Dynamics of Nonlinear and Disordered Systems
非线性和无序系统的动力学
基本信息
- 批准号:2350356
- 负责人:
- 金额:$ 46.02万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2024
- 资助国家:美国
- 起止时间:2024-06-01 至 2027-05-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Observations of solitary waves that maintain their shape and velocity during their propagation were recorded around 200 years ago. First by Bidone in Turin in 1826, and then famously by Russell in 1834 who followed a hump of water moving at constant speed along a channel for several miles. Today these objects are known as solitons. Lying at the intersection of mathematics and physics, they have been studied rigorously since the 1960s. For completely integrable wave equations, many properties of solitons are known, such as their elastic collisions, their stability properties, as well as their role as building blocks in the long-time description of waves. The latter is particularly important, as it for example predicts how waves carrying information decompose into quantifiable units. In quantum physics, quantum chemistry, and material science, these mathematical tools allow for a better understanding of the movement of electrons in various media. This project aims to develop the mathematical foundations which support these areas in applied science, which are of great importance to industry and society at large. The project provides research training opportunities for graduate students.The project’s goal is to establish both new results and new techniques in nonlinear evolution partial differential equations on the one hand, and the spectral theory of disordered systems on the other hand. The long-range scattering theory developed by Luhrmann and the Principal Investigator (PI) achieved the first results on potentials which exhibit a threshold resonance in the context of topological solitons. This work is motivated by the fundamental question about asymptotic kink stability for the phi-4 model. Asymptotic stability of Ginzburg-Landau vortices in their own equivariance class is not understood. The linearized problem involves a non-selfadjoint matrix operator, and the PI has begun to work on its spectral theory. With collaborators, the PI will engage on research on bubbling for the harmonic map heat flow and attempt to combine the recent paper on continuous-in-time bubbling with a suitable modulation theory. The third area relevant to this project is the spectral theory of disordered systems. More specifically, the PI will continue his work on quasiperiodic symplectic cocycles which arise in several models in condensed matter physics such as in graphene and on non-perturbative methods to analyze them.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.
