Date of Award
Fall 2012
Degree Type
Thesis
Degree Name
Master of Science (MSc)
Department
Mathematics
Supervisor
Dmitry Pelinovsky
Language
English
Abstract
We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads tends to zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist.
Recommended Citation
Betti, Matthew I., "Periodic Travelling Waves in Diatomic Granular Crystals" (2012). Open Access Dissertations and Theses. Paper 6991.
http://digitalcommons.mcmaster.ca/opendissertations/6991
McMaster University Library
Included in
Non-linear Dynamics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Physics Commons