New asymptotic methods and applications to physical problems

新的渐近方法及其在物理问题中的应用

• 批准号: 1108794
• 负责人: Saleh Tanveer
• 金额: $ 42万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1108794&HistoricalAwards=false
• 关键词: New; asymptotic; methods; applications; physical

The project focuses on further development of constructive andrigorous asymptotic analysis of linear and nonlinear partialdifferential equations that arise in a number of important physicalapplications. The applications include (a) evolution of smalldisturbances superposed on an oscillatory flow in a channel or pipe,of interest in transition to turbulence, (b) existence and stabilityof self-sustaining states in channel and pipe flows, believed to beomega-limits in intermediate Reynolds number turbulent flow, (c)nonlinear stability of steadily translating fingers and bubbles inHele-Shaw flow for small nonzero surface tension, of interest inpattern formation, (d) ionization of Hydrogen atoms in time-periodicdipole fields of arbitrary frequency and amplitude. Our understanding of the solutions of equations arising in fluidmotion and quantum mechanics is still very limited. The presentproject develops much needed new methods to study these problems.Among the immediate applications outside mathematics we note forinstance that understanding turbulent fluid flow can lead to a moreenergy-efficient transportation of fluids through pipes. Also, betterunderstanding of ionization processes has many applications, includingoptimal propagation of very intense laser beams through theatmosphere. Training of students --supported in the project-- willhelp maintain the high quality of research in the United States forthe coming generation.

该项目的重点是进一步发展线性和非线性偏微分方程的构造性渐近分析，这些方程出现在许多重要的物理应用中。这些应用包括：（a）叠加在槽道或管道中振荡流上的小扰动的演化，研究向湍流的转变;（B）槽道和管道流中自持态的存在和稳定性，在中等雷诺数湍流中被认为是ω极限;（c）Hele-Shaw流中稳定平移指状物和气泡的非线性稳定性，（d）氢原子在任意频率和振幅的时变偶极场中的电离。 我们对流体运动和量子力学方程的解的理解仍然非常有限。 本项目开发了急需的新方法来研究这些问题，在数学之外的直接应用中，我们注意到，例如，理解湍流可以导致更节能的流体管道输送.此外，更好地理解电离过程有许多应用，包括非常强的激光束通过大气的最佳传播。该项目支持的学生培训将有助于为美国的下一代保持高质量的研究。