Scaling in Colloidal and Biological Networks

Scaling and dimensional analysis is applied to networks that describe various physical systems. Some of these networks possess fractal, scale-free, and small-world properties. The amount of information contained in a network is found by calculating its Shannon entropy. First, we consider networks arising from granular and colloidal systems (small colloidal and droplet clusters) due to pairwise interaction between the particles. Many networks found in colloidal science possess self-organizing properties due to the effect of percolation and/or self-organized criticality. Then, we discuss the allometric laws in branching vascular networks, artificial neural networks, cortical neural networks, as well as immune networks, which serve as a source of inspiration for both surface engineering and information technology. Scaling relationships in complex networks of neurons, which are organized in the neocortex in a hierarchical manner, suggest that the characteristic time constant is independent of brain size when interspecies comparison is conducted. The information content, scaling, dimensional, and topological properties of these networks are discussed.