Boundary curvature-dependent dynamical trapping of undulating worms

Abstract: We investigate the behavior of {\it Lumbriculus variegatus} in polygonal chambers and show that the worms align with the boundaries as they move forward and get dynamically trapped at concave corners over prolonged periods of time before escaping. We develop a kinematic model to calculate and describe the evolution of the worm's mean body orientation angle relative to the boundary. Performing simulations with a minimal active elastic dumbbell model, we then show that both the boundary aligning and corner trapping behavior of the worm are captured by steric interactions with the boundaries. The dimensionless ratio of the strength of forward motion and diffusion caused by the worm's undulatory and peristaltic strokes is shown to determine the boundary alignment dynamics and trapping time scales of the worm. The simulations show that that the body angle with the boundary while entering the concave corner is important to the trapping time distributions with shallow angles leading to faster escapes. Our study demonstrates that directed motion and limited angular diffusion can give rise to aggregation which can mimic shelter seeking behavior in slender undulating limbless worms even when thigmotaxis or contact seeking behavior is absent.