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arxiv: 2606.01248 · v2 · pith:6ZIXI5XXnew · submitted 2026-05-31 · ❄️ cond-mat.mtrl-sci · cond-mat.soft

Stationarity-constrained representative volume elements for image-based homogenization of granular microstructures

Fernando Alonso-Marroquin , Abdullah Alqubalee , Eduardo Garzanti , Christian Tantardini This is my paper

Pith reviewed 2026-06-28 16:57 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.soft
keywords representative elementary volumegranular microstructuresimage-based analysisstationaritydune sandhomogenizationbackscattered electron
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The pith

A stationarity-constrained workflow identifies 2 mm as the representative volume size for dune-sand microstructures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an image-based method to size representative elementary volumes in heterogeneous granular materials by first locating stationary domains within the images. It applies this to backscattered electron maps of Arabian dune sand and finds that a window of 1536 pixels, or roughly 2 mm, satisfies the convergence criteria for mean and spectral properties. This size is confirmed separately through homogenization of mechanical and conductivity properties derived from chemical maps. The approach makes the dependence on stationarity and image characteristics explicit, offering a reproducible procedure for choosing simulation domains in such materials.

Core claim

The central claim is that the representative support for homogenization in chemically mapped granular microstructures is given by the persistent mean-spectral criterion applied inside stationary domains, which for the studied dune-sand BSE images yields L_REV = 1536 pixels (ℓ_REV ≈ 2.01 mm), and is independently supported by property-level homogenization giving L_REV^prop = 204 pixels (ℓ_REV^prop ≈ 2.04 mm).

What carries the argument

The persistent mean-spectral criterion, which requires both the apparent-mean residual and the low-wavenumber covariance-spectrum residual to remain within tolerance over the non-reference tail, applied within stationary domains screened by local mean and standard-deviation compatibility.

If this is right

  • The REV size is tied to the specific stationary domain and target observable rather than being a global image property.
  • Property homogenization curves for conductivity, stiffness, and directional Young modulus stabilize in the large-window regime at this scale.
  • The workflow can be used to make explicit the dependence of REV on stationarity, image field, window sequence, and observable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If applied to other heterogeneous materials, the method might show whether millimetre-scale REVs are common in granular systems.
  • Integrating this with finite-element simulations could test how REV choice affects predicted macroscopic behavior.
  • The stationarity screening step could be extended to multi-modal imaging data for more robust domain identification.

Load-bearing premise

Local mean and standard-deviation compatibility on full-resolution BSE maps is enough to find domains where the mean-spectral criterion reliably picks the representative window size.

What would settle it

Observing that the apparent mean or spectral residuals fail to stabilize within tolerance even at window sizes larger than 1536 pixels inside the identified stationary domains would falsify the claim that this size is representative.

Figures

Figures reproduced from arXiv: 2606.01248 by Abdullah Alqubalee, Christian Tantardini, Eduardo Garzanti, Fernando Alonso-Marroquin.

Figure 1
Figure 1. Figure 1: FIG. 1. Geological and aeolian-sand context of Arabia and the Gulf region. The principal sand seas include the Great Nafud [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. BSE scan of the polished dune sand section. The [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Conversion of a chemically mapped granular image into voxelized property fields. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. REV sizing inside detected stationary domains of the BSE gray/material-property maps. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Consistency checks for the stationary-domain REV [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Property-level finite-window homogenization inside detected stationary property domains. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

We present an image-based workflow for representative elementary volume (REV) sizing in chemically mapped granular microstructures, applied to Arabian dune-sand samples characterized by mineralogical and textural heterogeneity. The REV is treated as a finite-window convergence scale within approximately stationary material domains, rather than as a global length assigned to a non-stationary image. Full-resolution backscattered-electron (BSE) gray-level maps are screened by local mean and standard-deviation compatibility to identify stationary domains. Candidate windows are sampled only inside these domains, and the representative support is selected using a persistent mean--spectral criterion requiring both the apparent-mean residual and the low-wavenumber covariance-spectrum residual to remain within tolerance over the non-reference tail. Ensemble reproducibility is used as an auxiliary check. Applied to seven full-resolution BSE images of dune-sand microstructures, the strict stationary-domain criterion gives $(L_{\rm REV}=1536~\mathrm{pixels})$, corresponding to $(\ell_{\rm REV}\approx2.01~\mathrm{mm})$ for a BSE pixel size of $(1.31~\mu\mathrm{m})$. Property-level homogenization on QEMSCAN-derived numerical maps independently supports this millimetre-scale estimate: the converted support is $(L_{\rm REV}^{\rm prop}=201.2)$ pixels and is snapped to the nearest tested size, $(L_{\rm REV}^{\rm prop}=204)$ pixels $(\ell_{\rm REV}^{\rm prop}=2.04~\mathrm{mm})$. This length lies in the large-window regime of the apparent conductivity, stiffness, and directional Young-modulus curves. The workflow provides a reproducible route for REV sizing while making explicit its dependence on stationarity, image field, window sequence, and target observable.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript proposes an image-based workflow for determining representative elementary volumes (REVs) in granular microstructures with mineralogical and textural heterogeneity, using Arabian dune-sand samples. Full-resolution BSE gray-level maps are screened for stationary domains via local mean and standard-deviation compatibility. Candidate windows are then sampled within these domains, and the REV size is selected using a persistent mean-spectral criterion that requires both the apparent-mean residual and the low-wavenumber covariance-spectrum residual to stay within tolerance over the non-reference tail, with ensemble reproducibility as an auxiliary check. For seven BSE images, the strict criterion yields L_REV = 1536 pixels (ℓ_REV ≈ 2.01 mm at 1.31 μm/pixel). This is independently supported by property-level homogenization on QEMSCAN-derived maps, giving L_REV^prop = 204 pixels (ℓ_REV^prop = 2.04 mm) in the large-window regime for apparent conductivity, stiffness, and directional Young modulus. The workflow explicitly notes its dependence on stationarity, image field, window sequence, and target observable.

