On the Dynamics of Nonlinear Systems in Applied Sciences: From Theory, Computations, and Experiments to Insights
应用科学中的非线性系统动力学:从理论、计算、实验到见解
基本信息
- 批准号:2008568
- 负责人:
- 金额:$ 27万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2020
- 资助国家:美国
- 起止时间:2020-08-01 至 2024-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This research investigation focuses on the modeling and mathematical analysis of nonlinear systems of partial differential equations arising in physical applications. The analysis involves nonlinear systems for compressible flows, mixtures, and polymeric fluids, which are relevant to several practical applications in science and engineering, and kinetic models describing self-organized dynamics, which are important in biology, physics, and bioengineering. The project includes training and research opportunities for graduate students. The existence of statistically stationary states in randomly driven systems in fluid dynamics is of basic importance from both mathematical and experimental points of view. On the one hand, the existence of an invariant measure provides information on the generic long-time behavior of the system. On the other hand, under ergodicity assumptions, they provide a link between experimental observations, for example in turbulence theory. This project aims to (a) establish well-posedness results for variational solutions to deterministic systems and (b) analyze weak martingale solutions and invariant measures for randomly forced systems. The variational framework developed in this investigation will be employed for the construction of numerical algorithms for the approximation of nonlinear systems that arise in science and engineering. One of the goals of the project involves connecting the theoretical and computational results to experiments, in order to optimize theoretical models for more accurate predictions.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.
本研究调查的重点是在物理应用中产生的偏微分方程的非线性系统的建模和数学分析。该分析涉及可压缩流,混合物和聚合物流体的非线性系统,这些系统与科学和工程中的几个实际应用有关,以及描述自组织动力学的动力学模型,这些模型在生物学,物理学和生物工程中很重要。该项目包括为研究生提供培训和研究机会。从数学和实验的观点来看,流体动力学中随机驱动系统中统计定态的存在具有基本的重要性。一方面,不变测度的存在提供了系统的一般长时间行为的信息。另一方面,在遍历性假设下,它们提供了实验观测之间的联系,例如在湍流理论中。本计画的目的是(a)建立决定性系统变分解的适定性结果及(B)分析随机受迫系统的弱鞅解与不变测度。在这项调查中开发的变分框架将用于建设的数值算法的近似非线性系统,出现在科学和工程。该项目的目标之一是将理论和计算结果与实验联系起来,以优化理论模型,实现更准确的预测。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(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)
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Konstantina Trivisa其他文献
On the Motion of a Viscous Compressible Radiative-Reacting Gas
- DOI:
10.1007/s00220-006-1534-7 - 发表时间:
2006-03-09 - 期刊:
- 影响因子:2.600
- 作者:
Donatella Donatelli;Konstantina Trivisa - 通讯作者:
Konstantina Trivisa
On a free boundary problem for polymeric fluids: global existence of weak solutions
- DOI:
10.1007/s00030-017-0475-5 - 发表时间:
2017-08-05 - 期刊:
- 影响因子:1.200
- 作者:
Donatella Donatelli;Konstantina Trivisa - 通讯作者:
Konstantina Trivisa
Konstantina Trivisa的其他文献
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{{ truncateString('Konstantina Trivisa', 18)}}的其他基金
RTG: The Mathematics of Quantum Information Science
RTG:量子信息科学的数学
- 批准号:
2231533 - 财政年份:2023
- 资助金额:
$ 27万 - 项目类别:
Continuing Grant
On the Dynamics of Nonlinear Systems in Applied Sciences
应用科学中的非线性系统动力学
- 批准号:
1614964 - 财政年份:2016
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
ON THE DYNAMICS, STRUCTURE AND STABILITY OF CERTAIN NONLINEAR SYSTEMS IN APPLIED SCIENCES
应用科学中某些非线性系统的动力学、结构和稳定性
- 批准号:
1211519 - 财政年份:2012
- 资助金额:
$ 27万 - 项目类别:
Continuing Grant
ON THE DYNAMICS OF CERTAIN NONLINEAR SYSTEMS IN APPLIED SCIENCES: TRANSPORT, MOTION AND MIXING
应用科学中某些非线性系统的动力学:输运、运动和混合
- 批准号:
1109397 - 财政年份:2011
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
On the Dynamics, Structure and Stability of Certain Nonlinear Systems in Applied Sciences
应用科学中某些非线性系统的动力学、结构和稳定性
- 批准号:
0807815 - 财政年份:2008
- 资助金额:
$ 27万 - 项目类别:
Continuing Grant
Challenges in Systems with Semctic and Nematic Order
具有近序和向列序的系统面临的挑战
- 批准号:
0405853 - 财政年份:2004
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
PECASE: Systems of Conservation Laws and Related Models in Applied Sciences - Math Awareness and Outreach
PECASE:应用科学中的守恒定律体系和相关模型 - 数学意识和推广
- 批准号:
0239063 - 财政年份:2003
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
Hyperbolic Systems of Conservation Laws - Viscous Conservation Laws - Applications
守恒定律的双曲系统 - 粘性守恒定律 - 应用
- 批准号:
0196157 - 财政年份:2000
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
Hyperbolic Systems of Conservation Laws - Viscous Conservation Laws - Applications
守恒定律的双曲系统 - 粘性守恒定律 - 应用
- 批准号:
0072496 - 财政年份:2000
- 资助金额:
$ 27万 - 项目类别:
Standard Grant
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2001403 - 财政年份:2020
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$ 27万 - 项目类别:
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合作研究:微纳机械系统的非线性随机动力学
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