Supersonic Dispersive Fluid Dynamics

本计画研究分散流体中的超音速流动，其耗散效应可忽略不计。 主要目的是发展的基本激发色散流体的物理相关的一些系统，包括玻色-爱因斯坦凝聚，光学，等离子体和浅水的理解。 这样的激励包括斜向色散冲击波，它将被构造为一些非线性色散波方程。性质，包括稳定性和相互作用的色散激波的行为，将被研究和应用到多维边值问题的研究中。雷声，鞭子的噼啪声，以及从超过音速的喷气式飞机上听到的轰鸣声，都是人类经验中常见的现象，都是粘性激波产生的结果。该项目将专注于一种非常不同类型的冲击波，通过色散介质传播，如超流体玻色-爱因斯坦凝聚体（BEC），非线性光子晶体，等离子体和浅水。 该理论的应用包括非线性波的控制，促进了现代技术的进步，如物质激光，原子干涉测量和成像。

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.