Uniqueness of Reconstruction of Multiphase Morphologies from Two-Point Correlation Functions

Rozman, Michael G.; Utz, Marcel

doi:10.1103/physrevlett.89.135501

Cited by 59 publications

(35 citation statements)

References 33 publications

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“…Although there has been significant progress on reconstruction algorithms [1,[14][15][16], it remains a challenge to reconstruct accurately percolating microstructures, sets of essentially zero measure (e.g., cracked media and filamentary structures), and multiply connected microstructures. In this paper we introduce a procedure that enables one to begin to reconstruct such microstructures with heretofore unattained accuracy.…”

Section: Introductionmentioning

confidence: 99%

Improved reconstructions of random media using dilation and erosion processes

Zachary

Torquato

2011

Phys. Rev. E

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By using the most sensitive two-point correlation functions introduced to date, we reconstruct the microstructures of two-phase random media with heretofore unattained accuracy. Such media arise in a host of contexts, including porous and composite media, ecological structures, biological media, and astrophysical structures. The aforementioned correlation functions are special cases of the so-called canonical n-point correlation function H(n) and generalize the ones that have been recently employed to advance our ability to reconstruct complex microstructures [Y. Jiao, F. H. Stillinger, and S. Torquato, Proc. Natl. Acad. Sci. 106, 17634 (2009)]. The use of these generalized correlation functions is tantamount to dilating or eroding a reference phase of the target medium and incorporating the additional topological information of the modified media, thereby providing more accurate reconstructions of percolating, filamentary, and other topologically complex microstructures. We apply our methods to a multiply connected "donut" medium and a dilute distribution of "cracks" (a set of essentially zero measure), demonstrating improved accuracy in both cases with implications for higher-dimensional and biconnected two-phase systems. The high information content of the generalized two-point correlation functions suggests that it would be profitable to explore their use to characterize the structural and physical properties of not only random media, but also molecular systems, including structural glasses.

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Section: Introductionmentioning

confidence: 99%

Improved reconstructions of random media using dilation and erosion processes

Zachary

Torquato

2011

Phys. Rev. E

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“…It has also been shown that the structural ambiguity is considerably larger for a radial function without angular information, which is the only data available from small-angle scattering experiments. However, if angular information is employed successful microstructure reconstructions can often be obtained [18][19][20][21].…”

Section: S T R I B Umentioning

confidence: 99%

Density of States for a Specified Correlation Function and the Energy Landscape

2012

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The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.

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“…While models must be formulated and applied at macroscopic length scales that range from meters to kilometers, it is known that the microscopic arrangement of fluids within geologic materials has important consequences for fluid flow [12][13][14][15][16][17][18][19][20][21][22]. In particular, the snapoff and entrapment of fluid sub-regions at the pore-scale has been established as an important source of hysteresis [23][24][25][26][27].…”

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confidence: 99%

Geometric state function for two-fluid flow in porous media

McClure¹,

Armstrong²,

Berrill³

et al. 2018

Phys. Rev. Fluids

108

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Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a hysteretic description. As an alternative to the traditional perspective, we consider a geometrical description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of measures of the macroscale state. Synchrotron-based X-ray micro-computed tomography (µCT) and highresolution pore-scale simulation is applied to examine the uniqueness of the proposed relationship for six different porous media. We show that the geometric state function is able to characterize the microscopic fluid configurations that result from a wide range of simulated flow conditions in an averaged sense. The geometric state function can serve as a closure relationship within macroscale models to effectively remove hysteretic behavior attributed to the arrangement of fluids within a porous medium. This provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media. PACS numbers: 92.40Cy, 92.40.Kf, 91.60.Tn, 91.60.Fe

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Uniqueness of Reconstruction of Multiphase Morphologies from Two-Point Correlation Functions

Cited by 59 publications

References 33 publications

Improved reconstructions of random media using dilation and erosion processes

Improved reconstructions of random media using dilation and erosion processes

Density of States for a Specified Correlation Function and the Energy Landscape

Geometric state function for two-fluid flow in porous media

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