EQUIPARTITION, OPTIMAL ALLOCATION, AND THE CONSTRUCTAL APPROACH TO PREDICTING ORGANIZATION IN NATURE

This is a review of recent engineering developments in thermodynamic o ptimization, which shed light on a universal design principle that acc ounts for macroscopic organization in nature. It is shown that the opt imal performance of a finite-size system with purpose is always charac terized by the equipartition of driving forces or the optimal allocati on of material subject to overall constraints. Examples are drawn from natural inanimate systems (river basins, turbulent flow) and animate systems (living trees). It is shown that this principle also governs t he architecture of tree networks. Tree networks can be obtained in pur ely deterministic fashion by minimizing the flow resistance (or the ti me of travel) between one point and a finite area or a finite volume ( an infinite number of points). The shape of each volume element can be optimized for minimal flow resistance. The network is 'constructed' b y assembling the shape-optimized building blocks, and proceeding in ti me from the smallest volume element toward larger constructs. In const ructal theory small size and shapeless flow (diffusion) come first, an d larger sizes and geometrical form (channels, streams) come later. (C ) Elsevier, Paris.