Allometric scaling in evolutionary biology: implications for the metal-insulator and network glass stiffness transitions and high-temperature superconductivity, and the converse

The nature of appropriate microscopic models that can successfully describe anomalous transport properties, such as high-temperature superconductivity and giant magnetoresistance, in carefully selected and optimally processed complex inorganic materials such as doped layered multinary pseudoperovskite oxides is still unclear. This may be caused by lack of recognition, especially by theorists, of the consequences of the fundamental dichotomy between continuous and discrete (or network) systems. The simplest way to determine the generically correct choice of models in arch systems may be through scaling experiments associated with connectivity transitions. Here I show that the same approach is equally successful in explaining the origins of metabolic biometric (or allometric) scaling. From this one can conclude that the topological differences between conductivity networks in specially selected complex inorganic materials and circulatory systems of living animals and plants may be far smaller than is generally supposed.