Numerical simulation of flow in smectic liquid crystals

Merlin Fallahpour; Sean McKee; Ewa B. Weinmüller

doi:10.1016/j.apnum.2018.05.014

Numerical simulation of flow in smectic liquid crystals

Merlin Fallahpour, Sean McKee, Ewa B. Weinmüller

Mathematics And Statistics

Research output: Contribution to journal › Article

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.

Original language	English
Pages (from-to)	154-162
Number of pages	9
Journal	Applied Numerical Mathematics
Volume	132
Early online date	29 May 2018
DOIs	https://doi.org/10.1016/j.apnum.2018.05.014
Publication status	Published - 31 Oct 2018

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Keywords

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

Cite this

Fallahpour, M., McKee, S., & Weinmüller, E. B. (2018). Numerical simulation of flow in smectic liquid crystals. Applied Numerical Mathematics, 132, 154-162. https://doi.org/10.1016/j.apnum.2018.05.014

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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.

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KW - flow dynamics

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Access to Document

10.1016/j.apnum.2018.05.014