Dispersive Shocks in Continuous & Discrete Media

9500623 Venakides该提案的重点是研究色散波的产生和通过非线性离散或连续介质的传播。这些现象涉及两个不同时空尺度之间的相互作用。小尺度由强非线性的单个或多个行波组成，其波参数在大尺度上变化。最终在大空间区域传播的波在系统的色散性质使非线性产生的冲击平滑的点处产生。因此，振荡微结构将典型地由非振荡初始数据产生。 拟议的项目是有关的物理应用，涉及非线性和色散。这些应用包括量子半导体器件中的电子流和固态器件中杂质对传输特性的影响。我们对非线性粒子链的研究在很大程度上是出于通过材料的微观结构来理解其基本性质的愿望。

9500623 Venakides The proposal focuses on the study of dispersive wave generation and propaeation through nonlinear discrete or continuous media. The phenomena involve the interaction between two different space-time scales. The small scale consists of strongly nonlinear single or multiple traveling waves with wave parameters that vary in the large scale. The waves, that eventually spread over large space regions are generated at points where the dispersive nature of the system smoothens the shocks produced by the nonlinearity. An oscillatory microstructure will thus typically arise out of non-oscillatory initial data. The proposed projects are relevant to physical applications that involve nonlinearity and dispersion. Such applications, include electron flow in quantum semiconductor devices and the effect of impurities in the transmission characteristics in solid state devices. Our study of nonlinear particle chains is to a great extent motivated by the desire to understand basic properties of materials through their microscopic structure.