Minimal model for synchronization induced by hydrodynamic interactions

Qian, Baoliang; Jiang, Hongyuan; Gagnon, David A.; Breuer, Kenneth S.; Powers, Thomas

doi:10.1103/physreve.80.061919

Cited by 88 publications

(65 citation statements)

References 26 publications

(36 reference statements)

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“…This result is consistent with zero synchronization strength λ → 0 in the limit of a hard constraint A = A 0 for k → ∞. Several experimental realizations highlighted the role of elastic compliance for hydrodynamic synchronization in pairs of man-made oscillators, including helices rotating at low Reynolds numbers in a tank of highly viscous silicone oil [69], or micro-rotors driven by laser light [45]. A recent study of the synchronization of beating flagella by direct hydrodynamic interactions also suggested an important role of elastic waveform compliance of the flagellar beat for synchronization [39].…”

Section: Symmetry Breaking By Amplitude Compliancesupporting

confidence: 76%

Hydrodynamic synchronization of flagellar oscillators

Friedrich

2016

Eur. Phys. J. Spec. Top.

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Abstract. In this review, we highlight the physics of synchronization in collections of beating cilia and flagella. We survey the nonlinear dynamics of synchronization in collections of noisy oscillators. This framework is applied to flagellar synchronization by hydrodynamic interactions. The time-reversibility of hydrodynamics at low Reynolds numbers requires swimming strokes that break time-reversal symmetry to facilitate hydrodynamic synchronization. We discuss different physical mechanisms for flagellar synchronization, which break this symmetry in different ways.

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Section: Symmetry Breaking By Amplitude Compliancesupporting

confidence: 76%

Hydrodynamic synchronization of flagellar oscillators

Friedrich

2016

Eur. Phys. J. Spec. Top.

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“…In particular, in viscous fluids hydrodynamic coupling leads to the synchronization of rotating helical filaments such as bacterial flagella [31,32], rotating paddles [33], microfluidic rotors [34][35][36], the pair of beating flagella in Chlamydomonas [37], or flagella of neighboring sperm cells [38][39][40][41]. The most astonishing example for synchronization in viscous fluids are metachronal waves.…”

Section: Introductionmentioning

confidence: 99%

Metachronal waves in a chain of rowers with hydrodynamic interactions

2011

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Abstract. Hair-like appendages called cilia on the surface of a microorganism such as Paramecium or Opalina beat highly synchronized and form so-called metachronal waves that travel along the surfaces. In order to study under what principal conditions these waves form, we introduce a chain of beads, called rowers, each periodically driven by an external force on a straight line segment. To implement hydrodynamic interactions between the beads, they are considered point-like. Two beads synchronize in antiphase or in phase depending on the positive or negative curvature of their driving-force potential. Concentrating on in-phase synchronizing rowers, we find that they display only transient synchronization in a bulk fluid. On the other hand, metachronal waves with wavelengths of 7-10 rower distances emerge, when we restrict the range of hydrodynamic interactions either artificially to nearest neighbors or by the presence of a bounding surface as in any relevant biological system.

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“…Such reversible dynamics cannot give rise to any synchronization behavior that is, by definition, an irreversible process. This symmetry upon torque reversal can be broken by using phase dependent torques [6] or, alternatively, by introducing some degree of mechanical flexibility in the form of internal degrees of freedom with finite stiffness [15,16]. In the latter case, when we reverse the sign of applied torques, internal forces will not change their sign and the system will not trace back its history.…”

mentioning

confidence: 99%

“…As a consequence, synchronization in uniformly rotating systems is driven by small deviations from rigid dynamics and amounts to a tiny effect, despite the presence of strong hydrodynamic couplings. In such a situation, synchronization is highly sensitive to a small mismatch in the rotors' free rotational frequencies [16]. An extremely low Reynolds number is an important condition in mesoscopic dynamics, but even more peculiar is the unavoidable presence of noise.…”

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confidence: 99%

“…An extremely low Reynolds number is an important condition in mesoscopic dynamics, but even more peculiar is the unavoidable presence of noise. However, hydrodynamic synchronization of rotators has been investigated only by analytical [6,11] and numerical models [15] or macroscopic experiments [16] that do not take into account noise. A colloidal model for rotators, of the kind used [13] for modeling ciliar beating motions, is still lacking.…”

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confidence: 99%

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Hydrodynamic Synchronization of Light Driven Microrotors

et al. 2012

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Hydrodynamic synchronization is a fundamental physical phenomenon by which self-sustained oscillators communicate through perturbations in the surrounding fluid and converge to a stable synchronized state. This is an important factor for the emergence of regular and coordinated patterns in the motions of cilia and flagella. When dealing with biological systems, however, it is always hard to disentangle internal signaling mechanisms from external purely physical couplings. We have used the combination of two-photon polymerization and holographic optical trapping to build a mesoscale model composed of chiral propellers rotated by radiation pressure. The two microrotors can be synchronized by hydrodynamic interactions alone although the relative torques have to be finely tuned. Dealing with a micron sized system we treat synchronization as a stochastic phenomenon and show that the phase lag between the two microrotors is distributed according to a stationary Fokker-Planck equation for an overdamped particle over a tilted periodic potential. Synchronized states correspond to minima in this potential whose locations are shown to depend critically on the detailed geometry of the propellers. Synchronization is at the basis of a wide variety of fascinating and important phenomena in physics, biology, and engineering. From coupled Josephson junctions [1] to cardiac pacemaker cells [2], the presence of a weak interaction between two or more self-sustained oscillators often leads to the emergence of synchronous patterns [3]. At the micron scale of cells and bacteria, hydrodynamic interactions provide a strong and long-ranged mechanism for coupling [4]. Since synchronization phenomena are known to occur even in the presence of extremely weak and subtle couplings, it is quite natural to expect strong synchronous behavior in such a strongly coupled regime. The presence of a strong coupling, however, is not a sufficient condition for synchronization [5,6], and the role of hydrodynamic interactions for the emergence of synchronous behaviors in flagella [7][8][9] and cilia [10-13] is still the subject of a lively debate [14]. In the case of waving sheets [5], kinematic reversibility can destroy synchronization when the sheets have reflection symmetry. For the same reason, a collection of rigid rotors, spinning around fixed axes and coupled through hydrodynamic interactions, will appear as the same physical system evolving on a time reversed trajectory when we change sign to all applied torques. Such reversible dynamics cannot give rise to any synchronization behavior that is, by definition, an irreversible process. This symmetry upon torque reversal can be broken by using phase dependent torques [6] or, alternatively, by introducing some degree of mechanical flexibility in the form of internal degrees of freedom with finite stiffness [15,16]. In the latter case, when we reverse the sign of applied torques, internal forces will not change their sign and the system will not trace back its history. As a consequence, synchronization...

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Minimal model for synchronization induced by hydrodynamic interactions

Cited by 88 publications

References 26 publications

Hydrodynamic synchronization of flagellar oscillators

Hydrodynamic synchronization of flagellar oscillators

Metachronal waves in a chain of rowers with hydrodynamic interactions

Hydrodynamic Synchronization of Light Driven Microrotors

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