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Advisor(s)
Abstract(s)
Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter
profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either
(i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy
minimization. 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 multilayer
perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical
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 generalized to the richer experimental patterned-substrate geometries that are now experimentally
realizable but very problematic to conventional theoretical treatments.
Description
Keywords
Neural-network Modeling liquid crystals Complex confinement
Citation
SANTOS-SILVA, T.; TEIXEIRA, P. I. C.; ANQUETIL-DECK, C.; CLEAVER, D. J. - Neural-network approach to modeling liquid crystals in complex confinement. Physical Review E. ISSN 1539-3755. Vol. 89, nr. 5 (2014), p. 053316-1/053316-12.