The main objective of this work is to establish an analytical model to evaluate the rate of corrosion in a horizontal pipe downstream of an orifice under flow-accelerated corrosion (FAC). FAC is a serious issue in nuclear and fossil power plants. In this work, an experimental setup was built to observe the effect of the flow on corrosion inside a tube. The experiments confirmed that the flow inside the tube caused more corrosion. However, accurate experimental data from literature has been selected and correlated by dimensional analysis, the modelling method of repeating variables and the Buckingham Pi theorem. It was found that the Sh number and the relative distance from the orifice are the main dimensionless parameters influencing FAC downstream of an orifice. The maximum value of the FAC rate could be well-predicted for the OR of 0.25, while the location of the maximum FAC rate could be well predicted for the OR of 0.5. The maximum FAC rate occurs between 2D to 4D downstream of the orifice and increases with a decreasing OR. This work could be useful for professionals in industry and researchers in the field and could be the starting point for a new way of evaluating the FAC rate downstream of a flow’s singularity. / Dissertation (MSc)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / MSc / Unrestricted

This diplmoma thesis aims to answer three different questions. First aim of this thesis was to analyze measures of alfa and gama diversity based on Hill numbers and find out, if these measures fullfill the weak principle of taxonomic invariance. In other words, my aim was to proove, independetly of used order of diversity, alfa and gama diversity will be always lower for higher taxonomic groups (eg. genus), than for lower taxonoic groups (eg. species). For this purpose, I used direct mathematical proof, and I showed, that equations for alfa and gama diversity are both taxonomic invariant. Moreover, I analyzed one specific measure of beta diversity as well. I showed, that beta diversity of order zero may increase or decrease in taxonomic switch. Second aim of this thesis was to examine influence of abundances on visualising of preferences of species for different enviromental factors. For thi purpose I desinged new methodology based on well-known RANK plots. This methodology should filter the influence of irregular data collectioning. In other words, this methodology should consider the case, that values of enviromental factors in data are not uniform, which may result into apparent preferences of species. Moreover, this methodology is desinged to take into considerations abundances of species as...

An epidemiological model that incorporates individual adoption of protective behaviours due to fear of contracting an infectious disease is presented. These adaptive behaviours are assumed to lower an individual's risk of infection. The dynamics of this model are analyzed and the effects of fear on important public health metrics such as outbreak length, final size, and peak prevalence are investigated. It is concluded that the coupled dynamics of fear- and disease-spread are rich and can lead to counter-intuitive effects on the public health metrics considered. In particular, it is not always the case that more effective protective behaviours lead to the most favourable population-level outcomes; intermediate levels of effectiveness are optimal in some cases. This result depends on when fearful individuals become infected with respect to the main outbreak that is mostly driven by the infection of fully susceptible individuals. / Thesis / Master of Science (MSc)

Background: ​Infectious disease outbreaks are amongst the most threatening of disasters, capable of affecting the health and economies of millions of people around the world in a single occurrence. Mathematical models are a tool that can be used to synthesize information from different disciplines into a comprehensive model, which can further be used to guide public health in making appropriate economic and social decisions. However, the integration of modelling within public health is not maximized. This study aims to explore perceptions of key stakeholders in planning, producing and applying infectious disease mathematical models in public health. Methodology: ​Data was collected using semi-structured key informant interviews with key stakeholder groups (n=19), academic modellers (n=6), government modellers (n=5), government end-users (n=5) and professionals and practitioners who are end-users (n=4). Data was analyzed with thematic analysis with NVivo 11 (QSR International). A stakeholder analysis was used to map out the interrelatedness of key stakeholder issues, and a thematic analysis was used to abstract themes of collaboration between stakeholders, challenges with data and perceptions of predictive modelling. Results and Conclusion:​ The findings of this study identify and organize important insights