Wilkinson, M.; Mehlig, B. and Gustavsson, K.
Correlation dimension of inertial particles in random flows.
Europhysics Letters, 89(5) p. 50002.
We obtain an implicit equation for the correlation dimension D2 of dynamical systems in terms of an integral over a propagator. We illustrate the utility of this approach by evaluating D2 for inertial particles suspended in a random flow. In the limit where the correlation time of the flow field approaches zero, taking the short-time limit of the propagator enables D2 to be determined from the solution of a partial differential equation. We develop the solution as a power series in a dimensionless parameter which represents the strength of inertial effects.
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