Passive Defect Driven Morphogenesis in Nematic Membranes

Orientational order is a common feature of many biological and synthetic materials. Topological defects are discontinuities in this order that are often coupled to geometric features of the materials. Here, we study the equilibrium shapes of fluid membranes featuring a +1 topological defect as a model for morphogenesis. We show, through simulation and analytic calculation, that the membrane can spontaneously deform toward a conical shape with a defect at its apex. We show that the relative stability of the deformation is controlled by the balance of the elastic parameters. When boundary constraints are introduced, we observe three distinct modes of deformation. These deformation modes take advantage of the way in which splay, twist, and bend distortions of the director field can be exchanged on a curved surface. Finally, we demonstrate inverted solutions. Our findings demonstrate a mechanism for passive defect driven morphogenesis as well as the fusion of +1/2 topological defect pairs on deformable surfaces.