Abstract


We study the gradient flow model for the Landau--de Gennes energy functional for nematic liquid crystals at the nematic-isotropic transition temperature on prototype geometries. We study the dynamic model on a three-dimensional droplet and on a disc with Dirichlet boundary conditions and different types of initial conditions. In the case of a droplet with radial boundary conditions, a large class of physically relevant initial conditions generate dynamic solutions with a well-defined nematic-isotropic interface which propagates according to mean curvature for small times. On a disc, we make a distinction between “planar” and “nonplanar” initial conditions, and “minimal” and “nonminimal” Dirichlet boundary conditions. Planar initial conditions generate solutions with an isotropic core for all times, whereas nonplanar initial conditions generate solutions which escape into the third dimension. Nonminimal boundary conditions generate solutions with boundary layers, and these solutions can either have a largely ordered interior profile or an almost entirely disordered isotropic interior profile. Our examples suggest that while critical points of the Landau--de Gennes energy typically have highly localized disordered-ordered interfaces, the transient dynamics exhibits observable interfaces of potential experimental relevance.
LanguageEnglish
Pages1296-1320
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume76
Issue number4
DOIs
StatusPublished - 19 Jul 2016

Fingerprint

Front Propagation
Superconducting transition temperature
Initial conditions
Boundary conditions
Droplet
Dirichlet Boundary Conditions
Interior
Nematic liquid crystals
Transient Dynamics
Gradient Flow
Nematic Liquid Crystal
Dynamic models
Energy Functional
Boundary layers
Mean Curvature
Well-defined
Boundary Layer
Critical point
Dynamic Model
Geometry

Cite this

Front Propagation at the Nematic-Isotropic Transition Temperature. / Majumdar, Apala; Milewski, Paul A.; Spicer, Amy.

In: SIAM Journal on Applied Mathematics, Vol. 76, No. 4, 19.07.2016, p. 1296-1320.

Research output: Contribution to journalArticle

@article{a8ee56394e794298806c7eada520cf62,
title = "Front Propagation at the Nematic-Isotropic Transition Temperature",
abstract = "We study the gradient flow model for the Landau--de Gennes energy functional for nematic liquid crystals at the nematic-isotropic transition temperature on prototype geometries. We study the dynamic model on a three-dimensional droplet and on a disc with Dirichlet boundary conditions and different types of initial conditions. In the case of a droplet with radial boundary conditions, a large class of physically relevant initial conditions generate dynamic solutions with a well-defined nematic-isotropic interface which propagates according to mean curvature for small times. On a disc, we make a distinction between “planar” and “nonplanar” initial conditions, and “minimal” and “nonminimal” Dirichlet boundary conditions. Planar initial conditions generate solutions with an isotropic core for all times, whereas nonplanar initial conditions generate solutions which escape into the third dimension. Nonminimal boundary conditions generate solutions with boundary layers, and these solutions can either have a largely ordered interior profile or an almost entirely disordered isotropic interior profile. Our examples suggest that while critical points of the Landau--de Gennes energy typically have highly localized disordered-ordered interfaces, the transient dynamics exhibits observable interfaces of potential experimental relevance.",
author = "Apala Majumdar and Milewski, {Paul A.} and Amy Spicer",
year = "2016",
month = "7",
day = "19",
doi = "10.1137/15M1039250",
language = "English",
volume = "76",
pages = "1296--1320",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",

}

TY - JOUR

T1 - Front Propagation at the Nematic-Isotropic Transition Temperature

AU - Majumdar, Apala

AU - Milewski, Paul A.

AU - Spicer, Amy

PY - 2016/7/19

Y1 - 2016/7/19

N2 - We study the gradient flow model for the Landau--de Gennes energy functional for nematic liquid crystals at the nematic-isotropic transition temperature on prototype geometries. We study the dynamic model on a three-dimensional droplet and on a disc with Dirichlet boundary conditions and different types of initial conditions. In the case of a droplet with radial boundary conditions, a large class of physically relevant initial conditions generate dynamic solutions with a well-defined nematic-isotropic interface which propagates according to mean curvature for small times. On a disc, we make a distinction between “planar” and “nonplanar” initial conditions, and “minimal” and “nonminimal” Dirichlet boundary conditions. Planar initial conditions generate solutions with an isotropic core for all times, whereas nonplanar initial conditions generate solutions which escape into the third dimension. Nonminimal boundary conditions generate solutions with boundary layers, and these solutions can either have a largely ordered interior profile or an almost entirely disordered isotropic interior profile. Our examples suggest that while critical points of the Landau--de Gennes energy typically have highly localized disordered-ordered interfaces, the transient dynamics exhibits observable interfaces of potential experimental relevance.

AB - We study the gradient flow model for the Landau--de Gennes energy functional for nematic liquid crystals at the nematic-isotropic transition temperature on prototype geometries. We study the dynamic model on a three-dimensional droplet and on a disc with Dirichlet boundary conditions and different types of initial conditions. In the case of a droplet with radial boundary conditions, a large class of physically relevant initial conditions generate dynamic solutions with a well-defined nematic-isotropic interface which propagates according to mean curvature for small times. On a disc, we make a distinction between “planar” and “nonplanar” initial conditions, and “minimal” and “nonminimal” Dirichlet boundary conditions. Planar initial conditions generate solutions with an isotropic core for all times, whereas nonplanar initial conditions generate solutions which escape into the third dimension. Nonminimal boundary conditions generate solutions with boundary layers, and these solutions can either have a largely ordered interior profile or an almost entirely disordered isotropic interior profile. Our examples suggest that while critical points of the Landau--de Gennes energy typically have highly localized disordered-ordered interfaces, the transient dynamics exhibits observable interfaces of potential experimental relevance.

U2 - 10.1137/15M1039250

DO - 10.1137/15M1039250

M3 - Article

VL - 76

SP - 1296

EP - 1320

JO - SIAM Journal on Applied Mathematics

T2 - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 4

ER -