and recommendations required to optimize the utilization of infectious disease mathematical models in public health decision-making. The findings suggest that models that are most applicable to public health problems often go through iterative collaborations between end-users and modellers. The findings also suggest that there are growing challenges when it comes to the collection and interpretation of sources of infectious disease data and that mathematical models are valuable when used for understanding infectious disease outbreaks and/or interventions, rather than projecting the course of a specific outbreak. This study recommends actions be taken in education, practice and research to minimize the existing gap between mathematical models of infectious disease and their application for public health decision-making. / Thesis / Master of Science (MSc)

No / We consider and compare the various different kinds of flow that may take place in the anterior chamber of a human eye. The physical mechanisms re- sponsible for causing such flows may be classified as follows: (i) buoyancy-driven flow arising from the temperature difference between the anterior surface of the cornea and the iris, (ii) flow generated by the aqueous production of the ciliary body, (iii) flow generated by the interaction between buoyancy and gravity while sleeping while sleeping in a face-up position, (iv) flow generated by phakodenesis (lens tremor), (v) flow generated by Rapid Eye Movement (REM) during sleep. Each flow is studied using a traditional fluid mechanics/asymptotic analysis ap- proach. We also assess the veracity of a hypothesis that was recently advanced [see Maurice, D.M., 1998. The Von Sallman Lecture 1996: An ophthalmological explanation of REM sleep. Exp. Eye. Res. 66, 139¿145, for details] to suggest that, contrary to previous opinion, the purpose of REM during sleep is to ensure corneal respiration in the absence of the buoyant mixing that routinely takes place due to (i) above during waking conditions.

This thesis is concerned with the structure, analysis and numerical solution of the mathematical models used to estimate the transmission dynamics of the Human Immunodeficiency Virus (HIV)) the causative agent of Acquired Immune Deficiency Syndrome (AIDS). Investigations show that the devised deterministic mathematical models in term of system of first-order non-linear ordinary differential equations (ODEs) follow the stochastic nature of the problem at any time. In this thesis a generic form of the deterministic mathematical models is introduced which mirrors the transmission dynamics of HIV/AIDS in populations with different states of affairs, which leads to the division of large-scale and complex mathematical models. When analysing and;or solving a large-scale system of ODEs numerically, the key element in speeding up the process is selecting the maximum possible time step. This work introduces some new techniques used to estimate the maximum possible time step, avoiding the appearance of chaos and divergence in the solution when they are not features of the system. The solution to these mathematical models are presented graphically and numerically, aiming to identify the effect of the anti-HIV therapies and sex education in controlling the disease. The numerical results presented in this thesis indicate that lowering the average number of sexual partners per year is more effective in controlling the disease than the current anti-HIV treatments. For the purpose of this study the mathematical software 'Mathematica 3.0' was used to solve the system of differential equations, modelling HIV/AIDS propagation. This package also provided the graphical detail incorporated in the thesis.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The high sickle cell gene frequency has been hypothesised to be related to the protective advantage against malaria disease among heterozygous individuals. In this thesis, we study the interaction between the dynamics of malaria and sickle cell gene. The main aim is to investigate the impact of malaria treatment on the frequency of sickle cell gene. For this, we develop a mathematical model that describes the interactions between malaria and sickle cell gene under malaria treatment. The model includes both homozygous for the normal gene (AA) and heterozygous for sickle cell gene (AS) and assumes that AS individuals are not treated since they do not show clinical symptoms. We first analyse the model without malaria treatment, using singular perturbation techniques, basing on the fact that epidemiological and demographical dynamics occur on two different time scales (fast and slow dynamics). Our analysis on the fast time scale shows that high sickle cell gene frequency leads to high endemic levels for longer duration of parasitemia among heterozygous individuals. However, if the duration of parasitemia is reduced then high sickle cell gene frequency is