Statistical mechanics characterization of spatio-compositional inhomogeneity

Piasecki, R.

doi:10.1016/j.physa.2009.06.028

Cited by 8 publications

(13 citation statements)

References 38 publications

(80 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The hybrid pair, {S ∆ (k), C S (k)}, is often used for multi-scale statistical reconstruction via entropic descriptors [24,51,52]. The first descriptor, S ∆ (k) ≡ [S max (k) − S(k)]/λ(k), is a quantitative measure of the degree of spatial inhomogeneity per cell [21,24,48,49]. Here, S(k) is the current entropy for the real configuration, and S max (k) denotes the entropy for the theoretically most homogeneous system, while λ(k) = [L − k + 1] 2 describes the number of partially overlapping sampling cells k × k for a given length scale k. In turn, the second descriptor C S (k) ≡ S ∆ (k)γ (k) can be applied as a measure of the spatial statistical complexity [50], where the shortcut is used, 0…”

Section: Reconstruction Using Entropic Descriptors-stage Twomentioning

confidence: 99%

See 1 more Smart Citation

A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

et al. 2020

Self Cite

View full text Add to dashboard Cite

The main goal of our research is to develop an effective method with a wide range of applications for the statistical reconstruction of heterogeneous microstructures with compact inclusions of any shape, such as highly irregular grains. The devised approach uses multi-scale extended entropic descriptors (ED) that quantify the degree of spatial non-uniformity of configurations of finite-sized objects. This technique is an innovative development of previously elaborated entropy methods for statistical reconstruction. Here, we discuss the two-dimensional case, but this method can be generalized into three dimensions. At the first stage, the developed procedure creates a set of black synthetic clusters that serve as surrogate inclusions. The clusters have the same individual areas and interfaces as their target counterparts, but random shapes. Then, from a given number of easy-to-generate synthetic cluster configurations, we choose the one with the lowest value of the cost function defined by us using extended ED. At the second stage, we make a significant change in the standard technique of simulated annealing (SA). Instead of swapping pixels of different phases, we randomly move each of the selected synthetic clusters. To demonstrate the accuracy of the method, we reconstruct and analyze two-phase microstructures with irregular inclusions of silica in rubber matrix as well as stones in cement paste. The results show that the two-stage reconstruction (TSR) method provides convincing realizations for these complex microstructures. The advantages of TSR include the ease of obtaining synthetic microstructures, very low computational costs, and satisfactory mapping in the statistical context of inclusion shapes. Finally, its simplicity should greatly facilitate independent applications.

show abstract

Section: Reconstruction Using Entropic Descriptors-stage Twomentioning

confidence: 99%

“…Of course, we can use similar ideas to obtain gray-level equivalents of the above ED, which can be useful for multi-phase materials [21,24,55].…”

Section: Supplementary Materialsmentioning

confidence: 99%

A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Those statistical descriptors were obtained as a result of splitting of the adapted overall entropic descriptor of a pillar model applied to greyscale images [28]. Each of the phase descriptors describes separately the corresponding contribution to the overall spatial inhomogeneity of the system.…”

Section: Examplementioning

confidence: 99%

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

Olchawa

Piasecki

2015

Computational Materials Science

View full text Add to dashboard Cite

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.

show abstract

“…microstructure reconstruction, not on the other possible categories of spatio-compositional inhomogeneity or spatio-compositional complexity. The introduction to those broad topics can be found in the latest articles (Piasecki 2009b;Piasecki & Plastino 2010). This is a reason why only the list of the appropriate formulas and important details are given in the appendix.…”

Section: Introductionmentioning

confidence: 99%

Microstructure reconstruction using entropic descriptors

Piasecki

2010

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for a stochastic optimization method. The first of them measures a spatial inhomogeneity, for a binary pattern, or compositional one, for a greyscale image. The second one quantifies a spatial or compositional statistical complexity. The EDs reveal structural information that is dissimilar, at least in part, to that given by correlation functions at almost all discrete length scales. The method is tested on a few digitized binary and greyscale images. In each of the cases, the persuasive reconstruction of the microstructure is found.

show abstract

Statistical mechanics characterization of spatio-compositional inhomogeneity

Cited by 8 publications

References 38 publications

A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

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

Microstructure reconstruction using entropic descriptors

Contact Info

Product

Resources

About