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arXiv · 1806.08207

Fractal dimensions and trajectory crossings in correlated random walks

A. Dubey·J. Meibohm·K. Gustavsson·B. Mehlig
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Abstract

We study spatial clustering in a discrete, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions $D_q$ as functions of a dimensionless parameter, $α$, that plays the role of an inertia parameter. Using the fact that it suffices to consider the linearized dynamics of the model at small separations, we find that $D_q =D_2/(q-1)$ for $q=2,3,\ldots$. The correlation dimension $D_2$ turns out to be a non-analytic function of the inertia parameter in this model. We calculate $D_2$ for small $α$ up to the next-to-leading order in the non-analytic term.

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A. Dubey, J. Meibohm, K. Gustavsson, B. Mehlig. 2018-06-21. Fractal dimensions and trajectory crossings in correlated random walks. https://doi.org/10.1103/physreve.98.062117

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