http://hdl.handle.net/10500/2736 2013-05-23T00:49:33Z 2013-05-23T00:49:33Z Mukeru, Bahati http://hdl.handle.net/10500/8909 2013-04-13T22:00:44Z 2012-03-01T00:00:00Z

Bound states for A-body nuclear systems Mukeru, Bahati In this work we calculate the binding energies and root-mean-square radii for A−body nuclear bound state systems, where A ≥ 3. To study three−body systems, we employ the three−dimensional differential Faddeev equations with nucleon-nucleon semi-realistic potentials. The equations are solved numerically. For this purpose, the equations are transformed into an eigenvalue equation via the orthogonal collocation procedure using triquintic Hermite splines. The resulting eigenvalue equation is solved using the Restarted Arnoldi Algorithm. Ground state binding energies of the 3H nucleus are determined. For A > 3, the Potential Harmonic Expansion Method is employed. Using this method, the Schr¨odinger equation is transformed into coupled Faddeev-like equations. The Faddeevlike amplitudes are expanded on the potential harmonic basis. To transform the resulting coupled differential equations into an eigenvalue equation, we employ again the orthogonal collocation procedure followed by the Gauss-Jacobi quadrature. The corresponding eigenvalue equation is solved using the Renormalized Numerov Method to obtain ground state binding energies and root-mean-square radii of closed shell nuclei 4He, 8Be, 12C, 16O and 40Ca.

2012-03-01T00:00:00Z Nkuna, John Solly http://hdl.handle.net/10500/8828 2013-04-18T06:26:07Z 2012-06-01T00:00:00Z

Structure of hypernuclei studied with the integrodifferential equations approach Nkuna, John Solly A two-dimensional integrodi erential equation resulting from the use of potential harmonics expansion in the many-body Schr odinger equation is used to study ground-state properties of selected few-body nuclear systems. The equation takes into account twobody correlations in the system and is applicable to few- and many-body systems. The formulation of the equation involves the use of the Jacobi coordinates to de ne relevant global coordinates as well as the elimination of center-of-mass dependence. The form of the equation does not depend on the size of the system. Therefore, only the interaction potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon potentials are employed to construct the Hamiltonian of the systems. The results obtained are in good agreement with those obtained using other methods.

2012-06-01T00:00:00Z Venter, Geertien http://hdl.handle.net/10500/8603 2013-02-09T22:00:37Z 2013-02-06T00:00:00Z

Bydraes tot die oplossing van die veralgemeende knapsakprobleem Venter, Geertien In this thesis contributions to the solution of the generalised knapsack problem are given and discussed. Attention is given to problems with functions that are calculable but not necessarily in a closed form. Algorithms and test problems can be used for problems with closed-form functions as well. The focus is on the development of good heuristics and not on exact algorithms. Heuristics must be investigated and good test problems must be designed. A measure of convexity for convex functions is developed and adapted for concave functions. A test problem generator makes use of this measure of convexity to create challenging test problems for the concave, convex and mixed knapsack problems. Four easy-to-interpret characteristics of an S-function are used to create test problems for the S-shaped as well as the generalised knapsack problem. The in uence of the size of the problem and the funding ratio on the speed and the accuracy of the algorithms are investigated. When applicable, the in uence of the interval length ratio and the ratio of concave functions to the total number of functions is also investigated. The Karush-Kuhn-Tucker conditions play an important role in the development of the algorithms. Suf- cient conditions for optimality for the convex knapsack problem with xed interval lengths is given and proved. For the general convex knapsack problem, the key theorem, which contains the stronger necessary conditions, is given and proved. This proof is so powerful that it can be used to proof the adapted key theorems for the mixed, S-shaped and the generalised knapsack problems as well. The exact search-lambda algorithm is developed for the concave knapsack problem with functions that are not in a closed form. This algorithm is used in the algorithms to solve the mixed and S-shaped knapsack problems. The exact one-step algorithm is developed for the convex knapsack problem with xed interval length. This algorithm is O(n). The general convex knapsack problem is solved by using the pivot algorithm which is O(n2). Optimality cannot be proven but in all cases the optimal solution was found and for all practical reasons this problem will be considered as being concluded. A good heuristic is developed for the mixed knapsack problem. Further research can be done on this heuristic as well as on the S-shaped and generalised knapsack problems. Text in Afikaans

2013-02-06T00:00:00Z De Witt, Aletha http://hdl.handle.net/10500/7046 2013-05-02T11:18:05Z 2012-03-01T00:00:00Z

Radio astronomy techniques : the use of radio instruments from single dish radio telescopes to radio interferometers De Witt, Aletha New radio telescopes under development, will significantly enhance the capabilities of radio astronomy in the Southern Hemisphere. South Africa, in particular, is actively involved in the development of a new array (MeerKAT) as well as in the expansion of existing very long baseline interferometer arrays in the south. Participation in these new developments demands a thorough understanding of radio astronomy techniques, and data analysis, and this thesis focusses on two projects with the aim of gaining such experience. The Southern Hemisphere very long baselines array is not well served with calibrator sources and there are significant gaps in the present calibrator distribution on the sky. An adequately dense, well distributed, set of strong, compact calibrator or reference sources is needed. With this in mind, observations using the Southern Hemisphere long baseline array were conducted to investigate a sample of candidate calibrator sources. The compactness of the sources was investigated and new potential calibrators have been identified. Single antenna radio spectroscopy of OH masers has identified sources of 1720 MHz emission associated with supernova remnants at the shock interface between the expanding supernova remnant and a molecular cloud. Models indicate that these masers are shock excited and can only be produced under tight physical constraints. Out ows from newly-formed stars create nebulous regions known as Herbig-Haro objects when they interact with the surrounding medium, and these regions are potentially similar to those seen in supernova remnants. If conditions behind the shock fronts of Herbig-Haro objects are able to support 1720-MHz OH masers they could be a useful diagnostic tool for star formation. A survey toward Herbig-Haro objects using a single-dish radio telescope did detect 1720-MHz OH lines in emission, but neither their spectral signature nor follow-up observations with the Very Large Array showed evidence of maser emission.

2012-03-01T00:00:00Z