Field instabilities of Smectic A liquid crystals in 2D and 3D
AbstractWe study the de Gennes free energy to describe the undulations instability in smectic A liquid crystals subjected to magnetic fields. If a magnetic field is applied in the direction parallel to the smectic layers, an instability occurs above a threshold magnetic field. When the magnetic field reaches this critical threshold, periodic layer undulations are observed. We prove the existence and stability of the solution to the nonlinear system of de Gennes model using $\Gamma$-convergence method and bifurcation theory. Numerical simulations will be given near and well above the threshold. An efficient numerical scheme for some free energy containing the second order gradient will be presented. Undulation instabilities on three dimensional systems will be also discussed.
Co-author: Carlos J. Garcia-Cervera (UCSB)