Dispersion Relations for Active Undulators in Overdamped Environments.

Area of Science:

• Biophysics
• Fluid Dynamics
• Locomotion Biology

Background:

• Organisms using body undulation for locomotion must adapt to varying environments.
• Gait parameters like frequency ($\omega$) and wavenumber ($k$) are crucial for maintaining performance.

Purpose of the Study:

• To identify a unifying relationship between gait frequency and wavenumber for undulatory swimmers.
• To understand how environmental rheology influences locomotion strategies.

Main Methods:

• Analysis of experimental data from nematodes, spermatozoa, and small fish.
• Development of a viscoelastic beam model to simulate organismal movement.
• Investigating the impact of environmental dissipation on locomotion scaling.

Main Results:

• A universal active dispersion relation, $\omega\propto k^{\pm2}$, was identified for overdamped undulatory swimmers.
• The model successfully reproduced experimentally observed scaling laws.
• The observed scaling depends on the balance between organismal and environmental dissipation.

Conclusions:

• The identified scaling law provides a unified framework for understanding undulatory locomotion.
• Environmental properties and internal dynamics dictate the specific scaling regime ($k^2$ or $k^{-2}$).
• This highlights the adaptability of biological systems to complex fluid environments.