Coarsened Lattice Spatial Disorder in the Thermodynamic Limit

Physica Status Solidi (b)

2003

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PACS : 05.90.+m, 72.80.Ng, 72.80.Tm Using numerical simulations and analytical approximations we study a modified version of the twodimensional lattice model [R. Piasecki, phys. stat. sol. (b) 209, 403 (1998)] for random pH:(1 − p)L systems consisting of grains of high (low) conductivity for the H-(L-)phase, respectively. The modification reduces a spectrum of model bond conductivities to the two pure ones and the mixed one. The latter value explicitly depends on the average concentration γ(p) of the H-component per model cell. The effective conductivity as a function of content p of the H-phase in such systems can be modelled making use of three model parameters that are sensitive to both grain size distributions, GSD(H) and GSD(L). However, to incorporate into the model information directly connected with a given GSD, a computer simulation of the geometrical arrangement of grains is necessary. By controlling the polydispersity in grain sizes and their relative area frequencies, the effective conductivity could be raised or decreased and correlated with γ(p). When the phases are interchanged, a hysteresis-loop like behaviour of the effective conductivity, characteristic of dual media, is found. We also show that the topological non-equivalence of system's microstructure accompanies some GSDs, and it can be detected by the entropic measure of spatial inhomogeneity of model cells.

Section: Model and Resultsmentioning

confidence: 99%

“…c) The corresponding fractions of mixed bonds F M (p). d) The spatial inhomogeneity of coarsened lattice quantified by entropic measure S ∆ (p) in the thermodynamic limit [18,20].…”

Section: Model and Resultsmentioning

confidence: 99%

Effective conductivity in a lattice model for binary disordered media with complex distributions of grain sizes

Physica Status Solidi (b)

2003

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“…The morphological features of complex materials are vital for modelling and predicting their macroscopic properties, for instance, effective conductivity [1][2][3][4]. For binary micrographs of such materials, the quantitative characterization of the spatial distribution of pixels, in some cases allows correlate their properties and internal structure attributes.…”

Section: Introduction Sensitive Measuresmentioning

confidence: 99%

A versatile entropic measure of grey level inhomogeneity

Physica A: Statistical Mechanics and its Applications

2009

The entropic measure for analysis of grey level inhomogeneity (GLI) is proposed as a function of length scale. It allows us to quantify the statistical dissimilarity of the actual macrostate and the maximizing entropy of the reference one. The maximums (minimums) of the measure indicate those scales at which higher (lower) average grey level inhomogeneity appears compared to neighbour scales. Even a deeply hidden statistical grey level periodicity can be detected by the equally distant minimums of the measure. The striking effect of multiple intersecting curves (MIC) of the measure has been revealed for pairs of simulated patterns, which differ in shades of grey or symmetry properties, only. This indicates for a nontrivial dependence of the GLI on length scale. In turn for evolving photosphere granulation patterns, the stability in time of the first peak position has been found. Interestingly, at initial steps of the evolution clearly dominates the third peak. This indicates for a temporary grouping of granules at length scale that may belong to mesogranulation phenomenon. This behaviour has similarities with that reported by Consolini, Berrilli et al. (2003, 2005 for binarized granulation images of a different data set.

A generalization of the inhomogeneity measure for point distributions to the case of finite size objects

Physica A: Statistical Mechanics and its Applications

2008

The statistical measure of spatial inhomogeneity for n points placed in χ cells each of size k×k is generalized to incorporate finite size objects like black pixels for binary patterns of size L×L. As a function of length scale k, the measure is modified in such a way that it relates to the smallest realizable value for each considered scale. To overcome the limitation of pattern partitions to scales with k being integer divisors of L we use a sliding cell-sampling approach. For given patterns, particularly in the case of clusters polydispersed in size, the comparison between the statistical measure and the entropic one reveals differences in detection of the first peak while at other scales they well correlate. The universality of the two measures allows both a hidden periodicity traces and attributes of planar quasi-crystals to be explored. PACS: 05.90.+m