Date of Award

December 2020

Degree Type


Degree Name

Master of Science



First Advisor

Michael Nosonovsky

Committee Members

Junjie Niu, Mohammad H Rahman


The thesis we have studied, is about scaling and entropic content in various networks related to the material science, colloids and biological systems. The thesis is based on two papers:⦁ Nosonovsky M.; Roy P. Allometric scaling law and ergodicity breaking in the vascular system. Microfluidics and Nanofluidic-Springer. 2020 [Chapter 2 and 3] ⦁ Nosonovsky M.; Roy P. Scaling and Entropy in colloidal and neural networks. Entropy-MPDI. 2020 [Chapter 5 to 7] In chapter 2, we investigate scaling properties of vascular networks with fractal topology. Computational fluid dynamic (CFD) simulation of blood flow through one bifurcating vessel has been illustrated to demonstrate that complex dependencies cannot be approximated by a simple allometric scaling law. In chapter 3, this thesis investigates the ergodicity in the fractal vascular system by suggesting a generalized formulation of branching model. Ergodicity breaking is attributed to the fractal structure of the network as fluid flow in a fractal network system is not ergodic. The fractal branching is viewed as a source of ergodicity breaking in the biomechanical system. It is accounted that ergodicity is significant for a wide range of biomedical application where long observations time series are not practical. In chapter 4, dimensional and scaling analysis is implemented on networks, which contain fractal, scale-free and small-world properties. The quantity of information contained in a network could be estimated by the calculation of its Shannon entropy. Networks arising from tiny colloidal particles and droplet clusters due to pairwise interaction between the particles, have been considered in our work. In the colloidal science, due to influence of percolation and self-organized critically, networks have self-organizing properties and these properties tune the colloidal particles to the critical state, where system becomes unstable. In chapter 5, discussion of much more complex networks such neurons, which are organized in neocortex, has been demonstrated. Scaling relationship found in the neocortex suggests that characteristic time constant is independent of brain size when interspecies comparison is analyzed. In chapter 6, two physical concepts such as self-organizing criticality (SOC) and percolation, relevant to the self-organization of neural networks have been manifested. Then, sand-pile conceptual model of SOC and hypotheses of brain network formation by SOC, have been analyzed. To this end, the role of percolation to trigger avalanche in a system has been stated. In chapter 7, a review of experimental data about the scaling properties of cortical networks related to their temporal and spatial orientation, has been explored. Then, we extract the informational content of those cortical networks from entropic viewpoint. Scaling relationship of cortical networks suggest that characteristic time constant (rate of neural process) is independent of the brain size, when interspecies comparison is conducted.