Defect absorption and emission forp-atic liquid crystals on cones

Statics and diffusive dynamics of surfaces driven by p-atic topological defects

“…[8][9][10][11][12][13][14][15][16] In contrast, here we focus on viewing the intrinsic geometry as the fundamental field and study its dynamics. 17,18 However, unlike our previous work, 17 where we considered the effects of activity, here we show that even in a passive setting similar to that considered previously, [10][11][12] there is a simple and robust link between topological defects and the resulting geometry.…”

“…In this section, we review some basic facts that are useful for the study p -atic liquid crystals deep in the ordered limit on fixed curved surfaces. 18…”

“…Thus a solution to eqn (10) with defects j at z j with charge σ j isUsing eqn (11) and the Green's function G ( z , z ′), which satisfieswe can compute the contribution of defects to (eqn (9)), leading to(see ref. 18 for more details).…”

“…The first term in eqn (12) is the usual elastic interaction between defect pairs and the second term is the interaction between topological defects and the geometry, 18,24 where a topological defect of charge σ m acquires an effective charge of . The third term is an elastic contribution to the free energy from the geometry.…”

Active topological defect absorption by a curvature singularity

“…For a cone, this effective charge corresponds to negative topological charge concentrated at the apex, and a simple argument was recently presented in [32] for the case of free boundary conditions. Vafa et al [33] re-derived the induced charge result of Vitelli and Turner [31] and in the context of a cone with tangential boundary conditions used it to determine the ground state defect configuration given a fixed number of topological defects. As cones represent the simplest example of nontrivial curved geometry (flat everywhere except for the curvature singularity at the apex), we focus on studying the dynamics of active nematics on a cone.…”