Modeling networks in nanorod composites and power grids

Wang, Simi

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Last Modified

March 22, 2019

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Wang, Simi
- Affiliation: College of Arts and Sciences, Department of Mathematics

Abstract

Complex networks are ubiquitous in systems of physical, biological, social or technological origin. Components in complex systems range from as large as generators in power grids, to as small as nano-rod particles in nanocomposite materials, two applications that this dissertation considers. The work focuses on the implications of dynamics in establishing network structure and the impact of structural properties on dynamics on those networks. The first part of the thesis considers the network formed by perfectly conductive nanorods in nano-materials, and focuses on the dielectric properties of the composite to the structure change of the network. New scaling behaviors for the shear-induced anisotropic system is presented, a robust exponential tail of the pairwise charge distribution across the network is identified, and a hybrid material for storing charge in one dimension and conductive in another dimension is introduced. These results are relevant especially to active composite materials where materials are exposed to mechanical loading and strain deformations, that is, our tools can easily explore sensitivity to perturbations in the network due to applied loads. The second part of the thesis studies the electrical properties of the complex system, ranging from the nano-materials to power grids. Our attention has focused on building network models to simplify the problem, showing the new scaling of the conductance for anisotropic distribution and constructing contingency analysis of the large real-world power-grid system. In conclusion, the dissertation develops new network representations of physical material and power grid systems, and then develops tools which enable insights into the structure and dynamics of these systems. This work also advances network algorithms and provides new approaches to coherently articulated questions in real-world complex systems such as composite materials and power grid systems.

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