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ARMA manuscript No. (will be inserted by the editor)

Summary: ARMA manuscript No.
(will be inserted by the editor)
Analytic description of layer undulations in
smectic A liquid crystals
Carlos J. Garc´ia-Cervera, Sookyung Joo
We investigate the layer undulations that appear in smectic A liquid
crystals when a magnetic field is applied in the direction parallel to the
smectic layers. In an earlier work [12], the authors characterized the critical
field using the Landau-de Gennes model for smectic A liquid crystals. In
this paper, we obtain an asymptotic expression of the unstable modes us-
ing -convergence theory, and a sharp estimate of the critical field. Under
the assumption that the layers are fixed at the boundaries, the maximum
layer undulation occurs in the middle of the cell and the displacement am-
plitude decreases near the boundaries. Our estimate of the critical field is
consistent with the Helfrich-Hurault theory. When natural boundary con-
ditions are considered, the displacement amplitude does not diminish near
the boundary, in sharp contrast with the Dirichlet case, and the critical
field is reduced compared to the one calculated in the classical theory. This
is consistent with the experiments carried out by Lavrentovich et al. [17].


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics