### Browsing by Author "Mongwane, Bishop"

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- ItemOpen AccessCosmic electromagnetic fields due to perturbations in the gravitational field(American Physical Society, 2012) Mongwane, Bishop; Dunsby, Peter K S; Osano, Otieno BobWe use non-linear gauge-invariant perturbation theory to study the interaction of an inflation produced seed magnetic field with density and gravitational wave perturbations in an almost Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) spacetime with zero spatial curvature. We compare the effects of this coupling under the assumptions of poor conductivity, perfect conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of the electric field dominates the power spectrum on small scales, in agreement with previous arguments.
- ItemOpen AccessProblems in cosmology and numerical relativity(2015) Mongwane, Bishop; Dunsby, Peter K SA generic feature of most inflationary scenarios is the generation of primordial perturbations. Ordinarily, such perturbations can interact with a weak magnetic field in a plasma, resulting in a wide range of phenomena, such as the parametric excitation of plasma waves by gravitational waves. This mechanism has been studied in different contexts in the literature, such as the possibility of indirect detection of gravitational waves through electromagnetic signatures of the interaction. In this work, we consider this concept in the particular case of magnetic field amplification. Specifically, we use non-linear gauge-in variant perturbation theory to study the interaction of a primordial seed magnetic field with density and gravitational wave perturbations in an almost Friedmann-Lemaıtre-Robertson- Walker (FLRW) spacetime with zero spatial curvature. We compare the effects of this coupling under the assumptions of poor conductivity, perfect conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of the electric field dominates the power spectrum on small scales, in agreement with previous arguments. The second focus area of the thesis is the development a stable high order mesh refinement scheme for the solution of hyperbolic partial differential equations. It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. This approach combines the efficiency of local mesh refinement with the robustness and accuracy of higher order methods. To this end, different modifications of the standard Berger-Oliger adaptive mesh refinement a logarithm have been proposed. In this work we present a new fourth order convergent mesh refinement scheme with sub- cycling in time for numerical relativity applications. One of the distinctive features of our algorithm is that we do not use buffer zones to deal with refinement boundaries, as is currently done in the literature, but explicitly specify boundary data for refined grids instead. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena which is caused by inconsistent application of boundary data in the refined grids. Indeed, a peculiar feature of high order explicit Runge Kutta schemes is that they behave like low order schemes when applied to hyperbolic problems with time dependent Dirichlet boundary conditions. We present a new algorithm to deal with this phenomenon and through a series of examples demonstrate fourth order convergence. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothly match the phase velocity of coarser grids. We apply the method to test problems involving propagating waves and show a significant reduction in spurious reflections.
- ItemOpen AccessRelativistic neutron stars in general relativity and fourth order gravity(2021) Masetlwa, Nkosinathi; Mongwane, Bishop; van der Heyden, Kurt; Weltman, AmandaThis thesis investigates numerical instabilities arising from stiffness in the models of nonrotating, spherically symmetric single neutron star systems. The work deals with two distinct problems, each of which involves a stiff system of differential equations. In each case, we deal with stiffness by employing an IMEX Runge-Kutta scheme as opposed to the more computationally intensive fully implicit schemes or other adaptive Runge Kutta methods that may be impractical for partial differential equations. The first problem is focused on the mass-radius relation of a neutron star under a quadratic f(R) = R+αR2 theory for various realistic equations of state. This results in a coupled system of ODEs with stiff source terms which we discretize using an IMEX scheme. The observed maximum masses for different values of α, were consistent with the current neutron star maximum mass limit for some equations of state in both GR and beyond. In the second problem, we compute the frequencies of radial oscillations of neutron stars in the context of general relativity. This is achieved by linearly perturbing the ADM equations coupled to a matter source term. We discretize the resulting coupled system of PDEs with a third order WENO scheme in space and an IMEX scheme in time. We obtained 18 frequencies from the Fast Fourier Transform (FFT) of the evolved perturbation equations, which were consistent with the frequencies of the neutron star's Sturm-Liouville problem. The efficiency of the IMEX scheme as compared to other methods such as fully implicit schemes or adaptive methods makes it ideal for implementation in fully 3D numerical relativity codes for modified gravity.