Transient Dynamics and Nonlinear Instabilities of Spatially Extended Systems
by
Roman Grigoriev
Georgia Institute of Technology

The process of pattern formation in nonequilibrium spatially extended systems is usually associated with linear instability of the uniform state leading to exponential growth of arbitrarily small disturbances. There are a few important counter-examples to this rule, such as the transition to turbulence in a plane Couette flow which is linearly stable for all Reynolds numbers. I will discuss how the uniform state can be destabilized via a nonlinear instability in a class of systems characterized by strongly nonnormal evolution operators. In these systems finite-amplitude noise can be transiently amplified by many orders of magnitude, "bootstrapping" a positive-feedback loop involving the nonlinearities.

Date received: October 2, 2003