CAREER: Development and Applications of Weak Turbulence Theory

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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