researchy.jpg publicationsy.jpg personaly.jpg homey.jpg collaboratorsy.jpg back.jpg back.jpg
One of the most remarkable characteristics of systems like a school of fish or a swarm of locusts, is the emergence of states of collective order in which all the particles move together in the same direction, in spite of the fact that the interactions between the particles are (presumably) of short range.  Such systems are generally out of, and far from, equilibrium. Therefore, the emergence of ordered states in these systems cannot be accounted for by the standar theorems in statistical mechanics that explain the existence of long-range order phase transitions in equilibrium systems (like the Ising model).
Cristian Huepe, Hernan Larralde and I have put forward a formalism, based on networks and network dynamics, to explain the emergence of collective order in systems of autonomous particles. This formalism not only does explain the existence of colective order and phase transitions in these systems, but also allows us to analyze within the same framework the dynamics of flocks  and majority voter models.  In the first case each particle tends to move in the direction of motion in which the majority of its neighbors are moving. In the second case, a given individual in a society tends to be of the same opinion as the majority of his friends. In both cases there may be some noise in the enviroment that prevents the particles or individuals from blindly following the majority rule. In other words, while it is true that I tend to be of the same opinion as the majority of my friends, with a finite probability I can have the opposite opinion. 
The results that we have obtained using the network approach to analyze the onset of collective behavior in flocking-like systems and majority voter models suggest that the main ingredients needed for the emergence of ordered states are:
  1. Majority rule (each particle tends to follow the majority of its "friends" or "neighbors").
  2. Noise (with a given probability, the majority rule can be violated).
  3. Long-range interactions (particles far away from each other can interact).
Point number 3 is interesting. If we do not explicitely assume that distant particles can interact, then collective order is never achived. This means that for a school of fish to move collectively, two fish at opposite ends of the school should know what each other is doing. Our last work on this topic relates the topology of the network with the nature of the phase transition. It can be found here.       
The emergence of order in  flocks and majorities can be analyzed within the same theoretical framework.