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PreprintCC BY 4.0arXiv

Cutting, Shuffling and Diffusion as a Coarsening Process

  • Daniel Lester
  • Tanguy LeBorgne
  • Joris Heyman
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Abstract

Cutting and shuffling (CS) rearranges fluid without stretching, but homogenisation requires diffusion (D); this interaction is not well understood. We show that CSD is a coarsening process, with scale ℓ̅=L(ncPe/2)−1/3 rather than the Batchelor scale, and that cutting acts as a fractional Laplacian in wavenumber, giving the exact mixing rate γ=21/3|a1'|nc2/3λPe−1/3 for nc cuts per event at rate λ, with a1'=−1.0188… the first zero of Ai'. This holds in any dimension for random and deterministic protocols, extends to finite-time mixing, and places CSD in a known non-equilibrium universality class.

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Cite

BibTeXRIS
BibTeX
@misc{lester2026cutting,
  title = {{Cutting, Shuffling and Diffusion as a Coarsening Process}},
  author = {Daniel Lester and Tanguy LeBorgne and Joris Heyman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35979},
  eprint = {2610.35979},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35979},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Cutting, Shuffling and Diffusion as a Coarsening Process
AU  - Daniel Lester
AU  - Tanguy LeBorgne
AU  - Joris Heyman
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35979
UR  - https://arxiv.org/abs/2610.35979
AB  - Cutting and shuffling (CS) rearranges fluid without stretching, but homogenisation requires diffusion (D); this interaction is not well understood. We show that CSD is a coarsening process, with scale ℓ̅=L(n_cPe/2)^−1/3 rather than the Batchelor scale, and that cutting acts as a fractional Laplacian in wavenumber, giving the exact mixing rate γ=2^1/3|a_1'|n_c^2/3λPe^−1/3 for n_c cuts per event at rate λ, with a_1'=−1.0188… the first zero of Ai'. This holds in any dimension for random and deterministic protocols, extends to finite-time mixing, and places CSD in a known non-equilibrium universality class.
ER  -