Self-alignment driven by jump processes: Macroscopic limit and numerical investigation

In this paper, we are interested in studying self-alignment mechanisms described as jump processes. In the dynamics proposed, active particles are moving at a constant speed and align with their neighbors at random times following a Poisson process. This dynamics can be viewed as an asynchronous version of the so-called Vicsek model. Starting from this particle dynamics, we introduce the related kinetic description and then derive a continuum hydrodynamic model. We then introduce different discretization strategies for the hierarchy of proposed models, we numerically study the convergence of the schemes and compare the behaviors of the different systems for several test cases.