Comprehensive scaling laws across animals, microorganisms and plants

Source abstract

Scaling laws illuminate nature’s biological principles and guide bio-inspired materials and structural designs. In simple cases, they are based on the principle that all laws of nature remain invariant under a change of units. A more general framework is a change of variables for the governing laws that takes all equations, boundary and interaction conditions into themselves. We consider an accepted macroscale system of partial differential equations including coupled fluid dynamics, nonlinear elasticity and rigid body mechanics for a complex organism. We show that there is a set of scaling laws where length, time, density, elastic modulus, viscosity and gravitational constant undergo non-trivial scaling. We compare these results to extensive data sets mined from the literature on beating frequency of flying, swimming and running animals, speed of bacteria, insects, fish, mammals and reptiles, leg stiffness of mammals and modulus of elasticity of plants. The uniform agreement of the scaling laws with the dynamics of fauna, flora and microorganisms supports the dominating role of coupled nonlinear elasticity and fluid dynamics in evolutionary development. We conclude with predictions for some prehistoric cases for which observations are unavailable.