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arXiv 1902.10595cond-mat.soft
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电流介导的一对不同鞭毛的同步化

Current-mediated synchronization of a pair of beating non-identical flagella

V. Dotsenko, A. Maciolek, G. Oshanin, O. A. Vasilyev, S. Dietrich

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10 pages, 2 figures
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摘要：

实验观察到的同步的基本现象学（即，已知双鞭毛藻的相同的跳动鞭毛的随机锁相）被描述耦合的极限环噪声振荡器的动力学的极小模型（称为噪声Kuramoto模型）很好地捕获。如实验所示，其中的噪声项的幅度，这源于旋转马达的波动，取决于鞭毛的长度。在这里，我们解决概念上的重要问题，哪种同步发生，如果两个鞭毛有不同的长度，使噪音作用于他们每个人有不同的幅度。在一个极小模型的基础上，我们也表明，一种不同的同步出现，在这里，它是由一个电流携带，稳态介导的，它体现了自己通过相关的“漂移”的阶段。我们量化这样的同步机制，在适当的序参量$Q$和$Q_{\cal S}$ -为合奏的轨迹和持续时间${\cal S}$，分别为一个单一的实现噪声。通过数值模拟，我们表明，这两种方法变得相同的长观测时间${\cal S}$。这揭示了一个遍历行为，并意味着一个单一的实现序参量$Q_{\cal S}$是适合的实验分析，合奏平均并不总是可能的。

英文摘要：

The basic phenomenology of experimentally observed synchronization (i.e., a stochastic phase locking) of identical, beating flagella of a biflagellate alga is known to be captured well by a minimal model describing the dynamics of coupled, limit-cycle, noisy oscillators (known as the noisy Kuramoto model). As demonstrated experimentally, the amplitudes of the noise terms therein, which stem from fluctuations of the rotary motors, depend on the flagella length. Here we address the conceptually important question which kind of synchrony occurs if the two flagella have different lengths such that the noises acting on each of them have different amplitudes. On the basis of a minimal model, too, we show that a different kind of synchrony emerges, and here it is mediated by a current carrying, steady-state; it manifests itself via correlated "drifts" of phases. We quantify such a synchronization mechanism in terms of appropriate order parameters $Q$ and $Q_{\cal S}$ - for an ensemble of trajectories and for a single realization of noises of duration ${\cal S}$, respectively. Via numerical simulations we show that both approaches become identical for long observation times ${\cal S}$. This reveals an ergodic behavior and implies that a single-realization order parameter $Q_{\cal S}$ is suitable for experimental analysis for which ensemble averaging is not always possible.

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