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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{alvarado2026volume,
  title = {{The Volume Exchange Metric}},
  author = {Enrique Alvarado and Joseph Jung and Jeremy Mason and Shrunal Pothagoni and Benjamin Schweinhart},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26897},
  eprint = {2610.26897},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26897},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Volume Exchange Metric
AU  - Enrique Alvarado
AU  - Joseph Jung
AU  - Jeremy Mason
AU  - Shrunal Pothagoni
AU  - Benjamin Schweinhart
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.26897
UR  - https://arxiv.org/abs/2610.26897
AB  - 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.
ER  -