Faculty of Science (Research Outputs)

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A Technique to Solve a Parabolic Equation by Point Symmetries that Incorporate Initial Data
(Springer, 2025-03) Jamal, Sameerah; Maphanga, Rivoningo
In this paper, we show how transformation techniques coupled with a convolution integral can be used to solve a generalised option-pricing model, including the Black–Scholes model. Such equations are parabolic and the special convolutions are extremely involved as they arise from an initial value problem. New symmetries are derived to obtain solutions through an application of the invariant surface condition. The main outcome is that the point symmetries are effective in producing exact solutions that satisfy a given initial condition, such as those represented by a call-option.
Accurate hyperspectral imaging of mineralised outcrops: An example from lithium-bearing pegmatites at Uis, Namibia
(Elsevier Inc, 2021) Booysen, René; Nex, Paul A.M.; Lorenz, Sandra; Thiele, Samuel T.; Fuchsloch, Warrick C.; Marais, Timothy; Gloaguen, Richard
Efficient, socially acceptable and rapid methods of exploration are required to discover new deposits and enable the green energy transition. Sustainable exploration requires a combination of innovative thinking and new technologies. Hyperspectral imaging (HSI) is a rapidly developing technology and allows for fast and systematic mineral mapping, facilitating exploration of the Earth’s surface at various scales on a variety of platforms. Newly available sensors allow data capture over a wide spectral range, and provide information about the abundance and spatial location of ore and pathfinder minerals in drill-core, hand samples and outcrops with mm to cm precision. Conversely, the complex geometries of the imaged surfaces affect the spectral quality and signal-to-noise ratio (SnR) of HSI data at these very narrow spatial samplings. Additionally, the complex mineral assemblages found in hydrothermally altered ore deposits can make interpretation of spectral results a challenge. In this contribution, we propose an innovative approach that integrates multiple sensors and scales of data acquisition to help disentangle complex mineralogy associated with lithium and tin mineralisation in the Uis pegmatite complex, Namibia. We train this method using hand samples and finally produce a three-dimensional (3D) point cloud for mapping lithium mineralisation in the open pit. We were able to identify and map lithium-bearing cookeite and montebrasite at outcrop scale. The accuracy of the approach was validated by drill-core data, XRD analysis and LIBS measurements. This approach facilitates efficient mapping of complex terrains, as well as important monitoring and optimisation of ore extraction. Our method can easily be adapted to other minerals relevant to the mining industry.
Analysis of urban sprawl dynamics using machine learning, CA-Markov chain, and the Shannon entropy model: a case study in Mbombela City, South Africa
(SpringerOpen, 2024) Mhangara, Paidamwoyo; Gidey, Eskinder; Rabia Manjoo
Over half of the world’s population resides in urban areas. We anticipate that this pattern will become more evident, notably in South Africa. Therefore, research on urban spirals, both past and projected, is necessary for efficient urban land use planning and management. This study aims to assess the spatio-temporal urban sprawl dynamics from 2003 to 2033 in Mbombela, South Africa. We employed robust approaches such as machine learning, the cellular automata-Markov chain, and the Shannon entropy model to look at how urban sprawl changes over time using both the Landsat 4–5 Thematic Mapper and the 8 Operational Land Imagers. We conducted this study to bridge the gaps in existing research, which primarily focuses on past and current urban growth trends rather than future trends. The findings indicated that the coverage of built-up areas and vegetation has expanded by 1.98 km2 and 13.23 km2 between the years 2003 and 2023. On the other hand, the amount of land continues to decrease by -12.56 km2 and − 2.65 km2 annually, respectively. We anticipate an increase in the built-up area and vegetation to a total of 7.60 km2 and 0.57 km2, respectively, by the year 2033. We anticipate a total annual decline of -7.78 km2 and − 0.39 km2 in water bodies and open land coverage, respectively. This work has the potential to assist planners and policymakers in improving sustainable urban land-use planning.
Assessing runs of Homozygosity: a comparison of SNP Array and whole genome sequence low coverage data
(BMC, 2018) Ceballos, Francisco C.; Hazelhurst, Scott; Ramsay, Michèle
Background: Runs of Homozygosity (ROH) are genomic regions where identical haplotypes are inherited from each parent. Since their first detection due to technological advances in the late 1990s, ROHs have been shedding light on human population history and deciphering the genetic basis of monogenic and complex traits and diseases. ROH studies have predominantly exploited SNP array data, but are gradually moving to whole genome sequence (WGS) data as it becomes available. WGS data, covering more genetic variability, can add value to ROH studies, but require additional considerations during analysis. Results: Using SNP array and low coverage WGS data from 1885 individuals from 20 world populations, our aims were to compare ROH from the two datasets and to establish software conditions to get comparable results, thus providing guidelines for combining disparate datasets in joint ROH analyses. By allowing heterozygous SNPs per window, using the PLINK homozygosity function and non-parametric analysis, we were able to obtain non-significant differences in number ROH, mean ROH size and total sum of ROH between data sets using the different technologies for almost all populations. Conclusions: By allowing 3 heterozygous SNPs per ROH when dealing with WGS low coverage data, it is possible to establish meaningful comparisons between data using SNP array and WGS low coverage technologies.
Batch and semi-continuous fermentation with Parageobacillus thermoglucosidasius DSM 6285 for H2 production
(BMC, 2025) de Maayer, Pieter; Ardila, Magda S.; Aliyu, Habibu; Neumann, Anke
Background Parageobacillus thermoglucosidasius is a facultatively anaerobic thermophile that is able to produce hydrogen (H2) gas from the oxidation of carbon monoxide through the water–gas shift reaction when grown under anaerobic conditions. The water–gas shift (WGS) reaction is driven by a carbon monoxide dehydrogenase– hydrogenase enzyme complex. Previous experiments exploring hydrogenogenesis with P. thermoglucosidasius have relied on batch fermentations comprising defned media compositions and gas atmospheres. This study evaluated the efects of a semi-continuous feeding strategy on hydrogenogenesis. Results A batch and two semi-continuous fermentations, with feeding of the latter fresh media (with glucose) in either 24 h or 48 h intervals were undertaken and H2 production, carbon monoxide dehydrogenase (CODH) activity, and metabolite consumption/production were monitored throughout. Maximum H2 production rates (HPR) of 0.14 and 0.3 mmol min−1, were observed for the batch and the semi-continuous fermentations, respectively. Daily feeding attained stable H2 production for 7 days, while feeding every 48 h resulted in high variations in H2 production. CODH enzyme activity correlated with H2 production, with a maximum of 1651 U mL−1 on day 14 with the 48 h feeding strategy, while CODH activity remained relatively constant throughout the fermentation process with the 24 h feeding strategy. Conclusions The results emphasize the signifcance of a semi-continuous glucose-containing feed for attaining stable hydrogen production with P. thermoglucosidasius. The semi-continuous fermentations achieved a 46% higher HPR than the batch fermentation. The higher HPRs achieved with both semi-continuous fermentations imply that this approach could enhance the biohydrogen platform. However, optimizing the feeding interval is pivotal to ensuring stable hydrogen production.
Confocal microscopy and molecular analyses reveal anal secretory apparatus in immatures and recover transcontinental Clade of Gall Mites (Eriophyoidea) from Tamarisks
(MDPI, 2024-04) Sivu, Situngu; Chetverikov , Philipp E.; Ngubane-Ndhlovu, Nompumelelo P.; Elhalawan, Ashraf; Amrine, James
Tamarisk is an invasive evergreen shrub native to arid regions of Africa and Eurasia and is considered a weed in some countries with dry climates. The complex of gall mites from tamarisks includes fourteen species from four genera of the family Eriophyidae. We reinvestigated the type species of the genus Dicruvasates, D. tamaricis from Egypt, described D. ngubani n. sp. from Tamarix usneoides from South Africa, and revised the generic concept of Dicruvasates. This genus possesses cuticular plates marking longitudinal opisthosomal ridges typical of various phyllocoptine genera, e.g., Echinacrus. We sequenced three genes of Dicruvasates and Phyllocoptes mites from Tamarix and Echinacrus from Frangula, combined our sequences with the data from GenBank, and performed single-gene phylogenetic analyses. All analyses inferred the following: (1) a transcontinental clade Tam comprising Dicruvasates + Aceria + Phyllocoptes from Tamarix; (2) Echinacrus distantly related to Dicruvasates, suggesting the homoplastic nature of the cuticular plates on the opisthosomal ridges, and (3) polyphyly of the genera Aceria and Phyllocoptes. We also investigated partially cleared specimens of Dicruvasates under CLSM and, for the first time, visualized a well-developed anal secretory apparatus (ASA) in the immatures of gall mites, which was previously shown to be a specialized system evolved in Eriophyoidea for silk production. We hypothesize that the ASA contributes to finding nymphs by conspecific males and advocate for the importance of the future molecular biology studies of gall mite silk for developing new methods for controlling mites based on the knowledge of their ecology, behavior, and silk gene genetics.
Deep-crustal layered mafic complexes in the Mesoproterozoic oceanic-arc of the Tugela Terrane, South Africa
(Elsevier, 2025-03) Wilson, Allan H.
Layered mafic intrusions are important in understanding the generation of continental crust in oceanic arcs. The Mesoproterozoic (c. 1200 Ma) Tugela Terrane in southeast South Africa is made up of a series of thrust slices of varied rock-types purported to have been derived in oceanic arcs prior to accretion onto the southern margin of the Archean Kaapvaal Craton. They are not ophiolites. Mafic intrusions in two adjacent thrust slices are known as the Tugela Rand and Mambula Complexes. Both intrusions are intensely layered on scales of centimetres to several tens of metres but clear cyclic units are not apparent and crystal fractionation is limited indicating these were open systems with magma chamber through-flow. Tugela Rand is made up of dominantly olivine-bearing rocks ranging from dunite and pyroxenite to gabbro. In contrast, Mambula is dominantly gabbroic with only rare olivine-bearing rocks and is more evolved with layers of titaniferous-magnetite. Primary magmatic structures in both complexes include graded bedding, slumping and erosion features. Relatively high pressure of formation is indicated by the aluminous nature of the pyroxenes and corona textures by reaction between plagioclase and olivine. Chromitites in Tugela Rand range from massive to podiform with the rare orbicular variety indicating complex controls on chromite accretion. They include the high-Al compositional variety. There are no other similar chromitite occurrences in South Africa. The complexes, together with their enclosing rock-types, draw striking parallels with the lower arc crust observed in the late Cretaceous Kohistan arc complex in NE Pakistan. The Tugela Rand Complex shares many similarities with the Chilas Complex in that terrane, while the Mambula Complex is considered to be a more evolved derivative of the same magma. This study shows that generation of juvenile continental crust formation in mature island arc systems may have been firmly established by the Mesoproterozoic.
Detection of REEs with lightweight UAV‑based hyperspectral imaging
(Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations., 2020) Booysen, René; Nex, Paul A.M.; Zimmermann, Robert; Loren, Sandra; Kirsch, Moritz; Jackish, Robert; Gloaguen, Richard
Rare earth elements (REEs) supply is important to ensure the energy transition, e-mobility and ultimately to achieve the sustainable development goals of the United Nations. Conventional exploration techniques usually rely on substantial geological field work including dense in-situ sampling with long delays until provision of analytical results. However, this approach is limited by land accessibility, financial status, climate and public opposition. Efficient and innovative methods are required to mitigate these limitations. The use of lightweight unmanned aerial vehicles (UAVs) provides a unique opportunity to conduct rapid and non-invasive exploration even in socially sensitive areas and in relatively inaccessible locations. We employ drones with hyperspectral sensors to detect REEs at the earth’s surface and thus contribute to a rapidly evolving field at the cutting edge of exploration technologies. We showcase for the first time the direct mapping of REEs with lightweight hyperspectral UAV platforms. Our solution has the advantage of quick turn-around times (< 1 d), low detection limits (< 200 ppm for Nd) and is ideally suited to support exploration campaigns. This procedure was successfully tested and validated in two areas: Marinkas Quellen, Namibia, and Siilinjärvi, Finland. This strategy should invigorate the use of drones in exploration and for the monitoring of mining activities.
Developing a density functional theory model of glassy carbon via carbon defect induction and relaxation
(Elsevier, 2025-01) Falch, A.; Meerholz, K.; van Sittert, C.G.C.E.
Glassy Carbon (GC) is a non-graphitising carbon known for its thermal stability, conductivity, and resistance to chemical attack, making it valuable in industrial and scientific applications, especially as an electrode substrate in catalysis research. Despite its widespread use, GC’s precise structural characteristics is unclear due to synthesis variability. This study developed and validated a computational model to simulate GC’s structure. Starting from the R3-carbon allotrope, density functional theory calculations were used to construct a representative GC model, incorporating induced defects to mimic its structural imperfections. Multiple GC slab models were created for comparative analysis. Validation involved comparing theoretical X-ray diffraction data with published data, confirming the model’s accuracy in representing the GC’s structure. The model showed high correlation with existing models, particularly those by Jurkiewicz et al., emphasizing the effect of formation temperature on GC’s structural evolution. These findings enhance the understanding of GC’s structural complexities, providing a solid foundation for future research and applications in material science, especially for robust and conductive substrates used in electrocatalysis.
Draft genome sequence of the fungal pathogen Penicillium expansum (PPRI25879) isolated in South Africa
(Elsevier, 2025-02) Chan, Wai Yin; Rauwane, Molemi; Figlan, Sandiswa; Ntushelo, Khayalethu
Objectives: Penicillium expansum, a necrotrophic plant pathogen with a wide range of fruit hosts, is an important causal agent of blue mold rot. The fruit business suffers significant financial losses because of blue mold rot that occurs during fruit storage, transportation, and sale. The objective of this work was to generate a high-quality draft genome assembly of P. expansum, which will contribute to enhancing the management of blue mold, especially in stone and pome fruits, including grapes, by improving our understanding of the epidemiology of the pathogen and its interactions with the host. Data description: Here, we describe the genome sequence of Penicillium expansum isolate PPRI25879, one of the most virulent strains isolated from grapes in South Africa. Sequencing reads from P. expansum produced approximately 3.5 Gb. The assembly generated a draft genome of size 32.1 Mb, consisting of 1648 contigs, with an N50 of 508 KB. Examination of the genome completeness with Benchmarking Universal Single-Copy Orthologs (BUSCO) showed the draft genome carries 97.9% of the 746 genes in the Eurotiomycetes_odb10 database. The draft genome sequence will allow improved genomic comparisons among the most important pathogens belonging to the Penicillium genus, with the aim of improving our knowledge of their plant-pathogen interactions, population biology, and control.
Entanglement beating in free space through spin–orbit coupling
(Springer Nature, 2018) Rosales-Guzmán, Carmelo; Denz, Cornelia; Otte, Eileen; Ndagano, Bienvenu; Forbes, Andrew
It is well known that the entanglement of a quantum state is invariant under local unitary transformations. This rule dictates, for example, that the entanglement of internal degrees of freedom of a photon remains invariant during free-space propagation. Here, we outline a scenario in which this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, the so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and product states (purely scalar). We outline the spin–orbit interaction behind these novel propagation dynamics and confirm the results experimentally, demonstrating spin–orbit coupling in paraxial beams. This demonstration highlights a hitherto unnoticed property of classical entanglement and simultaneously offers a device for the on-demand delivery of vector states to targets, for example, for dynamic laser materials processing, switchable resolution within stimulated emission depletion (STED) systems, and a tractor beam for entanglement.
Evidence for igneous differentiation in Sudbury Igneous Complex and impact-driven evolution of terrestrial planet proto-crusts
(Nature Research, 2019-01) Latypov, Rais; Chistyakova, Sofya; Grieve, Richard; Huhma, Hannu
Bolide impact is a ubiquitous geological process in the Solar System, which produced craters and basins filled with impact melt sheets on the terrestrial planets. However, it remains controversial whether these sheets were able to undergo large-scale igneous differentiation, or not. Here, we report on the discovery of large discrete bodies of melanorites that occur throughout almost the entire stratigraphy of the 1.85-billion-year-old Sudbury Igneous Complex (SIC) – the best exposed impact melt sheet on Earth – and use them to reaffirm that conspicuous norite-gabbro-granophyre stratigraphy of the SIC is produced by fractional crystallization of an originally homogeneous impact melt of granodioritic composition. This implies that more ancient and compositionally primitive Hadean impact melt sheets on the Earth and other terrestrial planets also underwent large-volume igneous differentiation. The near-surface differentiation of these giant impact melt sheets may therefore have contributed to the evolution and lithological diversity of the proto-crust on terrestrial planets.
