- 4607B South Hall
- Applied Math/PDE Seminar
We study de Gennes and Chen-Lubensky free energies for smectic A liquid crystals over S2 valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. As the applied field increases well above the critical field, the sinusoidal shape of the smectic layer at the onset of undulation will change into the chevron patterns with a longer period. We consider a square domain to represent the cross section of a three dimensional smectic A liquid crystal sample. Well above the instability threshold, we show via ?"-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. Numerical simulations illustrating the chevron structures for both models will be presented. This is a joint work with T. Giorgi and C. J. Garc?a-Cervera.