associated with low endemic levels. We also note that on the slow time scale, the invasion ability of sickle cell gene is dependent on the malaria epidemiological parameters. The invasion coefficient given as the difference in the weighted death rates of AA and AS individuals is used as a measure to determine the establishment of sickle cell gene in the population. Results show that, the gene may establish itself if the weighted death rate of AA individuals is greater than that of AS individuals otherwise it fails. We note that, high mortality of AA individuals leads to establishment of sickle cell gene in the population. Then we analysed the model with treatment, our results indicate that the frequency of sickle cell gene decreases with an increase in the recovery rate of AA individuals. We thus conclude that eradication of malaria disease will lead to a reduction in sickle cell gene frequency. / AFRIKAANSE OPSOMMING: Daar word veronderstel dat die hoë sekelsel geenfrekwensie onder heterosigotiese individue verwant is aan die beskermende voordeel teen malaria siekte. In hierdie verhandeling ondersoek ons die wisselwerking tussen die dinamika van malaria en die sekelsel geen. Die hoofdoel is om die invloed van malaria behandeling op die frekwensie van die sekelsel geen te ondersoek. Hiervoor het ons ‘n wiskundige model ontwikkel, wat die wisselwerking tussen die dinamika van malaria en die sekelsel geen met malaria behandeling, beskryf. Die model sluit beide homosigotiese vir die normale geen (AA) en heterosigotiese vir die sekelsel geen (AS) in, en neem aan dat AS individue nie behandel is nie omdat hulle nie die eerste kliniese simptome getoon het nie. Ons ontleed eers die model sonder malaria behandeling, deur gebruik te maak van enkelvoudige pertubasie tegnieke, wat gegrond is op die feit dat epidemiologiese en demografiese dinamika plaasvind op twee verskillende tydskale (vinnige en stadige dinamika). Ons ontleding op die vinnige tydskaal dui dat hoë sekelsel geenfrekwensie onder heterosigotiese individue lei tot hoë endemiese vlakke vir ‘n langer duur van parasitemie. Nietemin, as die duur van parasitemie afneem, dan word hoë sekelsel geenfrekwensie verbind met lae endemiese vlakke. Ons neem ook waar dat op die stadige skaal die indringingsvermoë van die sekelsel afhanklik is van malaria se epidemiologiese parameters. Die indringingskoëffisiënt wat bereken word as die verskil van die geweegde sterftekoerse van AA en AS individue, word gebruik as ‘n maatstaf om die vestiging van die sekelsel geen in die bevolking te bepaal. Resultate toon dat die geen homself kan vestig as die geweegde sterftekoers van AA individue groter is as di e van die AS individue, andersins misluk dit. Ons let op dat hoë mortaliteit van AA individue lei tot die vestiging van die sekelsel geen in die bevolking. Daarna het ons die model wat behandeling insluit ge-analiseer en ons resultate toon dat die frekwensie van die sekelsel geen afneem met ‘n toename in die herstelkoers van AA individue. Ons kom dus tot die gevolgtrekking dat die uitwissing van malaria siekte sal lei tot die afname in sekelsel geenfrekwensie.

The analysis of large disordered complex networks has recently received enormous attention motivated by both academic and commercial interest. The most important results in this discipline have come from the analysis of stochastic models which mimic the growth and evolution of real networks as they change over time. The purpose of this thesis is to introduce various novel processes which dictate the development of a network on a small scale, and use techniques learned from statistical physics to derive the dynamical and structural properties of the network on the macroscopic scale. We introduce each model as a set of mechanisms determining how a network changes over a small period in time, from these rules we derive several topological properties of the network after many iterations, most notably the degree distribution. 1. In the rst mechanism, nodes are introduced and linked to older nodes in the network in such a way as to create triangles and maintain a high level of clustering. The mechanism resembles the growth of a citation network and we demonstrate analytically that the mechanism introduced su ces to explain the power-law form commonly found in citation distributions. 2. The second mechanism involves edge rewiring processes - detaching one end of an edge and reattaching it, either to a random node anywhere in the network or to one selected locally. 3. We analyse a variety of processes based around a novel fragmentation mechanism. 4. The nal model concerns the problem of nding the electrical resistance across a network. The network grows as a random tree, as it grows the distribution of resistance converges towards a steady state solution. We nd an application of the relatively recent concept of a random Fibonacci sequence in deriving the rate of convergence of the mean.

