Euler-Poincaré characteristics of classes of disordered media

Arns, Christoph H.; Knackstedt, Mark; Pinczewski, W.V.; Mecke, Klaus

doi:10.1103/physreve.63.031112

Cited by 93 publications

(103 citation statements)

References 34 publications

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“…These tools are commonly used in other disciplines (e.g, digital image analysis [48]) but have only recently been developed in a systematic way as measures of complex media [3]. A family of measures, the Minkowski functionals in particular seem to be promising measures for describing the morphology of complex materials.…”

Section: Integral Geometric Measuresmentioning

confidence: 99%

“…In particular, integral geometry provides powerful formulae for the Boolean model. A review of these measures and applications in physics is given in [3,32,34]. In this study we consider the integral geometric measures of digitized representations of complex media.…”

Section: Integral Geometric Measuresmentioning

confidence: 99%

“…A digitised set of either component can be described by a collection of voxels of compact (closed and bounded) convex sets. The global morphology of a Boolean model, i.e., of a structure ∪ i K i made up of individual overlapping grains K of number density ρ are [3,32,34];…”

Section: Integral Geometric Measuresmentioning

confidence: 99%

“…In this equation we assume the particulate phase is the continuous phase-each voxel has 26 neighbour connections, while the inverse phase is 6-connected. The dependence of these measures on the definition of the voxel-neighbourhood is discussed in detail in [3] as well as in the contribution by Ohser et al in this volume. In the examples discussed below, the resolution of the digitisation was always smaller than the size of typical spatial features, so that the differences between neighbourhood definitions can be neglected since they are usually smaller than the symbol size used.…”

Section: Integral Geometric Measuresmentioning

confidence: 99%

“…/N for each configuration are obtained by configuration counts over all vertices on any voxelated structure after normalizing by the total number N = L 3 of vertices [3,17,33].…”

Section: Calculation Of Integral Geometric Measures the Intensities mentioning

confidence: 99%

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Characterising the Morphology of Disordered Materials

Arns

Knackstedt

Mecke

2002

Morphology of Condensed Matter

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Abstract. We introduce Minkowski functionals to characterise, reconstruct and discriminate different complex material microstructures, for instance, experimental data sets generated from X-ray computer tomography imaging; samples include a suite of Fontainebleau sandstone, and a heterogeneous cross-bedded sandstone. Three distinct classes of digitised complex microstructure are considered: particle based Boolean models, structures generated by level-cuts through Gaussian fields, and models based on a Voronoi tesselation of space. One can define a set of measures for random composite media from a single image at any phase fraction φ which allows one to accurately reconstruct the medium for all other phase fractions and to predict, for instance, the percolation threshold pc. The evolution of the Minkowski functions during erosion and dilation operations on non-convex morphologies leads to a very accurate discrimination of morphologybetter than commonly used techniques such as structure functions or chord length distributions. Spatial Structures: Experimental Data and Stochastic ModelsThe structure of a disordered material -an oil bearing rock, a piece of paper, or a polymer composite -is a remarkably incoherent concept. Despite this, scientists and engineers are asked to predict the properties of a disordered material based on the "structure" of its constituent components. A major shortcoming in the understanding of processes involving complex materials has been an inability to accurately characterize microstructure. The specification of "structure" requires topological as well as geometric descriptors to characterize the connectivity and the shape of the spatial configuration. In oil recovery from petroleum reservoir rocks, an area of particular interest to the authors, recovery depends crucially on the topology of the pore space and on the mean curvature of the surfaces where immiscible phases meet at a contact angle. To determine accurate flow models and to devise intelligent recovery strategies requires an accurate characterization of reservoir rocks in terms of topology and geometry.To date, the main toolkit used to quantify complex structures has been primarily that of the statistical physicist and not the advanced techniques developed in spatial statistics [11,59]

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Section: Integral Geometric Measuresmentioning

confidence: 99%

Section: Integral Geometric Measuresmentioning

confidence: 99%

Section: Integral Geometric Measuresmentioning

confidence: 99%

Section: Integral Geometric Measuresmentioning

confidence: 99%

“…/N for each configuration are obtained by configuration counts over all vertices on any voxelated structure after normalizing by the total number N = L 3 of vertices [3,17,33].…”

Section: Calculation Of Integral Geometric Measures the Intensities mentioning

confidence: 99%

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Characterising the Morphology of Disordered Materials

Arns

Knackstedt

Mecke

2002

Morphology of Condensed Matter

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Mapping permeability in low‐resolution micro‐CT images: A multiscale statistical approach

Botha

Sheppard

2016

Water Resources Research

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We investigate the possibility of predicting permeability in low‐resolution X‐ray microcomputed tomography (µCT). Lower‐resolution whole core images give greater sample coverage and are therefore more representative of heterogeneous systems; however, the lower resolution causes connecting pore throats to be represented by intermediate gray scale values and limits information on pore system geometry, rendering such images inadequate for direct permeability simulation. We present an imaging and computation workflow aimed at predicting absolute permeability for sample volumes that are too large to allow direct computation. The workflow involves computing permeability from high‐resolution µCT images, along with a series of rock characteristics (notably open pore fraction, pore size, and formation factor) from spatially registered low‐resolution images. Multiple linear regression models correlating permeability to rock characteristics provide a means of predicting and mapping permeability variations in larger scale low‐resolution images. Results show excellent agreement between permeability predictions made from 16 and 64 µm/voxel images of 25 mm diameter 80 mm tall core samples of heterogeneous sandstone for which 5 µm/voxel resolution is required to compute permeability directly. The statistical model used at the lowest resolution of 64 µm/voxel (similar to typical whole core image resolutions) includes open pore fraction and formation factor as predictor characteristics. Although binarized images at this resolution do not completely capture the pore system, we infer that these characteristics implicitly contain information about the critical fluid flow pathways. Three‐dimensional permeability mapping in larger‐scale lower resolution images by means of statistical predictions provides input data for subsequent permeability upscaling and the computation of effective permeability at the core scale.

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Virtual Materials Design: Properties of Cellular Solids Derived from 3D Tomographic Images

et al. 2005

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The physical properties of cellular solids are a direct consequence of their complex microstructure. Linking properties to structure will lead to an understanding of how cellular solids can be optimised and materials engineered for given applications. In this paper we illustrate a 3D imaging and analysis study of a number of industrial cellular foam morphologies; structural characteristics (porosity, pore size, interconnectivity and tortuosity) and physical properties (diffusivity, elasticity, permeability and conductivity) are calculated directly on the large three dimensional digitised images. Comparisons with common empirical estimates and theoretical formulae are encouraging.Manufactured cellular materials (e.g, polymer, ceramic or metallic foams) are an extremely attractive option as materials engineered for a range of applications ranging from light weight structures to packaging, insulation and crash protection. The useful properties of cellular solids are a direct consequence of their microstructure. Relevant aspects of the structure of cellular materials include porosity or apparent COMMUNICATIONS 238

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Euler-Poincaré characteristics of classes of disordered media

Cited by 93 publications

References 34 publications

Characterising the Morphology of Disordered Materials

Characterising the Morphology of Disordered Materials

Mapping permeability in low‐resolution micro‐CT images: A multiscale statistical approach

Virtual Materials Design: Properties of Cellular Solids Derived from 3D Tomographic Images

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