Characterisation of irregular spatial structures by parallel sets and integral geometric measures

Abstract

A new method of characterising the morphology of disordered systems is presented based on the evolution of a family of integral geometric measures during erosion and dilation operations. The method is used to determine the accuracy of model reconstructions of random systems. It is shown that the use of erosion/dilation operations on the original image leads to an accurate discrimination of morphology. We consider the morphology of an experimental system and use the method to optimally match a reconstructed model morphology.

Shape- and size-dependent electronic capacitance in nanostructured materials

“…Typical value of spill length in parallel-plate capacitor of a pair of graphite sheets is approximately 0.1 nm [22]. In order to calculate the electronic capacitance at the spillover plane [13,14,20,24], we have to take the modified mean H and Gaussian K curvatures which are, respectively, [25,26] (see the appendix for derivation of curvatures) 19) where δ is the electron spillover distance. For small δ, we have H ≈ H and K ≈ K. Now the electronic capacitance c s E of arbitrary nanostructured material with spillover correction is …”

“…But for a general arbitrary surface, the curvatures mean H and Gaussian K may be obtained from the Monge formula as follows: (b) Curvature and area correction of parallel surfaces at spillover plane [25,26] (Sterner's formula)…”

Mark Correlations: Relating Physical Properties to Spatial Distributions

“…These data trace a 4.52 mm diameter cylindrical core extracted from a block with bulk porosity φ = 13%,, where the bulk porosity is the volume fraction occupied by the pores. A piece with 2.91mm length (resulting in a 46.7 mm 3 volume) of the core was imaged and tomographically reconstructed [23,54,3,2]. Further details of this sample are presented in the contribution by C. Arns et al in this volume.…”

Parallel Sets and Morphological Measurements of CT Images of Soil Pore Structure in a Vineyard

“…These functions account for the evolution of Minkowski functionals as the radius of dilation/erosion performed to the object varies. Arns et al [5] analyzed these Minkowski functions to characterize 3D images of Fontainebleau sandstone. Vogel et al [6] took advantage of Minkowski functions based on openings (i.e.…”

“…Parallel sets, which can be understood in terms of dilations and erosion, were introduced by Mecke [3] to characterize and model 2D structures beyond two point correlation functions and predict percolations threshold in porous media. Arns et al [5] also made use of parallel sets to determine the accuracy of the model they developed for the Fontainebleau sandstone.…”