Universal conductivity curve for a plane containing random holes

Garboczi, Edward J.; Thorpe, M. F.; DeVries, M. S.; Day, Anthony R.

doi:10.1103/physreva.43.6473

Cited by 88 publications

(53 citation statements)

References 22 publications

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“…A mathematically equivalent problem of effective conductivity in presence of random overlapping dielectric inclusions of various shapes was stud- ied numerically by Garboczi et al 13 They observed the collapse of the data obtained for individual obstacle shapes onto a single curve and found that for a number of different of shapes, α A c varied only slightly ( A c is the critical area density of inclusions, an analogue of V c in 3D). Based on these observations, Garboczi et al proposed a universal curve for the 2D conductivity, attributing differences of α A c to computational errors.…”

Section: Similarities Of Effective Diffusion In 2dmentioning

confidence: 99%

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

Novak

Gao

Kraikivski

et al. 2011

The Journal of Chemical Physics

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Efficient and accurate numerical techniques are used to examine similarities of effective diffusion in a void between random overlapping obstacles: essential invariance of effective diffusion coefficients (D eff ) with respect to obstacle shapes and applicability of a two-parameter power law over nearly entire range of excluded volume fractions (φ), except for a small vicinity of a percolation threshold. It is shown that while neither of the properties is exact, deviations from them are remarkably small. This allows for quick estimation of void percolation thresholds and approximate reconstruction of D eff (φ) for obstacles of any given shape. In 3D, the similarities of effective diffusion yield a simple multiplication "rule" that provides a fast means of estimating D eff for a mixture of overlapping obstacles of different shapes with comparable sizes.

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Section: Similarities Of Effective Diffusion In 2dmentioning

confidence: 99%

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

Novak

Gao

Kraikivski

et al. 2011

The Journal of Chemical Physics

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“…In order to obtain an estimation of the area of a digitized circle with less than 1% of error, a number of 15 pixels/ diameter is generally required. 16,17 To overcome this difficulty, and taking into account the limited resolution of the apparatus, a continuum disk may be associated to each digitized disk, leading to a kind of continuous idealization of the medium. That is the idea which will be applied throughout this article.…”

Section: Reconstruction Of Three-dimensional Objectsmentioning

confidence: 99%

Periodic unit cell reconstruction of porous media: Application to open-cell aluminum foams

Perrot

Panneton

Olny

2007

Journal of Applied Physics

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In this article, the issue of reconstructing an idealized periodic unit cell ͑PUC͒ to represent a porous medium is examined by means of microcomputed tomography ͑ CT͒. Using CT, three-dimensional images of open-cell foam are collected and used to characterize the representative parameters of its cellular morphology. These parameters are used in order to reconstruct the porous medium by means of an idealized PUC: a tetrakaidecahedron with ligaments of triangular cross sections, whose characteristic dimensions have been measured on the CT images. The proposed reconstruction of the idealized PUC is applied to four aluminum foams. The averaged macroscopic properties of the foams ͑open porosity and thermal characteristic length͒ are deduced from their respective PUC model and compared to experimental measurements and literature data. Good correlations are obtained. For each of the foams, this provides a parameterized idealized periodic unit cell on which the partial differential equations governing sound dissipation and propagation in foams can be solved with a view to studying the microphysical basis of the acoustical macrobehavior.

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“…Many control tests were run in order to replicate the results of Weddell et al 1 We collected 5 runs of data for 1000 circle cuts and found an average pc of 0.34 ± 0.073, close to the theoretical value Xia and Thorpe cite, 0.33, and Weddell's value, 0.36. 1,7 From this result, we can conclude that this experimental method is repeatable and valid.…”

mentioning

confidence: 55%

The Effect of Different Geometries on Percolation in Two Dimensions

Morgan

Wedell

Feinerman

2013

J Undergrad Research UIC

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Using the model simulation developed by Weddell and Feinerman, this study found results for the percolation threshold as a function of aspect ratio for rectangle shaped holes and then compared these results to Weddell's elliptical ones.1 We developed a slightly different experimental set-up than Weddell, proving that this method for collecting percolation data is repeatable and valid. The percolation threshold for both shapes has been found to exhibit a similar trend -as aspect ratio decreases, percolation threshold increases. At small aspect ratios, when both shapes are almost indistinguishable lines, the percolation threshold results are very similar. For larger aspect ratios, the differences in percolation threshold are much greater. More shapes need to be considered, but these results imply that there exists a point at which the aspect ratio of a shape does influence the percolation threshold.

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Universal conductivity curve for a plane containing random holes

Cited by 88 publications

References 22 publications

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

Diffusion amid random overlapping obstacles: Similarities, invariants, approximations

Periodic unit cell reconstruction of porous media: Application to open-cell aluminum foams

The Effect of Different Geometries on Percolation in Two Dimensions

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