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Abstract
We introduce a generic model of a weakly nonlinear self-sustained oscillator as a simplified tool to study synchronization in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronization. Furthermore, we find that synchronization is strongly enhanced when the oscillators are nonisochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Nonisochronity is determined by a nonlinear coupling α being nonzero. We find that its (α) sign determines if they synchronize in phase or antiphase. We then study an infinite array of oscillators in the long-wavelength limit, in the presence of noise. For α>0, hydrodynamic interactions can lead to a homogeneous synchronized state. Numerical simulations for a finite number of oscillators confirm this and, when α<0, show the propagation of waves, reminiscent of metachronal coordination.
Original language | English |
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Article number | 040901 |
Number of pages | 4 |
Journal | Physical Review E: Statistical, Nonlinear, and Soft Matter Physics |
Volume | 85 |
Issue number | 4 |
DOIs | |
Publication status | Published - 5 Apr 2012 |
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Dive into the research topics of 'Hydrodynamic synchronization of nonlinear oscillators at low Reynolds number'. Together they form a unique fingerprint.Projects
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NSF MATERIALS WORLD NETWORK: MICROSCOPIC MODELS OF CROSS-LINKED ACTIVE GELS
Liverpool, T. B. (Principal Investigator)
1/03/09 → 1/03/12
Project: Research