Variational problems for liquid crystals with variable degree of orientation

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]¹₀[k (sʹ)² + s² (([phi]ʹ)² + cos²[phi]/r²)]rdr subject to s(1) = s₀, [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."