Wednesday Evening, October 25

Applied Nonlinear Dynamics of Partial Differential Equations

The speakers in this minisymposium will discuss problems that lie at the interface between applied dynamical systems and partial differential equations, in the context of four different applications: materials science (microstructure in shape-memory alloys), laser optics (low-dimensional regular and chaotic behavior in ring-cavity lasers), dynamics of space-curves and DNA molecules (completely-integrable, continuum Heisenberg spin-chain models), and water waves (a new integrable model for waves in shallow water). The speakers will emphasize how geometric structures that exist in the corresponding infinite-dimensional phase spaces, such as homoclinic orbits, invariant manifolds, soliton solutions with discontinuous derivatives, or low-dimensional attractors can be used to describe the physical features of the problems at hand. They will present comparisons between analytical and computational.

Organizers: Annalisa Calini, Case Western Reserve University; Roberto Camassa, Los Alamos National Laboratory; and Gregor Kovacic, Rensselaer Polytechnic Institute

5:00 Dynamics, Hysteresis and Memory in a Class of Shape-Memory Alloys
Pieter J. Swart, Los Alamos National Laboratory

5:30 Regular and Chaotic Dynamics of the Maxwell-Bloch Equations
Thomas A. Wettergren, Naval Undersea Warfare Center

6:00 Dynamics of Curves and Integrable Equations
Annalisa Calini, Organizer

6:30 New Completely Integrable Evolution Equations
Roberto Camassa, Organizer

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