The constructal law origin of the logistics S curve

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. © 2011 American Institute of Physics.

Full Text

Duke Authors

Cited Authors

  • Bejan, A; Lorente, S

Published Date

  • 2011

Published In

Volume / Issue

  • 110 / 2

International Standard Serial Number (ISSN)

  • 0021-8979

Digital Object Identifier (DOI)

  • 10.1063/1.3606555

Citation Source

  • SciVal