Cosentino Lagomarsino M, Jona P, Bassetti B
FOM Institute for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ Amsterdam, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Aug;68(2 Pt 1):021908. doi: 10.1103/PhysRevE.68.021908. Epub 2003 Aug 18.
We employ a model system, called rowers, as a generic physical framework to define the problem of the coordinated motion of cilia (the metachronal wave) as a far from equilibrium process. Rowers are active (two-state) oscillators in a low Reynolds number fluid, and interact solely through the forces of hydrodynamic origin. In this work, we consider the case of fully deterministic dynamics, find analytical solutions of the equation of motion in the long-wavelength (continuum) limit, and investigate numerically the short-wavelength limit. We prove the existence of metachronal waves below a characteristic wavelength. Such waves are unstable and become stable only if the sign of the coupling is reversed. We also find that with normal hydrodynamic interaction, the metachronal pattern has the form of stable trains of traveling wave packets sustained by the onset of anti-coordinated beating of consecutive rowers.
我们采用一种名为“划桨者”的模型系统，作为一个通用的物理框架，将纤毛的协调运动问题（即同步波动）定义为一个远离平衡态的过程。“划桨者”是低雷诺数流体中的主动（双态）振荡器，仅通过流体动力学起源的力相互作用。在这项工作中，我们考虑完全确定性动力学的情况，在长波长（连续介质）极限下找到运动方程的解析解，并对短波长极限进行数值研究。我们证明了在一个特征波长以下存在同步波动。这种波动是不稳定的，只有当耦合的符号反转时才会变得稳定。我们还发现，在正常的流体动力学相互作用下，同步模式具有由连续“划桨者”的反协调搏动引发的稳定行波包列的形式。
