Thesis--Paris XI. / Includes bibliographical references.

Thesis (doctoral)--Universität Karlsruhe. / Vita. Includes bibliographical references (p. 91-92).

Thesis (doctoral)--Universität Bonn, 1988. / Includes bibliographical references (p. 179-184).

Originally presented as author's thesis, Bonn, 1983. / Bibliography: p. [221]-[225]

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1991. / Includes bibliographical references (p. 199-201).

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2005. / Includes bibliographical references: p. 116-119.

In this dissertation we analyse from a qualitative standpoint motion in a quasihomogeneous potential field: we offer a complete description of the flow associated with the two-body problem in quasihomogeneous field, obtain necessary and sufficient conditions for the block regularization of the flow and we propose an alternative model for the helium atom within the framework of a Manev-type interaction. We call a potential quasihomogeneous if it is of the form A/rᵃ + B/rᵝ, where r is the distance between the two mass points, 0 < α < β are real parameters and A > 0 and B > 0 inertia factors. To obtain the full description of the flow associated with the two-body problem in quasihomogeneous fields, we use diffeomorphic transformations that lead to an equivalent analytic system and at least differentiable integral energy relation. For each level of energy, we introduce the fictional invariant collision manifold and the infinity manifolds. We offer and analyse the global flow picture and we point out the Lebesgue measure of the set of initial conditions that lead to collision for each different case with respect to α and β. The next chapter focuses on the smoothness of the flow in the neighborhood of the collision manifold. In question is the possibility of extending solutions beyond singularities maintaining good properties with respect to initial data. In this case the singularity set for the system is said to be block regularizable. It is proved that the singularity set block regularizable if and only if β = 2 − [special characters omitted], where n is a positive integer, n ≥ 2. Also, the physical interpretation of this result is pointed out, namely that block regularization is in fact the mathematical expression of constrain imposed over the classical scattering angle. The last chapter presents a model for the Helium atom within the framework of classical mechanics. The set up consists of a planar isosceles 3-body problem formed by one neutron and two electrons, whose law of motion is given by a Manev-type potential with charges. We first describe the qualitative features of the local flow near triple collision, find several properties of the global flow and finally we prove the existence of a large open, connected, positive-measure manifold of bounded and collisionless solution. / Graduate

An oscillating electric dipole emits radiation, and the flow of energy is represented by the field lines of the Poynting vector. In the most general state of oscillation the dipole moment vector traces out an ellipse. We have evaluated analytically and numerically the field lines of the Poynting vector for the emitted light, and it appears that each field line lies on a cone, which has its axis perpendicular to the plane of the ellipse. The field lines exhibit a vortex structure near the location of the dipole, and they approach a straight line in the far field. The spatial extent of the optical vortex is well below the wavelength of the emitted radiation. It is shown that the asymptotic limit of a field line is displaced as compared to a ray which would come directly out of the source. This nearield vortex pattern will also lead to a shift of the intensity distribution of the radiation in the far field. The emission of radiation by a linearly oscillating electric dipole is drastically altered when the dipole is close to a mirror. The energy is not emitted along optical rays, as for a free dipole, but as a set of four optical vortices. At a larger distance from the dipole singularities and isolated vortices appear. It is shown that most of these interference vortices are due to the vanishing of the magnetic field at their centers. In the plane of the mirror there is a singular circle with a diameter which is proportional to the distance between the dipole and the mirror. Inside this circle, all energy flows to a singularity on the mirror surface. We have also demonstrated a peculiar property of energy transport of optical dipole radiation in a negative index of refraction material (NIM). When the particle is embedded in a NIM and the dipole moment is rotating, the direction of rotation of the field lines of energy flow is reversed as compared to the rotation of the field lines for emission in a dielectric.

No description available.

First, a regularity property for global solutions of some superlinear parabolic problems is established. We obtain some new a priori estimates on the global classical solutions. Applying this property to the blow-up problem, we obtain a general criterion for the occurrence of blow-up. When applied to the study of global weak solutions, we obtain some regularity results, which answers some open questions in this topic. / In this thesis, we obtain some new results on the formation of singularities for parabolic problems. We are interested in two typical singularities in parabolic evolution problems: blow-up and quenching. / Second, dichotomy properties for some porous medium equations and some semilinear parabolic equations are discussed. Some conditions on universal quenching are also obtained. When the space dimension is one, we establish a new, strong dichotomy property. Bifurcation analysis of some stationary solutions in high dimension is also investigated. / by Zheng Gaofeng. / "June 2005." / Adviser: Chou Kai-Seng. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0310. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 84-89). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.