Vortices induced by topological forcing in nematic liquid crystal layers
In two-dimensional systems, dissipative vortices are described by a complex Ginzburg-Landau equation (CGLE) which has a universal character and describes such different systems as fluids, superfluids, superconductors, liquid crystals, granular media, magnetic media, and optical dielectrics, to menti...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Chile |
| OAI Identifier: | oai:repositorio.anid.cl:10533/237755 |
| Acceso en línea: | https://hdl.handle.net/10533/237755 |
| Access Level: | acceso abierto |
| Palabra clave: | Ciencias Naturales Ciencias Físicas Optica |
| Sumario: | In two-dimensional systems, dissipative vortices are described by a complex Ginzburg-Landau equation (CGLE) which has a universal character and describes such different systems as fluids, superfluids, superconductors, liquid crystals, granular media, magnetic media, and optical dielectrics, to mention just a few. Vortices occur in complex fields and can be identified as topological defects, that is, pointlike singularities which locally breaks the symmetry. Liquid crystals with negative anisotropic dielectric constant and homeotropic anchoring are a natural physical context where dissipative vortices are observed. Dissipative vortices are known in this context as umbilical defects. This thesis is composed of seven chapters and one appendix that contain the article published during this work. The first three chapters serve as an introduction: In Chapter 1 we present motivations and preliminary notions about topological defects, while Chapter 2 and 3 are focused on presenting general results about Ginzburg-Landau type equations. Chapter 4 is devoted to establishing analytically the origin of vortex lattices observed in illuminated liquid crystal layers, we give a theoretical description in terms of an approximate vortex solution that we called Rayleigh vortex valid under the Fr\'eederickzs transition and induced by a topological forcing. In Chapter 5 we study a new type of topological forcing that induces vortex-like defects inspired by experimental observations with inhomogeneous magnetic fields in a nematic liquid-crystal light valve (LCLV). We give a theoretical description in terms of a Ginzburg-Landau type amplitude equation and also we derive an analytical solution which describes accurately the system behavior and shows fair agreement with numerical simulations and experimental observations. In Chapter 6 we study the dynamics of defects in one (kinks) and two dimensional (vortices) cases, deriving in each one the dynamical motion equation for the defect position under topological forcing. Finally, in Chapter 7 we show qualitative properties of global minimizers of the Ginzburg-Landau energy, prove the existence of global minimizers and state the main results about symmetry breaking scenarios. |
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