Graph Spectra and Modal Dynamics of Oscillatory Networks  

Abstract Category: Engineering
Course / Degree: Electrical Engineering and Computer Science
Institution / University: Massachusetts Institute of Technology (MIT), United States
Published in: 2002

Thesis Abstract / Summary:

Our research focuses on developing design-oriented analytical tools that enable us to better understand how a network comprising dynamic and static elements behaves when it is set in oscillatory motion, and how the interconnection topology relates to the spectral
properties of the system. Such oscillatory networks are ubiquitous, extending from miniature electronic circuits to large-scale power networks.

We tap into the rich mathematical literature on graph spectra, and develop theoretical extensions applicable to networks containing nodes that have finite nonnegative weights—including nodes of zero weight, which occur naturally in the context of power networks.

We develop new spectral graph-theoretic results spawned by our engineering interests, including generalizations (to node-weighted graphs) of various structure-based eigenvalue
bounds. The central results of this thesis concern the phenomenon of dynamic coherency, in which clusters of vertices move in unison relative to each other. Our research exposes the relation between coherency and network structure and parameters. We study both approximate and exact dynamic coherency. Our new understanding of coherency leads to a number of results. We expose a conceptual link between theoretical coherency and the confinement of an oscillatory mode to a node cluster. We show how the eigenvalues of a coherent graph relate to those of its constituent clusters. We use our eigenvalue expressions to
devise a novel graph design algorithm; given a set of vertices (of finite positive weight) and a desired set of eigenvalues, we construct a graph that meets the specifications. Our novel graph design algorithm has two interesting corollaries: the graph eigenvectors have regions of support that monotonically decrease toward faster modes, and we can construct graphs that exactly meet our generalized eigenvalue bounds.

It is our hope that the results of this thesis will contribute to a better understanding of the links between structure and dynamics in oscillatory networks.

Thesis Keywords/Search Tags:
slow coherency, exact coherency, theoretical coherency, laplacian matrix, mode confinement, localization, weighted nodes, levis node, gravis node, schur contraction, eigenvalues, eigenvectors

This Thesis Abstract may be cited as follows:
Babak Ayazifar, "Graph Spectra and Modal Dynamics of Oscillatory Networks," Ph.D. Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, September 2002.

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Engineering - Graph Spectra and Modal Dynamics of Oscillatory Networks Thesis Abstract
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Submission Details: Thesis Abstract submitted by Babak Ayazifar from United States on 21-Dec-2004 03:38.
Abstract has been viewed 4459 times (since 7 Mar 2010).

Babak Ayazifar Contact Details: Email: ayazifar@alum.mit.edu

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