CAREER: Development and Applications of Weak Turbulence Theory

获奖摘要获奖编号：0134955PI: Lvov， Yuri机构：Rensselaer理工学院项目：应用数学项目经理：Catherine mavriplis标题：职业：弱湍流理论的发展与应用弱湍流理论为研究大类别弱非线性或弱耦合物理系统所表现出的稳态统计特性提供了一个广泛的框架。在这个框架内，这项工作的研究部分将集中在物理学的三个基本问题上：海洋内波的Garrett-Munk谱，半导体中应用于半导体激光器的有限通量谱，以及玻色爱因斯坦凝聚体。在每种情况下，将开发新的弱湍流启发技术来计算所研究现象的平稳能谱，这将提供其长期动力学的分析统计描述。这项工作的应用包括海洋动力学的环境方面，半导体制造和激光效率的提高，以及低温下的凝聚态物理和材料科学。教育部分包括本科和研究生水平的课程开发，将在本科数学建模课程中包含实验部分，以及波浪和弱湍流理论的研究生课程。海底深处的内部波、半导体激光和极冷的金属蒸汽有什么共同之处？它们都是非常复杂的物理系统，由相互作用微弱的简单组件组成。弱湍流理论解决了这类系统，并预测了它们所包含的能量在长时间内的平均行为。海洋内部波浪的能量如何取决于波浪的长度，这个问题有一个优雅的实验答案，它指出了一个普遍规律，但30多年来一直没有得到理论解释。这项工作旨在提供这样一个解释，这将为海洋环境提供新的见解。半导体和半导体激光器的制造和运行对效率的要求越来越高。这项工作将探索一种基于更有效地向工作的半导体和半导体激光器输送能量的改进方法。四分之三个世纪以前，玻色和爱因斯坦预言了物质的新相——玻色-爱因斯坦凝聚体，这种物质只能在极低的温度下出现。最后，在六年前，这个阶段通过实验实现了，实验的创造者获得了今年的诺贝尔奖。这项工作将为极冷的金属蒸汽如何进入玻色-爱因斯坦凝聚相提供理论解释。日期：2001年12月17日

DMS Award AbstractAward #: 0134955PI: Lvov, Yuri Institution: Rensselaer Polytechnic InstituteProgram: Applied MathematicsProgram Manager: Catherine MavriplisTitle: CAREER: Development and Applications of Weak Turbulence TheoryWeak turbulence theory provides a broad framework for the study ofsteady-state statistical properties exibited by large classes ofweakly nonlinear or weakly coupled physical systems. Within thisframework, the research component of this work will focus on threefundamental problems in physics: the Garrett-Munk spetrum of internalwaves in the ocean, finite-flux spectra in semiconductors withapplications to semiconductor lasers, and Bose Einstein condensates.In each case, novel weak-turbulence-inspired techniques will bedeveloped to compute the stationary energy spectra of the phenomenaunder investigation, which will provide an analytic statisticaldescription of their long-term dynamics. Applications of this workinclude environmental aspects of ocean dynamics, semiconductormanufacturing and increases in laser efficiency, and condensed-matterphysics and materials science at low temperatures. The educationalcomponent includes course development on undergraduate and graduatelevel that will incorporate an experimental component in anundergraduate mathematical modelling course, and a graduate course onwaves and weak turbulence theory.What do internal waves deep below the ocean surface, semiconductorlasers, and extremely cold metallic vapors have in common? They areall very complicated physical systems composed of simple componentsthat interact weakly. Weak turbulence theory addresses these type ofsystems, and precdicts how the energy they contain will behave onaverage over long times. The question of how the energy of aninternal ocean wave depends on this wave's length has an elegantexperimental answer pointing to a universal law, but has eludedtheoretical explanation for more than thirty years. This work aims toprovide such an explanation, which will furnish new insights into theoceanic environment. Semiconductors and semiconductor lasersmanufacturing and operation requires ever increasing efficiency. Thiswork will explore an improvement that is based on a more efficient wayof delivering energy to the working semiconductors and semiconductorlasers. Three quarters of a century ago Bose and Einstein predicted anew phase of materials, the Bose-Einstein condensate, that can onlyoccur at extremely low temperatures. Finally, six years ago, thisphase was realized experimentally, and the the creators of theexperiment received this year's Nobel Prize. This work will provide atheoretical explanation of how extremely cold metal vapors settle intothe Bose-Einstein condensate phase.Date: December 17, 2001