Laser-Matter Interactions and Highly Nonlinear Geometrical Optics; Dynamics of Reacting Flows

激光与物质相互作用和高度非线性几何光学；

• 批准号: 0505780
• 负责人: Kevin Zumbrun
• 金额: --
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505780&HistoricalAwards=false
• 关键词: Laser; Matter; Interactions; Highly; Nonlinear

Abstract: This project investigates mathematical properties of models equations describing a) laser-matter interactions, and b) reacting flows, specifically: a) High-frequency, large-amplitude solutions of the Maxwell-Euler and Maxwell-Landau equations. Systems of equations based on the fundamental equations of physics are too complex to serve as a basis for numerical simulations. Hence the need of simple model systems. This project addresses the question of the validity of model systems describing laser-matter interactions, such as the Zakharov and the Davey-Stewartson models. b) Stability issues for reacting flows. The project will provide a simple mathematical description of one-dimensional instabilities occurring in reacting flows by studying bifurcations of simple model systems. Ultimately, the analysis will be carried out to the more complex framework of the reacting Navier-Stokes equations, where recent techniques using pointwise Green's functions bounds will have to be used. The motivation for these projects comes from actual experiments: large-scale experiments of high-energy lasers show important enerngy losses; detonation waves are seen to develop longitudinal instabilities. This project will contribute to a rigorous mathematical analysis of relevant model equations describing these phenomena. Such an analysis is a key step in the development of predictive tools, as a deep mathematical understanding of the models is needed in order to devise efficient numerical simulations.

摘要：该项目研究了描述a）激光互动的模型方程的数学特性，而b）反应流，特别是：a）Maxwell-euler和Maxwell-landau方程的高频，大振幅解。基于物理基础方程的方程式系统太复杂，无法作为数值模拟的基础。因此，需要简单的模型系统。该项目解决了描述激光互动的模型系统的有效性问题，例如Zakharov和Davey-Stewartson模型。 b）反应流动的稳定性问题。该项目将通过研究简单模型系统的分叉在反应流中发生的一维不稳定性提供简单的数学描述。最终，分析将进行到反应的Navier-Stokes方程的更复杂的框架，其中最新的技术必须使用Pointwince Green的功能边界。这些项目的动机来自实际的实验：高能量激光器的大规模实验显示出重要的递观损失；爆炸波被认为发展出纵向不稳定性。该项目将有助于对描述这些现象的相关模型方程进行严格的数学分析。这种分析是开发预测工具的关键步骤，因为需要对模型的深刻数学理解来设计有效的数值模拟。