Levy Random Motion and Fractional Calculus in the .. (LeFrac)
Levy Random Motion and Fractional Calculus in the Kinetic Theory of Systems Far from Equilibrium
Start date: Apr 1, 2009,
End date: Mar 31, 2011
The aim of the Project is a combined theoretical, numerical and empirical investigation of anomalous diffusion and relaxation processes which are intrinsic to a broad range of phenomena in complex non-equilibrium systems (in areas of physics, chemistry, environmental and geosciences). An adequate statistical description of these phenomena requires non - Gaussian Lévy statistics and the use of fractional calculus, namely both integrals and derivatives of fractional order. Fractional kinetic equations go beyond Fick’s second law and the Fokker-Planck equation by taking into account memory effects such as the stretching of polymers under external fields and the occupation of deep traps by charge carriers in amorphous semiconductors. Fractional kinetic equations allow physicists to describe complex systems with anomalous behavior in much the same way as simpler systems. We expect to generalize the standard fractional kinetic equations and develop methods to solve them analytically and numerically, and introduce fractional equations for multidimensional, anisotropic and non-homogeneous media. New Monte Carlo algorithms will be developed and applied for modeling anomalous relaxation and diffusion phenomena governed by generalized fractional kinetics. The new fractional equations and random walk models will be applied in order to get insight into various processes: wind fluctuations in surface layers of the atmosphere; underground water pollution (as the result of Chernobyl accident); scale free random search observed in different biological systems ranging from a search by an ensemble of proteins of DNA to intermittent foraging behavior of animals; and rare events studied in biomolecules. Based on the central role played by the Tel Aviv School in the area of fractional kinetics and on the broad spectrum of collaborations of the Tel Aviv group, it is expected that European involvement in research of anomalous diffusion and related phenomena will be strengthened.
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