The British cattle population hosts a diverse community of endemic pathogens that impact the sustainability of beef and dairy production. As such, there has been a tremendous amount of ongoing research to develop more cost-effective strategies for controlling disease at the industry level. Cattle movements have come under particular scrutiny over the past decade both because of their role in spreading many economically important diseases and because the movements of individual cattle in Great Britain have been explicitly recorded in a centralized electronic database since 1998. Numerous studies have shown that these cattle movements organize into complex networks with key structural and temporal features that influence transmission dynamics. Building on previous work, this thesis used a variety of epidemiological and statistical models to highlight limitations in the current approaches to controlling disease as well as opportunities for reducing endemic disease prevalence through targeted interventions. Empirical disease data from the national bovine tuberculosis (bTB) control programme and from two seroprevalence studies of bovine viral diarrhoea virus (BVDV) in Scottish cattle herds were used in conjunction with movement data from the Cattle Tracing System (CTS) database. Endemic diseases are often challenging to control due to lack of affordable and accurate diagnostic tests as well as the presence of subclinically infected carriers that can easily escape detection. There was evidence that combined issues with the sensitivity and specificity of routine surveillance methods for bTB were contributing to a low level of disease transmission within and between Scottish cattle herds from 2002 to 2009. For BVDV, herds that purchased pregnant beef dams, beef dams with a calf at foot, and open dairy heifers were significantly more likely to be seropositive even though these movements were responsible for only a small number of network contacts. In both cases, targeting the subset of high risk movements with disease specific biosecurity measures may be a more cost-effective use of limited national disease control resources. Other researchers have suggested that control strategies should target multiple diseases simultaneously to reduce trade-offs in resource allocation. Using key indicators of herd reproductive performance derived from the CTS database, it was shown that improving the reproductive management of herds operating below industry standards could reduce endemic disease prevalence by reducing the movements of replacement breeding cattle. A series of network generation algorithms were also developed to study the effects of restricting contact formation based on key demographic and network characteristics of actively trading cattle farms. Strategies that increased network fragmentation either by forcing highly connected farms to form contacts with other highly connected farms or preventing the formation of movements with a high predicted betweenness centrality were found to be particularly effective in limiting disease transmission. For these models to be useful in guiding future policy decisions, it is important to incorporate financial and behavioural drivers of dynamic network change. Following the introduction of pre- and post-movement testing requirements for cattle imported into Scotland from endemic bTB regions, there was a significant decline in cross-border movements, which has likely contributed to the decreasing risk of bTB outbreaks as much as testing itself. Many endemic cattle diseases such as BVDV also spread through local transmission mechanisms, which may undermine the success of disease control programmes that exclusively target cattle movements. There was also evidence that in the absence of national animal legislation, few farmers were likely to adopt biosecurity measures against BVDV. This may be related to the perceived inefficacy of recommendations as well as general unawareness of farm disease status due to the non-specific clinical signs of BVDV outbreaks. Although the CTS database was originally intended for use in slaughter traceback investigations, results from this thesis show how the basic records of births, deaths, and movements can be used to generate valuable insights into the epidemiology of endemic cattle diseases. The findings also emphasize that the management decisions of individual herds can have a substantial impact on industry level transmission dynamics, which offers unique opportunities to develop novel and more cost-effective disease control programmes.

