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Driving innovations in manufacturing: Open Access research from DMEM

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Design, Manufacture & Engineering Management (DMEM).

Centred on the vision of 'Delivering Total Engineering', DMEM is a centre for excellence in the processes, systems and technologies needed to support and enable engineering from concept to remanufacture. From user-centred design to sustainable design, from manufacturing operations to remanufacturing, from advanced materials research to systems engineering.

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Stability of non-constant equilibrium states in a finite sample of ferroelectric liquid crystals

Anderson, D.A. and Stewart, Iain W. (2001) Stability of non-constant equilibrium states in a finite sample of ferroelectric liquid crystals. International Journal of Engineering Science, 39 (11). pp. 1191-1215. ISSN 0020-7225

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Abstract

The non-constant equilibrium solutions to a dynamic equation governing the director reorientation within a finite sample of ferroelectric liquid crystal are obtained in terms of Jacobian elliptic integrals of the first kind. The stability results for these solutions, for various values of the measurable parameters of the problem, depend upon proving the positivity of the eigenvalues of a regular Sturm-Liouville problem which arises from applying a perturbation analysis to such equilibrium solutions in a quite general setting. A Hardy-type integral inequality is further employed to prove the positivity of eigenvalues in a more restricted class of perturbations which allows improved results on the ranges of parameters for which stability holds.