Integral One-Point Statistical Characteristics of Magnetic Field

  • Valery I. KlyatskinEmail author
Part of the Understanding Complex Systems book series (UCS)


Above, we derived the equation for the one-point probability densities of the magnetic field under the assumption that effects of dynamic diffusion are absent. The one-point probability densities allow calculating arbitrary one-point characteristics of this field. Combined with the ideas of statistical topography, they are sufficient to obtain the conditions of possible formation of cluster structures. However, the analysis of derivatives of this field requires the knowledge of at least the two-point probability densities. In principle, the equations for such probability densities can be obtained in standard manner, by using the general procedure for the linear partial differential equations of the first order. However, this derivation requires very cumbersome calculations, and examination of consequences of such description is a very difficult task. Moreover, effects of dynamic diffusion cannot be included in such probabilistic description.


Average Energy Moment Function Variational Derivative Linear Partial Differential Equation Dynamic Diffusion 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.A.M. Obukhov Institute of Atmospheric Physics Russian Academy of SciencesMoscowRussia

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