Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation:Large-scale behavior of the turbulent transport coefficient - art. no. 047301
Av. Milovanov, Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation:Large-scale behavior of the turbulent transport coefficient - art. no. 047301, PHYS REV E, 6304(4), 2001, pp. 7301
The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [
Physica D 76, 110 (1994)] has led to important advances in the description
of the stochastic dynamics of Hamiltonian systems. Here, the long-time beha
vior of the basic transport processes obeying the fractional FPK equation i
s analyzed. A derivation of the large-scale turbulent transport coefficient
for a Hamiltonian system with 1 1/2 degrees of freedom is proposed in conn
ection with the fractal structure of the particle chaotic trajectories. The
principal transport regimes (i.e., a diffusion-type process, ballistic mot
ion, subdiffusion in the limit of the frozen Hamiltonian, and behavior asso
ciated with self-organized criticality) are obtained as partial cases of th
e generalized transport law. A comparison with recent numerical and experim
ental studies is given.