Supersonic Dispersive Fluid Dynamics

这个项目研究了色散流体中的超音速流动，其耗散效应可以忽略不计。主要目的是发展对色散流体中的基本激发的理解，这些基本激发对包括玻色-爱因斯坦凝聚、光学、等离子体和浅水在内的许多系统具有物理意义。这种激励包括斜色散激波，它将被构造为一些非线性色散波方程。包括稳定性和相互作用的频散冲击波行为在内的性质将被研究并应用于多维边值问题的研究。雷声、鞭子的响声和喷气式飞机超过音速的轰鸣声是人类经验中常见的现象，都是由粘性激波产生的。该项目将专注于一种非常不同类型的冲击波，它通过色散介质传播，如超流玻色-爱因斯坦凝聚体(BEC)、非线性光子晶体、等离子体和浅水。这一理论的应用包括控制非线性波，促进物质激光、原子干涉测量和成像等现代技术的进步。

This project examines supersonic flows in dispersive fluids experiencing negligible dissipative effects. The main objective is to develop an understanding of fundamental excitations in dispersive fluids which are physically relevant for a number of systems including Bose-Einstein condensates, optics, plasma, and shallow water. Such excitations include oblique dispersive shock waves which will be constructed for a number of nonlinear dispersive wave equations. Properties, including stability and the behavior of interacting dispersive shock waves, will be investigated and applied to the study of multidimensional boundary value problems.Thunder, the crack of a whip, and the boom heard from a jet plane surpassing the speed of sound are familiar occurrences in human experience and all result from the generation of viscous shock waves. This project will focus on a very different type of shock wave that propagates through dispersive media such as the superfluidic Bose-Einstein condensate (BEC), nonlinear photonic crystals, plasma, and shallow water. Applications of this theory include the control of nonlinear waves, fostering advances in modern technologies such as matter lasers, atomic interferometry, and imaging.