Thesis (PhD)--Stellenbosch University, 2001. / ENGLISH ABSTRACT: In this dissertation we set out to develop the first relativistic model for calculating complete sets of (p, 2p) spin transfer observables. In addition to this a new technique has been developed which allows us to evaluate the transition amplitude, which is used to calculate the scattering observables for the reaction directly. The influence of various modiuin-modificd parameters ()1I the scattered wave functions anr] NN interact ion lH-IVC' })('('11 invest igatcd DlIC t,C) (I,llIlJigllitic's surrounding the nNN coupling we have included both pseudosoalar and pseudovector coupling into the nucleon-nucleon interaction model. Furthermore we have included two different kinematic prescriptions to obtain the effective NN laboratory kinetic energy and center of mass scattering angle, which are used to obtain the NN scattering amplitudes. The aim of this study is to investigate the effects of the various model parameters on complete sets of scattering observables. Our investigation has shown that although the analyzing power is not very sensitive to nuclear medium effects, and the various other spin transfer observables such as Dnn should provide valuable insight. Further refinements of the model would be to include nuclear distortions as well as the IA2 model of the NN interaction. / AFRIKAANSE OPSOMMING: In hierdie tesis ontwikkel ons die eerste relatiwistiese model vir die berekening van 'n volledige stel (p, 2p) spin waarneembares. Verder word 'n nuwe tegniek ingevoer wat ons toelaat om die oorgangsamplitude, wat gebruik word in berekening van die verstrooings waarneembares vir die reaksie, direk te evalueer. Die invloed van verskeie medium-gemodifiseerde parameters op die verstrooide golffunksies en die NN wisselwerking word bestudeer. As gevolg van onsekerhede betreffende die лNN koppeling word beide die pseudoskalaar en pseudovektor koppeling in die nukleon-nukleon interaksie model ingesluit. Ons sluit ook twee verskillende kinematiese preskripsies in om die effektiewe NN laboratorium kinetiese energie en die massa middelpunt verstrooiings hoek, wat gebruik word vir die berekening van die NN verstrooiings amplitude, te bereken. Die doel van hierdie studie is om die effek van verskeie model parameters op 'n volledige stel spin waarneembares te ondersoek. Die studie toon dat alhoewel die analiseervermoë nie baie sensitief is vir medium effekte nie, die ander spin waarneembares soos byvoorbeeld Dnn waardevolle insig lewer. Daar word voorgestel dat die model verfyn word deur kerndistorsies as ook die meer algemele IA2 model vir die NN interaksie in te sluit.

In this thesis we study relativistic models of gravitating uids with heat ow and electric charge. Firstly, we derive the model of a charged shear-free spherically symmetric cosmological model with heat ow. The solution of the Einstein-Maxwell equations of the system is governed by the pressure isotropy condition. This condition is a highly nonlinear partial di erential equation. We analyse this master equation using Lie's group theoretic approach. The Lie symmetry generators that leave the equation invariant are found. We provide exact solutions to the gravitational potentials using the rst symmetry admitted by the equation. Our new exact solutions contain the earlier results of Msomi et al (2011) without charge. Using the second symmetry we are able to reduce the order of the master equation to a rst order highly nonlinear di erential equation. Secondly, we study a shear-free spherically symmetric cosmological model with heat ow in higher dimensions. We establish the Einstein eld equations and nd the governing pressure isotropy condition. We use an algorithm due to Deng (1989) to provide several new classes of solutions to the model. The four-dimensional case is contained in our general result. Solutions due to Bergmann (1981), Maiti (1982), Modak (1984) and Sanyal and Ray (1984) for the four-dimensional case are regained. We also establish a new class of solutions that contains the results of Deng (1989) from four dimensions. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.

