Analysis of a Self-Propelled Particle Model for Understanding Flocking Transition in Sperm

Self-propelled particle (SPP) models have been used to derive useful knowledge in active matter systems for more than two decades. When the self-propelled velocities tend to align, there can be a flocking transition in certain regions of parameter space. The goal of our SPP model is to help us understand and predict our experimental observations of flocking in bull sperm. Here, we present preliminary results from our simulations. When we analyze simulations with a quadratic repulsion potential and no alignment, the mean squared displacement (MSD) scales linearly with time to show a purely diffusive motion, as expected. When alignment is introduced, we observe flocking behavior, where the MSD scales quadratically with time, as expected for a flock of particles moving together in a fixed direction. Future work will focus on whether distributions of self-propelled velocities and persistence times can help explain the statistics of flocking (including cluster size distributions) seen in our experiments.