Statistical theory of structure formation: self-organization
  We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent structure is utilized for the prediction of the PDFs, revealing strong intermittency with exponential tails. Numerical simulations confirm these results. The predicted power spectra are also in a good agreement with simulation results. The results imply a significant probability of supercritical states due to stochastic perturbation in a variety of systems. 
Eun-jin Kim, Han-Li Liu, and Johan Anderson