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Shape and structure morphing of systems with internal flows 67

1/2 2
by the mass diffusion in this interval is M B At . Using the scaling tB A= _m and
utilizing _mBM 3=4 yields
ABM 7=8 and tBM 1=4 : ð2:35Þ

This allometric law is sustained by the large body of observations archived in the
literature, for example, Schmidt-Nielsen (1984), Peters (1983), Vogel (1988).
The evolutionary design shaped through the laws of physics for animate or inani-
mate systems is now explained through the constructal law and the theories that rely
on it. The power law relations produced by the allometric laws and other theoretical
or empirical observations have been seen as a signs of possible fractal shapes. Fractal
geometry might present so convincingly some then but it is physics that explains
them—from functioning to shape. In the constructal philosophy, vascularized tissues
and organs, the organism, work, adapt, morph, and survive as a optimally balanced
whole, and are the result of a constrained evolution as described by the laws of phys-
ics, following the time arrow.

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