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Mathematics 2017, 5(1), 3; doi:10.3390/math5010003

From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description

Center for Complexity and Biosystems and Department of Physics, University of Milano, Via Celoria 16, 20133 Milano, Italy
Academic Editor: Rui A. C. Ferreira
Received: 8 November 2016 / Revised: 12 December 2016 / Accepted: 19 December 2016 / Published: 6 January 2017
(This article belongs to the Special Issue Fractional Differential and Difference Equations)
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Abstract

The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusive stages of the stochastic dynamics. We derive the generalized Langevin equation for a probe particle and we show that this equation reduces to the usual Langevin equation for Brownian motion, and to the fractional Langevin equation on the long-time limit. View Full-Text
Keywords: fractional calculus; stochastic processes; Langevin equation fractional calculus; stochastic processes; Langevin equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Taloni, A. From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description. Mathematics 2017, 5, 3.

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