Generation of long-range correlations in large systems as an optimization problem

Abstract

We propose an efficient method of generating long-range correlations in large systems. The development of this method was motivated by the problem of constructing an optimal model for a large-scale porous medium. There are typically long-range correlations in the properties of such porous media, such as their permeability and porosity, for which there are usually only limited data. The optimal model must not only honor (preserve) the available data and their correlation function, but also accurately predict the future behavior of fluid flow in the media. We formulate the problem of generating the long-range correlations as one of optimization, and utilize simulated annealing to generate a d-dimensional array which contains the correlations and honors the existing data. The optimization process is based on the data's correlation function. The method is, therefore, free of the many numerical difficulties and/or limitations that most previous techniques suffer from. It is completely general and may be used for generating long-range correlations with any type of correlation function, in both isotropic and anisotropic media. Representative examples are presented, and the method's efficiency and accuracy are discussed.