Fall 2015

Seminars are held on Mondays from 2:30 - 3:30PM in Cullimore Hall, Room 611, unless noted otherwise. For questions about the seminar schedule, please contact David Shirokoff.


Date: November 16, 2015

Speaker: Te-Sheng Lin
Department of Applied Mathematics,
National Chiao Tung University

University Profile

Title: "Weak-Interaction Theory and Bound State Formation in Electrified Falling Liquid Films"

Abstract:

We consider a perfectly conducting viscous liquid film flowing down an inclined wall and subjected to a normal electric field. The electric field introduces a destabilizing non-local term in the long-wave evolution equation and the solutions may evolve into arrays of interacting pulses. We develop a weak-interaction theory for these pulses. We show that the standard first-neighbor approximation is no longer valid and it is essential to take into account long-range interactions. We also develop numerical continuation techniques to explore bifurcation diagrams in systems processing translational symmetry, including traveling waves and spatially varying time-periodic solutions. We find that each bound state bifurcates from the primary branch when continuing with respect to the domain size, and we then construct full bifurcation diagrams taking into account all the bound states. Finally, we compare the bound state for the long-wave evolution equation with the ones found in Stokes calculations and find excellent agreement.