It has been seen experimentally that ring patterns occur when planar aligned samples of SmC* are subjected to a rotating in-plane electric field . We shall model this problem mathematically by approximating the ring patterns and considering a circular domain embedded within a rectangular sample. The ring patterns will be modelled by travelling wave solutions. We shall then investigate the stability of these travelling wave solutions via a linearised perturbation, a Hardy-type inequality and an isoperimetric minimisation problem. This allows a calculation of the lowest eigenvalue which we use to determine the response time of perturbations to the travelling wave solution.
- ring patterns
- smectic C liquid crystals