Seeing the S-curve in everything

July 21, 2011

S-curve (credit: Wikipedia)

The ubiquitous logistics S-curve (also known as the sigmoid function) has long been recognized by economists and scientists. Now professor Adrian Bejan at Duke University, with collaborator Sylvie Lorente from the University Toulouse, has developed a theory that explains the reason for the prevalence of this particular pattern throughout nature and the man-made world.

Economic trends, population growth, the spread of cancer, or the adoption of new technology seem to follow certain patterns, says Bejan. A new technology, for example, begins with slow acceptance, followed by explosive growth, only to level off before “hitting the wall.”

Bejan’s theory, known as the constructal law, uses a large river basin as a visual description of flow systems, growing fast and far, with smaller branches growing laterally from the main channels. It is based on the principle that designs of flow systems develop over time by facilitating flow access — reducing and distributing friction or other forms of resistance.

  • A new technology, for example, after a slow initial acceptance can be imagined moving fast through established, though narrow, channels into the marketplace. This is the steep upslope of the “S.”
  • As this technology matures, and its penetration slows, any growth, or flow, moves outward from the initial penetration channels in a shorter and slower manner.

Ref.: A. Bejan and S. Lorente, The constructal law origin of the logistics S curve, Journal of Applied Physics, 110, 024901 (2011); [DOI:10.1063/1.3606555]