Forward scattering on the line with a transfer condition
(SpringerOpen [Commercial Publisher], 2013-12) Currie, Sonja; Nowaczyk, Marlena; Watson, Bruce A.
We consider scattering on the line with a transfer condition at the origin. Under suitable growth conditions on the potential, the spectrum consists of a finite number of eigenvalues which are negative real numbers, while the remainder is continuous spectrum which is comprised of the positive real axis. Asymptotics are provided for the Jost solutions. Conditions which characterize transfer conditions resulting in self-adjoint problems are found. Properties are given of the scattering coefficient linking it to the spectrum.
Geological Remote Sensing
(Acdemic Press, United Kingdom, 2021) Booysen, René; Nex, Paul A.M.; Gloaguen, Richard; Lorenz, Sandra; Zimmermann, Robert; Alderton, David; Elias, Scott A.
The field of remote sensing has recently witnessed major innovations that have been translated to Earth science applications. Before they can be used, remote sensing data must be corrected for effects originating from the sensors, the platforms on which they are deployed, atmospheric characteristics, and geometrical constraints. When the data are calibrated and geolocated, they can be used either as physical quantities, such as reflectance and temperatures, or as images. The recent development of new sensors has permitted the remote measurement of a large area of the Earth's surface, with direct geological applications. Additionally, advances in machine vision, machine learning and artificial intelligence, combined with an unprecedented increase in computer processing power, have led to innovative remote sensing data processing techniques that simplify the handling of large amounts of complex data. As a consequence, it is now possible to characterize the geological settings of large areas with precision and even their changes through time. Remote sensing data are now directly integrated into modelling algorithms that describe surface and subsurface processes at different scales. Geological remote sensing currently encompasses multi temporal, multi-source and multi scale approaches. The retrieval of big data in disseminated archives, as well as (near) real time processing are the challenges that remain to be solved. These new applications in geology ensure cost efficient, safe, and rapid surveys and monitoring that not only benefit the research community but society at large.
Insights into the genetics of blood pressure in black South African individuals: the Birth to Twenty cohort
(BMC, 2018) Hendry, Liesl M.; Sahibdeen, Venesa; Choudhury, Ananyo; Norris, Shane A.; Ramsay, Michèle; Lombard, Zané
Background: Cardiovascular diseases (CVDs) are the leading cause of non-communicable disease deaths globally, with hypertension being a major risk factor contributing to CVDs. Blood pressure is a heritable trait, with relatively few genetic studies having been performed in Africans. This study aimed to identify genetic variants associated with variance in systolic (SBP) and diastolic (DBP) blood pressure in black South Africans. Methods: Genotyping was performed using the Metabochip in a subset of participants (mixed sex; median age 17.9) and their adult female caregivers (median age 41.0) from the Birth to Twenty cohort (n = 1947). Data were analysed as a merged dataset (all participants and caregivers together) in GEMMA (v0.94.1) using univariate linear mixed models, incorporating a centered relatedness matrix to account for the relatedness between individuals and with adjustments for age, sex, BMI and principal components of the genotype information. Results: Association analysis identified regions of interest in the NOS1AP (DBP: rs112468105 - p = 7.18 × 10−5 and SBP: rs4657181 - p = 4.04 × 10−5), MYRF (SBP: rs11230796 - p = 2.16 × 10−7, rs400075 - p = 2.88 × 10−7) and POC1B (SBP: rs770373 - p = 7.05 × 10−5, rs770374 - p = 9.05 × 10−5) genes and some intergenic regions (DACH1|LOC440145 (DBP: rs17240498 - p = 4.91 × 10−6 and SBP: rs17240498 - p = 2.10 × 10−5) and INTS10|LPL (SBP: rs55830938 - p = 1.30 × 10−5, rs73599609 - p = 5.78 × 10−5, rs73667448 - p = 6.86×10−5)). Conclusions: The study provided further insight into the contribution of genetic variants to blood pressure in black South Africans. Future functional and replication studies in larger samples are required to confirm the role of the identified loci in blood pressure regulation and whether or not these variants are African-specific.
