Numerical simulation of flow in smectic liquid crystals

Merlin Fallahpour, Sean McKee, Ewa B. Weinmüller

Research output: Contribution to journalArticle

Abstract

Our aim is to simulate a nonlinear system of ODEs describing the flow in smectic liquid crystals. The nonlinear system is first linearized. We present a direct approach to compute the exact analytic solution of this linear system and use this solution as a starting profile in the MATLAB package bvpsuite2.0 to obtain the approximate solution to the nonlinear system. Although, the solution of the nonlinear system has steep boundary layers and therefore is difficult to resolve, we demonstrate that bvpsuite2.0 can cope with the problem and provide an approximation with reasonable accuracy.

LanguageEnglish
Pages154-162
Number of pages9
JournalApplied Numerical Mathematics
Volume132
Early online date29 May 2018
DOIs
Publication statusPublished - 31 Oct 2018

Fingerprint

Smectic liquid crystals
Liquid Crystal
Nonlinear systems
Nonlinear Systems
Numerical Simulation
Computer simulation
Analytic Solution
MATLAB
Linear systems
Boundary Layer
Resolve
Boundary layers
Approximate Solution
Linear Systems
Approximation
Demonstrate

Keywords

  • adaptive grids
  • boundary value problems in ODEs
  • collocation method
  • flow dynamics
  • smectic A liquid crystals

Cite this

Fallahpour, Merlin ; McKee, Sean ; Weinmüller, Ewa B. / Numerical simulation of flow in smectic liquid crystals. In: Applied Numerical Mathematics. 2018 ; Vol. 132. pp. 154-162.
@article{3de499e992b4417d8378df762430f440,
title = "Numerical simulation of flow in smectic liquid crystals",
abstract = "Our aim is to simulate a nonlinear system of ODEs describing the flow in smectic liquid crystals. The nonlinear system is first linearized. We present a direct approach to compute the exact analytic solution of this linear system and use this solution as a starting profile in the MATLAB package bvpsuite2.0 to obtain the approximate solution to the nonlinear system. Although, the solution of the nonlinear system has steep boundary layers and therefore is difficult to resolve, we demonstrate that bvpsuite2.0 can cope with the problem and provide an approximation with reasonable accuracy.",
keywords = "adaptive grids, boundary value problems in ODEs, collocation method, flow dynamics, smectic A liquid crystals",
author = "Merlin Fallahpour and Sean McKee and Weinm{\"u}ller, {Ewa B.}",
year = "2018",
month = "10",
day = "31",
doi = "10.1016/j.apnum.2018.05.014",
language = "English",
volume = "132",
pages = "154--162",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",

}

Numerical simulation of flow in smectic liquid crystals. / Fallahpour, Merlin; McKee, Sean; Weinmüller, Ewa B.

In: Applied Numerical Mathematics, Vol. 132, 31.10.2018, p. 154-162.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Numerical simulation of flow in smectic liquid crystals

AU - Fallahpour, Merlin

AU - McKee, Sean

AU - Weinmüller, Ewa B.

PY - 2018/10/31

Y1 - 2018/10/31

N2 - Our aim is to simulate a nonlinear system of ODEs describing the flow in smectic liquid crystals. The nonlinear system is first linearized. We present a direct approach to compute the exact analytic solution of this linear system and use this solution as a starting profile in the MATLAB package bvpsuite2.0 to obtain the approximate solution to the nonlinear system. Although, the solution of the nonlinear system has steep boundary layers and therefore is difficult to resolve, we demonstrate that bvpsuite2.0 can cope with the problem and provide an approximation with reasonable accuracy.

AB - Our aim is to simulate a nonlinear system of ODEs describing the flow in smectic liquid crystals. The nonlinear system is first linearized. We present a direct approach to compute the exact analytic solution of this linear system and use this solution as a starting profile in the MATLAB package bvpsuite2.0 to obtain the approximate solution to the nonlinear system. Although, the solution of the nonlinear system has steep boundary layers and therefore is difficult to resolve, we demonstrate that bvpsuite2.0 can cope with the problem and provide an approximation with reasonable accuracy.

KW - adaptive grids

KW - boundary value problems in ODEs

KW - collocation method

KW - flow dynamics

KW - smectic A liquid crystals

UR - http://www.scopus.com/inward/record.url?scp=85047986078&partnerID=8YFLogxK

UR - https://www.sciencedirect.com/journal/applied-numerical-mathematics

U2 - 10.1016/j.apnum.2018.05.014

DO - 10.1016/j.apnum.2018.05.014

M3 - Article

VL - 132

SP - 154

EP - 162

JO - Applied Numerical Mathematics

T2 - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -