论文标题
伦纳多规则的统计液压模型
Statistical hydraulic model for the Leonardo's rule
论文作者
论文摘要
超过五百年前，莱昂纳多·达·芬奇（Leonardo da Vinci）在如今被称为莱昂纳多（Leonardo）统治的树木生长中发现了一种模式。该规则将茎的厚度与分叉阶段的分支的厚度联系起来，以毕达哥拉斯的方式。他认为他的统治是保护SAP通量的结果。在目前的工作中，我们通过假设每个木质部元素的SAP通量作为非理想的流体以及木质部元素的尺寸分布来探讨这一想法。我们发现，莱昂纳多统治的同时实现和对SAP通量的保存，在所有Xylem元素概括之后，会导致SAP的全球行为，就像理想的流体一样。这些结果得到了现场和实验工作的支持。特别是，我们通过测量不同分叉阶段的茎分支厚度来证实莱昂纳多在不同树种中的规则。我们还通过浸渍过程确定了木质部元素的统计尺寸分布，发现它对应于一个接近三个指数的功率定律分布，这是莱昂纳多规则所需的指数。据我们所知，这是第一次为Leonardo规则提供了由实验数据支持的统计液压模型。
More than five hundred years ago Leonardo Da Vinci found a pattern in the growth of trees nowadays known as the Leonardo's rule. This rule relates the thickness of the stem with the thickness of the branches at different bifurcation stages in a Pythagorean fashion. He argued that his rule was the result of the conservation of sap flux. In the present work, we explore this idea by assuming that the sap flux through each xylem element behaves as a non-ideal fluid and the size-distribution of the xylem elements obeys a power law distribution. We find that the simultaneous fulfillment of Leonardo's rule and the conservation of the sap flux, lead to a global behavior of the sap like that of an ideal fluid after summing over all xylem elements. These results are supported by field and experimental work. In particular, we corroborated the Leonardo's rule in different tree species by measuring the stem-branches thickness at different bifurcations stages. We also determined the statistical size-distribution of the xylem elements through a maceration process, finding that it corresponds to a power law distribution with an exponent close to three, which is the exponent required for the Leonardo's rule. As far as we know this is the first time that a statistical hydraulic model supported by experimental data is presented for the Leonardo's rule.
