DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491