IP3 ~ Sunday, May 21, 1995 ~ 5:00 PM
The speaker will illustrate how universal order parameter equation descriptions in terms of complex Swift-Hohenberg, complex Ginzburg-Landau type pde's. arise naturally in the description of the emergence of patterns near a Hopf bifurcation point in a large aspect ratio laser. Such models prove to be remarkably robust in predicting pattern selection, not only near, but well beyond the initial bifurcation point. For many important laser systems, the physically relevant Maxwell-Bloch mathematical models prove to be extremely stiff and the relevant order parameter equation must be coupled to a mean flow. As a consequence, the domain of stable patterns is extremely narrow and a weakly turbulent behavior becomes evident in both experimental observations and numerical simulations.
Jerome V. Moloney
Department of Mathematics, University of Arizona