# MUIC Math

Mathematics at MUIC

### Internal

seminar:ma_scaling

# Scaling Laws in Complex Systems

Michael A. Allen
Physics Department, Mahidol University, Bangkok

16:00 Wednesday 18th January 2017, Room 3303, MUIC

### Abstract

It has been known since the 1930s that living organisms obey a variety of scaling laws involving quarter powers. For example, the metabolic rate of organisms of mass $M$ is generally proportional to $M^{3/4}$ and the heart-rate scales as $M^{-1/4}$. On purely (Euclidean) geometric grounds one would expect one-third powers. It was only 20 years ago that an explanation for the quarter-power laws was found: the key to this was the fact that all organisms have a space-filling fractal distribution network. If time permits we will also look at scaling laws in complex systems derived from social networks. Organisms scale sublinearly and consequently show sigmoidal growth and attain a finite size. Certain systems based on social networks, however, scale superlinearly which results in a finite-time singularity in their growth.

### Resources

Last modified: 2017/01/19 10:42