title: Neural-network approach to modeling liquid crystals in complex confinement.
abstract: 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.
authors.affiliation: Faculdade de Engenharia, Universidade Católica Portuguesa, Estrada de Talaíde, P-2635-631 Rio de Mouro, Portugal.
authors.forename: T
authors.initials: T
authors.lastname: Santos-Silva
authors.affiliation: Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, P-1950-062 Lisbon, Portugal and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, P-1649-003 Lisbon, Portugal.
authors.forename: P I C
authors.initials: PI
authors.lastname: Teixeira
authors.affiliation: Materials and Engineering Research Institute, Sheffield Hallam University, Pond Street, Sheffield S1 1WB, United Kingdom.
authors.forename: C
authors.initials: C
authors.lastname: Anquetil-Deck
authors.affiliation: Materials and Engineering Research Institute, Sheffield Hallam University, Pond Street, Sheffield S1 1WB, United Kingdom.
authors.forename: D J
authors.initials: DJ
authors.lastname: Cleaver