by Lai Chi Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves [104]-107). / Text in English; abstract also in Chinese. / by Lai Chi Wai. / Abstract --- p.i / Acknowledgment --- p.iv / List of Figures --- p.xi / List of Tables --- p.xii / Chapter 1 --- Introduction to Numerical Relativity --- p.1 / Chapter 1.1 --- The need for numerical approach --- p.2 / Chapter 1.2 --- A brief history of numerical relativity --- p.3 / Chapter 1.3 --- What this thesis concern --- p.4 / Chapter 2 --- Mathematical Formulation --- p.6 / Chapter 2.1 --- The initial value problem --- p.6 / Chapter 2.2 --- The space-plus-time (3+1) formalism --- p.8 / Chapter 3 --- Methods in Numerical Relativity --- p.17 / Chapter 3.1 --- General numerical methods --- p.17 / Chapter 3.2 --- Consistency and stability --- p.18 / Chapter 3.3 --- Difficulties and limitations --- p.20 / Chapter 3.4 --- Strategies specific to numerical relativity --- p.21 / Chapter 3.5 --- Boundary conditions --- p.27 / Chapter 4 --- Detweiler's Scheme --- p.29 / Chapter 4.1 --- Constrainted evolution in numerical relativity --- p.29 / Chapter 4.2 --- Detweiler's Scheme --- p.31 / Chapter 5 --- Constraint Enforcement in Plane Waves --- p.36 / Chapter 5.1 --- General solution for a linearized plane wave --- p.36 / Chapter 5.2 --- Code test --- p.40 / Chapter 5.3 --- Comparison of results with and without Detweiler's scheme --- p.41 / Chapter 5.4 --- Stability of evolution --- p.46 / Chapter 5.5 --- Comparison of Detweiler's scheme and simple diffusion method --- p.50 / Chapter 5.6 --- Two parameter extension of Detweiler's scheme --- p.55 / Chapter 5.7 --- Long time behavior --- p.59 / Chapter 5.8 --- Comparison of Hamiltonian and momentum constraint --- p.63 / Chapter 5.9 --- Indicator of Detweiler's scheme --- p.67 / Chapter 5.10 --- The maximal slicing condition --- p.70 / Chapter 5.11 --- The leaking problem --- p.73 / Chapter 5.12 --- The near-linear plane waves --- p.75 / Chapter 6 --- Constraint Enforcement in MTW Waves --- p.83 / Chapter 6.1 --- MTW waves --- p.83 / Chapter 6.2 --- Linear regime --- p.85 / Chapter 6.3 --- Comparison of results with and without Detweiler's scheme --- p.85 / Chapter 6.4 --- The indicator --- p.90 / Chapter 6.5 --- A comparison of simple diffusion method and Detweiler's scheme with a large amplitude wave --- p.92 / Chapter 7 --- Summary and Conclusion --- p.97 / Chapter A --- The Numerical Scheme of the Code --- p.98 / Chapter B --- Convergence Test --- p.100 / Chapter B.1 --- Plane wave --- p.100 / Chapter B.2 --- MTW wave --- p.102 / Bibliography --- p.104

The growing fields of spintronics and nanotechnology have created increased interest in developing the means to manipulate the spin of electrons. One such method arises from the combination of the spin-orbit interaction and the broken inversion symmetry that arises at surfaces and interfaces, and has prompted many recent investigations on metallic surfaces. A method by which surface states, in the absence of spin orbit effects, have been successfully investigated is the Green function embedding scheme of Inglesfield. This has been integrated into a self consistent FLAPW density functional framework based on the scalar relativistic K¨olling Harmon equation. Since the spin of the electron is a direct effect of special relativity, calculations involving the spin orbit interaction are best performed using solutions of the Dirac equation. This work describes the extension of Green’s function embedding to include the Dirac equation and how fully relativistic FLAPW surface electronic structure calculations are implemented. The general procedure used in performing a surface calculation in the scalar relativistic case is closely followed. A bulk transfer matrix is defined and used to generate the complex band structure and an embedding potential. This embedding potential is then used to produce a self consistent surface potential, leading to a Green’s function from which surface state dispersions and splittings are calculated. The bulk embedding potential can also be employed in defining channel functions and these provide a natural framework in which to explore transport properties. A relativistic version of a well known expression for the ballistic conductance across a device is derived in this context. Differences between the relativistic and nonrelativistic methods are discussed in detail. To test the validity of the scheme, a fully relativistic calculation of the extensively studied spin orbit split L-gap surface state on Au(111) is performed, which agrees well with experiment and previous calculations. Contributions to the splitting from different angular momentum channels are also provided. The main advantages of the relativistic embedding method are the full inclusion of the spin orbit interaction to all orders, the true semi infinite nature of the technique, allowing the full complex bands of the bulk crystal to be represented and the fact that a only small number of surface layers is needed in comparison to other existing methods.

