Tamás Vicsek

Novel type of phase transition in a system of self-driven particles

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation

Uncovering the overlapping community structure of complex networks in nature and society

(\ensuremath{\eta})

Evolution of the social network of scientific collaborations

added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity,

Quantifying social group evolution

|{\mathbf{v}}_{a}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

CFinder: locating cliques and overlapping modules in biological networks

) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since

Global organization of metabolic fluxes in the bacterium Escherichia coli

|{\mathbf{v}}_{a}|

Dynamics of fractal surfaces

is found to scale as

Hierarchical group dynamics in pigeon flocks.

({\ensuremath{\eta}}_{c}\ensuremath{-}\ensuremath{\eta}{)}^{\ensuremath{\beta}}

Clique percolation in random networks

with

Deterministic scale-free networks

\ensuremath{\beta}\ensuremath{\simeq}0.45