Thesis (Ph.D.)--Ohio University, November, 2004. / Includes bibliographical references (p. 168-177)

Thesis (M.S.)--Brigham Young University. Dept. of Statistics, 2007. / Includes bibliographical references (p. 35-37).

Thesis (Ph.D.)--Ohio University, November, 2004. / Title from PDF t.p. Includes bibliographical references (p. 168-177)

Bibliography: p. 143-147. / Issued also as a Ph.D. thesis in the Dept. of Electrical Engineering, 1968. / M.I.T. DSR Project no. 76265 NASA Research Grant NGR-22-009-124

Bibliography: p. 102-104. / NASA Research Grant NGR-22-009-124. M.I.T. Project no. DSR 76265.

In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the family of the trial functions). Thus, the residual is calculated, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that only the parameter regimes for the existence of solitary waves had previously been analyzed for the microstructure PDE considered here, the results obtained here are both new and timely.

During strong ground shaking structures often become inelastic and respond hysteretically. Therefore, in this study some hysteretic models commonly used in seismic structural analysis are studied. In particular the characteristics of a popular endochronic model proposed by Bouc and Wen are examined in detail. In addition, analytical expressions have also been developed for most commonly used bilinear model as well as another model, herein called as the hyperbolic model.</p> / Master of Science

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Microfiche copy available in Archives and Science. / Bibliography: leaves 122-123. / by Charles A. Moo. / Ph.D.

M.S.

Singularly perturbed systems with or without delays commonly appear in mathematical modeling of physical and chemical processes, engineering applications, and increasingly, in mathematical biology. There has been intensive work for singularly perturbed systems, yet most of the work so far focused on systems without delays. In this thesis, we provide a new set of tools for the stability analysis for singularly perturbed control systems with time delays. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection