Published In
Mathematics and Computers in Simulation
Document Type
Pre-Print
Publication Date
3-2024
Subjects
Eigenvectors
Abstract
We analyze the eigenvectors of the generalized Laplacian for two metric graphs occurring in practical applications. In accordance with random network theory, localization of an eigenvector is rare and the network should be tuned to observe exactly localized eigenvectors. We derive the resonance conditions to obtain localized eigenvectors for various geometric configurations and their combinations to form more complicated resonant structures. These localized eigenvectors suggest new indicators based on the energy density; in contrast to standard criteria, ours provide the number of active edges. We also suggest practical ways to design resonating systems based on metric graphs. Finally, numerical simulations of the time-dependent wave equation on the metric graph show that localized eigenvectors can be excited by a broadband initial condition, even with leaky boundary conditions.
Rights
© Copyright the author(s) 2024
Locate the Document
DOI
10.1016/j.matcom.2023.07.011
Persistent Identifier
https://archives.pdx.edu/ds/psu/41432
Citation Details
Published as: Kravitz, H., Brio, M., & Caputo, J. G. (2023). Localized eigenvectors on metric graphs. Mathematics and Computers in Simulation, 214, 352-372.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication as Kravitz, H., Brio, M., & Caputo, J. G. (2023). Localized eigenvectors on metric graphs. Mathematics and Computers in Simulation, 214, 352-372.