Systems with Competing Periodicities: Localization and Fractal Fluctuations

9700808 Satija本基金将支持一名女性理论家的工作，该理论家的研究项目在国际上得到认可，并且有大量本科生参与。该研究涉及具有竞争长度尺度的系统的性质。这些系统的一个重要方面是具有分形特征的奇异相的存在。大部分工作的概念联系是局部化（以及许多与局部化相关的现象）和普遍分形波动之间的关系。研究中提出的系统包括具有动态局域性的量子混沌模型和具有奇异非混沌吸引子的经典驱动振子。这些系统将通过使用PI和她的合作者最近开发的重整化方法进行研究。可能的应用包括具有巨磁阻的超晶格的摩擦和磁性的微观模型。%%%资助一名女性PI的理论研究。非线性动力系统的研究涉及复杂的数学技术，需要本科生和研究生的积极参与。它是一个国际公认的项目的一部分，与来自世界各地的同事长期合作。她的工作已经应用到几个目前活跃的材料领域；包括摩擦的微观模型和磁超晶格的性质。＊＊＊

9700808 Satija This grant will support the work of a female theorist who has a research program of international recognition with a strong participation of undergraduate students. The research involves properties of systems with competing length scales. One of the important aspects of these systems is the existence of an exotic phase with fractal characteristics. The conceptual linkage through much of this work is the relationship between localization (and many phenomena related to localization) and the universal Fractal fluctuations. The proposed systems under investigation include quantum chaos models exhibiting dynamical localization and classical driven oscillators with strange non-chaotic attractors. These systems will be studied by using a renormalization methodology developed recently by the PI and her collaborators. The possible applications include a microscopic model of friction and magnetic properties of superlattices exhibiting giant magnetoresistance. %%% This grant supports theoretical research of a female PI. The research on nonlinear dynamical systems involves sophisticated mathematical techniques with active participation by undergraduate and graduate students. It is part of an internationally recognized program with long- standing collaborations with colleagues from around the world. Her work has applications to several currently active areas in materials; including microscopic models of friction and properties of magnetic superlattices. ***