Modulations of Periodic Waves in Applied Mathematics
应用数学中的周期波调制
基本信息
- 批准号:2108749
- 负责人:
- 金额:$ 19.8万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2021
- 资助国家:美国
- 起止时间:2021-09-01 至 2024-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project analyzes the existence and behavior of spatially periodic solutions to models for viscous fluid dynamics and optical signal propagation, with an emphasis on the stability of such patterns, that is their ability to persist when subjected to small perturbations. The study of the stability of a pattern is of practical interest since only stable solutions are expected to be observed in nature. Results of this research will provide scientists with new analytical tools and methodologies to understand observed laboratory experiments in both fluid dynamics and optical signal propagation contexts, and will lead to experimental design principles that will be used to better explain patterns observed in experiments, to predict the presence of new structures and patterns not previously observed, and to provide insight into the experimental construction of patterns. Both undergraduate and graduate students will receive training through research involvement in the project.The research project naturally divides into two sets of questions according to their fundamentally different physical applications. The first set seeks to develop and analyze new mathematical models relating to buoyancy driven viscous interfacial wave dynamics, such as magma rising through a porous rock. The results of this analysis is expected to provide mathematically rigorous justifications for currently unexplained laboratory observations. The second relates to the dynamics of optics waveguides and optical resonators and will resolve several outstanding issues that are of interest to both experimentalists and theoreticians alike. Importantly, both components involve mathematical work that can be experimentally tested and compared to laboratory experiments.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.
这个项目分析了粘性流体动力学和光信号传播模型的空间周期解的存在和行为,重点是这种模式的稳定性,即它们在受到小扰动时的持续能力。对模式稳定性的研究具有实际意义,因为自然界中只能观察到稳定的解。这项研究的结果将为科学家提供新的分析工具和方法,以理解在流体动力学和光学信号传播环境中观察到的实验室实验,并将导致实验设计原则,这些原则将被用于更好地解释实验中观察到的模式,预测以前没有观察到的新结构和模式的存在,并提供对模式的实验结构的洞察。本科生和研究生都将通过参与项目的研究进行培训。根据他们根本不同的物理应用,研究项目自然分为两组问题。第一组试图开发和分析与浮力驱动的粘性界面波动力学有关的新的数学模型,例如岩浆从多孔岩石中上升。这一分析的结果预计将为目前无法解释的实验室观察提供严格的数学理由。第二个涉及光学、波导和光学谐振器的动力学,将解决实验者和理论家都感兴趣的几个悬而未决的问题。重要的是,这两个部分都涉及数学工作,可以进行实验测试并与实验室实验进行比较。这一奖项反映了NSF的法定使命,并通过使用基金会的智力优势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(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Subharmonic dynamics of wave trains in the Korteweg‐de Vries/Kuramoto‐Sivashinsky equation
Korteweg–de Vries/Kuramoto–Sivashinsky 方程中波列的分谐波动力学
- DOI:10.1111/sapm.12475
- 发表时间:2021
- 期刊:
- 影响因子:2.7
- 作者:Johnson, Mathew A.;Perkins, Wesley R.
- 通讯作者:Perkins, Wesley R.
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Mathew Johnson其他文献
Minimum wages and the multiple functions of wages
最低工资和工资的多重功能
- DOI:
- 发表时间:
2021 - 期刊:
- 影响因子:0
- 作者:
J. Rubery;Mathew Johnson;D. Grimshaw - 通讯作者:
D. Grimshaw
Examination of gender differences using the multiple groups DINA model
使用多组 DINA 模型检查性别差异
- DOI:
- 发表时间:
2013 - 期刊:
- 影响因子:0
- 作者:
Mathew Johnson;Young;R. Sachdeva;Jianzhou Zhang;M. Waldman;Jung Yeon Park - 通讯作者:
Jung Yeon Park
Campus Classification, Identity, and Change: The Elective Carnegie Classification for Community Engagement
校园分类、身份和变化:社区参与的选修卡内基分类
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
John A. Saltmarsh;Mathew Johnson - 通讯作者:
Mathew Johnson
Civil society organisations in and against the state: Advice, advocacy and activism on the margins of the labour market
国家内部和反对国家的民间社会组织:劳动力市场边缘的建议、倡导和行动
- DOI:
- 发表时间:
2023 - 期刊:
- 影响因子:1.4
- 作者:
S. Mustchin;Mathew Johnson;Marti Lopez‐Andreu - 通讯作者:
Marti Lopez‐Andreu
Towards More Disorganised Decentralisation? Collective Bargaining in the Public Sector Under Pay Restraint
走向更加无组织的权力下放?
- DOI:
10.1111/irj.12166 - 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
D. Grimshaw;Mathew Johnson;S. Marino;J. Rubery - 通讯作者:
J. Rubery
Mathew Johnson的其他文献
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{{ truncateString('Mathew Johnson', 18)}}的其他基金
Conference: 2024 KUMUNU-ISU Conference on PDE, Dynamical Systems and Applications
会议:2024 年 KUMUNU-ISU 偏微分方程、动力系统和应用会议
- 批准号:
2349508 - 财政年份:2024
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Stochastic Calculus of Variations and Limit Theorems
随机变分和极限定理
- 批准号:
2054735 - 财政年份:2021
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
4th Annual KUMUNU Conference in Partial Differential Equations, Dynamical Systems and Applications
第四届偏微分方程、动力系统和应用 KUMUNU 年度会议
- 批准号:
1753332 - 财政年份:2018
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Existence, Stability, and Dynamics of Nonlinear Waves
非线性波的存在性、稳定性和动力学
- 批准号:
1614785 - 财政年份:2016
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
Stability of Nonlinear Waves in Dissipative and Dispersive PDE
耗散和色散偏微分方程中非线性波的稳定性
- 批准号:
1211183 - 财政年份:2012
- 资助金额:
$ 19.8万 - 项目类别:
Standard Grant
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