The Hydrodynamics of Stretching, Buckling Filaments

Michael Shelly (Courant Institute)

Experimental observations of an Isotropic -> Smectic/A (liquid crystal) phase transition show the rapid growth of slender, buckling filaments. This creates beautiful, space-filling patterns that apparently arise from the combination of filament elasticity and growth, with hydrodynamic self-interaction.

Accordingly, I have been studying the Stokes hydrodynamics of stretching buckling filaments. Our modelling combines slender-body theory with filament elasticity and tension, and gives an integro-differential system for the filament dynamics. Solving numerically such a system is very delicate, and brings forward issues of the interaction of asymptotics with constructing numerically tractable models. This is joint work with Ted Ueda (Courant).