Frequency Locking in Spatially Extended Systems

Frequency locking in spatially extended systems.

A variant of the complex Ginzburg-Landau equation is used to investigate the frequency-locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, pi fronts, labyrinths, and 2pi/3 fronts emerge. We show that in spatially extended systems, frequency locking can be enhanced or suppressed by diffusive coupling. Novel p...

Entropy Production in Driven Spatially Extended Systems

This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production can be identified with a logarithmic ratio of microstate multiplicities of the original macrostate with respect to the time-reversed state. A special role is t...

Finite Propagation Speeds in Spatially Extended Systems

Rogue Waves in Spatially Extended Optical Systems

Giant anomalous events may occur in systems characterized by many waves, with extremely high amplitude waves appearing with a probability much higher than expected for a random dynamics. Such rare, and giant, events are known to occur on the ocean surface and have been named, in that context, “rogue waves”. We present here some recent experimental results on the statistical properties of giant ...

Subcritical bifurcation in spatially extended systems

A theory for noise-driven subcritical instabilities in spatially extended systems is put forward. The theory allows one to calculate the critical bifurcation parameter for a first-order phase transition in such non-equilibrium systems in the thermodynamic limit and analyse the mechanism of phase transition. Two examples with distinctive features are studied in detail to demonstrate the usefulne...