Thèse doctorat : Physique : Dijon : 2004. / Titre provenant de l'écran-titre. Bibliogr. p. 209-217, [230] réf.

Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2004. / John A. Buck, Committee Chair ; Stephen E. Ralph, Committee Member ; Gee-Kung Chang, Committee Member ; Rick Trebino, Committee Member ; Glenn S. Smith, Committee Member. Includes bibliographical references (leaves 102-104).

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (M. Phil.)--University of Hong Kong, 1985.

Thesis (Ph. D. in Applied Mathematics)--Naval Postgraduate School, June 2003. / Dissertation supervisors: Beny Neta, Dan Givoli. Includes bibliographical references (p. 131-133). Also available online.

In 2002, Feldman, Ilmanen, and Knopf constructed the first example of a non-trivial (i.e. non-constant curvature) complete non-compact shrinking soliton, and conjectured that it models a Ricci flow singularity forming on a closed four-manifold. In this thesis, we confirm their conjecture and, as a consequence, show that limits of blow-ups of Ricci flow singularities on closed four-dimensional manifolds do not necessarily have non-negative Ricci curvature. / text

Not available / text

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published_or_final_version / Physics / Doctoral / Doctor of Philosophy

The purpose of this work is to study the initial value problem for coherent pulse propagation (SIT) for zero area pulses. We employ the machinery of the newly developed mathematical technique of the inverse scattering method (ISM) to deduce general rules by which one can predict the kind of output pulses for a given input pulse impinging on a resonant attenuator. This study is relevant since the area theorem cannot provide unambiguous information about zero area pulses. Thus in effect we introduce an equivalent and more general formulation to the theorem in terms of the reflection coefficient, r(ν), of the ISM. The poles of r(ν) correspond to the steady state solitary pulses called solitons. We show that the threshold for soliton generation, including breathers, is for an absolute initial area of about π, a result consistent with the predictions of the area theorem. We solve an example of an input zero area profile. We also show that if the input pulse has an odd profile with respect to time, only breathers can be expected as solitons. We demonstrate that the conservation equations are of limited use when applied to zero area pulses. They give satisfactory results only in a limited region. We compare the predictions of the conservation equations to the predictions of the ISM, and come to the conclusion that for zero area pulses, the ISM is the only known satisfactory approach.