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Friday, March 13, 2009 - 1:00pm

John Wesley Cain

Virginia Commonwealth University

Location

Drexel University

Korman 245

Note the time change...

I will discuss electrical wave propagation in excitable media, with special emphasis on cardiac tissue. In the cardiac context, the waves are called "action potentials", and the standard model of the action potential is a reaction-diffusion PDE known as the "cable equation". I will analyze the cable equation in one spatial dimension with periodic forcing: v_t = kv_xx + f(v) + J(t), where k is a diffusion coefficient, f(v) is a suitably chosen reaction term with cubic nonlinearity, and J(t) is a periodic square-wave impulse. In particular, I will provide an analytical description of the progress of each propagating wave without regard to the full solution profile. Wave speeds will be estimated by seeking periodic traveling wave solutions of the PDE, and the separation between consecutive wavefronts and wavebacks will be approximated by deriving a Poincare-like mapping from the above equation with k = 0.