57 citations · 134 across the 10 of their papers we have counts for
7 papers · 1 filter
Quantum statistics on graphs
JM Harrison, JP Keating, JM Robbins
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for…
Liquid crystals and harmonic maps in polyhedral domains
A Majumdar, JM Robbins, M Zyskin
Unit-vector fields $\nvec$ on a convex polyhedron subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The e…
Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions
A Majumdar, JM Robbins, M Zyskin
A unit-vector field n:P \to S^2 on a convex polyhedron P \subset R^3 satisfies tangent boundary conditions if, on each face of P, n takes values tangent to that face. Tangent unit-…
Elastic energy for reflection-symmetric topologies
A. Majumdar, J. M. Robbins, M. Zyskin
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider…
Elastic energy of liquid crystals in convex polyhedra
A Majumdar, JM Robbins, M Zyskin
We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-co…
Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra
A. Majumdar, J. M. Robbins, M. Zyskin
We derive a lower bound for energies of harmonic maps of convex polyhedra in to the unit sphere with tangent boundary conditions on the faces. We also establish tha…