PreprintCC BY 4.0arXiv
Dimension-dependent continuum limits in tissue mechanics
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)∝ργ. 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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BibTeX
@misc{simpson2026dimensiondependent,
title = {{Dimension-dependent continuum limits in tissue mechanics}},
author = {Matthew J Simpson and Pascal R Buenzli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.07000},
eprint = {2607.07000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07000},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dimension-dependent continuum limits in tissue mechanics
AU - Matthew J Simpson
AU - Pascal R Buenzli
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2607.07000
UR - https://arxiv.org/abs/2607.07000
AB - 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)∝ρ^γ. Exponents in nonlinear diffusivities are fixed by microscopic mechanics and dimensionality, providing a novel physical mechanism for emergent macroscopic transport phenomena.
ER -