论文标题
如何生长扁平叶子
How to grow a flat leaf
论文作者
论文摘要
如果没有一些反馈来稳定易于触发的长波长模式，就几乎不可能种植诸如叶片的平坦薄片，因为它们在能量上便宜。在这里，我们将薄弹性板的物理学与反馈控制理论相结合，以探索叶子在生长时如何保持平坦。我们研究了面内（度量）和平面外（曲率）生长变化，并解释了局部和非局部反馈定律。我们表明，一种线性化反馈理论，该理论既说明了空间非局部和时间延迟的效果，就足以抑制长波长波动，并解释了最近观察到的烟草叶片生长的统计特征。我们的工作提供了一个框架，以了解对叶子和其他层流对象的形状调节。
Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other laminar objects.
