Speaker
Laurette Tuckerman
Description
For systems making a transition from simple (uniform,
laminar, steady) to more complex (non-uniform, periodic,
quasiperiodic, chaotic, turbulent) behavior, a bifurcation
diagram summarizes the information necessary for
understanding the system. A complete bifurcation diagram,
including unstable states and limit cycles, is inaccessible to
experiment, but is, in principle, obtainable numerically from
the governing equations. This is seldom done in practice if
the equations are two or three dimensional PDEs.
In this talk, we will show how to adapt a time-stepping code
so as to calculate steady states and rotating waves via
Newton's method and to calculate leading eigenpairs and
Floquet multipliers via the Arnoldi method.
We will show how this information can be used to
understand various hydrodynamic pattern-forming systems,
such as convection in cylindrical and spherical geometries.
