论文标题
部分可观测时空混沌系统的无模型预测
Planar Rotational Equilibria of Two Non-identical Microswimmers
论文作者
论文摘要
我们研究了两个流体动力耦合的非相同微晶状体的平面运动，每个微磁带均模型为具有内在自我启动的力偶极子。使用图像方法，我们证明了我们的结果与大部分流体一样，在无压力的液态气体界面上同样适用。提出了一对两个拉特和两个推动器的圆形周期轨道的封闭分析形式，并根据两维扰动确定其线性稳定性。构建了相对于二维扰动的轨道的通用稳定图，并显示出两个非相同的推动器或两个在无压力界面上移动的非相同的拉杆可能形成稳定的旋转平衡。 对于两个非相同的拉斯，我们发现稳定的准周期性局部状态与相位空间中二维圆环上的运动有关。稳定的Tori是由于圆环分叉而源自圆形的周期轨道。相对于三维扰动，所有稳定的平衡在两个维度上均单调不稳定。
We study a planar motion of two hydrodynamically coupled non-identical micro-swimmers, each modelled as a force dipole with intrinsic self-propulsion. Using the method of images, we demonstrate that our results remain equally applicable at a stress-free liquid-gas interface as in the bulk of a fluid. A closed analytical form of circular periodic orbits for a pair of two pullers and a pair of two pushers is presented and their linear stability is determined with respect to two- and three-dimensional perturbations. A universal stability diagram of the orbits with respect to two-dimensional perturbations is constructed and it is shown that two non-identical pushers or two non-identical pullers moving at a stress-free interface may form a stable rotational equilibrium. For two non-identical pullers, we find stable quasi-periodic localized states, associated with the motion on a two-dimensional torus in the phase space. Stable tori are born from circular periodic orbits as the result of a torus bifurcation. All stable equilibria in two dimensions are shown to be monotonically unstable with respect to three-dimensional perturbations.
