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Active topological defect absorption by a curvature singularity
Farzan Vafa, David R. Nelson, Amin Doostmohammadi
Using the Born-Oppenheimer approximation, we present a general description of topological defects dynamics in -atic materials on curved surfaces, and simplify it in the case of…
Curvature as an external field in mechanical antiferromagnets
Abigail Plummer, Paul Z. Hanakata, David R. Nelson
A puckered sheet is a freestanding crystalline membrane with an embedded array of bistable buckled units. Recent work has shown that the bistable units behave like spins in a two-d…
Defect absorption and emission for -atic liquid crystals on cones
Farzan Vafa, Grace H. Zhang, David R. Nelson
We investigate the ground state configurations of -atic liquid crystals on fixed curved surfaces. We focus on the intrinsic geometry and show that isothermal coordinates are par…
Fractional defect charges in -atic liquid crystals on cones
Grace H. Zhang, David R. Nelson
Conical surfaces, with a delta function of Gaussian curvature at the apex, are perhaps the simplest example of geometric frustration. We study two-dimensional liquid crystals with…
Phonon eigenfunctions of inhomogeneous lattices: Can you hear the shape of a cone?
Grace H. Zhang, David R. Nelson
We study the phonon modes of interacting particles on the surface of a truncated cone resting on a plane subject to gravity, inspired by recent colloidal experiments. We derive the…
Buckling and metastability in membranes with dilation arrays
Abigail Plummer, David R. Nelson
We study periodic arrays of impurities that create localized regions of expansion, embedded in two-dimensional crystalline membranes. These arrays provide a simple elastic model of…