236 research outputs found
Markovian embedding of fractional superdiffusion
The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized
Brownian Motion with long time persistence (superdiffusion), or
anti-persistence (subdiffusion) of both velocity-velocity correlations, and
position increments. It presents a case of the Generalized Langevin Equation
(GLE) with a singular power law memory kernel. We propose and numerically
realize a numerically efficient and reliable Markovian embedding of this
superdiffusive GLE, which accurately approximates the FLE over many, about r=N
lg b-2, time decades, where N denotes the number of exponentials used to
approximate the power law kernel, and b>1 is a scaling parameter for the
hierarchy of relaxation constants leading to this power law. Besides its
relation to the FLE, our approach presents an independent and very flexible
route to model anomalous diffusion. Studying such a superdiffusion in tilted
washboard potentials, we demonstrate the phenomenon of transient hyperdiffusion
which emerges due to transient kinetic heating effects.Comment: EPL, in pres
Some Insights in Superdiffusive Transport
In this paper we deal with high-order corrections for the Fractional
Derivative approach to anomalous diffusion, in super-diffusive regime, which
become relevand whenever one attempts to describe the behavior of particles
close to normal diffusion.Comment: 14 pages, 7 figure
Non-Markovian Levy diffusion in nonhomogeneous media
We study the diffusion equation with a position-dependent, power-law
diffusion coefficient. The equation possesses the Riesz-Weyl fractional
operator and includes a memory kernel. It is solved in the diffusion limit of
small wave numbers. Two kernels are considered in detail: the exponential
kernel, for which the problem resolves itself to the telegrapher's equation,
and the power-law one. The resulting distributions have the form of the L\'evy
process for any kernel. The renormalized fractional moment is introduced to
compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure
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