Dispersion Relations for Active Undulators in Overdamped Environments

Organisms that locomote by propagating waves of body bending can maintain performance across heterogeneous environments by modifying their gait frequency \(\omega\) or wavenumber \(k\). We identify a unifying relationship between these parameters for overdamped undulatory swimmers (including nematod...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Pierce, Christopher J, Irvine, Daniel, Peng, Lucinda, Lu, Xuefei, Lu, Hang, Goldman, Daniel I
Format: Article
Language:English
Subjects:
Gait
Parameter identification
Parameter modification
Rheological properties
Scaling
Spermatozoa
Wave propagation
Wavelengths
Online Access:Get full text
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Summary:Organisms that locomote by propagating waves of body bending can maintain performance across heterogeneous environments by modifying their gait frequency \(\omega\) or wavenumber \(k\). We identify a unifying relationship between these parameters for overdamped undulatory swimmers (including nematodes, spermatozoa, and mm-scale fish) moving in diverse environmental rheologies, in the form of an active `dispersion relation' \(\omega\propto k^{\pm2}\). A model treating the organisms as actively driven viscoelastic beams reproduces the experimentally observed scaling. The relative strength of rate-dependent dissipation in the body and the environment determines whether \(k^2\) or \(k^{-2}\) scaling is observed. The existence of these scaling regimes reflects the \(k\) and \(\omega\) dependence of the various underlying force terms and how their relative importance changes with the external environment and the neuronally commanded gait.
ISSN:2331-8422