Abstract
The aim of this paper is to consider theoretically a Freedericksz transition for concentric toroidal layers of smectic C liquid crystal arising from a simple geometric setup, thereby extending the results of Atkin and Stewart [Q. Jl Mech. Appl. Math., 47, 1994] who considered spherical layers of smectic C in the usual cone and plate geometry. Application of smectic continuum theory leads, after suitable approximations are made, to a linear governing equilibrium equation which is satisfied by both the trivial solution and a variable solution involving Bessel functions. We are able to determine the critical magnitude cH of the magnetic field H at which this variable solution exists, and a standard energy comparison reveals that the variable solution is expected to be more energetically favourable than the zero solution provided H > cH. Numerical examples of critical thresholds are given, which are comparable to those in the literature for nematics. The paper ends with a discussion section and some indication of possible future work.
Original language | English |
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Pages (from-to) | 387-409 |
Number of pages | 22 |
Journal | IMA Journal of Applied Mathematics |
Volume | 66 |
Issue number | 4 |
DOIs | |
Publication status | Published - Aug 2001 |
Keywords
- Freedericksz transitions
- liquid crystals
- smetic