TL;DR
This paper explains the Vicsek model for collective motion, covering its implementation, fundamental properties, and the role of symmetries, supported by numerical simulations and analytical insights.
Contribution
It provides an accessible overview of the Vicsek model's properties, universality class, and the influence of symmetries, with simplified analytical arguments and simulation results.
Findings
The Vicsek model exhibits a well-defined universality class.
Symmetries and conservation laws significantly influence collective behavior.
Numerical simulations support the analytical insights into the model's properties.
Abstract
In these lecture notes, prepared for the Microswimmers Summer School 2015 at Forschungszentrum Juelich, I discuss the well known Vicsek model for collective motion and its main properties. In particular, I discuss its algorithmical implementation and the basic properties of its universality class. I present results from numerical simulations and insist on the role played by symmetries and conservation laws. Analytical arguments are presented in an accessible and simplified way, but ample references are given for more advanced readings.
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