树木与埃菲尔铁塔的共同之处

最近，爱思唯尔期刊《理论生物学杂志》(Journal of Theoretical Biology)刊登了美国杜克大学的一项最新研究。研究发现，著名的法国埃菲尔铁塔与树木有很多相似的地方——二者都是优化的流体和固体力学的典型例子，都符合构造理论。

对于大多数工程师来说，流体力学和固体力学的原理如同油和水不相容。但是最近美国杜克大学的工程师提出，这些不同的力可以并存于同一理论。研究人员以树木为例，树主主要疏运水分到树干、树叶等各部分，树木的结构会方便水从地面疏运。大自然这个伟大的“工程师”，在设计树木结构时候，不仅要考虑到让树木本身最大限度地流动水，同时还要适应自然世界的需要，要承受来自外界的力，比如风。世界著名的建筑埃菲尔铁塔也与树木有类似的地方。埃菲尔铁塔是巴黎的标志之一，它和纽约的帝国大厦、东京的电视塔同被誉为西方三大著名建筑。它被誉为19世纪世界上最伟大的土木工程之一，体现了外在美和内在美的统一。同树木一样，埃菲尔铁塔要“疏运”力到各个部分，同时也要考虑来自外界的力量。研究表明，这个重达7000多吨的铁塔对地面的压强每平方厘米只有4公斤，和一个人坐在椅子上的压强相当。

树木与埃菲尔铁塔都遵循了构造理论，这是由美籍罗马尼亚科学家Bejan在2O世纪9O年代中期首先提出的。构造理论是一种最优设计方法，它从系统的基本单元结构开始优化，之后再将这些经过优化的最小单元结构通过优化逐级组合起来，一直到满足设计要求。（生物谷Bioon.com）

生物谷推荐原始出处：

Journal of Theoretical Biology，doi:10.1016/j.jtbi.2008.06.026，A. Bejan, J. Lee

Unifying constructal theory of tree roots, canopies and forests

A. Bejana, S. Lorenteb and J. Lee

Here, we show that the most basic features of tree and forest architecture can be put on a unifying theoretical basis, which is provided by the constructal law. Key is the integrative approach to understanding the emergence of “designedness” in nature. Trees and forests are viewed as integral components (along with dendritic river basins, aerodynamic raindrops, and atmospheric and oceanic circulation) of the much greater global architecture that facilitates the cyclical flow of water in nature (Fig. 1) and the flow of stresses between wind and ground. Theoretical features derived in this paper are: the tapered shape of the root and longitudinally uniform diameter and density of internal flow tubes, the near-conical shape of tree trunks and branches, the proportionality between tree length and wood mass raised to 1/3, the proportionality between total water mass flow rate and tree length, the proportionality between the tree flow conductance and the tree length scale raised to a power between 1 and 2, the existence of forest floor plans that maximize ground-air flow access, the proportionality between the length scale of the tree and its rank raised to a power between −1 and −1/2, and the inverse proportionality between the tree size and number of trees of the same size. This paper further shows that there exists an optimal ratio of leaf volume divided by total tree volume, trees of the same size must have a larger wood volume fraction in windy climates, and larger trees must pack more wood per unit of tree volume than smaller trees. Comparisons with empirical correlations and formulas based on ad hoc models are provided. This theory predicts classical notions such as Leonardo's rule, Huber's rule, Zipf's distribution, and the Fibonacci sequence. The difference between modeling (description) and theory (prediction) is brought into evidence.