Extracting spectral density function of a binary composite without a-priori assumption

TL;DR

This paper introduces a numerical algorithm combining Monte Carlo integration and constrained least squares to extract the spectral density function of binary composites without prior assumptions, enhancing microstructural analysis.

Contribution

The paper presents a novel numerical method for resolving spectral density functions in composites without requiring a priori assumptions, verified against known models and applied to real systems.

Findings

Method accurately reproduces known spectral functions

Provides microstructural insights into composite behavior

Applicable to complex rock-and-brine systems

Abstract

The spectral representation separates the contributions of geometrical arrangement (topology) and intrinsic constituent properties in a composite. The aim of paper is to present a numerical algorithm based on the Monte Carlo integration and contrainted-least-squares methods to resolve the spectral density function for a given system. The numerical method is verified by comparing the results with those of Maxwell-Garnett effective permittivity expression. Later, it is applied to a well-studied rock-and-brine system to instruct its utility. The presented method yields significant microstructural information in improving our understanding how microstructure influences the macroscopic behaviour of composites without any intricate mathematics.