Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 27, Issue 6, Pages 1905-1932Publisher
SPRINGER
DOI: 10.1007/s00332-017-9390-5
Keywords
Nematic; Landau-de Gennes; Gamma-convergence; Thin film
Categories
Funding
- NSF [DMS-1434969, DMS-1101290, DMS-1362879]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1434969] Funding Source: National Science Foundation
Ask authors/readers for more resources
We use the method of -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach in Golovaty et al. (J Nonlinear Sci 25(6):1431-1451, 2015) where we considered a similar problem for a planar surface. Since the anchoring energy dominates when the thickness of the film is small, it is essential to understand its influence on the structure of the minimizers of the limiting energy. In particular, the anchoring energy dictates the class of admissible competitors and the structure of the limiting problem. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and strong Dirichlet boundary conditions on the lateral boundary of the film when the surface is not closed. We establish a general convergence result to an energy defined on the surface that involves a somewhat surprising remnant of the normal component of the tensor gradient. Then we exhibit one effect of curvature through an analysis of the behavior of minimizers to the limiting problem when the substrate is a frustum.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available