分形介质的动力学性质
Kinetic properties of fractal media
摘要：
分形恒星介质中的动力学过程是根据我们早期论文（Chumak \& Rastorguev，2015）中开发的方法进行分析的，该方法涉及将最近邻和随机力分布推广到分形介质。在分析相应朗之万方程解的基础上，研究了尺度依赖条件密度近似下的扩散问题。结果表明，动力学参数（时间尺度，动摩擦系数，扩散等），对于分形恒星介质，它可以从定性和定量上显著不同于具有有限波动的准均匀随机介质的相应参数。最重要的区别是，在分形的情况下，动力学参数取决于空间尺度的长度和分形维数的介质研究。在考虑到空间恒星密度分布的分形性质的情况下，在Fokker-Planck近似下导出了恒星介质的广义动力学方程（恒星动力学基本方程）。导出了描述分形引力介质偏离平衡态的极限形式。
英文摘要：
Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper (Chumak \& Rastorguev, 2015) involving a generalization of the nearest neighbour and random force distributions to fractal media. Diffusion is investigated in the approximation of scale-dependent conditional density based on an analysis of the solutions of the corresponding Langevin equations. It is shown that kinetic parameters (time scales, coefficients of dynamic friction, diffusion, etc.) for fractal stellar media can differ significantly both qualitatively and quantitatively from the corresponding parameters for a quasi-uniform random media with limited fluctuations. The most important difference is that in the fractal case kinetic parameters depend on spatial scale length and fractal dimension of the medium studied. A generalized kinetic equation for stellar media (fundamental equation of stellar dynamics) is derived in the Fokker-Planck approximation with the allowance for the fractal properties of the spatial stellar density distribution. Also derived are its limit forms that can be used to describe small departures of fractal gravitating medium from equilibrium.
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