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The constructal law origin of the logistics S curve

Publication ,  Journal Article
Bejan, A; Lorente, S
Published in: Journal of Applied Physics
2011

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.

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Published In

Journal of Applied Physics

DOI

ISSN

0021-8979

Publication Date

2011

Volume

110

Issue

2

Related Subject Headings

  • Applied Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Bejan, A., & Lorente, S. (2011). The constructal law origin of the logistics S curve. Journal of Applied Physics, 110(2). https://doi.org/10.1063/1.3606555
Bejan, A., and S. Lorente. “The constructal law origin of the logistics S curve.” Journal of Applied Physics 110, no. 2 (2011). https://doi.org/10.1063/1.3606555.
Bejan A, Lorente S. The constructal law origin of the logistics S curve. Journal of Applied Physics. 2011;110(2).
Bejan, A., and S. Lorente. “The constructal law origin of the logistics S curve.” Journal of Applied Physics, vol. 110, no. 2, 2011. Scival, doi:10.1063/1.3606555.
Bejan A, Lorente S. The constructal law origin of the logistics S curve. Journal of Applied Physics. 2011;110(2).

Published In

Journal of Applied Physics

DOI

ISSN

0021-8979

Publication Date

2011

Volume

110

Issue

2

Related Subject Headings

  • Applied Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences