Work

Correlations in a generalized elastic model: Fractional Langevin equation approach

Year: 2010

Type: article

Abstract: The generalized elastic model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, and growing interfaces. On the other hand a probe (tracer) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a fractional Langevin equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree with the corresponding quantities calculated from the GEM. Furthermore we show that the Fox H -function formalism appears to be very convenient to describe the correlation properties within the FLE approach.

Source: Physical Review E

DOI: 10.1103/physreve.82.061104

Authors: Alessandro Taloni, Aleksei Chechkin, Joseph Klafter

Institutions: Tel Aviv University, Kharkiv Institute of Physics and Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: European Commission

Award: Levy Random Motion and Fractional Calculus in the Kinetic Theory of Systems Far from Equilibrium