Speaker:Brenton LeMesurier, College of Charleston
Title: Airy-like pulses in models of large molecular chains, and conservative numerical methods for quasi-linear Hamiltonian systems

Abstract: The phenomenon of coherent energetic pulse propagation in macromolecular chains such as alpha-helix protein is studied using the Davydov-Scott model, with both numerical studies using a new unconditionally stable fourth order accurate energy-momentum conserving time discretization, and with analysis based on ideas of center manifold theory. It is shown that for physically natural impulsive initial data, the coherent traveling pulses seen have a form related to the Airy function, but with rapid variation of phase along the chain. This can be explained in terms of a new continuum limit approximation by the third derivative nonlinear Schrodinger equation, which differs from the previous continuum limit approximations related to the standard NLS equation. A theorem is given describing the construction of such conservative time discretizations for a large class of Hamiltonian systems.

Time: Friday, February 1, 2013, 1:30-2:30 p.m.

Place: Planetary Hall (formerly S & T I), Room 242

Department of Mathematical Sciences
George Mason University
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