Defects in nematic shells: a \(\Gamma\)-convergence discrete-to-continuum approach. (English) Zbl 1401.82047
A nematic shell is a rigid colloidal particle with a typical dimension in the micrometer scale coated with a thin film of nematic liquid crystal whose molecular orientation is subjected to a tangential anchoring. In this paper, the authors investigate the emergence of defects on nematic shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment of the director field. Defects emerge when the mesh size of the triangulation goes to zero, namely in the discrete-to-continuum limit. The discrete-to-continuum limit in two different asymptotic regimes is investigated. The first scaling promotes the appearance of a finite number of defects and the second scaling produces the so-called renormalized energy that governs the equilibrium of the configurations with defects.
Reviewer: Nasir N. Ganikhodjaev (Kuantan)
MSC:
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 76A15 | Liquid crystals |
| 35Q35 | PDEs in connection with fluid mechanics |
Software:
TriangleReferences:
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