Using Steepest Descent to Find Energy-Minimizing Maps Satisfying Nonlinear Constraints
Description:
The method of steepest descent is applied to a nonlinearly constrained optimization problem which arises in the study of liquid crystals. Let Ω denote the region bounded by two coaxial cylinders of height 1 with the outer cylinder having radius 1 and the inner having radius ρ. The problem is to find a mapping, u, from Ω into R^3 which agrees with a given function v on the surfaces of the cylinders and minimizes the energy function over the set of functions in the Sobolev space H^(1,2)(Ω; R^3) h…
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Date:
August 1994
Creator:
Garza, Javier, 1965-
Partner:
UNT Libraries