EVENT DETAILS AND ABSTRACT

Title: Instability of local deformations of an elastic filament
Speaker: Joceline Lega
Speaker Info: U. Arizona
Brief Description:
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Abstract:

When subject to sufficient twist, an elastic filament kept under tension typically undergoes a writhing bifurcation. Near threshold, the dynamics of the filament may be modeled by two coupled nonlinear Klein- Gordon equations, which are envelope equations for the amplitudes of the local deformations and twist. I will consider the question of the spectral stability of a two-parameter family of pulse-like solutions of these envelope equations. More precisely, I will explain how to obtain a criterion on the speed of propagation of the pulses, which is a necessary and sufficient condition for their spectral stability. This will involve Evans function techniques as well as Hamiltonian methods. I will also discuss the numerical evaluation of the Evans function. This work is joint with Stephane Lafortune and Silvia Madrid-Jaramillo.