Optimal Control of Active Nematics
Optimal Control of Active Nematics
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DOI：
10.1103/physrevlett.125.178005
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发表时间：
2020-10-23
影响因子：
8.6
通讯作者：
Fraden, Seth
中科院分区：
文献类型：
--
作者：
Norton, Michael M.;Grover, Piyush;Fraden, Seth
在这项工作中，我们提出了第一个系统框架来塑造主动向列系统，利用最优控制理论和主动向列系统的流体动力学模型。我们演示了使用两个不同的控制场，(I)外加涡度和(Ii)活动强度，来塑造限制在圆盘上的伸展活动向列相的动力学。在没有控制输入的情况下，系统表现出两个吸引子，即顺时针和逆时针的循环态，其特征是两个同向旋转的拓扑+1/2缺陷。我们特别寻找将系统从一个吸引子切换到另一个吸引子的时空输入，我们还研究了相移扰动。我们通过优化具有三个贡献的惩罚函数来识别控制输入：总控制力、控制中的空间梯度和与期望轨迹的偏差。这项工作表明，最优控制理论可以用来计算能够以经济、平稳和快速的方式重组活动向列的非平凡输入，因此将对控制活性物质的实验工作起到指导作用。
In this work we present the first systematic framework to sculpt active nematic systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (i) applied vorticity and (ii) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological +1/2 defects. We specifically seek spatiotemporal inputs that switch the system from one attractor to the other, we also examine phase-shifting perturbations. We identify control inputs by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control, and deviations from the desired trajectory. This work demonstrates that optimal control theory can be used to calculate nontrivial inputs capable of restructuring active nematics in a manner that is economical, smooth, and rapid, and therefore will serve as a guide to experimental efforts to control active matter.