Dispersive Shocks in Continuous & Discrete Media

连续分散激波

• 批准号: 9500623
• 负责人: Stephanos Venakides
• 金额: $ 9.3万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-09-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500623&HistoricalAwards=false
• 关键词: Dispersive; Shocks; Continuous; & Discrete

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.

该提案侧重于研究色散波在非线性离散或连续介质中的产生和传播。这种现象涉及两个不同时空尺度之间的相互作用。小尺度由强烈非线性的单行波或多行波组成，其波参数在大尺度上变化。最终在大空间区域传播的波是在系统的色散特性平滑非线性产生的冲击的点上产生的。因此，振荡微观结构通常是由非振荡初始数据产生的。提议的项目与涉及非线性和色散的物理应用有关。这些应用包括量子半导体器件中的电子流和固体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微观结构了解材料基本性质的愿望。