Applied Math Seminar with Griffin Smith, "A PDE Model for Janus-Particle Swarming"
- Thursday, September 9, 2021 from 3:00pm to 4:00pm
- Wilson Hall, 1-143 - view map
We consider a system of orientable Janus particles in the plane.Particles are subject to Brownian motion and can exhibit active forward drift. Forward drift is controlled by quorum sensing of a particle’s peers in its conical field of view. It has been shown experimentally that this set of rules can lead to clustering behavior in certain perception configurations (Lavergne et al., 2018). Here, we explore the group formation and cohesion of Janus particles using both an agent-based computer model and an advection-diffusion partial differential equation (PDE) model. Our PDE model can recreate the behavior from both physical experimentation and agent-based simulations. Indeed, agent-based simulations run with increasingly more particles approach the PDE results. Additionally, the PDE model highlights an annular structure which was not apparent in prior work. Through a histogramming process this structure can be verified in the agent-based computer simulations. Batches of simulations were run to produce a phase diagram offering insight into the group formation of particles at varying vision model parameter values. Allowing the initial condition to be a symmetrical group, a similar phase diagram can be. constructed offering insight into the cohesion of groups at certain parameter values. Our simulations show that interesting group patterns can emerge from governing rules that are substantially different from classical swarming models.
This is joint work between Griffin Smith, Nathan Stouffer, Scott
McCalla, Dominique P Zosso, MSU.
- Tomas Gedeon