title: Using convex quadratic programming to model random media with Gaussian random fields.
abstract: Excursion sets of Gaussian random fields (GRFs) have been frequently used in the literature to model two-phase random media with measurable phase autocorrelation functions. The goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function. In this paper, we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization. Unlike previous methods, this technique efficiently optimizes over all admissible field autocorrelation functions, instead of optimizing only over a predetermined parametrized family. The results from using this technique indicate that the GRF model is significantly more versatile than observed in previous studies. An application to modeling a base-catalyzed tetraethoxysilane aerogel system given small-angle neutron scattering data is also presented.
authors.affiliation: Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, Texas 76203, USA. jquintanilla@unt.edu
authors.forename: John A
authors.initials: JA
authors.lastname: Quintanilla
authors.forename: W Max
authors.initials: WM
authors.lastname: Jones