https://ir.unisa.ac.za/handle/10500/3056 Tue, 23 Jun 2026 01:32:31 GMT 2026-06-23T01:32:31Z https://ir.unisa.ac.za/handle/10500/32632 A study of synchronisation in the classical phase-oscillator model of an electrical power grid Olivier, Christiaan In this work, we study synchronisation in power grids using a classical phase oscillator model that can be thought of as a variant of the famous Kuramoto model for coupled phase oscillators. In the recent literature, the connection between a Kuramoto-like model and power grids has been made by Filatrella, Nielsen and Pedersen. Here, we will show that this connection goes much further back, to the so-called Classical Model of power grids that was introduced in 1951 by the work of Boast and Rector. We also observe that in 2018, Arinushkin and Anishchenko developed a Kuramotolike model for power grids in which, for the first time, there appear non-negligible phase-lag parameters as a result of the Kron reduced approximation. Although a single phase-lag (or frustration) parameter had been introduced much earlier in the so-called Kuramoto-Sakaguchi model (from 1986), Arinushkin and Anishchenko were the first to introduce multiple phase-lag parameters into a Kuromoto-like model for power grids. Unfortunately, our attempts to replicate their results soon revealed that they used a too-large, fixed time step for the numerical time integration of their equations, and that this led them to make several erroneous conclusions about the grid which they modelled. Therefore, in Chapter 3, we give a detailed critique of the 2018 paper by Arinushkin and Anishchenko. Then, in a follow-up work by Arinushkin and Vadivasova, from 2021, we observe that use was made of nonlinear damping to control the synchronicity of the Kron reduced grid. In this case, we were able to reproduce all the results of Arinushkin and Vadivasova. We were able to develop a more efficient proportional control scheme, based on the global order parameter. Our proposed control scheme and its results were presented at the 2023 International Conference on Electrical, Computer, and Energy Technologies (ICECET). The resulting conference proceeding is included here, in slightly revised form, as Chapter 4. Finally, in Chapter 5, we provide a brief summary of our main findings and some suggestions for future work. Sun, 01 Feb 2026 00:00:00 GMT https://ir.unisa.ac.za/handle/10500/32632 2026-02-01T00:00:00Z https://ir.unisa.ac.za/handle/10500/32266 Density functional theory study of oxygen reduction reaction (ORR) products with graphene Matloga, Mahlatse The 2D crystal lattice graphene has attracted tremendous research interest due to its exceptional properties that provide interesting opportunities for many applications, including energy storage technologies. Graphene has revealed remarkable potential in electrochemical energy capacity and conversion, particularly in rechargeable metal-air batteries. However currently metal air batteries (MABs) are faced with challenges such as anode issues (corrosion, dendrite formation at the metal anode and passivation) [1]. In this study, first-principle density functional theory was employed to investigate reaction mechanisms between graphene and oxygen reduction reaction (ORR) products XxOy, where X= Li, Na, Mg and K with x,y = 1 or 2, specifically for energy storage application of the 2D graphene in an effort to address the energy crisis. The reaction mechanisms of a single atom-, double atom-, and molecules (XO-, X2O-,XO2- and X2O2-) adsorbed onto graphene was investigated. For single-atom adsorption, the three adsorption sites, i.e., top, hollow and bridge sites were considered. The calculated adsorption energies revealed that single Li atom adsorbs stronger on graphene than all the alkaline metals and oxygen, with the hollow site being the most preferred site. For double atom adsorption, the calculated adsorption energies revealed that Na2 has a strong interaction with graphene layer and as a result the hollow site being the most preferred adsorption site. Furthermore, the order of stability was found to be Na2 >K2 > Li2 > O2 > Mg2. The ORR product NaO2 was found to be the most favoured reaction product with a calculated adsorption energy of -4.209 eV, followed by KO2 with the adsorption energy of -2.808 eV The results show a stronger interaction between oxygen atom and carbon atoms, which could potentially suggest a formation of C-O bond. In addition, the study revealed that adsorbates molecules move away from graphene layer together with two neighboring carbon atoms (possibly forming CO, CO2, LiCO3, NaCO2, KCO3 and MgCO3). The electronic properties of all the systems predicted metallic behaviour along the Fermi level due to no energy band gap between the valence and conduction bands. Thus, the electronic properties of XO-, X2O-,XO2-and X2O2- adsorbed graphene systems indicated that the typical electronic model of pristine graphene remains a conductor even after adsorption. Overall Na atom adsorption as a double and reaction product was the most stable system when adsorbed onto graphene implying that graphene could be considered as a better alternative anode electrode for sodium batteries, particularly sodium air batteries (SIBs) Mon, 01 Dec 2025 00:00:00 GMT https://ir.unisa.ac.za/handle/10500/32266 2025-12-01T00:00:00Z https://ir.unisa.ac.za/handle/10500/32123 First-principles studies of impurity defects formation and their implications on electronic and magnetic properties in a two-dimensional solid : the case of silicene Maboe, Doctor Paul Aggripa We report on first-principles density functional theory (DFT) calculations of interactions between extrinsic defects and intrinsic structural defects in silicene. Specifically, we investigate the stability, structural, magnetic and electronic properties of a monolayer silicene containing vanadium (V), hydrogen (H) and oxygen (O) atoms. Vanadium is a magnetic transition-metal and its incorporation in silicene lattice introduces magnetization. Thus, we have considered various configurations of vanadium either as interstitial or substitutional atoms, and their interactions with silicene vacancies. Hydrogen and oxygen are ubiquitous elements which are inadvertently introduced during material synthesis. Therefore, for practical purposes, it is important to investigate how their presence impact on the host material which in this case, are silicene or silicene containing vanadium impurities. We show that a monovacancy introduces a magnetic moment of 2.02 μB in an otherwise non-magnetic monolayer silicene. Nonetheless, the vacancy possesses a significant formation energy of 3.52 eV, which suggest that it may only be produced through external perturbation such as electron irradiation. Also, we show that a divacancy is more stable than a single vacancy, but unlike a single vacancy, it has a zero magnetic moment. Also, divacancies at different separation in silicene lattice have a similar formation energy irrespective of their separation. Furthermore, when a silicene atom is substituted by a vanadium atom, the latter makes the monolayer silicene metallic while introducing a magnetic moment of 2.61 μB. The presence of a vacancy at a different atomic separation from vanadium shows that the nearest-neighbour vanadium-vacancy defect complex, that is, vanadium in a divacancy has the highest stability, however, all the substitutional vanadium-vacancy configurations are stable and both types of defects can co-exist in a monolayer silicene. Regarding small vanadium clusters consisting of a pair of vanadium at varying separations, we found that the relative stability of the V-V pair is sublattice dependent, which oscillates between ferromagnetic (FM) and antiferromagnetic (AFM) configuration as the substitutional lattice sites of the V-V pair varies. When the V-V dimer are on a similar sublattice type, they prefer to couple together antiferromagnetically. However, when they are on a different sublattice type, the V-V dimer prefer to be in ferromagnetic configuration. Comparison between the binding energy of substitutional V-vacancy pair and V-V pair shows that vanadium clustering is more probable without the vacancy than with vacancy. Consideration of interstitial hole V-V pair, that is, V-V pair at the centre of silicene hexagons affirms that indeed, small V-V pair are stable without vacancies. The presence of V atoms, however, induces finite magnetic moment in monolayer silicene, while annihilating the Dirac point and opening a narrow band gap of under 0.1 eV in the monolayer silicene electronic band structures. We found that the V atom attracts the O and H either in atomic or molecular form, and when adsorbed they impact on the magnetization of V-doped monolayer silicene by reducing or annihilating its magnetic moment. Furthermore, a V-doped silicene having adsorbed atomic H and O behaves like a ferromagnetic semiconductor. On the other hand, molecular H2 and O2 adsorbed on a V-doped silicene do not result in a ferromagnetic semiconductor, although the resulting structures are metallic with a finite magnetization. We also found that the impact of H and O on the electronic and magnetic properties of V-doped silicene depends on their respective lattice locations, that is, whether these adsorbates are on the V atom or on the silicene atom near to the V dopant. Wed, 31 Jul 2024 00:00:00 GMT https://ir.unisa.ac.za/handle/10500/32123 2024-07-31T00:00:00Z https://ir.unisa.ac.za/handle/10500/31602 Breakup dynamics of a neutron-halo system at sub-barrier incident energies Sithole, Tapuwa The understanding of the nuclear breakup dynamics at sub-barrier incident energies, remains a hot subject in Nuclear Physics. In this dissertation, the breakup of the weaklybound neutron-halo 11Be nucleus impinging on a lead target is investigated for sub-barrier and around the Coulomb barrier incident energies. As theoretical framework, the continuum discretized coupled channels (CDCC) formalism is used. The fundamental mathematical description of this formalism leading to a discretized set of coupled di erential equations is outlined and the analytical expressions of the resulting coupling matrix elements as well as the breakup cross sections are derived. The convergence of the angular-distributions breakup cross section is rst checked against various numerical parameters that are used in the numerical solution of the coupled di erential equations. The stability of the numerical calculations is further tested by comparing the numerical results with the available experimental data. Comparison of breakup cross section with the total fusion cross section, it is reported that for incident energies below the Coulomb barrier, the breakup cross section is more important than the total fusion cross section. This observation has also been reported in the breakup of the proton-halo 8B on the same target nucleus, in a similar incident energy range. It is found that this importance of the breakup cross section over its fusion counterpart is due to a strong enhancement of the breakup cross section by the continuumcontinuum couplings. These couplings are otherwise known to strongly suppress the breakup cross section for incident energies above the Coulomb barrier. In order to further probe the enhancement of the breakup cross section by the continuumcontinuum couplings, the e ect of these couplings on its Coulomb and nuclear breakup components is analysed. It is shown that at sub-barrier incident energies, the continuumcontinuum couplings strongly enhance the Coulomb breakup cross section, whereas they strongly suppress the nuclear breakup cross section. It followed that the enhancement of the total breakup cross section by these couplings comes exclusively from its Coulomb component. The argument is that the enhancement of the Coulomb breakup cross section below the Coulomb barrier by the continuum-continuum couplings can be explained by the projectile breakup on its outgoing trajectory. A dominant breakup channel over other reaction channels at deep sub-barrier energies could be comprehensive to breakup of weakly-bound systems and may be justified by the projectile breakup on its outgoing trajectory. A paper manuscript based on these results has been submitted for review in the journal of European Physical Letters. Thu, 01 Feb 2024 00:00:00 GMT https://ir.unisa.ac.za/handle/10500/31602 2024-02-01T00:00:00Z