Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, school of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.Comment: Four pages, four figures. Submitted to PR

Parametric instability of linear oscillators with colored time-dependent noise

The goal of this paper is to discuss the link between the quantum phenomenon of Anderson localization on the one hand, and the parametric instability of classical linear oscillators with stochastic frequency on the other. We show that these two problems are closely related to each other. On the base of analytical and numerical results we predict under which conditions colored parametric noise suppresses the instability of linear oscillators.Comment: RevTex, 9 pages, no figure

Cohesive motion in one-dimensional flocking

A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique group behaviour that contrasts with previous studies. Our results show that the largest cluster of particles, in the condensed states, develops a mean velocity slower than the preferred one in the absence of noise. For strong noise, the system also develops a non-vanishing mean velocity, alternating its direction of motion stochastically. This allows us to address the directional switching phenomenon. The effects of different sources of stochasticity on the system are also discussed.Comment: 24 pages, 11 figure

Fractal to Non-Fractal Morphological Transitions in Stochastic Growth Processes

From the formation of lightning-paths to vascular networks, diverse nontrivial self-organizing and self-assembling processes of pattern formation give rise to intricate structures everywhere and at all scales in nature, often referred to as fractals. One striking feature of these disordered growth processes is the morphological transitions that they undergo as a result of the interplay of the entropic and energetic aspects of their growth dynamics that ultimately manifest in their structural geometry. Nonetheless, despite the complexity of these structures, great insights can be obtained into the fundamental elements of their dynamics from the powerful concepts of fractal geometry. In this chapter, we show how numerical and theoretical fractal analyses provide a universal description to the well observed fractal to nonfractal morphological transitions in particle aggregation phenomena