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Analysis of a Ginzburg-Landau type energy model for smectic $$C^\ast$$ liquid crystals with defects. (English) Zbl 1288.35443
Summary: This work investigates properties of a smectic $$C^\ast$$ liquid crystal film containing defects that cause distinctive spiral patterns in the film’s texture. The phenomena are described by a Ginzburg-Landau type model and the investigation provides a detailed analysis of minimal energy configurations for the film’s director field. The study demonstrates the existence of a limiting location for the defects (vortices) so as to minimize a renormalized energy. It is shown that if the degree of the boundary data is positive then the vortices each have degree $$+1$$ and that they are located away from the boundary. It is proved that the limit of the energies for a sequence of minimizers minus the sum of the energies around their vortices, as the G-L parameter $$\epsilon$$ tends to zero, is equal to the renormalized energy for the limiting state.

##### MSC:
 35Q56 Ginzburg-Landau equations 82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) 76A15 Liquid crystals 49K20 Optimality conditions for problems involving partial differential equations 35R09 Integro-partial differential equations
##### Keywords:
liquid crystal film; Ginzburg-Landau type model; minimizers
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##### References:
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