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Time evolution of interacting vortices under overdamped motion

Mauricio S. Ribeiro^1,*, Fernando D. Nobre^1,†, and Evaldo M. F. Curado^1,2,‡

¹Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil
²Laboratoire APC, Université Paris Diderot, 10 rue A. Domon et L. Duquet, 75205 Paris, France

^*ribeiro@cbpf.br
^†fdnobre@cbpf.br
^‡evaldo@cbpf.br

Phys. Rev. E 85, 021146 – Published 27 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.021146

Abstract

A system of interacting vortices under overdamped motion, which has been commonly used in the literature to model flux-front penetration in disordered type-II superconductors, was recently related to a nonlinear Fokker-Planck equation, characteristic of nonextensive statistical mechanics, through an analysis of its stationary state. Herein, this connection is extended by means of a thorough analysis of the time evolution of this system. Numerical data from molecular-dynamics simulations are presented for both position and velocity probability distributions $P (x, t)$ and $P (v_{x}, t)$ , respectively; both distributions are well fitted by similar $q$ -Gaussian distributions, with the same index $q = 0$ , for all times considered. Particularly, the evolution of the system occurs in such a way that $P (x, t)$ presents a time behavior for its width, normalization, and second moment, in full agreement with the analytic solution of the nonlinear Fokker-Planck equation. The present results provide further evidence that this system is deeply associated with nonextensive statistical mechanics.

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Time evolution of interacting vortices under overdamped motion

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