Limit-cycle oscillation of an elastic filament and caterpillar motion

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    Abstract

    Soft biological materials can exhibit various active motion such as limit-cycle oscillation. The limit-cycle oscillation of active matter might be used for a mechanism of locomotion. We propose a simple model of an active elastic chain as an extension of the van der Pol equation. The uniform state is unstable, and exhibits a limit cycle of breathing motion. If the breathing motion is mirror symmetric, the elastic chain does not move as a whole. However, the breathing motion becomes a caterpillar motion and a unidirectional motion is induced, if an additional heterogeneity is involved or the chain is set on a spatially periodic sawtooth potential. We also analyze the model equation with coupled mode equations, and try to understand the bifurcation to the collective oscillation and the directional motion.

    Original languageEnglish
    Article number026216
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume79
    Issue number2
    DOIs
    Publication statusPublished - Feb 2 2009

    Fingerprint

    Caterpillar
    Filament
    Limit Cycle
    filaments
    Oscillation
    oscillations
    cycles
    Motion
    breathing
    Van Der Pol Equation
    Saw tooth
    locomotion
    Locomotion
    coupled modes
    Mirror
    Bifurcation
    Unstable
    mirrors
    Model

    All Science Journal Classification (ASJC) codes

    • Condensed Matter Physics
    • Statistical and Nonlinear Physics
    • Statistics and Probability

    Cite this

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    abstract = "Soft biological materials can exhibit various active motion such as limit-cycle oscillation. The limit-cycle oscillation of active matter might be used for a mechanism of locomotion. We propose a simple model of an active elastic chain as an extension of the van der Pol equation. The uniform state is unstable, and exhibits a limit cycle of breathing motion. If the breathing motion is mirror symmetric, the elastic chain does not move as a whole. However, the breathing motion becomes a caterpillar motion and a unidirectional motion is induced, if an additional heterogeneity is involved or the chain is set on a spatially periodic sawtooth potential. We also analyze the model equation with coupled mode equations, and try to understand the bifurcation to the collective oscillation and the directional motion.",
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