Code from: Effect of fluid elasticity on the emergence of oscillations in an active elastic filament

Many microorganisms propel through complex media by deformations of their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, passive elastic response from deformations of the flagellum, and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there is limited data on how systematic changes in elasticity alter the beat. This work analyzes a related problem with fixed-strength driving force: the emergence of the beating of an elastic planar filament driven by a follower force at the tip in a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Usi..., , , # Code from: Effect of fluid elasticity on the emergence of oscillations in an active elastic filament

[https://doi.org/10.5061/dryad.9p8cz8wqs](https://doi.org/10.5061/dryad.9p8cz8wqs)

## Code/Software

MATLAB programs related to the paper. There are three main routines: two for computing eigenvalues and one for performing the dynamic simulation of a filament subject to a follower force at the tip in a linear viscoelastic fluid. Supporting routines, including those that set parameters for the simulation, are in the src/ directory.

#### make\_viscous\_evals.m

Compute the eigenvalues of the operator L*y=-y''''-sigma *y'' subject to the boundary conditions y(0)=y'(0)=y''(1)=y'''(1)=0 for a range of values of sigma. The output is saved in the file viscous_eigenvalues.mat. The output will contain two arrays:

* sigma: values of the follower force strength
* vis_eigs: eigenvalues of L

#### compute\_VE\_evals.m

Compute the corresponding eigenvalues in a linear viscoelastic fluid fo...