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arXiv physics/0511096physics.space-phnlin.AOphysics.plasm-ph
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太阳风- magnetosphere耦合数据的多尺度行为和分数动力学

Multiscale behavior and fractional kinetics from the data of solar wind - magnetosphere coupling

G. M. Zaslavsky, P. N. Guzdar, M. Edelman, M. I. Sitnov, A. S. Sharma

摘要:

多尺度现象在自然界和实验室中普遍存在。一个广泛的相互作用的空间和时间尺度决定了许多系统的动力学本质上是多尺度的。在大多数研究学科中,多尺度现象不仅十分突出,而且往往占据主导地位。在太阳风-磁层相互作用中,多尺度特征与整体或相干特征并存。这些现象的基础是数学和理论的方法,如相变,湍流,自组织,分数动力学,渗流等分数动力学方程提供了一个合适的数学框架的多尺度行为。分数阶动力学方程的多尺度性质通过分数阶导数来描述,这些方程的解产生非收敛矩,表现出很强的多尺度行为。使用Lévy-flights方法,我们分析了磁层和太阳风的数据。在此基础上,我们提出了一个模型的多尺度功能,并比较它与扩散型方程的解决方案。具有分数阶空间导数的方程表现出很强的多尺度行为和发散矩。另一方面,与空间相关的扩散系数的方程产生收敛的时刻,高斯型的解决方案和缺乏长尾通常与多尺度行为。

英文摘要:

Multiscale phenomena are ubiquitous in nature as well in laboratories. A broad range of interacting space and time scales determines the dynamics of many systems which are inherently multiscale. In most research disciplines multiscale phenomena are not only prominent, but also they have often played the dominant role. In the solar wind - magnetosphere interaction, multiscale features coexist along with the global or coherent features. Underlying these phenomena are the mathematical and theoretical approaches such as phase transitions, turbulence, self-organization, fractional kinetics, percolation, etc. The fractional kinetic equations provide a suitable mathematical framework for multiscale behavior. In the fractional kinetic equations the multiscale nature is described through fractional derivatives and the solutions of these equations yield non-convergent moments, showing strong multiscale behavior. Using a Lévy-flights approach, we analyze the data of the magnetosphere and the solar wind. Based on this analysis we propose a model of the multiscale features and compare it with the solutions of diffusion type equations. The equation with fractional spatial derivative shows strong multiscale behavior with divergent moments. On the other hand the equation with space dependent diffusion coefficients yield convergent moments, indicating Gaussian type solutions and absence of long tails typically associated with multiscale behavior.

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