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Hopping on a wave: from periodic to chaotic transport

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Abstract

We study the dynamics of a particle on an elastic surface carrying a harmonic traveling wave. The particle–surface interaction is assumed to be inelastic both normally and tangentially, and the surface is assumed to provide a kinematic boundary condition to the particle. In this setting, we search for periodic hopping solutions of the particle. The results point to a rich variety of possible particle trajectories which include periodic and chaotic motions. Interestingly, coexisting distinct multi-period attractors, (one with period-3 and its multiples, and including coexisting periodic–chaotic attractors) are observed over a frequency band. In the case of a mutually non-interacting multi-particle system, we observe ballistic and diffusive transport in inter-leaved frequency bands. These results indicate tunability of transport without/with mixing.

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Authors and Affiliations

  1. Department of Mechanical Engineering, IIT Kharagpur, Kharagpur, India

    Gaurang Ruhela

  2. Department of Mechanical Engineering, Center of Theoretical Studies, IIT Kharagpur, Kharagpur, India

    Anirvan DasGupta

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  1. Gaurang Ruhela
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  2. Anirvan DasGupta
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Correspondence to Gaurang Ruhela.

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Ruhela, G., DasGupta, A. Hopping on a wave: from periodic to chaotic transport. Nonlinear Dyn 86, 1663–1672 (2016). https://doi.org/10.1007/s11071-016-2984-x

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  • DOI: https://doi.org/10.1007/s11071-016-2984-x

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