منابع مشابه
S-valued harmonic maps on polyhedra with tangent boundary conditions
A unit-vector field n : P → S2 on a convex polyhedron P ⊂ R3 satisfies tangent boundary conditions if, on each face of P , n takes values tangent to that face. Tangent unit-vector fields are necessarily discontinuous at the vertices of P . We consider fields which are continuous elsewhere. We derive a lower bound E P (h) for the infimum Dirichlet energy Einf P (h) for such tangent unit-vector f...
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Unit-vector fields n on a convex polyhedron P subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The equilibrium and metastable configurations correspond to minimisers and local minimisers of the Dirichlet energy, and may be regarded as S-valued harmonic maps on P . We consider unit-vector fields which are continuous away fro...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2010
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.11.008