Award Abstract #0134955
CAREER: Development and Applications of Weak Turbulence Theory

NSF Org:	DMS Division of Mathematical Sciences
Initial Amendment Date:	February 1, 2002
Latest Amendment Date:	February 1, 2002
Award Number:	0134955
Award Instrument:	Standard Grant
Program Manager:	Henry A. Warchall DMS Division of Mathematical Sciences MPS Directorate for Mathematical & Physical Sciences
Start Date:	June 1, 2002
Expires:	May 31, 2008 (Estimated)
Awarded Amount to Date:	$350000
Investigator(s):	Yuri Lvov lvovy@rpi.edu (Principal Investigator)
Sponsor:	Rensselaer Polytechnic Institute 110 8TH ST Troy, NY 12180 518/276-6000
NSF Program(s):	APPLIED MATHEMATICS
Field Application(s):	0000099 Other Applications NEC
Program Reference Code(s):	OTHR,1187,1045,0000
Program Element Code(s):	1266

ABSTRACT

DMS Award Abstract

Award #: 0134955

PI: Lvov, Yuri

Institution: Rensselaer Polytechnic Institute

Program: Applied Mathematics

Program Manager: Catherine Mavriplis

Title: CAREER: Development and Applications of Weak Turbulence Theory

Weak turbulence theory provides a broad framework for the study of

steady-state statistical properties exibited by large classes of

weakly nonlinear or weakly coupled physical systems. Within this

framework, the research component of this work will focus on three

fundamental problems in physics: the Garrett-Munk spetrum of internal

waves in the ocean, finite-flux spectra in semiconductors with

applications to semiconductor lasers, and Bose Einstein condensates.

In each case, novel weak-turbulence-inspired techniques will be

developed to compute the stationary energy spectra of the phenomena

under investigation, which will provide an analytic statistical

description of their long-term dynamics. Applications of this work

include environmental aspects of ocean dynamics, semiconductor

manufacturing and increases in laser efficiency, and condensed-matter

physics and materials science at low temperatures. The educational

component includes course development on undergraduate and graduate

level that will incorporate an experimental component in an

undergraduate mathematical modelling course, and a graduate course on

waves and weak turbulence theory.

What do internal waves deep below the ocean surface, semiconductor

lasers, and extremely cold metallic vapors have in common? They are

all very complicated physical systems composed of simple components

that interact weakly. Weak turbulence theory addresses these type of

systems, and precdicts how the energy they contain will behave on

average over long times. The question of how the energy of an

internal ocean wave depends on this wave's length has an elegant

experimental answer pointing to a universal law, but has eluded

theoretical explanation for more than thirty years. This work aims to

provide such an explanation, which will furnish new insights into the

oceanic environment. Semiconductors and semiconductor lasers

manufacturing and operation requires ever increasing efficiency. This

work will explore an improvement that is based on a more efficient way

of delivering energy to the working semiconductors and semiconductor

lasers. Three quarters of a century ago Bose and Einstein predicted a

new phase of materials, the Bose-Einstein condensate, that can only

occur at extremely low temperatures. Finally, six years ago, this

phase was realized experimentally, and the the creators of the

experiment received this year's Nobel Prize. This work will provide a

theoretical explanation of how extremely cold metal vapors settle into

the Bose-Einstein condensate phase.

Date: December 17, 2001

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