Thesis (MSc)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: The United Nations Convention on the Law of the Sea (UNCLOS) provides an opportunity for qualifying coastal signatory states to claim extended maritime estate. The opportunity to claim rests on the precept that in certain cases a continental shelf extends beyond the traditionally demarcated two hundred nautical mile (200M) Exclusive Economic Zone (EEZ) mark. In these cases a successful claim results in states having sovereign rights to the living and non-living resources of the seabed and subsoil, as well as the sedentary species, of the area claimed. Where the continental shelf extends beyond the 200M mark, the Foot of the Continental Slope (FoS) has to be determined as one of the qualifying criteria. Article 76 of UNCLOS de nes the FoS as ". . . the point of maximum change in the gradient at its base." Currently Caris Lots is the most widely used software which incorporates public domain data to determine the FoS as a step towards defining the offshore extent of an extended continental shelf. In this software, existing methods to compute the FoS are often subjective, typically involving an operator choosing the best perceived foot point during consideration of a two dimensional profile of the continental slope. These foot points are then joined by straight lines to form the foot line to be used in the desk top study (feasibility study). The purpose of this thesis is to establish a semi-automated and mathematically based three dimensional method for determination of the FoS using South African data as a case study. Firstly, a general background of UNCLOS is given (with emphasis on Article 76), including a brief discussion of the geological factors that influence the characteristics of a continental shelf and thus factors that could influence the determination of the FoS. Secondly, a mathematical method for determination of the surfaces of extremal curvature (on three dimensional data), originally proposed by Vanicek and Ou in 1994, is detailed and applied to two smooth, hypothetical sample surfaces. A discussion of the bathymetric data to be used for application introduces the factors to be taken into account when using extensive survey data as well as methods to process the raw data for use. The method is then applied to two sets of gridded bathymetric data of differing resolution for four separate regions around the South African coast. The ridges formed on the resulting surfaces of maximum curvature are then traced in order to obtain a foot line definition for each region and each resolution. The results obtained from application of the method are compared with example foot points provided by the subjective two dimensional method of computation within the Caris Lots software suite. A comparison of the results for the different resolutions of data is included to provide insight as to the effectiveness of the method with differing spatial coarseness of data. Finally, an indication of further work is provided in the conclusion to this thesis, in the form of a number of recommendations for possible adaptations of the mathematical and tracing methods, and improvements thereof. / AFRIKAANSE OPSOMMING: Die Verenigde Nasies se Konvensie oor die Wet van die See (UNCLOS) bied 'n geleentheid aan kwalifiserende state wat ondertekenaars van die Konvensie is om aanspraak te maak op uitgebreide maritieme gebied. Die geleentheid om op uitgebreide gebied aanspraak te maak berus op die veronderstelling dat 'n kontinentale tafel in sekere gevalle tot buite die tradisioneel afgebakende 200 seemyl eksklusiewe ekonomiese zone (EEZ) strek. In sulke gevalle het 'n suksesvolle aanspraak die gevolg dat die staat soewereine reg oor die lewende en nie-lewende bronne van die seevloer en ondergrond verkry, sowel as die inwonende spesies van die gebied buite die EEZ waarop aanspraak gemaak word. Die voet van die kontinentale tafel (FoS) moet vasgestel word as een van die bepalende kriteria vir afbakening van die aanspraak waar die kontinentale tafel tot buite die EEZ strek. Artikel 76 van UNCLOS defineer die FoS as ". . . die punt van maksimale verandering in die helling by sy basis." Die mees algemeen gebruikte rekenaar sagteware wat openbare domein data aanwend om die voet van die helling te bepaal, is tans "Caris Lots." Die metodes wat in die program gebruik word om die voet van die helling te bepaal, is dikwels subjektief en berus tipies op 'n operateur se keuse van die beste afgeskatte punt van die voet van die helling uit 'n oorweging van 'n twee dimensionele profiel van die kontinentale tafel. Die berekende voet-punte word dan deur middel van reguit lyne verbind om 'n hellingsvoetlyn te vorm. Hierdie voetlyn kan dan in die Suid-Afrikaanse lessenaarstudie (doenlikheidstudie) oor die bepaling van die voet van die kontinentale tafel gebruik word. Die doel van hierdie verhandeling is om 'n semi-outomatiese en wiskundig gebaseerde drie-dimensionele metode te beskryf vir die vasstelling van die FoS, deur as 'n gevallestudie van Suid-Afrikaanse data gebruik te maak. 'n Algemene agtergrond van UNCLOS, met beklemtoning van Artikel 76, word eerstens gegee. 'n Kort bespreking van die geologiese faktore wat die kontinentale tafel beïnvloed en wat gevolglik 'n invloed kan hê op die vasstelling van die voet van die helling, is ingesluit. Tweedens word 'n wiskundige metode, wat oorspronklik in 1994 deur Vanicek en Ou voorgestel is, vir bepaling van die oppervlaktes van maksimale kromming (gebaseer op drie-dimensionele data) in detail bespreek en 'n voorbeeld van 'n toepassing op twee gladde, denkbeeldige oppervaktes word beskryf. Die faktore wat in ag geneem moet word wanneer omvattende dieptemeting data gebruik word, en die metodes wat gebruik word om die rou data te verwerk, word ingelei deur 'n bespreking van die aard van die dieptemeting data wat gebruik is. Die metode word dan toegepas op twee stelle geruite dieptemeting data van verskillende resolusies vir vier afsonderlike streke om die Suid-Afrikaanse kus. Die riwwe wat op die resulterende oppervlaktes van maksimale kromming gevorm word, word dan nagetrek ten einde 'n lyndefinisie van die voet van die kontinentale tafel vir elke streek teen elke resolusie te bepaal. Die resultate verkry uit toepassings van die metode word vergelyk met hellingsvoetpunte soos bepaal deur die subjektiewe twee dimensionele berekeningsmetode in die "Caris Lots" rekenaar-program. 'n Vergelyking van die resultate vir die verskillende data resolusies word ingesluit om die doeltreffendheid van die metode met betrekking tot die hantering van verskillende ruimtelike data resolusies te ondersoek. 'n Aanduiding van verdere werk, bestaande uit 'n aantal aanbevelings vir moontlike aanpassings en verbeterings van die wiskundige en natrek metodes, word ten slotte in die gevolgtrekking van die verhandeling verskaf.

