论文标题
时间周期性粘性流的柔性细丝：形状混乱和三个周期
Flexible filament in time-periodic viscous flow: shape chaos and period three
论文作者
论文摘要
我们在线性剪切流中研究一个单一的自由浮动，不可扩展的弹性细丝：$ \ mathbf {u} _ {0}（x，x，y）= \dotγy \ hat {x} $。在我们的模型中：弹性能仅取决于弯曲；汇率，$ \dotγ= s \ sin（ωt）$是时间的定期功能，$ t $;灯丝和流量之间的相互作用是通过局部各向同性阻力近似的。基于细丝的形状，我们发现了五个不同的动态阶段：直，弯曲，周期性（周期第三，第四周，等等），混乱，一个混乱的瞬变。在混乱阶段，我们表明，角度的迭代图（灯丝的端到端向量与切线的一端都具有三个时期的解决方案）。因此，这是混乱的。此外，在混乱阶段，流量是有效的混合器。
We study a single, freely--floating, inextensible, elastic filament in a linear shear flow: $\mathbf{U}_{0}(x,y) = \dotγ y \hat{x}$. In our model: the elastic energy depends only on bending; the rate-of-strain, $\dotγ = S \sin(ωt)$ is a periodic function of time, $t$; and the interaction between the filament and the flow is approximated by a local isotropic drag force. Based on the shape of the filament we find five different dynamical phases: straight, buckled, periodic (with period two, period three, period four, etc), chaotic, and one with chaotic transients. In the chaotic phase, we show that the iterative map for the angle, which the end-to-end vector of the filament makes with the tangent its one end, has period three solutions; hence it is chaotic. Furthermore, in the chaotic phase the flow is an efficient mixer.
