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arXiv · 2607.07000

Dimension-dependent continuum limits in tissue mechanics

Matthew J Simpson·Pascal R Buenzli
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Abstract

Continuum descriptions of epithelial tissue mechanics can replace expensive individual-based simulations with tractable macroscopic models, yet the link between cell-scale forces and tissue-scale transport remains poorly understood. We show that dimensionality controls this link: long-time mechanical relaxation rates reveal generalized porous-media-type nonlinear transport phenomena, $D(ρ)\proptoρ^γ$. Exponents in nonlinear diffusivities are fixed by microscopic mechanics and dimensionality, providing a novel physical mechanism for emergent macroscopic transport phenomena.

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Matthew J Simpson, Pascal R Buenzli. 2026-09-21. Dimension-dependent continuum limits in tissue mechanics. https://arxiv.org/abs/2607.07000

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