Whitney Taylor J, Mitchell Kevin A
<a href="https://ror.org/00d9ah105">University of California Merced</a>, 5200 Lake Rd, Merced, California 95343, USA.
Phys Rev E. 2024 Sep;110(3-1):034203. doi: 10.1103/PhysRevE.110.034203.
We study the transport of rigid ellipsoidal swimmers in a periodic vortex array via numerical simulation and dynamical systems analysis. Via ensemble simulations, we show the counterintuitive result that slower swimming speeds can generate fast ballistic transport, while faster swimming speeds generate chaotic and diffusive transport, which is inherently slower in the long run. To explain this, we use the symmetry of the flow to construct a time-reversible Poincaré return map on a two-dimensional surface of section in phase space. For sufficiently small swimming speeds, we find stable periodic orbits on the surface of section surrounded by invariant tori, similar to Kolmogorov-Arnold-Moser curves. Trajectories within these tori are ballistic. As the swimming speed is increased, the periodic orbits undergo a sequence of period-doubling bifurcations that destroys the ballistic tori. These bifurcations exactly match the ballistic to diffusive transition from the ensemble simulations. Additional ensemble simulations are used to test the robustness of these results to noise. The ballistic behavior is destroyed as the strength of rotational diffusion increases. However, we estimate that the ballistic tori might still be seen in experiments.
我们通过数值模拟和动力系统分析研究了刚性椭球体游动者在周期性涡旋阵列中的输运。通过系综模拟，我们展示了一个违反直觉的结果：较慢的游动速度能够产生快速的弹道输运，而较快的游动速度则产生混沌和扩散输运，从长远来看，扩散输运本质上要慢得多。为了解释这一点，我们利用流场的对称性在相空间的二维截面表面上构建了一个时间可逆的庞加莱返回映射。对于足够小的游动速度，我们在截面表面上发现了被不变环面包围的稳定周期轨道，类似于柯尔莫哥洛夫 - 阿诺尔德 - 莫泽曲线。这些环面内的轨迹是弹道式的。随着游动速度的增加，周期轨道经历一系列倍周期分岔，从而破坏了弹道环面。这些分岔与系综模拟中从弹道到扩散的转变完全匹配。额外的系综模拟用于测试这些结果对噪声的鲁棒性。随着旋转扩散强度的增加，弹道行为被破坏。然而，我们估计在实验中可能仍然可以看到弹道环面。
