Free Boundary-Value Problems for Liquid Crystals

Update: 2014-07-11

Description

We discuss modelling strategies for free boundary-value problems arising in liquid crystal applications. We have recently modelled stable liquid crystal patterns in shallow cuboid-shaped nematic wells and have computed phase diagrams as a function of geometrical aspect ratio and anchoring strength on well boundaries. Recent work by Telo da Gama group (CFTC, Lisbon) shows that our computed patterns are also relevant to wedge-shaped nematic-filled wells at the isotropic-nematic transition temperature. At the isotropic-nematic transition temperature, the isotropic and nematic phases are separated by a free boundary, depending on the geometry and the surface effects at play. We discuss modelling approaches to this free-boundary problem and the role of such free boundaries in applications. This is joint work with Chong Luo, Samo Kralj and Samo Kralj.

Comments

In Channel

$Shock diffraction by convex cornered wedges$

Shock diffraction by convex cornered wedges

2014-07-1430:44

Plenary Lecture 14: Free boundary problems for mechanical models of tumor growth

2014-07-1151:32

Plenary Lecture 13: Shock Reflection, von Neumann conjectures, and free boundary problems

2014-07-1152:54

Plenary Lecture 11: Numerical simulation of endocytosis

2014-07-1153:14

Plenary Lecture 12: Slamming in flexible-channel flows

2014-07-1146:01

Plenary Lecture 10: Absence of the interface splash singularity for the two-fluid Euler equations

2014-07-1152:24

On a thermodynamically consistent Stefan problem with variable surface energy

2014-07-1134:38

Plenary Lecture 9: Curvature flow on graphs for large data classification

2014-07-1155:17

$Free boundaries in fractional filtration equations$

Free boundaries in fractional filtration equations

2014-07-1134:50

Obstacle problems in unbounded domains and related issues

2014-07-1132:38

Pointwise estimates and regularity for the parabolic obstacle problem

2014-07-1126:45

Deterministic Pattern Formation in Diffusion-Limited Systems

2014-07-1138:55

A phase field approach for shape optimization in fluids

2014-07-1124:13

On the production of high-porosity metallic solids

2014-07-1128:55

Existence and Qualitative Properties of Grounds States to the Choquard-Type Equations

2014-07-1127:48

Plenary Lecture 8: Interfaces arising from solid phase transformations

2014-07-1155:14

Free Boundary-Value Problems for Liquid Crystals

2014-07-1132:42

Free boundary problems in glacial hydrology

2014-07-1127:09

Numerical approximation of phase-field models for multiphase flow

2014-07-1131:23

A stable discretization for the simulation of two-phase flow

2014-07-1127:10

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Free Boundary-Value Problems for Liquid Crystals

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Free Boundary-Value Problems for Liquid Crystals

Vincenzo Abete

Free Boundary-Value Problems for Liquid Crystals