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Garncarek, Zbigniew; Majcherczyk, T.; Potoczna-Petru, D.; Piasecki, R.

doi:10.1023/a:1006709417525

Cited by 4 publications

(7 citation statements)

References 8 publications

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“…As a result, the current value of the two-phase interface can be kept under control. The utility of monitoring of the interface has been shown using the examples of islands of miscellaneous shapes and poly-dispersed in sizes, mentioned above [13,25]. It is important to emphasize that in the present approach, a competition appears between the two pairs of the considered statistical descriptors.…”

Section: Introductionmentioning

confidence: 87%

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Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands

Olchawa

Piasecki

2015

Computational Materials Science

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H I G H L I G H T S  A weighted doubly-hybrid method of statistical reconstruction of patterns isreported.  The weighting factors account in part for an irregularity of islands shapes.  A final pattern has the same value of interface and number of islands as the target.  This competitive approach offers morphologically credible patterns.A B S T R A C T We report a fast, efficient and credible statistical reconstruction of any two-phase patterns of islands of miscellaneous shapes and poly-dispersed in sizes. In the proposed multi-scale approach called a weighted doubly-hybrid, two different pairs of hybrid descriptors are used. As the first pair, we employ entropic quantifiers, while correlation functions are the second pair. Their competition allows considering a wider spectrum of morphological features. Instead of a standard random initial configuration, a synthetic one with the same number of islands as that of the target is created by a cellular automaton. This is the key point for speeding-up of microstructure reconstruction, making use of the simulated annealing technique. The program procedure allows requiring the same values for the reconstructed and target interface. The reconstruction terminates when three conditions related to the accuracy, interface and number of islands are fulfilled. We verify the approach on digitized images of a thin metallic film and a concrete sample cross-section. For a given accuracy, our method significantly reduces the number of accepted Monte Carlo steps when compared to the standard approach. At the same time, it provides credible shapes and similar areas of islands, keeping their number and the total interface of the target. To the best of our knowledge, this is the first attempt to obtain such an outcome. The cost-effective reconstructions suggest that the present technique could also be used for patterns of islands with strongly jagged border lines.

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Section: Introductionmentioning

confidence: 87%

“…1a. A comparison of the representative 180  180 digitized sub-domain of the poly-dispersed metallic islands adapted from Ref [25]. with its typical WDH reconstructions for a given random seed and chosen parameters.…”

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confidence: 99%

Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands

Olchawa

Piasecki

2015

Computational Materials Science

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“…The approach of Refs. [10,11] can be regarded as exact for investigating the degree of inhomogeneity in a phase space. When the entropic measures are used for the same binary image, that is, (1)-pixel = ÿnite-sized object, exact measure, and (2)-pixel ∼ = point marker as a punctual object, approximated measure that is, however, qualitatively correct, a simple relation between them can be established (see Eq.…”

Section: Recapitulation Of the Microcanonical Formalism And Of The Avmentioning

confidence: 99%

“…The second measure (see formula (3b)) refers to the simpler case of "point" objects (POs) and was used in Refs. [10,11] under a di erent guise (it was called "f(S)" in these references). The method of Ref.…”

Section: Recapitulation Of the Microcanonical Formalism And Of The Av...mentioning

confidence: 99%

Inhomogeneity and complexity measures for spatial patterns

Piasecki

Martín

Plastino

2002

Physica A: Statistical Mechanics and its Applications

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In this work, we examine two di erent measures for inhomogeneity and complexity that are derived from non-extensive considerations Â a la Tsallis. Their performance is then tested on theoretically generated patterns. All measures are found to exhibit a most sensitive behaviour for Sierpinski carpets. The procedures here introduced provide us with new, powerful Tsallis' tools for analysing the inhomogeneity and complexity of spatial patterns.

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“…Let us indicate some other examples of media with a complex spatial distribution of objects such as metallic islands, carbon black or grains. A simple mathematical method [2] for the quantitative characterization of spatial inhomogeneity of point object distribution was employed to analyze transmission electron micrographs of thin metallic films [3,4] and polymer ⁄ carbon black composites [5]. Also other methods used in mathematical statistics were considered.…”

Section: Introductionmentioning

confidence: 99%

What is a physical measure of spatial inhomogeneity comparable to the mathematical approach?

Garncarek¹,

Piasecki²

1999

Eur. Phys. J. AP

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Abstract.A linear transformation f(S) of configurational entropy with length scale dependent coefficients as a measure of spatial inhomogeneity is considered. When a final pattern is formed with periodically repeated initial arrangement of point objects the value of the measure is conserved. This property allows for computation of the measure at every length scale. Its remarkable sensitivity to the deviation (per cell) from a possible maximally uniform object distribution for the length scale considered is comparable to behaviour of strictly mathematical measure h introduced by Garncarek et al. in [2]. Computer generated object distributions reveal a correlation between the two measures at a given length scale for all configurations as well as at all length scales for a given configuration. Some examples of complementary behaviour of the two measures are indicated.PACS. 05.90.+m Other topics in statistical physics, thermodynamics and nonlinear dynamical systems -68.55.-a Thin film structure and morphology

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Cited by 4 publications

References 8 publications

Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands

Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands

Inhomogeneity and complexity measures for spatial patterns

What is a physical measure of spatial inhomogeneity comparable to the mathematical approach?

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