在传播过程中保持其形状和速度的孤立波的观测记录在大约200年前。首先是1826年在都灵的比多内,然后是1834年著名的罗素,他沿着沿着一条通道以恒定速度移动的一个驼峰走了几英里。今天,这些物体被称为孤子。它们位于数学和物理的交叉点,自20世纪60年代以来一直受到严格的研究。对于完全可积的波动方程,孤立子的许多性质都是已知的,例如它们的弹性碰撞、它们的稳定性特性以及它们在波的长期描述中作为构建块的作用。后者尤其重要,因为它可以预测携带信息的波如何分解成可量化的单位。在量子物理学、量子化学和材料科学中,这些数学工具可以更好地理解电子在各种介质中的运动。该项目旨在开发支持应用科学这些领域的数学基础,这些领域对工业和整个社会都非常重要。该项目为研究生提供研究训练机会。该项目的目标是一方面建立非线性发展偏微分方程的新结果和新技术,另一方面建立无序系统的光谱理论。由Luhrmann和主要研究者(PI)开发的长程散射理论在拓扑孤子的背景下首次获得了关于表现出阈值共振的势的结果。这项工作的动机是基本问题的φ-4模型的渐近扭结稳定性。Ginzburg-Landau涡在它们自己的等方差类中的渐近稳定性还不清楚。线性化问题涉及非自伴矩阵算子,PI已经开始研究其谱理论。与合作者一起,PI将从事谐波映射热流的起泡研究,并尝试将最近关于连续时间起泡的论文与合适的调制理论联合收割机结合起来。第三个与这个项目有关的领域是无序系统的光谱理论。更具体地说,PI将继续他在凝聚态物理学(如石墨烯)的几个模型中出现的准周期辛上循环以及分析它们的非微扰方法方面的工作。该奖项反映了NSF的法定使命,并通过使用基金会的智力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)
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Wilhelm Schlag其他文献
Correction to: On Localization and the Spectrum of Multi-frequency Quasi-periodic Operators
- DOI:
10.1007/s10013-025-00736-z - 发表时间:
2025-03-27 - 期刊:
- 影响因子:0.700
- 作者:
Michael Goldstein;Wilhelm Schlag;Mircea Voda - 通讯作者:
Mircea Voda
石英のESR信号強度と結晶化度によるタクラマカン砂漠における砂の供給源と運搬システムの解明
基于ESR信号强度和石英结晶度阐明塔克拉玛干沙漠沙子来源和输送系统
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
Joachim Krieger;Kenji Nakanishi;Wilhelm Schlag;勝山正則,谷誠;数土直紀;烏田明典 - 通讯作者:
烏田明典
A perturbation theory for core operators of Hilbert-Schmidt submodules
Hilbert-Schmidt子模核心算子的摄动理论
- DOI:
- 发表时间:
2011 - 期刊:
- 影响因子:0.8
- 作者:
Kenji Nakanishi;Wilhelm Schlag;Michio Seto - 通讯作者:
Michio Seto
On codimension one stability of the soliton for the 1D focusing cubic Klein-Gordon equation
一维聚焦三次Klein-Gordon方程孤子的余维一稳定性
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Jonas Lührmann;Wilhelm Schlag - 通讯作者:
Wilhelm Schlag
Biharmonic Lagrangean submanifolds in Kaehler manifolds
凯勒流形中的双调和拉格朗日子流形
- DOI:
- 发表时间:
2013 - 期刊:
- 影响因子:0.5
- 作者:
Joachim Krieger;Kenji Nakanishi;Wilhelm Schlag;H. Urakawa and S. Maeta - 通讯作者:
H. Urakawa and S. Maeta
Wilhelm Schlag的其他文献
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{{ truncateString('Wilhelm Schlag', 18)}}的其他基金
Global Dynamics of Nonlinear Dispersive Evolution Equations and Spectral Theory
非线性色散演化方程的全局动力学和谱理论
- 批准号:
1764384 - 财政年份:2018
- 资助金额:
$ 46.02万 - 项目类别:
Standard Grant
Long-Term Dynamics of Nonlinear Evolution Partial Differential Equations
非线性演化偏微分方程的长期动力学
- 批准号:
1842197 - 财政年份:2018
- 资助金额:
$ 46.02万 - 项目类别:
Continuing Grant
Global Dynamics of Nonlinear Dispersive Evolution Equations and Spectral Theory
非线性色散演化方程的全局动力学和谱理论
- 批准号:
1902691 - 财政年份:2018
- 资助金额:
$ 46.02万 - 项目类别:
Standard Grant
Long-Term Dynamics of Nonlinear Evolution Partial Differential Equations
非线性演化偏微分方程的长期动力学
- 批准号:
1500696 - 财政年份:2015
- 资助金额:
$ 46.02万 - 项目类别:
Continuing Grant
Global dynamics for nonlinear dispersive equations
非线性色散方程的全局动力学
- 批准号:
1160817 - 财政年份:2012
- 资助金额:
$ 46.02万 - 项目类别:
Continuing Grant
Harmonic Analysis, Mathematical Physics, and Nonlinear PDE
调和分析、数学物理和非线性偏微分方程
- 批准号:
0653841 - 财政年份:2007
- 资助金额:
$ 46.02万 - 项目类别:
Continuing Grant
Harmonic Analysis with Applications to Mathematical Physics
调和分析及其在数学物理中的应用
- 批准号:
0617854 - 财政年份:2005
- 资助金额:
$ 46.02万 - 项目类别:
Continuing Grant
Harmonic Analysis with Applications to Mathematical Physics
调和分析及其在数学物理中的应用
- 批准号:
0300081 - 财政年份:2003
- 资助金额:
$ 46.02万 - 项目类别:
Continuing Grant
Nonperturbative methods for quasiperiodic discrete Schroedinger equations on the line
在线准周期离散薛定谔方程的非微扰方法
- 批准号:
0241930 - 财政年份:2002
- 资助金额:
$ 46.02万 - 项目类别:
Standard Grant
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