A metagenomic viral discovery approach identifies potential zoonotic and novel mammalian viruses in Neoromicia bats within South Africa
(Public Library of Science, 2018-03) Geldenhuys, M.; Mortlock, M.; Weyer, J.; Bezuidt, O.; Seamark, E.C.J.; Kearney, T.
Species within the Neoromicia bat genus are abundant and widely distributed in Africa. It is common for these insectivorous bats to roost in anthropogenic structures in urban regions. Additionally, Neoromicia capensis have previously been identified as potential hosts for Middle East respiratory syndrome (MERS)-related coronaviruses. This study aimed to ascertain the gastrointestinal virome of these bats, as viruses excreted in fecal material or which may be replicating in rectal or intestinal tissues have the greatest opportunities of coming into contact with other hosts. Samples were collected in five regions of South Africa over eight years. Initial virome composition was determined by viral metagenomic sequencing by pooling samples and enriching for viral particles. Libraries were sequenced on the Illumina MiSeq and NextSeq500 platforms, producing a combined 37 million reads. Bioinformatics analysis of the high throughput sequencing data detected the full genome of a novel species of the Circoviridae family, and also identified sequence data from the Adenoviridae, Coronaviridae, Herpesviridae, Parvoviridae, Papillomaviridae, Phenuiviridae, and Picornaviridae families. Metagenomic sequencing data was insufficient to determine the viral diversity of certain families due to the fragmented coverage of genomes and lack of suitable sequencing depth, as some viruses were detected from the analysis of reads-data only. Follow up conventional PCR assays targeting conserved gene regions for the Adenoviridae, Coronaviridae, and Herpesviridae families were used to confirm metagenomic data and generate additional sequences to determine genetic diversity. The complete coding genome of a MERS-related coronavirus was recovered with additional amplicon sequencing on the MiSeq platform. The new genome shared 97.2% overall nucleotide identity to a previous Neoromicia-associated MERS-related virus, also from South Africa. Conventional PCR analysis detected diverse adenovirus and herpesvirus sequences that were widespread throughout Neoromicia populations in South Africa. Furthermore, similar adenovirus sequences were detected within these populations throughout several years. With the exception of the coronaviruses, the study represents the first report of sequence data from several viral families within a Southern African insectivorous bat genus; highlighting the need for continued investigations in this regard.
New modern and Pleistocene fossil micromammal assemblages from Swartkrans, South Africa: Paleobiodiversity, taphonomic, and environmental context
(Elsevier, 2024-03) Steininger, Christine; Clarke, Ronald J.; Caruana, Matthew V.; Kuman, Kathleen; Pickering, Travis Rayne; Linchamps, Pierre; Stoetzel, Emmanuelle; Amberny, Laurie
The oldest deposit at the hominin-bearing cave of Swartkrans, South Africa, is the Lower Bank of Member 1, dated to ca. 2.2 million years ago. Excavations of this unit have produced a diverse and extensive mammalian fossil record, including Paranthropus robustus and early Homo fossils, along with numerous Oldowan stone tools. The present study focuses on the taxonomic analysis of the micromammalian fossil assemblage obtained from recent excavations of the Lower Bank, conducted between 2005 and 2010, as part of the Swartkrans Paleoanthropological Research Project. The taxonomic composition of this assemblage is dominated by Mystromys, a rodent indicative of grassland environments. Taphonomic analysis indicates an accumulation of prey by Tyto alba (Barn owl) or a related species. Environments inferred from this evidence reflect an open landscape primarily covered by grassland vegetation, but they also feature components of wooded areas, rocky outcrops, and the proximity of a river. The Swartkrans fossil assemblage is compared with Cooper's D (dated to ca. 1.4 Ma) and a modern coprocoenosis of Bubo africanus (spotted eagle-owl) collected within the Swartkrans cave for taxonomic, taphonomic, and paleoecological perspectives. Contrasting fossil and modern micromammalian data provide a better understanding of accumulation processes and facilitate a diachronic reconstruction of changes in climate and landscape evolution. Issues regarding paleoenvironmental reconstruction methodologies based on micromammals are also discussed.
