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Updated: Jul 8, 2025

Simultaneous Measurement of Turbulence and Particle Kinematics Using Flow Imaging Techniques
Published on: March 12, 2019
Goal quest for an intelligent surfer moving in a chaotic flow
Klaus M Frahm1, Dima L Shepelyansky1
1Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France.
Abstract:
We consider a model of an intelligent surfer moving on the Ulam network generated by a chaotic dynamics in the Chirikov standard map. This directed network is obtained by the Ulam method with a division of the phase space in cells of fixed size forming the nodes of a Markov chain. The goal quest for this surfer is to determine the network path from an initial node A to a final node B with minimal resistance given by the sum of inverse transition probabilities. We develop an algorithm for the intelligent surfer that allows us to perform the quest in a small number of transitions which grows only logarithmically with the network size. The optimal path search is done on a fractal intersection set formed by nodes with small Erdös numbers of the forward and inverted networks. The intelligent surfer exponentially outperforms a naive surfer who tries to minimize its phase space distance to target B. We argue that such an algorithm provides unique hints for motion control in chaotic flows.
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