Nematic liquid crystals on curved surfaces: a thin film limit
| Autor: | Ingo Nitschke, Simon Praetorius, Michael Nestler, Hartmut Löwen, Axel Voigt |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Surface (mathematics)
Materials science General Mathematics FOS: Physical sciences General Physics and Astronomy Condensed Matter - Soft Condensed Matter 01 natural sciences 010305 fluids & plasmas Mathematics - Analysis of PDEs Liquid crystal 0103 physical sciences FOS: Mathematics Limit (mathematics) Thin film 010306 general physics Research Articles Mathematical Physics 35Q82 53Z05 58J99 58Z05 82D30 76A15 Partial differential equation Condensed matter physics Continuous transition General Engineering Mathematical Physics (math-ph) Flow (mathematics) Phase space Soft Condensed Matter (cond-mat.soft) Analysis of PDEs (math.AP) |
| Zdroj: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 474:20170686 |
| ISSN: | 1471-2946 1364-5021 |
| DOI: | 10.1098/rspa.2017.0686 |
| Popis: | We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties. Comment: 20 pages, 4 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|