Effective long-range interactions and active flocking: the role of boundary conditions.

The study of systems composed by active particles has become an important research topic in the last decade. In Statistical Mechanics it raises questions about nonequilibrium phase transitions since active particles are endowed with internal free energy depot which keep themselves out-of-equilibrium and, when interacting, can generate collective motion (flocking) and dynamical aggregation (clustering). Many diverse models, implementing the basic ingredients which allow collective motion, have been proposed in order to capture the global features displayed by these active systems. However a sufficiently wide and predictive model has yet to be found. In this thesis we study a continuous time model for the description of a two-dimensional coherent motion in groups of locally interacting biological units, based on the well established Vicsek model. We examine this system, in analytical and numerical fashions, in domains with different boundary conditions. We show that changing such boundary conditions dramatically influences the properties of particles dynamics. With reflecting boundary conditions in a static disk, typically a rotating behaviour along the border arises. While, with a moving disk confinement a much richer phenomenology occurs.