Wave Propagation and Scattering for Periodic and Randomly Perturbed Periodic Media.

这个项目将提供一个完整的渐近分析的传播波包与窄频谱通过有限板的周期性分层介质和周期性量子图形。 这项工作将确定条件下，小群速度伴随着近透明。 这种分析将补充的影响，由于紧凑和随机扰动的介质的研究，特别是，从绝对连续的频谱模型的过渡到完整的本地化将进行调查。 有效的统计估计将给出脉冲的物理特性的噪声在media.The项目将提供一个基本的问题，一直在物理文献中非常活跃的讨论，在过去几年中的数学背景：有效的光学设备的建设光信号的减速。这些器件可以找到许多应用，例如在使非常快的光学元件的工作与慢得多的电子器件同步方面。

This project will provide a complete asymptotic analysis of the propagation of wave packets with narrow spectra through finite slabs of periodic layered media and periodic quantum graphs. The work will identify conditions under which small group velocity is accompanied by near transparency. This analysis will be complemented by a study of the effects due to compact and random perturbations of the media; in particular, the transition from models with absolutely continuous spectrum to complete localization will be investigated. Effective statistical estimates will be given for physical characteristics of the pulses in terms of the noise in the media.The project will furnish the mathematical background for a fundamental problem that has been very actively discussed in physical literature during the last several years: construction of efficient optical devices for slowing down of optical signals. These devices can find many applications, for example in synchronizing the work of very fast optical elements with much slower electronics.