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George C. Verghese. Ayazifar, Babak, 1967- Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2005-05-19T15:16:09Z 2005-05-19T15:16:09Z 2002 2003 http://hdl.handle.net/1721.1/16913 52699710 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2003. Includes bibliographical references (leaves 186-191). This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. 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. (cont.) 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. by Babak Ayazifar. Ph.D. 191 leaves 1004633 bytes 1004415 bytes application/pdf application/pdf eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Graph spectra and modal dynamics of oscillatory networks Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="de19fe85-ed61-4209-aa5a-cd31b9363988"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Graph spectra and modal dynamics of oscillatory networks</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2003</PublicationDate> <Authors> <Author> <DisplayName>Ayazifar, Babak, 1967-</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>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.</Abstract> <Abstract>(cont.) 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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>