Seminar in Applied Mathematics

Richard Jordan Department of Mathematical Sciences Worcester Polytechnic Institute Self-organization in nonlinear wave turbulence Monday, February 14, 2000 3:00pm Pierce 116

Abstract:   In this talk, I will describe a statistical equilibrium model of self-organization in a generic class of nonlinear Schrodinger equations. These equations, whose dynamics is nonintegrable and nonsingular, provide natural prototypes for nonlinear dispersive wave turbulence. The main result is that the statistically preferred state of such a system is a macroscopic coherent structure coupled with fine-scale random fluctuations. The coherent structure is seen to be a ground-state solution of the NLS equation. The predictions of the statistical model will be compared with direct numerical simulations of the NLS equation, and it will be demonstrated that the model captures the long-time average behavior of solutions remarkably well. Finally, some unanswered questions and open problems related to the statistical model will be discussed.

Coffee and refreshments will be available immediately following the talk. For additional information contact Patrick Miller  or Yi Li.