Constructing a Theory for Scaling and More

Abstract

The developments that Geoffrey West and James Brown review in their article “Life’s Universal Scaling Laws” (Physics Today, September 2004, page 36) are important, but they fit into a much greater theoretical framework. West and coauthors’ first paper appeared in April 1997. 1 1. G. B. West, J. H. Brown, B. J. Enquist, Science 276, 122 (1997) https://doi.org/10.1126/science.276.5309.122. I published the basic idea behind their approach to the modeling of tree flows one year earlier 2 2. A. Bejan, J. Adv. Transportation 30, 85 (1996) https://doi.org/10.1002/atr.5670300207. as part of the constructal theory of organization in nature. Constructal theory, reviewed in my 1997 book Advanced Engineering Thermodynamics , 2nd edition (Wiley) and more recently, 3 3. A. Bejan, Shape and Structure: From Engineering to Nature, Cambridge U. Press, New York (2000). is now a growing field, with articles appearing regularly, including in physics journals. 4 4. L. Ghodoossi, N. Egrican, J. Appl. Phys. 93, 4922 (2003) https://doi.org/10.1063/1.1562008 S. M. Senn, D. Poulikakos, J. Appl. Phys. 96, 842 (2004) https://doi.org/10.1063/1.1757028. Constructal theory is about the generation of shape and structure in nonequilibrium thermodynamic systems—flow systems—in general. Simply put, the constructal law states, “For a finite-size flow system to persist in time (to live), it must evolve in such a way that it provides easier access to the currents that flow through it.” 2,3 2. A. Bejan, J. Adv. Transportation 30, 85 (1996) https://doi.org/10.1002/atr.5670300207.3. A. Bejan, Shape and Structure: From Engineering to Nature, Cambridge U. Press, New York (2000). The constructal law is not about what flows—fluid, energy, momentum, goods, or people—but about how the flow system generates its architecture. The three key assumptions that West and coauthors stated in 1997 and that West and Brown reviewed in their Physics Today article are present in constructal theory, not as convenient assumptions to make a model work, but as invocations of the constructal law. In particular, a space-filling tree architecture can be deduced from the constructal law. Constructal trees are not fractal objects.In a constructal tree there are at least two flow modes. The slow mode, which describes low-conductivity, low-permeability, high-unit-cost processes such as diffusion or walking, corresponds to interstices in the tree architecture. The fast mode, which describes high-conductivity, high-permeability, low-unit-cost processes such as flowing water and moving vehicular traffic, corresponds to channels in the architecture. Interstices and channels optimally connect to form a “tree,” in which the resistance across interstices is balanced against the resistance along channels.Because West’s three assumptions are consequences of constructal theory, every successful derivation of an allometric law that West and coworkers make is an affirmation of the validity of that theory.In return, every successful invocation of the constructal law in domains far removed from the living flow systems of West and coauthors is an indication not only that their model is correct but that it is an integral part of a theoretical framework that unites biology with physics and engineering. In addition to allometric laws, constructal theory covers many phenomena that fall well outside the biological scaling reviewed by West and Brown. Some examples are turbulent flow structure in various flow configurations, cracks in shrinking solids, the structure of animal hair, refraction in geographical economics, flight, atmospheric and oceanic circulation, and the structure of power plants and refrigeration plants—that is, the architecture of “human-plus-machine” species.West and Brown conclude by asking, Is all life organized by a few fundamental principles? According to constructal theory, the answer is yes.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. G. B. West, J. H. Brown, B. J. Enquist, Science 276, 122 (1997) https://doi.org/10.1126/science.276.5309.122. Google ScholarCrossref, ISI2. A. Bejan, J. Adv. Transportation 30, 85 (1996) https://doi.org/10.1002/atr.5670300207. Google ScholarCrossref, ISI3. A. Bejan, Shape and Structure: From Engineering to Nature, Cambridge U. Press, New York (2000). Google Scholar4. L. Ghodoossi, N. Egrican, J. Appl. Phys. 93, 4922 (2003) https://doi.org/10.1063/1.1562008 , Google ScholarCrossref, ISI S. M. Senn, D. Poulikakos, J. Appl. Phys. 96, 842 (2004) https://doi.org/10.1063/1.1757028. , Google ScholarCrossref, ISI© 2005 American Institute of Physics.