者:
    Yasutaka Fushimi;Tomohisa Okada;Sonoko Oshima;Yusuke Yokota;Hikaru Fukutomi;Gosuke Okubo;Satoshi Nakajima;Akira Yamamoto;Wei Liu;Sinyeob Ahn;Thomas Beck;and Kaori Togashi.;Masutani Satoshi
  • 通讯作者:
    Masutani Satoshi
The isoperimetric inequality for convex subsets of the sphere
球体凸子集的等周不等式
Control of the actin cytoskeleton by extracellular signals.
通过细胞外信号控制肌动蛋白细胞骨架。

Thomas Beck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('Thomas Beck', 18)}}的其他基金

Quantum-Designed Models of Bulk and Interfacial Solvation
体相和界面溶剂化的量子设计模型
  • 批准号:
    1955161
  • 财政年份:
    2020
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Continuing Grant
Estimates on eigenvalues and eigenfunctions in convex settings
凸设置中特征值和特征函数的估计
  • 批准号:
    2042654
  • 财政年份:
    2020
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Continuing Grant
Quantum Models of Ion Solvation Thermodynamics
离子溶剂化热力学的量子模型
  • 批准号:
    1565632
  • 财政年份:
    2016
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant
Theory and Modeling of Specific Ion Solvation in Water and Non-Aqueous Solvents with Applications to Energy Storage
水和非水溶剂中特定离子溶剂化的理论和建模及其在储能中的应用
  • 批准号:
    1266105
  • 财政年份:
    2013
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant
Theory and Modeling of Specific Ion Effects in Chemistry and Biology
化学和生物学中特定离子效应的理论和建模
  • 批准号:
    1011746
  • 财政年份:
    2010
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant
Modeling specific-ion effects in aqueous solutions and ion channels
模拟水溶液和离子通道中的特定离子效应
  • 批准号:
    0709560
  • 财政年份:
    2007
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant
ITR/AP+SY(DMR): Multiscale Quantum Simulations of Electron Transport in Molecular Devices
ITR/AP SY(DMR):分子器件中电子传输的多尺度量子模拟
  • 批准号:
    0112322
  • 财政年份:
    2001
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant
Multigrid Methods for Simulation of Complex Materials
复杂材料模拟的多重网格方法
  • 批准号:
    9632309
  • 财政年份:
    1996
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Continuing Grant
Theory of Tethered Polymer-Solution Interfaces and Quantum Impurities
系留聚合物溶液界面和量子杂质理论
  • 批准号:
    9225123
  • 财政年份:
    1993
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Continuing Grant
An Interdisciplinary Design and Manufacturing Laboratory
跨学科设计和制造实验室
  • 批准号:
    9250928
  • 财政年份:
    1992
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant

相似海外基金

LEAPS-MPS: Investigation on Spectral Geometry of Steklov Eigenvalues
LEAPS-MPS:Steklov 特征值的谱几何研究
  • 批准号:
    2316620
  • 财政年份:
    2023
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant
Distribution of Hecke eigenvalues for automorphic representations
自守表示的 Hecke 特征值分布
  • 批准号:
    RGPIN-2021-03032
  • 财政年份:
    2022
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Discovery Grants Program - Individual
Analysis on spectral and embedded eigenvalues for non-local Schrodinger operators
非局部薛定谔算子的谱和嵌入特征值分析
  • 批准号:
    21KK0245
  • 财政年份:
    2022
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Fund for the Promotion of Joint International Research (Fostering Joint International Research (A))
Fluctuations of random matrix eigenvalues and disordered systems
随机矩阵特征值的涨落和无序系统
  • 批准号:
    RGPIN-2022-03118
  • 财政年份:
    2022
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Discovery Grants Program - Individual
Fluctuations of random matrix eigenvalues and disordered systems
随机矩阵特征值的涨落和无序系统
  • 批准号:
    DGECR-2022-00435
  • 财政年份:
    2022
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Discovery Launch Supplement
Far apart: outliers, extremal eigenvalues, and spectral gaps in random graphs and random matrices
相距较远:随机图和随机矩阵中的异常值、极值特征值和谱间隙
  • 批准号:
    2154099
  • 财政年份:
    2022
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Standard Grant
Gaps between Robin and Neumann eigenvalues
Robin 和 Neumann 特征值之间的差距
  • 批准号:
    562327-2021
  • 财政年份:
    2021
  • 资助金额:
    $ 10.72万
  • 项目类别:
    University Undergraduate Student Research Awards
Eigenvalues of Stochastic Matrices with Prescribed Stationary Distribution
具有规定平稳分布的随机矩阵的特征值
  • 批准号:
    564391-2021
  • 财政年份:
    2021
  • 资助金额:
    $ 10.72万
  • 项目类别:
    University Undergraduate Student Research Awards
Distribution of Hecke eigenvalues for automorphic representations
自守表示的 Hecke 特征值分布
  • 批准号:
    DGECR-2021-00121
  • 财政年份:
    2021
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Discovery Launch Supplement
Distribution of Hecke eigenvalues for automorphic representations
自守表示的 Hecke 特征值分布
  • 批准号:
    RGPIN-2021-03032
  • 财政年份:
    2021
  • 资助金额:
    $ 10.72万
  • 项目类别:
    Discovery Grants Program - Individual
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了