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Variational problems for liquid crystals with variable degree of orientation
journal contributionposted on 1991-01-01, 00:00 authored by Victor J. Mizel
Abstract: "The analysis of a nematic liquid crystal, filling a bounded cylindrical container, whose free energy is a (simplified) version of Ericksen's model with variable degree of orientation, leads to a variational problem of the form F[s,[phi]] = [integral]┬╣ΓéÇ[k (s╩╣)┬▓ + s┬▓ (([phi]╩╣)┬▓ + cos┬▓[phi]/r┬▓)]rdr subject to s(1) = sΓéÇ, [phi](1) = 0, with k a positive constant. It will be shown that a surprisingly explicit solution is obtainable. Moreover an interesting bifurcation takes place at k = 1."