Neural-network approach to modeling liquid crystals in complex confinement

SANTOS-SILVA, T, TEIXEIRA, P.I.C., ANQUETIL-DECK, C. and CLEAVER, Doug (2014). Neural-network approach to modeling liquid crystals in complex confinement. Physical Review E, 89 (5), 053316.

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Abstract

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are non-uniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a non-linear, integral Euler-Lagrange equation, or (ii) perform a direct multi-dimensional free energy minimisation. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the Multi-Layer Perceptron (MLP) artificial neural network for minimising the free energy of a fluid of hard non-spherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible and refinable. Furthermore, it can be readily generalised to the richer experimental patterned-substrate geometries that are now experimentally realisable but very problematic to conventional theoretical treatments.

Item Type:	Article
Research Institute, Centre or Group - Does NOT include content added after October 2018:	Materials and Engineering Research Institute > Modelling Research Centre > Materials Modelling group
Identification Number:	https://doi.org/10.1103/PhysRevE.89.053316
Page Range:	053316
Depositing User:	Doug Cleaver
Date Deposited:	17 Jul 2014 09:30
Last Modified:	18 Mar 2021 04:31
URI:	https://shura.shu.ac.uk/id/eprint/8170

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