Ribeiro Mauricio S, Nobre Fernando D, Curado Evaldo M F
Centro 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.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):021146. doi: 10.1103/PhysRevE.85.021146. Epub 2012 Feb 27.
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.
一个处于过阻尼运动状态下的相互作用涡旋系统，该系统在文献中常用于对无序II型超导体中的磁通前沿渗透进行建模，最近通过对其稳态的分析，与非广延统计力学所特有的非线性福克 - 普朗克方程建立了联系。在此，通过对该系统时间演化的深入分析，扩展了这种联系。分别给出了分子动力学模拟中位置和速度概率分布(P(x,t))和(P(v(x),t))的数值数据；在所有考虑的时刻，这两种分布都能很好地由具有相同指数(q = 0)的类似(q) - 高斯分布拟合。特别地，系统的演化使得(P(x,t))在其宽度、归一化和二阶矩方面呈现出一种时间行为，这与非线性福克 - 普朗克方程的解析解完全一致。目前的结果进一步证明了该系统与非广延统计力学有着深刻的关联。