At present several groups are analysing quasar absorption spectra to search for variation of the fine structure constant, alpha, across space and time. These studies compare the wavelengths of several transitions observed in the absorption clouds with those seen in the laboratory, and interpret anomalies as variation in alpha. One group has already presented evidence that alpha may have been smaller at an early epoch. Other groups using different telescopes see no variation. These studies use the ???many-multiplet??? method, which relies on the utilisation of many transitions in many ions to enhance the size of the effects and remove sources of systematic error. While this method offers an order-of-magnitude improvement in sensitivity over the previously used alkali-doublet method, the alpha-dependence (relativistic shift) of every transition used in the analysis must be calculated ab initio. In this thesis we present a method for the precise calculation of relativistic shifts, based on an energy calculation involving combination of the configuration interaction method and many-body perturbation theory. The many-multiplet method also introduces a potential systematic error: if the relative isotope abundances of the absorbers differ from terrestrial abundances then there can be spurious shifts in the measured wavelengths, which may be incorrectly interpreted as variation of alpha. A ???conspiracy??? of several isotopic abundances may provide an alternative explanation for the observed spectral anomalies. To account for these systematic errors we need accurate values of the isotope shift. We calculate these shifts using the finite-field method to reduce the problem to that of an energy calculation, which in turn is done using the same method used for the relativistic shift. We present the results of our calculations for a variety of atoms and ions seen in quasar absorption spectra. The results of this research should allow astrophysicists to measure isotope abundances in the absorbers directly. This can provide a test for models of nuclear reactions in stars and supernovae, and of the chemical evolution of the Universe. Our calculations can also be used in conjunction with measurements to extract changes in nuclear charge radii between isotopes.

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 206-219). Available also in a digital version from Dissertation Abstracts.

No description available.

At present several groups are analysing quasar absorption spectra to search for variation of the fine structure constant, alpha, across space and time. These studies compare the wavelengths of several transitions observed in the absorption clouds with those seen in the laboratory, and interpret anomalies as variation in alpha. One group has already presented evidence that alpha may have been smaller at an early epoch. Other groups using different telescopes see no variation. These studies use the ???many-multiplet??? method, which relies on the utilisation of many transitions in many ions to enhance the size of the effects and remove sources of systematic error. While this method offers an order-of-magnitude improvement in sensitivity over the previously used alkali-doublet method, the alpha-dependence (relativistic shift) of every transition used in the analysis must be calculated ab initio. In this thesis we present a method for the precise calculation of relativistic shifts, based on an energy calculation involving combination of the configuration interaction method and many-body perturbation theory. The many-multiplet method also introduces a potential systematic error: if the relative isotope abundances of the absorbers differ from terrestrial abundances then there can be spurious shifts in the measured wavelengths, which may be incorrectly interpreted as variation of alpha. A ???conspiracy??? of several isotopic abundances may provide an alternative explanation for the observed spectral anomalies. To account for these systematic errors we need accurate values of the isotope shift. We calculate these shifts using the finite-field method to reduce the problem to that of an energy calculation, which in turn is done using the same method used for the relativistic shift. We present the results of our calculations for a variety of atoms and ions seen in quasar absorption spectra. The results of this research should allow astrophysicists to measure isotope abundances in the absorbers directly. This can provide a test for models of nuclear reactions in stars and supernovae, and of the chemical evolution of the Universe. Our calculations can also be used in conjunction with measurements to extract changes in nuclear charge radii between isotopes.

