Fokker-Planck equation for the energy cascade in turbulence

Free energy and the Fokker-Planck equation

We establish a new and intriguing connection between the FokkerPlanck equation with gradient drift term and an associated free energy functional. Namely, we demonstrate that such a Fokker-Planck equation may be interpreted as a gradient flux, or a steepest descent, of a free energy functional with respect to a certain metric. This is accomplished through the construction of a time-discrete iter...

The Fokker-Planck equation

In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one variable, several variables, methods of solution and its applications, especially dealing with laser statistics. There has been a considerable progress on the topic as well as the topic has received greater...

The Fokker-Planck Equation

Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, ...

Iterative methods for solving non linear Fokker-Planck equation

Fokker-Planck Equation

The Langevin equation approach to the evolution of the velocity distribution for the Brownian particle might leave you uncomfortable. A more formal treatment of this type of problem is given by the Fokker-Planck equation. We can either formulate the question in terms of the evolution of a nonstationary probability distribution from a defined initial condition, or in terms of the evolution of th...