Semi-linear Poisson-mediated Flocking in a Cucker-Smale Model
Abstract
We propose a family of compactly supported parametric interaction functions in the general Cucker-Smale flocking dynamics such that the mean-field macroscopic system of mass and momentum balance equations with non-local damping terms can be converted from a system of partial integro-differential equations to an augmented system of partial differential equations in a compact set. We treat the interaction functions as Green's functions for an operator corresponding to a semi-linear Poisson equation and compute the density and momentum in a translating reference frame, i.e. one that is taken in reference to the flock's centroid. This allows us to consider the dynamics in a fixed, flock-centered compact set without loss of generality. We approach the computation of the non-local damping using the standard finite difference treatment of the chosen differential operator, resulting in a tridiagonal system which can be solved quickly.
Cite
@article{arxiv.2102.08772,
title = {Semi-linear Poisson-mediated Flocking in a Cucker-Smale Model},
author = {Christos N. Mavridis and Amoolya Tirumalai and John S. Baras and Ion Matei},
journal= {arXiv preprint arXiv:2102.08772},
year = {2021}
}