In nature, simple building units can be assembled into complex shapes through long-term time-varying external stimuli that are often spatially nonlinear. In contrast, most artificial methods of externally directed assembly rely on field- or template-based energy minimization. However, methods directing the assembly process by controlling time-varying external stimuli instead of attaining the lowest-energy state remain largely unexplored. In this study, we introduce a method that applies time-varying and spatially nonlinear vibration fields to assemble particles into a desired two-dimensional shape. Our assembly method predicts, controls, and monitors the vibration-induced particle motion to iteratively minimize the difference between the desired shape and the actual particle distribution. We applied our method to a centrally actuated vibrating plate, also known as a Chladni plate, and assembled up to a hundred submillimeter particles into complex recognizable shapes. The method allows programmable formation of shapes beyond the intrinsic limits of periodic patterning of the plate.

中文翻译：

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在 Chladni 板上可编程的粒子组装

在自然界中，简单的建筑单元可以通过长期时变的外部刺激组装成复杂的形状，这些刺激通常在空间上是非线性的。相比之下，大多数外部定向组装的人工方法依赖于基于场或模板的能量最小化。然而，通过控制随时间变化的外部刺激而不是达到最低能量状态来指导组装过程的方法在很大程度上仍未得到探索。在这项研究中，我们介绍了一种方法，该方法应用时变和空间非线性振动场将粒子组装成所需的二维形状。我们的组装方法可以预测、控制和监控振动引起的粒子运动，以迭代地最小化所需形状与实际粒子分布之间的差异。我们将我们的方法应用于中央驱动的振动板，也称为克拉尼板，并将多达一百个亚毫米颗粒组装成复杂的可识别形状。该方法允许可编程的形状形成超出板的周期性图案化的固有限制。