Towards the mid-frequency regime - combining wave chaos methods and 'Statistical Energy Analysis'

提议的奖学金旨在建立机械工程界和应用数学之间在大尺度结构振动和线性波动方程短波长的渐近界面上的联系。研究者从短波长的角度以及从统计的角度广泛地研究了波问题的特征谱的性质-这一研究领域通常被称为量子或波混沌。该领域在历史上与量子力学中的问题密切相关，但可以通过修改应用于其他线性波动方程，如弹性动力学的波动方程。本文提出了将量子混沌方法纳入统计能量分析（SEA）方法的可能性，统计能量分析（SEA）方法在机械工程界广泛用于分析复杂结构（如建筑物，飞机等）高频振动的能量流。这里将讨论通过重新评估和修改该技术的一些基本假设，可以改进SEA中的误差估计，并且可以纳入系统特定的特征，从而使该方法也适用于中频范围。方法本身及其应用范围的详细知识对于这项任务至关重要，这是研究者在奖学金的一生中寻求获得的

The proposed fellowship aims at forging links between the Mechanical Engineering community and Applied Mathematics at the interface of vibrations in large-scale structures and short wavelength asymptotics of linear wave equations. The investigator has worked extensively on the properties of eigenspectra of wave problems both from a short wavelength perspective as well as from a statistical point of view - an area of research often referred to as quantum - or wave - chaos. The field is historically closely linked to problems in quantum mechanics, but can with modifications be applied to other linear wave equations such as the wave equations of elastodynamics. It is proposed here to evaluate the possibility of incorporating quantum chaos methods in a Statistical Energy Analysis (SEA) approach, widely used in the mechanical engineering community for analysing energy flow of high-frequency vibrations in complex structures such as buildings, aeroplanes and so on. It will be argued here that by re-evaluating and modifying some of the basic assumptions of the technique, error estimates in SEA may be improved and system specific features may be incorporated which would make the method applicable also in the medium frequency range. Detailed knowledge of the method itself and its range of applications is essential for this task, which the investigator seeks to obtain during the lifetime of the fellowship