Platinum-bearing chromite layers are caused by pressure reduction during magma ascent
(Nature Research, 2018) Latypov, Rais; Costin, Gelu; Chistyakova, Sofya; Hunt, Emma J.; Mukherjee, Ria; Naldrett, Tony
Platinum-bearing chromitites in mafic-ultramafic intrusions such as the Bushveld Complex are key repositories of strategically important metals for human society. Basaltic melts saturated in chromite alone are crucial to their generation, but the origin of such melts is controversial. One concept holds that they are produced by processes operating within the magma chamber, whereas another argues that melts entering the chamber were already saturated in chromite. Here we address the problem by examining the pressure-related changes in the topology of a Mg2SiO4–CaAl2Si2O8–SiO2–MgCr2O4 quaternary system and by thermodynamic modelling of crystallisation sequences of basaltic melts at 1–10 kbar pressures. We show that basaltic melts located adjacent to a so-called chromite topological trough in deep-seated reservoirs become saturated in chromite alone upon their ascent towards the Earth’s surface and subsequent cooling in shallow-level chambers. Large volumes of these chromite-only-saturated melts replenishing these chambers are responsible for monomineralic layers of massive chromitites with associated platinum-group elements.
Self-adjoint higher order differential operators with eigenvalue parameter dependent boundary conditions.
(SpringerOpen [Commercial Publisher], 2015-12) Möller, Manfred; Zinsou, Bertin
Eigenvalue problems for even order regular quasi-differential equations with boundary conditions which depend linearly on the eigenvalue parameter λ can be represented by an operator polynomial (Formula presented.) where M is a self-adjoint operator. Necessary and sufficient conditions are given such that also K and A are self-adjoint.
Spatio-temporal trends in daily precipitation extremes over the Enkangala escarpment of South Africa: 1961–2021
(Springer, 2025-02) Abubakar, Hadisu Bello; Scholes, Mary C.; Engelbrecht, Francois A.
The Intergovernmental Panel on Climate Change in its Sixth Assessment Report reported that increases in extreme weather events can already be detected in every region in the world. For eastern southern Africa the report provides evidence of an increasing trend in extreme precipitation events, but more research is needed to understand how this change is manifesting over regions as diverse as South Africa’s eastern escarpment and northern Mozambique. This study evaluates the trends in extreme precipitation over the Enkangala Escarpment, part of South Africa’s eastern escarpment, over the period 1961 to 2021. Daily precipitation data covering 22 stations with fewer than 10% missing values over 61 years were obtained from the South African Weather Service. A total of twelve extreme events precipitation indices were computed using the ClimPACT2 package, and a time series trend analysis was performed using the Trend Free Whitening Mann Kendal test and a field significance test. The results indicate significant increasing trends in nine out of the twelve extreme events indices that were investigated. The three indices which have shown significant decreasing trends include Consecutive Wet days (CWD) at (0.03 day/year total annual rainfall (PRCPTOT) (0.61 mm/decade) and the annual count of days when precipitation≥10 mm (R10mm) of 0.32 days/decade. Indices such Rx1 days, Rx3 days and Rx5 days exhibited increasing trends of 0.2 days/decade each. Other indices with an increasing trend are CDD (3.6 day/decade), R20mm (0.2 days/decade) and R30mm (0.2 days/decade). The R95p (11.2 mm/decade) and R99p (6.0 mm/decade) indices, and Simple Daily Intensity Index(0.4 mm/decade) also exhibit positive trends over the study period. Overall the analysis is indicative of a change in the nature of rainfall over the Enkangala escarpment of South Africa, with annual rainfall totals, the number of consecutive wet days and the frequency of events with smaller thresholds such as 10 mm/day decreasing, but with extreme events of larger thresholds occurring more frequently. That is, when it rains, it tends to rain more intensely than in the past. The use of a field significance test was useful to formalise when relatively small but spatially homogeneous trends detected at separate weather stations yield statistical significance. The findings of the paper are relevant to decision and policy in multiple of socio-economic sectors active in South Africa’s eastern escarpment.