Chepizhko O. Kinetics of the order-disorder transition for the systems of self-propelled particles

The thesis is devoted to the investigation of the behavior of self-propelled particles, which align their directions of motion according to the Vicsek algorithm. The particle relaxation to the average direction of motion of its neighbors is considered, and the mean-field approach was developed. In the framework of the mean-field approach allows to show the dependency of the kind of the phase (order-disorder) transition on the type of the stochastic perturbation that is applied to the direction of motion of a particle. Kinetic equation for the fluid made up from self-propelled particles is obtained with the use of the method of microscopic phase density. An equation, analogous to the Euler equation is obtained from the kinetic equation. It is used to describe the hydrodynamics of the ideal self-propelled fluid. The dynamics of ordering in such approach is shown. As an example an inhomogeneous system is considered where the inhomogeneities are modeled as obstacles, which particles try to avoid. It is shown that the presence of obstacles leads to a non-trivial change in the behavior of the dependency of the order parameter on the noise strength: the dependency exhibits a maximum, so there is an optimal noise, at which the collective motion is the most ordered. It is shown that obstacles change the behavior of non-interacting active particles, changing their transport properties: they change the value of the diffusion coefficient and lead to the transfer from diffusive to subdiffusive regime.