Diffusive Influence Systems

Diffusive Influence Systems

Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while Turing-complete, influence dynamics of the diffusive type is almost surely asymptotically periodic. Besides resolving the dynamics of a popular family of multiagent systems, t...

Diffusive instabilities in heterogeneous systems

We investigate the behavior of a system composed of two small identical water droplets loaded with an activator-inhibitor system possessing only a single stable steady state and coupled through a third, ‘‘signaling’’ species able to diffuse through the interdroplet medium. Depending on whether the third species is coupled to the activator or the inhibitor, the system can exhibit wave instabilit...

Coherence and interactions in diffusive systems

This lecture is a tutorial introduction to coherent effects in disordered electronic systems. Avoiding technicalities as most as possible, I present some personal points of view to describe well-known signatures of phase coherence like weak localization correction or universal conductance fluctuations. I show how these physical properties of phase coherent conductors can be simply related to th...

Diffusive Behavior of Interacting Particle Systems

Renormalization Group Analysis of Driven Diffusive Systems

The critical properties of statistical systems in thermal equilibrium are well understood, thanks to renormalization group analysis. For systems driven into non-equilibrium steady states, many surprising new features appear. For example, when the Ising lattice gas is driven with biased diffusion or coupled to two thermal baths, long range correlations exist at all temperatures. The second order...