Kinetic properties of fractal media

TL;DR

This paper investigates the kinetic properties of fractal stellar media, revealing scale-dependent parameters and deriving a generalized kinetic equation that accounts for fractal spatial distributions in stellar dynamics.

Contribution

It introduces a generalized kinetic framework for fractal stellar media, extending classical models to include fractal density distributions and their impact on kinetic parameters.

Findings

Kinetic parameters depend on spatial scale and fractal dimension.

Derived a generalized kinetic equation for fractal stellar media.

Identified significant qualitative and quantitative differences from uniform media.

Abstract

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.