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arXiv · 2610.26897

The Volume Exchange Metric

Enrique Alvarado·Joseph Jung·Jeremy Mason·Shrunal Pothagoni·Benjamin Schweinhart
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Abstract

The volume exchange metric between cell structures embedded in Euclidean space is introduced. Intuitively, it measures the minimum amount of volume that must be swept out to continuously transform one cell structure into another. The main result is that the volume exchange metric coincides with a discrete analogue defined as a minimum over matchings between cells. Algorithms are described to compute the discrete volume exchange metric and illustrate its effectiveness at distinguishing polycrystalline microstructures in computational experiments.

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Enrique Alvarado, Joseph Jung, Jeremy Mason, Shrunal Pothagoni, Benjamin Schweinhart. 2026-10-16. The Volume Exchange Metric. https://arxiv.org/abs/2610.26897

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