The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be relevant for in vitro reconstructed actomyosin-membrane system. Different from a membrane coupled to a polar active fluid, this model predicts that only when the viscosity of the fluid above the membrane is sufficiently large, a contractile active fluid is able to slow down the relaxation of the membrane for perturbations with wavelength comparable to the thickness of the active fluid. Hence, our model predicts a finite-wavelength instability in the limit of strong contractility, which is different from a membrane coupled to a polar active fluid. However, a membrane coupled to an extensile active fluid is always unstable against long-wavelength perturbations due to active extensile stress enhanced membrane undulation.

中文翻译：

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与活性流体耦合的膜的动力学。

从理论上考虑了与活性流体耦合的膜在衬底顶部的动力学。假设活性流体的指向矢场在膜平面内具有旋转对称性。这种情况可能与体外重建的肌动球蛋白-膜系统有关。与耦合至极性活性流体的膜不同，该模型预测，只有当膜上方的流体的粘度足够大时，收缩性活性流体才能够减慢膜的松弛，从而产生与波长可比的扰动。活性流体的厚度。因此，我们的模型预测了在强收缩性极限内的有限波长不稳定性，这与偶联至极性活性流体的膜不同。然而，