Splay ostracism on ferroelectric nematic shells

Abstract

Ostracism was the practice in use in Athens and other ancient Greek cities to send into exile citizens whose influence was deemed to be dangerous. Quite similarly, splay ostracism is here the approximation that bans splay distortion from thin films of ferroelectric nematic liquid crystals on a curved shell in space. This reduces to a mere geometric problem the quest for equilibria of director vortexes and the walls isolating them, as splay ostracism requires the director field lines to be everywhere orthogonal to systems of geodesics on the shell. Consequences of this theorem are explored for shells with Gaussian curvature of either sign. The resulting quasi static dynamics reveals both cases where walls escape from the shell and cases where they are trapped on it, with possibly different reflections on the vortex dynamics.