Light-scattering experiments in dye-doped liquid crystals both to determine crystal parameters and to construct consistent neural network empirical physical formulas for scattering amplitudes

Abstract

The aim of this paper is two-fold. Firstly, static laser light-scattering amplitude measurements in azo-dye doped nematic liquid crystals (NLCs) were made versus scattering angle, temperature and applied bias voltage. Three NLC parameters were determined: the elastic constant ratios K-11/K-22 by regression, phase transition temperatures, and Freedericksz voltages from the graphs. They were all doping ratio dependent. Secondly, as a novel approach, by a nonlinear universal function approximator layered feedforward neural network (LFNN) we constructed an explicit form of empirical physical formulas (EPFs) for theoretically unknown nonlinear azo-dye doped NLC scattering amplitude functions. Excellent LFNN test set (i.e. yet-to-be measured experimental data) predictions prove that the constructed LFNN-EPPs estimate unknown amplitude functions consistently. The LFFN-EPFs, too, confirmed the doping-ratio dependency. Also, comparing LFNN and regression amplitude fits, the LFNN fits were significantly better. In conclusion, physical laws embedded in the physical data can be consistently extracted by LFNN. One major potential application in the nonlinear optics domain is that these LFNN-EPFs, by differentiation, integration, minimization, etc., can be used to obtain further NLC scattering amplitude related molecular structural physical quantities. This could in turn help us to develop new nonlinear optical materials. (C) 2011 Elsevier B.V. All rights reserved.