Stability and vibrations of catenoid-shaped smectic films

Catenoid-shaped smectic films are spanned between two coaxial circular frames separated by a distance H. It is shown that there exists a critical height H* such that below it two shapes of the catenoid are possible. The stability of these two shapes is analysed in terms of their vibrations. The spectrum of eigenfrequencies is calculated as a function of the catenoid height. It is shown that the frequency of the fundamental mode is real for the stable shape and imaginary for the other shape. Experimental study of vibrational eigenmodes performed on stable SCE4 films confirms this theoretical prediction.