Significance. If the stationarity screening is adequate, this work contributes a reproducible procedure for REV sizing that treats the REV as a convergence scale within stationary domains rather than a global property of potentially non-stationary images. The cross-validation between image-based spectral criteria and property homogenization is a notable strength. Explicit acknowledgment of the method's dependencies on specific choices enhances transparency. Such approaches are valuable in computational homogenization of heterogeneous materials where standard REV concepts may not apply directly.

major comments (1)
  1. [Abstract (workflow description)] The workflow's central premise—that local mean and standard-deviation screening on BSE maps sufficiently identifies stationary domains for reliable application of the persistent mean-spectral criterion—is not validated against controlled non-stationary test cases. Without such tests, it remains unclear whether longer-range correlations or drifts missed by first- and second-moment screening could affect the selected L_REV=1536 pixels. This assumption is load-bearing for the reported millimetre-scale REV and its QEMSCAN corroboration.
minor comments (2)
  1. [Abstract] Clarify how the value 201.2 pixels for L_REV^prop is obtained before snapping to 204 pixels, and specify the exact residual tolerances used in the mean-spectral criterion.
  2. [Abstract] The manuscript should include error bars or variability measures across the seven images and the supporting validation figures to allow independent assessment of the reported REV sizes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the validation of the stationarity screening. We respond point by point below.

read point-by-point responses

  1. Referee: The workflow's central premise—that local mean and standard-deviation screening on BSE maps sufficiently identifies stationary domains for reliable application of the persistent mean-spectral criterion—is not validated against controlled non-stationary test cases. Without such tests, it remains unclear whether longer-range correlations or drifts missed by first- and second-moment screening could affect the selected L_REV=1536 pixels. This assumption is load-bearing for the reported millimetre-scale REV and its QEMSCAN corroboration.

    Authors: We agree that the stationarity identification relies on local mean and standard-deviation compatibility and that the manuscript does not present controlled tests on synthetic non-stationary microstructures to quantify the impact of undetected higher-order correlations. The workflow is explicitly conditioned on approximate stationarity within the screened domains, as stated in the abstract and methods, and the QEMSCAN-derived property homogenization provides independent support for the reported REV size on the specific dune-sand images. To address the concern, we will revise the discussion section to include an explicit statement on this limitation of moment-based screening and its potential implications for the selected L_REV. revision: yes

Circularity Check

0 steps flagged

No circularity: workflow applies explicit stationarity and convergence criteria directly to image data

full rationale

The derivation selects L_REV by screening BSE maps for local mean/std compatibility, then applying the persistent mean-spectral residual criterion inside those domains, with ensemble checks and an independent QEMSCAN property homogenization cross-check. No equation or step reduces by construction to a fitted parameter renamed as prediction, no self-definitional loop appears, and no load-bearing premise rests on a self-citation chain or imported ansatz. The reported millimetre-scale REV follows from direct application of the stated image-analysis rules to the given microstructures; the workflow is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim of a specific millimetre-scale REV size rests on the domain assumption that local mean and standard-deviation compatibility identifies usable stationary domains, plus an unspecified tolerance threshold in the convergence criterion.

free parameters (1)
  • residual tolerance
    The persistent mean-spectral criterion requires both apparent-mean residual and low-wavenumber covariance-spectrum residual to remain within tolerance, but the specific tolerance value is not stated in the abstract.
axioms (1)
  • domain assumption Local mean and standard-deviation compatibility identifies stationary domains suitable for REV sampling
    Invoked to screen full-resolution BSE gray-level maps before sampling candidate windows inside those domains.

pith-pipeline@v0.9.1-grok · 5855 in / 1378 out tokens · 36093 ms · 2026-06-28T16:57:06.237125+00:00 · methodology

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