Statistical admissibility and long-wavelength structural convergence determine representative support in granular materials
Abstract
Representative elementary areas and volumes provide the scale bridge between resolved granular microstructure and continuum-scale material properties, yet they are still commonly selected from the apparent stabilization of a single scalar observable. Such plateaus can be false indicators of representativeness when statistically incompatible regions are averaged together or when long-wavelength structural correlations remain unresolved. We introduce a general representative-support framework for granular materials based on three sequential requirements: statistical admissibility of the sampled domain, persistent convergence of the apparent field mean and the low-wavenumber covariance spectrum, and validation against independent effective properties. The concept is tested on seven large-area backscattered-electron images of Arabian dune sands and mineral-resolved QEMSCAN maps. The structure-only criterion identifies a representative elementary area of $1536$ pixels, corresponding to approximately 2.01 mm. Without property-specific fitting or recalibration, the same physical scale transferred to the QEMSCAN grid (≈ 2.04 mm) coincides with the onset of weak size dependence in apparent thermal conductivity, elastic stiffness, and directional Young's moduli. Thus, the representative scale inferred from long-wavelength granular organization independently predicts the convergence of distinct constitutive responses. The results show that representative support should be assigned only after both statistical compatibility and long-range structural convergence have been established. Although demonstrated here on two-dimensional dune-sand sections, the criterion is formulated for granular materials generally and has a direct mathematical extension to three-dimensional voxelized volumes.
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BibTeX
@misc{tantardini2026statistical,
title = {{Statistical admissibility and long-wavelength structural convergence determine representative support in granular materials}},
author = {Christian Tantardini and Fernando Alonso-Marroquin and Abdullah Alqubalee and Eduardo Garzanti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.01248},
eprint = {2606.01248},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.01248},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Statistical admissibility and long-wavelength structural convergence determine representative support in granular materials
AU - Christian Tantardini
AU - Fernando Alonso-Marroquin
AU - Abdullah Alqubalee
AU - Eduardo Garzanti
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2606.01248
UR - https://arxiv.org/abs/2606.01248
AB - Representative elementary areas and volumes provide the scale bridge between resolved granular microstructure and continuum-scale material properties, yet they are still commonly selected from the apparent stabilization of a single scalar observable. Such plateaus can be false indicators of representativeness when statistically incompatible regions are averaged together or when long-wavelength structural correlations remain unresolved. We introduce a general representative-support framework for granular materials based on three sequential requirements: statistical admissibility of the sampled domain, persistent convergence of the apparent field mean and the low-wavenumber covariance spectrum, and validation against independent effective properties. The concept is tested on seven large-area backscattered-electron images of Arabian dune sands and mineral-resolved QEMSCAN maps. The structure-only criterion identifies a representative elementary area of $1536$ pixels, corresponding to approximately 2.01 mm. Without property-specific fitting or recalibration, the same physical scale transferred to the QEMSCAN grid (≈ 2.04 mm) coincides with the onset of weak size dependence in apparent thermal conductivity, elastic stiffness, and directional Young's moduli. Thus, the representative scale inferred from long-wavelength granular organization independently predicts the convergence of distinct constitutive responses. The results show that representative support should be assigned only after both statistical compatibility and long-range structural convergence have been established. Although demonstrated here on two-dimensional dune-sand sections, the criterion is formulated for granular materials generally and has a direct mathematical extension to three-dimensional voxelized volumes.
ER -