CAREER: Development and Applications of Weak Turbulence Theory

DMS奖摘要奖#：0134955PI：LVOV，尤里学院：伦斯勒理工学院项目：应用数学项目经理：Catherine Mavriplis标题：职业：弱湍流理论的发展和应用弱湍流理论为研究大类弱非线性或弱耦合物理系统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中的三个基本问题：海洋中内波的Garrett-Munk谱，半导体中的有限通量谱及其在半导体激光器中的应用，以及玻色爱因斯坦凝聚体。在每一种情况下，新的弱湍流激发的技术将被开发来计算被研究现象的稳定能谱，这将为它们的长期动力学提供解析的统计描述。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质物理和材料科学。教育部分包括本科生和研究生阶段的课程开发，这将包括本科数学建模课程中的实验部分，以及关于波浪和弱湍流理论的研究生课程。海洋表面深处的内波、半导体激光和极冷的金属蒸气有什么共同之处？它们都是非常复杂的物理系统，由相互作用很弱的简单组件组成。弱湍流理论解决了这些类型的系统，并预测了它们所包含的能量在很长一段时间内将如何平均表现。内部海浪的能量如何依赖于该波的长度这个问题有一个优雅的实验答案，它指向了一个普遍定律，但三十多年来一直难以从理论上解释。这项工作旨在提供这样一种解释，这将为人们对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营需要不断提高效率。这项工作将探索一种改进，这种改进基于一种更有效地向工作的半导体和半导体激光器输送能量的方式。四分之三个世纪前，玻色和爱因斯坦预言了一种新的物质--玻色-爱因斯坦凝聚体，它只能在极低的温度下发生。最后，六年前，这一阶段在实验中实现，实验的创造者获得了今年的诺贝尔奖。这项工作将从理论上解释极冷的金属蒸气如何进入玻色-爱因斯坦凝聚相。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