Title: Spatial dynamics of flexible nano-swimmers under a rotating magnetic field Show Chinese title

Title: 旋转磁场下柔性纳米游动器的空间动力学

Abstract: Micro-nano-robotic swimmers have promising potential for future biomedical tasks such as targeted drug delivery and minimally-invasive diagnosis. An efficient method for controlled actuation of such nano-swimmers is applying a rotating external magnetic field, resulting in helical corkscrew-like locomotion. In previous joint work, we presented fabrication and actuation of a simple magnetic nano-swimmer composed of two nano-rods connected by a short elastic hinge. Experiments under different actuation frequencies result in different motion regimes. At low frequencies, in-plane tumbling; at higher frequencies, moving forward in a spatial helical path in synchrony with the rotating magnetic field; in further frequency increase, asynchronous swimming is obtained. In this work, we present mathematical analysis of this nano-swimmer motion. We consider a simple two-link model and explicitly formulate and analyze its nonlinear dynamic equations, and reduce them to a simpler time-invariant system. For the first time, we obtain explicit analytic solutions of synchronous motion under simplifying assumptions, for both solutions of in-plane tumbling and spatial helical swimming. We conduct stability analysis of the solutions, presenting stability transitions and bifurcations for the different solution branches. Furthermore, we present analysis of the influence of additional effects, as well as parametric optimization of the swimmer's speed. The results of our theoretical study are essential for understanding the nonlinear dynamics of experimental magnetic nano-swimmers for biomedical applications, and conducting practical optimization of their performance. Show Chinese abstract

Abstract: 微纳机器人游泳器在未来的生物医学任务（如靶向药物递送和微创诊断）中具有巨大的潜力。 对于这种纳米游泳器的有效操控方法之一是施加旋转的外部磁场，从而产生类似螺旋桨的运动。 在之前的合作研究中，我们展示了由两个通过短弹性铰链连接的纳米棒组成的简单磁性纳米游泳器的制造与驱动。 在不同驱动频率下的实验结果显示了不同的运动模式：低频时表现为平面内翻滚；高频时沿空间螺旋路径同步于旋转磁场向前移动；进一步增加频率则得到非同步游动。 在这项工作中，我们提出了对该纳米游泳器运动的数学分析。 我们考虑了一个简单的两连杆模型，并明确推导并分析了其非线性动力学方程，将其简化为一个更简单的时不变系统。 首次在简化假设下获得了平面翻滚和平面螺旋游泳两种情况同步运动的显式解析解。 我们对这些解进行了稳定性分析，展示了不同解分支的稳定性转换和分岔。 此外，我们还分析了额外效应的影响以及游泳器速度的参数优化。 我们的理论研究结果对于理解实验磁性纳米游泳器在生物医学应用中的非线性动力学至关重要，并为其实用性能优化提供了依据。