Thesis (MSc)--University of Stellenbosch, 2002. / See article for abstract

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Flow and reactive transport of chemical species is a very common phenomenon that occurs in natural and artificial systems. However in this study, the topic is related to acid mine drainage in the South African mining environment. Due to the hazards associated with acid mine drainage, prevention or treatment of mine effluent water before discharging to receiving waters and other environments is a necessity. A new time-dependent mathematical model is developed for a passive treatment method, based on multi-scale modelling of the coupled physico-chemical processes such as diffusion, convection, reactions and filtration, that are involved in the treatment process. The time-dependent model is simulated on a two-dimensional domain using finite volume discretization to obtain chemical species distributions. / AFRIKAANSE OPSOMMING: Vloei en reagerende transport van chemiese spesies is ’n baie algemene verskynsel wat in natuurlike en kunsmatige stelsels plaasvind. In hierdie studie is die onderwerp egter verwant aan suurmyndreinering in die Suid-Afrikaanse mynbou-omgewing. As gevolg van die gevare wat verband hou met suurmyndreinering, is die voorkoming of die behandeling van die afval-mynwater voor dit in opvangswaters en ander omgewings beland ’n noodsaaklikheid. ’n Nuwe tydafhanklike wiskundige model vir ’n passiewe behandelingsmetode is ontwikkel. Dit is gebaseer op die multi-skaal modulering van gekoppelde fisies-chemiese prosesse soos diffusie, konveksie, reaksies en filtrasie, wat by die behandelingsproses betrokke is. Die tydafhanklike model word gesimuleer op ’n twee-dimensionele domein met behulp van eindige volume diskretisasie om die verspreiding van chemiese spesies te bepaal.

