This is a series of four lectures presented at the 2015 Enrico Fermi Summer School in Varenna. The aim of the lectures is to give an introduction to the hydrodynamics of active matter concentrating on low-Reynolds-number examples such as cells and molecular motors. Lecture 1 introduces the hydrodynamics of single active particles, covering the Stokes equation and the Scallop Theorem, and stressing the link between autonomous activity and the dipolar symmetry of the far flow field. In lecture 2 I discuss applications of this mathematics to the behaviour of microswimmers at surfaces and in external flows, and describe our current understanding of how swimmers stir the surrounding fluid. Lecture 3 concentrates on the collective behaviour of active particles, modelled as an active nematic. I write down the equations of motion and motivate the form of the active stress. The resulting hydrodynamic instability leads to a state termed “active turbulence” characterised by strong jets and vortices in the flow field and the continual creation and annihilation of pairs of topological defects. Lecture 4 compares simulations of active turbulence to experiments on suspensions of microtubules and molecular motors. I introduce lyotropic active nematics and discuss active anchoring at interfaces.

中文翻译：

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主动系统的流体动力学

这是在瓦伦纳（Varenna）2015恩里科·费米（Enrico Fermi）暑期学校上演的四个系列讲座。演讲的目的是介绍活性物质的流体动力学，这些动力学集中于低雷诺数的例子，例如细胞和分子马达。第1课介绍了单个活动粒子的流体动力学，涵盖了斯托克斯方程和扇贝定理，并强调了自主活动与远流场的偶极对称性之间的联系。在第2课中，我讨论了该数学方法对微游泳者在表面和外部流动中的行为的应用，并描述了我们目前对游泳者如何搅拌周围流体的理解。第3讲集中于建模为主动向列的主动粒子的集体行为。我写下运动方程式并激发主动应力的形式。所产生的流体动力学不稳定性导致一种状态为“活动湍流”，其特征是流场中的强射流和涡流以及拓扑缺陷对的不断产生和and灭。第4课将主动湍流的模拟与微管和分子马达悬架的实验进行了比较。我介绍了溶致活性向列，并讨论了界面处的主动锚定。