Title: Designing optimal elastic filaments for viscous propulsion Show Chinese title

Title: 设计用于粘性推进的最佳弹性细丝

Abstract: The propulsion of many eukaryotic cells is generated by flagella, flexible slender filaments that are actively oscillating in space and time. The dynamics of these biological appendages have inspired the design of many types of artificial microswimmers. The magnitude of the filament's viscous propulsion depends on the time-varying shape of the filament, and that shape depends in turn on the spatial distribution of the bending rigidity of the filament. In this work, we rigorously determine the relationship between the mechanical (bending) properties of the filament and the viscous thrust it produces using mathematical optimisation. Specifically, by considering a model system (a slender elastic filament with an oscillating slope at its base), we derive the optimal bending rigidity function along the filament that maximises the time-averaged thrust produced by the actuated filament. Instead of prescribing a specific functional form, we use functional optimisation and adjoint-based variational calculus to formally establish the link between the distribution of bending rigidity and propulsion. The optimal rigidities are found to be stiff near the base, and soft near the distal end, with a spatial distribution that depends critically on the constraints used in the optimisation procedure. These findings may guide the optimal design of future artificial swimmers. Show Chinese abstract

Abstract: 许多真核细胞的运动是由鞭毛产生的，这些鞭毛是柔性细长的丝状物，在空间和时间上主动振荡。这些生物附属物的动力学启发了许多类型的人工微游泳器的设计。丝状物的粘性推进力的大小取决于丝状物随时间变化的形状，而该形状又反过来取决于丝状物弯曲刚度的空间分布。在本工作中，我们通过数学优化严格确定了丝状物的机械（弯曲）特性与所产生的粘性推力之间的关系。具体来说，通过考虑一个模型系统（基部具有振荡斜率的细长弹性丝状物），我们推导出沿丝状物的最优弯曲刚度函数，以最大化由驱动丝状物产生的时间平均推力。而不是规定特定的功能形式，我们使用功能优化和基于伴随的变分法来正式建立弯曲刚度分布与推进力之间的联系。发现最优刚度在基部较硬，而在远端较软，其空间分布关键地依赖于优化过程中使用的约束条件。这些发现可能指导未来人工游泳器的最佳设计。