Nonlinear Dynamics Seminar

David Sanz, Institute for Fusion Studies, UT-Austin

"Explosive attractor solutions in plasmas and fluids"

1:00pm, RLM 11.204

Abstract: This talk presents new solutions to a universal equation that has been studied in both the fluid mechanics and the plasma literature. This equation describes the evolution of weakly nonlinear waves close to marginal stability, a scenario that is likely to occur in additional areas of physics. The structure of these 'explosive' solutions varies for different values of a control parameter that characterizes different physical systems. We use two methods to find the solutions: (a) computation, where we developed an iterative scheme that allows us to resolve the asymptotic behavior of the solutions as they 'explode'; (b) analytic approximations that replicate the simulations. A physical result of these solutions is the development of frequency chirping of the observed wave. This effect continues beyond the applicability of the universal equation, and thus the attractor solutions that we study represent precursors to long-lived phenomena that may be used in an experimental situation to understand the nature of a system's equilibrium.