In this thesis, I present 4 new, high-resolution observations of the Galactic microquasar SS 433, obtained from the Very Long Baseline Array (VLBA). I show that we can resolve the same ejecta in successive observations separated by ~ 35 d. I will demonstrate a method to uniquely determine launch vectors of the jet bolides, and I use this unprecedented baseline in time to show that the expansion rate of these bolides may reach 0.03c. I also present the first scientific results from the study of the radio jets in a unique set of historic observations of SS 433: the 39 images that comprise the 2003 VLBA movie of Mioduszewski et al. (2004). This unmatched time sampling allows us to see daily changes in the dynamics of SS 433's jets. I present evidence that these observations caught SS 433 as it transitioned from quiescence into a flare, and I show that this manifests itself as an increase in both the jet launch speed and the brightness of the jet bolides. Using these data, I examine the evolution of the particle energies, densities and magnetic fields within the bolides. We see that the estimates of the mass-loss rates via the jets cannot be reconciled with the those inferred from X-ray or optical data, if we posit equipartition of energy in synchrotron emitting plasma. The time resolution of the 2003 data allows us to observe the flux evolution of the jet bolides, and I show that the bolides undergo a power law decay as t^−2.8. Lastly, I examine X-ray monitoring data from the Swift/BAT satellite and the MAXI All-Sky- Monitor. From these lightcurves, I examine the geometry of the X-ray emission from close to the compact object itself, and I discuss SS 433's place within the current paradigm of accretion in microquasars. Throughout, we will see that it is the accessible time scales of the SS 433 phenomenon that allow us to learn about its exciting, complex physics.

Relativistic effects are extremely important for heavy atoms and heavy atom containing molecules. Therefore, a relativistic treatment is needed when calculating molecular properties of these species. The fully- relativistic Dirac treatment involves electronic and positronic wavefunctions and a very large basis set is required. This leads to calculations that are too costly and time-consuming for larger molecules. The Zeroth-Order Regular Approximation (ZORA) is an approximation to the Dirac approach, which only deals with the electronic wavefunction. However, unfortunately this method is plagued by the gauge-dependence problem. The gauge-independent ZORA (ZORA-GI) and strictly atomic ZORA approaches provide solutions to this problem.In this work, the ZORA-GI and strictly atomic ZORA codes have been successfully implemented into the Gaussian 09 program. They have been used to calculate the bond lengths, harmonic vibrational frequencies and dissociation energies of the I2, Au2 and Pt2 diatomic molecules. The results show good agreement with experiment and previous theoretical studies. The non-relativistic, ZORA-GI, strictly atomic ZORA and pseudopotential approximations have been used to investigate the electronic structure of the actinide monoxides, AnO, and actinide monoxide cations, AnO+ (An = Th – Cm). It was found that the ground state configurations were dependent on the relativistic approximation chosen. The bond lengths, harmonic vibrational frequencies and dissociation energies were also calculated, with the ZORA methods generally outperforming the pseudopotential approximation. The first theoretical g-tensor study of the organouranium(V) complexes [U(C7H7)2]-, [U(η8-C8H8)(NEt2)(THF)]+, [U(η5-C5H5)(NMe2)3(THF)]+, [U(η8-C8H8)(NEt2)3], [U(η5-C5H5)2(NEt2)2]+ and [U(η8-C8H8)(η5-C5H5)(NEt2)2] has been carried out. It was demonstrated that the choice of density functional affects the way in which the g-tensor axes are assigned. The ground state spin density and SOMO are also sensitive to the choice of density functional. It is these factors that determine the value of the g-tensor.