论文标题
主动命名的最佳控制
Optimal Control of Active Nematics
论文作者
论文摘要
在这项工作中，我们介绍了使用最佳控制理论和活性nematics的流体动力学模型来雕刻主动命员系统的第一个系统框架。我们证明了使用两个不同的对照场的使用，（1）应用涡度和（2）活性强度，以塑造局限于磁盘的延伸活性列的动力学。在没有控制输入的情况下，该系统显示了两个吸引子，顺时针和逆时针循环状态，其特征在于两个共旋转拓扑$+\ \ \ frac {1} {1} {2} $缺陷。我们专门寻求时空输入，以将系统从一个吸引子切换到另一个吸引子；我们还检查相移扰动。我们通过优化具有三个贡献的惩罚功能来识别控制输入：总控制努力，控制中的空间梯度以及与所需轨迹的偏差。这项工作表明，最佳控制理论可用于计算能够以经济，平滑和快速的方式重组活跃词法的非平凡输入，因此将作为控制主动物质的实验努力的指南。
In this work we present the first systematic framework to sculpt active nematics systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (1) applied vorticity and (2) 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 $+\frac{1}{2}$ 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 non-trivial 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.
