- A. Bejan and S. Lorente, The constructal law origin of the logistics S curve,
Journal of Applied Physics, vol. 110
pp. 1-4, American Institute of Physics (024901.) [1.3606555], [doi] .
(last updated on 2013/03/25)
The S curve is one of the most common phenomena in nature: the spreading of populations, tumors, contaminants, innovations, economic activity. Here we show that this phenomenon can be predicted entirely by recognizing in it a flow. The flow is not by diffusion alone, rather it is a combination of tree-shaped “invasion” by convection, followed by “consolidation” by diffusion perpendicular to the invasive lines. The S curve is not unique: its scales depend on the relative magnitude of the speed of the invading lines and the diffusivity perpendicular to the lines. Tree-shaped invasion covers the territory with diffusion much faster than line-shaped invasion. The predicted S-curve flow architecture unites the designs of spreading flows and collecting flows (e.g., mining, fossil fuel extraction, Hubbert peak) in all the realms of nature: animate, inanimate, and human-made.