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Fractal dimensions and trajectory crossings in correlated random walks

Journal article
Authors Anshuman Dubey
Jan Meibohm
Kristian Gustavsson
Bernhard Mehlig
Published in Physical Review E
Volume 98
ISSN 2470-0045
Publication year 2018
Published at Department of Physics (GU)
Language en
Subject categories Other Physics Topics


© 2018 American Physical Society. We study spatial clustering in a discrete-time, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions Dq 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 Dq=D2/(q-1) for q=2,3,. The correlation dimension D2 turns out to be a nonanalytic function of the inertia parameter in this model. We calculate D2 for small α up to the next-to-leading order in the nonanalytic term.

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