Dinâmica de Partículas Auto - Propelidas

Abstract

In this work, we study the collective behaviour of living systems whose aggregates form organized groups such as flocks of birds, herds of mamals and schools of fishes. Through numerical simulations, we model the collective movement of a school of fishes using behavioural rules similar to the ones proposed by Couzin et al. [23], that investigates the spatial dynamics of animals groups. The model presents three interaction zones: repulsion, orientation and attraction. Our results for the distributions of nearest neighbour distance, the diference of orientation between the velocities of neighbour fishes and the cooperativeness of the school are in good agreement with experimental measurements. A simpler way to describe the collective motion of several groups of organisms was introduced by Vicsek et al. [10]. This model presents only one interaction region, called orientation zone and considers point particles moving off lattice at constant speed adjusting their direction of motion to that of the average velocity of their neighbors, being subject to some noisy term. A second-order transition between an ordered state and a disordered regime was found. However, Gregoire and Chate [12] contest the nature of such phase transition as being of first order. Indeed, this transition is related to the way of introducing the noise into the system. In this sense, we present a comparative study on noise in two system of self-propelled particle (Vicsek model and Gregoire model) with the aim of understanding the role of the noise on some observables such as polarization, distributions of the nearest neighbour distances, difference of orientations between neighbour particles, the order parameter and the Binder cumulant.