Trees, forests and the Eiffel tower reveal theory of design in nature

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Eiffel Tower. Credit: Adrian Bejan

What do a tree and the Eiffel Tower have in common? According to a Duke University engineer, both are optimized for flow. In the case of trees, the flow is of water from the ground throughout the trunk, branches and leaves, and into the air. The Eiffel Tower's flow carries stresses throughout the structure without collapsing under its own weight or being downed by the wind.

For most engineers, the laws governing fluid and solid mechanics like these examples are like oil and water – they just don't mix.

However, a theory developed by Adrian Bejan, J.A. Jones Professor of Mechanical Engineering at Duke's Pratt School of Engineering and colleague Sylvie Lorente, professor of civil engineering at the University of Toulouse, France, explains how these disparate forces can co-exist within the same theory.

"We believe that the main function of the tree is to facilitate the flow of water from the ground and into the atmosphere," Bejan said. "To achieve that function, the tree is ideally designed to not only maximize the flow of water, but in order to be successful in the real world, it must also be able to withstand the stresses of the wind. It is exquisitely designed to do just that."

The constructal theory, which Bejan started describing in 1996, is based on the principle that flow systems evolve to balance and minimize imperfections, reducing friction or other forms of resistance, so that the least amount of useful energy is lost. While the tree is the most common model used by Bejan to explain the theory, other similar examples exist in nature, such as the rivers and streams that make up a delta or the intricate airways of the lungs.

In their latest theoretical formulation, the engineers focused on fundamental principles to explain the "designedness" of nature, or why things are constructed the way they are. Using the constructal theory, they deduced the structure of the individual tree, as well as its root system and its place in the forest, as a microcosm of the flow of water in nature.

This new application of the constructal theory was published early online in the Journal of Theoretical Biology. Bejan and Lorente's work was supported by the Air Force Office of Scientific Research.

"The tree is a physical flow architecture that has evolved to meet two main objectives – maximum mechanical strength against wind and maximum access for water coming from the ground through the tree and into the atmosphere," Bejan said. "In the larger sense, the forest itself is a flow system with the same mechanical properties and functions as the individual tree, facilitating the flow of water across the globe."

As the branches grow out from the trunk, the ratio of their circumferences decreases in proportion to the trunk's decreasing circumference as it rises.

"Winds come in many speeds, but their ultimate effect is cutting off trunks, branches and leaves, so whatever is too long or sticks out too much is shaved off," Bejan said. "So the pattern of the tree is the result of the never-ending assault by the wind."

The resulting patterns and proportions, like the similar ones of the Eiffel Tower, are predicted by the constructal theory, Bejan said.

"If the purpose of a tree was not to transport water, it would look like the Eiffel Tower," said Bejan, half jokingly. "It looks like Mr. (French engineer Gustave) Eiffel, without knowing it, designed a structure that corresponds with our constructal theory."

Source: Duke University

   

• Alizee - Aug 14, 2008
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  By AWT the matter, life or civilization artifacts were created to fulfill the principle of least action in low energy density conditions from the same reason, like every other phase transition. For example, during cooling of saturated vapor the system of density gradients of higher complexity appears, because it enables the molecules to spread the energy by higher energy density (the actual energy speed decreases, which can be intepreted as an inflation of local space-time). The water surface can spread the energy with higher density because the air is too lighweight and the water is of low compressibility. Therefore the spontaneous symmetry breaking, i.e. the formation of compactified Aether density gradients (i.e. phase transform followed by formation of water surface or life in bisphere) is the straightforward solution of this optimization problem. And not just formation of particles, dropplets, life or trees - but most of civilization artifacts: the establishing of monetary economy, IP/TCP/HTTP protocols or even Eiffel tower. Everything is serving for intensification of inertial mass/energy spreading through Universe.
  
  While the constructal theory is in many good point definitelly, I can see a problem similar to unparticle or process physics in somewhat ad-hoced / empirical character of these theories, which are supposed to become replaced by more general approach of AWT. After all, the formation of nested foam of theories is just another attempt to intensify the information/energy spreading through civilization.
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• OregonWind - Aug 14, 2008
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  to Alizee
  
  Could you explain the whole thing again?
  
  
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• Alizee - Aug 14, 2008
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  Could you explain the whole thing again?

  From which point? Do you know, for example, what the principle of least action is? The matter/energy is always trying to spread as effectively, as possible. For example, the reconnaissance of unknown terrain can be done in line of skirmishers, or in colum of soldiers. But the most effective strategy line is the fractal one, which alternates both approaches and as such it enables to cover the largest area by the smallest amount of soldiers by the highest speed. And this is the way, how to observe the largest volume of chaotic environment in shortest time interval as a vacuum space. The vacuum is of nested foam structure because such way of energy spreading enables to see it as large as possible.
  
  http://superstrun...rchy.gif
  http://superstrun...Foam.gif
  
  The Eiffel tower is trying to spread its material towards gravitational potential as effectivelly, as possible, thus following such fractal shape too. And we can find an infinite number of other analogies of such conical geometry, for example the shape of river deltas or the shape of diffusive fog spreading, etc.
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