Dynamical Boundary Following and Corner Trapping of Undulating Worms

Abstract

We investigate the behavior of {\it Lumbriculus variegatus} in circular and polygonal chambers and show that the worms align with the boundaries as they move forward and then become dynamically trapped at the concave corners over prolonged periods. We model the worm as a self-propelled rod and derive analytical expressions for the evolution of its orientation when it encounters the flat and the circular boundaries of the chamber. By further incorporating translational and rotational diffusion, arising due to the undulatory and peristaltic body strokes, we demonstrate through numerical simulations that the self-propelled rod model can capture both the boundary aligning and the corner trapping behavior of the worm. The P\'eclet number $Pe$, representing the ratio of forward propulsion to rotational diffusion, is found to characterize the boundary alignment dynamics and trapping time distribution of the worm. Simulations show that the angle of the worm's body with the boundary while entering a concave corner plays a key role in determining the trapping time, with shallow angles leading to faster escapes. Our study demonstrates that directed motion combined with limited angular diffusion can lead to spatial localization that mimics shelter seeking behavior in slender undulating limbless worms, even in the absence of thigmotaxis or contact seeking behavior.