Dissertation (PhD)--University of Stellenbosch, 2001. / ENGLISH ABSTRACT: The efficient management of renewable resources may ensure sustainable income to communities and countries. In the past the mathematical modelling used in the management decisions, in South Africa, was based on biological considerations only. In this thesis we include economic factors in the models and aim to determine steady state harvesting levels such that a maximum present value of all future revenues may be reached. A bio-economical approach is followed throughout the study and applied to the South African Cape Rock Lobster (Jasus lalandii) resource. We first address the problem using the simplest surplus production models. The model is applied to the Cape Rock Lobster, finding that the economical factors do indeed influence the steady state results, emphasising that they should be incorporated in the modelling process. A more descriptive two-sex-delay-difference model is then applied, which includes delay times for juveniles to reach sexual maturity and distinguishes between sexes. Yet further involved stage-class models are also studied and we propose a solution to the non-linear programming problem reached. These models may assist decision makers in future as knowledge on, for example, the growth of the two sexes, proper size limits and the influence of price differences are gained. Finally, we propose a harvesting strategy where catch is taken from alternative spatial lanes and apply here results from reaction diffusion theory. This theoretical approach might provide guidelines to new and underdeveloped fisheries in future, but also influence current inshore fisheries towards new management strategies. / AFRIKAANSE OPSOMMING: Die doeltreffende bestuur van hernubare hulpbronne kan 'n volhoubare ekonomiese opbrengs aan gemeenskappe en lande verseker. In die verlede is die wiskundige modelle wat in die besluitnemingsproses gebruik is, in Suid Afrika, gebaseer op biologiese oorwegings alleen. In hierdie studie word ook ekonomiese faktore in die modelle ingesluit en word ewewigstoestande bepaal vir vangste, sodanig dat 'n maksimum huidige waarde van toekomstige inkomste uit 'n vissery bereik word. 'n Bio-ekonomiese benadering word deurgaans gevolg en modelle word toegepas op die Suid-Afrikaanse Weskus Kreefbron (Jasus lalandii). Die studie begin deur basiese surplus produksie modelle te gebruik. Die resultate van die toepassing op die Weskus Kreefbron toon dat die ekonomiese faktore 'n groot invloed op die voorgestelde ewewigstoestand van die populasie het. Dit benadruk dus die feit dat hierdie faktore in die modelleringsproses ingesluit behoort te word. Meer beskrywende twee-geslag-vertragings-verskil modelle word daarna toegepas, en sluit in 'n vertragings periode vir vis om 'n volwasse stadium te bereik. Hierdie tydfaktor verskil dikwels vir mannetjies en wyfies en daarom word hier 'n twee-geslag model gebruik. Meer gevorderde klasse modelle word ook bespreek. Ons stel 'n oplossing vir hierdie nie-lineêre programmeringsprobleem voor. Hierdie gevorderde modelle mag in die toekoms handige hulpmiddels wees wanneer inligting rakende 'n spesie gesoek word. Sulke inligting mag insluit die groeitempos van mannetjies en wyfies, geskikte grootte beperkings vir vangste en die invloed van prysverskille vir verskillende groottes vis. 'n Nuwe vangste strategie word ook voorgestel waar vangste slegs geneem word uit alternatiewe ruimtelike bane en pas ons hier resultate uit die reaksie-diffusie teorie toe. Hierdie teoretiese oplossings mag riglyne bied wanneer nuwe visserye in die toekoms ontgin word, maar ook huidige visserye beïnvloed in die rigting van 'n nuwe bestuur strategie.

In this dissertation a study will be made of university performance in the Science Faculty of the University of Natal, Durban. In particular, we will develop models that can be used to predict the success rate of a student based on his or her matriculation results. These models will prove useful for selecting students to universities. They may also be used to assist sponsors, bursars and donors in allocating funds to deserving students. In addition, these models may be used to identify students who might experience difficulties in their studies at university. / Thesis (M.Sc.)-University of Natal, Durban, 1994.

Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2005. / The process of modelling the fruit export infrastructure capacity of South Africa formed part of a larger project called the \Fruit Logistics Infrastructure Capacity Optimisation Study," which was coordinated by the Transportek division of the CSIR in Stellenbosch during the period August 2002 to March 2004. The aim of this project was to create efficiencies for, and enhance the competitiveness of, the South African fruit industry by improved usage of, and investment in, shared logistics infrastructure. After putting the size of the fruit industry into perspective, numerous aspects of the export process are considered in this thesis so as to be able to perform a comprehensive cost analysis of the export of fruit, including the cost of handling, cooling and transportation. The capacities of packhouses, cold stores and terminals are found and presented. This information, combined with fruit export volumes of 2003, then allow an estimation of the current utilisation of the South African ports with respect to fruit export.