Thesis (PhD)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: The investigation of reservoir sedimentation has become an important and valuable research topic in engineering practice. Sediment deposition in reservoirs can affect ood levels, drainage for agriculture land, pumpstation and hydropower operation and navigation. An extensive review of the technical literature pertaining to suspended sediment transports as well as deposited sediment ushing from reservoirs has shown that most studies on sediment are still based on empirical formulas and experimental work, despite the availability of sophisticated computers. This is because sediment transport and particularly sediment deposition and erosion are complex processes, that involve the interaction of many physical factors which are not easily modelled numerically. In addition, most of the existing three-dimensional numerical models are not coupled hydrodynamic and sediment transport models. They first simulate the velocity field and water depth and then the concentration and bed change are calculated. Furthermore, they are not fully three-dimensional models for using layer-averaged approaches in conjunction with Saint-Venant equations. The key objective of the present research was to develop a coupled fully three-dimensional (3D) numerical model based on Navier-Stokes equations which includes both the sediment transport component and hydrodynamic parameters. In this regard, a physical model was set up in a laboratory ume in order to investigate the bottom outlet sediment ushing under pressure in a controlled environment. The proposed coupled fully 3D numerical model was used to simulate the experimental tests. Results from these simulations were in good agreement with the measurements. The geometric features of the scour hole (temporal and spatial hole development) upstream of the bottom outlet were reasonably well predicted compared to the experimental data. Furthermore, the velocity field upstream of the bottom outlet was in good agreement with measurements. The proposed numerical model can be considered reliable provided that the model is correctly set up to reflect the condition of a particular case study. Finally, the coupled fully 3D numerical model for turbulent suspended sediment transport in reservoirs was validated against a range of typical reservoir sediment transport and deposition laboratory flume cases. The proposed suspended sediment transport model successfully predicted both sediment deposition and entrainment processes and therefore, it can be used for turbulent suspended sediment transport assessments in reservoirs. / AFRIKAANSE OPSOMMING: Die ondersoek van damtoeslikking het 'n belangrike navorsing onderwerp in ingenieurswese praktyk geword. Sedimentdeponering in damme kan vloed vlakke, dreinering van landbo grond sowel as pompstasie en hidrokrag werking en navigasie benvloed. 'n Omvattende ontleding van die tegniese literatuur met betrekking tot gesuspendeerde sedimentvervoer asook die spoel van gedeponeerde sediment uit reservoirs het getoon dat die meeste studies oor sediment steeds op empiriese formules en eksperimentele werk gebaseer is, ten spyte van die beskikbaarheid van gesofistikeerde rekenaars. Dit is omdat sedimentvervoer en veral sedimentafsetting en -erosie komplekse prosesse is, wat die interaksie van baie fisiese faktore behels en nie moeiteloos numeries gemodelleer kan word nie. Daarbenewens, in die meeste van die bestaande drie -dimensionele numeriese modelle is die hidrodinamika en sedimentvervoer modelle nie gekoppel nie. Die numeriese modelle simuleer eerstens die snelheid veld en waterdiepte en dan word die sedimentkonsentrasie en bedverandering bereken. Verder is die bestaande modelle nie ten volle driedimensioneel nie, en gebruik laag-gemiddelde benadering in samewerking met Saint- Venant vergelykings. Die hoofdoelwit van die huidige navorsing was om 'n gekoppelde volle drie -dimensionele (3D) numeriese model gebaseer op Navier -Stokes-vergelykings wat beide die sediment vervoer komponent en hidrodinamiese parameters insluit, te ontwikkel. In hierdie verband is 'n fisiese model opgestel in 'n laboratorium kanaal om die bodem uitlaat spoel van sediment onder druk in 'n beheerde omgewing te ondersoek. Die voorgestelde gekoppelde 3D numeriese model is gebruik om die eksperimentele toetse na te boots. Resultate van hierdie simulasies het goed ooreengestem met die metings. Die geometriese eienskappe van die erosie gat (tyd en ruimtelike gatontwikkeling) stroomop van die bodemuitlaat was redelik goed voorspel vergeleke met die eksperimentele data. Verder is die snelheid veld stroomop van die bodem uitlaat ook goed voorspel. Die voorgestelde numeriese model kan beskou word as betroubaar met die wete dat die model korrek opgestel is om die toestand van 'n bepaalde gevallestudie te weerspiel. Ten slotte, is n gekoppelde 3D numeriese model vir turbulente gesuspendeerde sediment vervoer in reservoirs ontwikkel en getoets teen 'n reeks laboratorium kanaal eksperimente. Die voorgestelde gesuspendeerde sediment vervoer model voorspel suksesvol beide die sediment afsetting- en erosieprosesse en daarom kan dit gebruik word vir die simulasie van turbulente gesuspendeerde sediment vervoer in damme.