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Time evolution of interacting vortices under overdamped motion

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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Mauricio Ribeiro, Fernando Nobre, Evaldo M. F. Curado. Time evolution of interacting vortices under overdamped motion. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2012, 85 (2), ⟨10.1103/PhysRevE.85.021146⟩. ⟨hal-02881463⟩



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