MULTISCALE WAVELET ANALYSIS IN POROUS MEDIA

An active area of experimental and theoretical research is to determine the relationship between microstructure and material properties such as mechanical, electrical, etc. [1]. Numerous studies have led to a better understanding of issues such as deformation, fracture, strength, electrical conductivity. However, it has been recognized that several open questions in this area could benefit significantly from recognizing that material heterogeneity (microstructure) is scale dependent, i.e. it is multiscale for (most) materials. Describing the relationship of material properties at different scales is quite a complex task [2]. Traditionally, problems of a multiscale nature, in particular the description of the porosity of inhomogeneous materials, are dealt with by different models using wavelet transforms. The composite wavelet matrix method consists of an approach in which different computational methodologies (molecular dynamics simulations, Monte Carlo simulations, and Potts Q-states) are applied to a region of a material simultaneously at coarse and fine spatial scales [3, 4].