Conservative, Dissipative and Super-diffusive Behavior of a Particle Propelled in a Regular Flow

Abstract

A recent model of Ariel et al. [1] for explaining the observation of Lévy walks in swarming bacteria suggests that self-propelled, elongated particles in a periodic array of regular vortices perform a super-diffusion that is consistent with Lévy walks. The equations of motion, which are reversible in time but not volume preserving, demonstrate a new route to L'evy walking in chaotic systems. Here, the dynamics of the model is studied both analytically and numerically. It is shown that the apparent super-diffusion is due to "sticking" of trajectories to elliptic islands, regions of quasi-periodic orbits reminiscent of those seen in conservative systems. However, for certain parameter values, these islands coexist with asymptotically stable periodic trajectories, causing dissipative behavior on very long time scales.

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Cited by in corpus (5)

• Anomalous diffusion and Lévy walks distinguish active from inertial turbulence
• Trapping of swimmers in a vortex lattice
• Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows
• Noise-induced aggregation of swimmers in the Kolmogorov flow
• Attractor-repeller collision and the heterodimensional dynamics