Local entropy characterization of correlated random microstructures

Abstract

A rigorous connection is established between the local porosity entropy introduced by Boger et al. (Physica A 187, 55 (1992)) and the configurational entropy of Andraud et al. (Physica A 207, 208 (1994)). These entropies were introduced as morphological descriptors derived from local volume fluctuations in arbitrary correlated microstructures occuring in porous media, composites or other heterogeneous systems. It is found that the entropy lengths at which the entropies assume an extremum become identical for high enough resolution of the underlying configurations. Several examples of porous and heterogeneous media are given which demonstrate the usefulness and importance of this morphological local entropy concept.

Information entropy in solar atmospheric fields

“…As a matter of fact, morphology and topology information may be extracted by applying the Gibbs-Shannon entropy concept. For example, Andraud et al (1994Andraud et al ( , 1997 introduced an entropic measure, named configuration entropy, as a descriptor of random morphologies. Such configuration entropy is a measure of the local fluctuations of some measurable quantity over the random system, defined as follows.…”

“…Such a definition is equivalent to the usual Gibbs-Shannon entropy normalised by the factor log(a + 1), which plays a role similar to the "multiplicative renormalization in the theory of critical phenomena" (Andraud et al 1997). When applied to a disordered system, this entropic measure is able to extract some useful information dealing with the typical length scale at which inhomogeneities are present and so on.…”

Spectral density analysis of the optical properties of Ni-Al 2 O 3 nano-composite films

“…6 suggest that local density distributions should be looked into as a way to characterize nanocomposite samples and to predict their optical and electrical properties. Significant work along these lines have been done in the field of geophysics by Hilfer and coworkers 45 , but only little attention has been devoted to optical properties of nanoparticle films 46 using closely related concepts 47 .…”

Inhomogeneity and complexity measures for spatial patterns

“…Fig. 3b depicts the typical behaviour of S ; q (k; PO; B), versus the length scale k, for a given q-parameter and also for its associated 1=q-value, for both the DSC (3,8,3) and the R patterns. Note that the behaviour displayed in Fig.…”