Asymptotics of the exponentially small

渐近分析在研究复杂的界面动力学方面起着至关重要的作用，这些界面动力学是流体力学中实际问题的基础，例如从地下储油层中提取石油和天然气，以及优化船体设计以使波浪阻力最小。这些应用表现出极小的物理效应，这些效应可能是至关重要的，但不能用经典的渐近分析来描述。该项目将发展最先进的指数渐近数学技术，以解决经典理论中的这一不足，并提供对两种流体之间界面上的图案形成、不稳定性和波传播的更深层次的了解。

Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of the art mathematical techniques in exponential asymptotics to address this deficiency in the classical theory, and provide a deeper understanding of pattern formation, instabilities and wave propagation on the interface between two fluids.