Yes / This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using RBF neural network while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be included as 1) an output entropy model is presented using neural network; 2) a nonlinear filter design algorithm is developed as the main result and 3) a solution of entropy assignment problem is obtained which is an extension of the presented framework.

Yes / Reverse Osmosis (RO) is one of the most widely used technologies for wastewater treatment for the removal of toxic impurities, such as phenol and phenolic compounds from industrial effluents. In this research, performance of multi-stage RO wastewater treatment system is evaluated for the removal of chlorophenol from wastewater using model-based techniques. A number of alternative configurations with recycling of permeate, retentate, and permeate-retentate streams are considered. The performance is measured in terms of total recovery rate, permeate product concentration, overall chlorophenol rejection and energy consumption and the effect of a number of operating parameters on the overall performance of the alternative configurations are evaluated. The results clearly show that the permeate recycling scheme at fixed plant feed flow rate can remarkably improve the final chlorophenol concentration of the product despite a reduction in the total recovery rate.

The exploratory study sought to elicit and document mathematics teachers‟ views on how they enacted the process of transition between contexts and mathematics. The study pursued to understand teachers‟ beliefs and knowledge of mathematics. A mixed methods sequential explanatory research design was employed where a quantitative phase was followed by the connecting phase and concluded through a qualitative phase involving three case studies. A purposive sample of 165 practicing teachers who had registered for a professional advancement developmental course at a university participated in the study by voluntarily completing a survey questionnaire. From this sample, three cases of individual teachers were pursued. The first two cases involved conducting in-depth interviews with the teacher who had rated sentences in the questionnaire differently while the last case involved the recording of an interview of one individual using field notes. The questionnaire sought teachers‟ biographical details (section A), their views on contexts and mathematics (section B) and their rating of sentences in a passage with regard to the mathematics embedded in the sentences (section C). Semi-structured interviews were conducted in the qualitative phase to elicit in-depth views of the teachers‟ regarding the research problem. All the instruments were tested for validity and reliability. Quantitative data gathered was analysed using frequencies, percentages, cross tabulations, bar charts and pie charts as well as the calculation of Pearson chi-square tests (Cohen, Manion & Morrison, 2011). Descriptive and inferential statistics were used to collate teachers‟ views from which themes were drawn and related to make inferences. It was found that teachers‟ positive views about contexts and mathematics did not translate into them recognising mathematics in some mathematics potent contexts as captured in their ratings in section C of the questionnaire. Statistically significant associations were recorded to support this. The study also conceptualised a mathematical participation model (MP-model) as a tool to describe and analyse participation that involves the use of real world data in the teaching and learning of mathematics. The MP-model involves four components, viz. the community of practice (CoP), real world data, mathematics and a model in which members of the CoP tap into the real world data and mathematics to model their participation. The study recommends the MP-model as tool for description and enactment of full mathematical participation. / Mathematical Sciences / D.Litt.et. Phil. (Mathematics Education)

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2008. / This thesis aims to contribute to the modelling and analysis of MEMS gyroscope technologies. Various gyroscope types are studied, and the phase-based vibratory gyroscope is then selected for further investigation. In the literature, vibratory MEMS gyroscopes are mostly used in a single excitation and amplitude detection mode. However, a dual excitation and phase detection mode has recently been proposed, since phase-based detection, as opposed to amplitude-based detection modes, may be expected to increase measurement accuracy (in turn since improved signal-to-noise ratios may be expected). However, the presented analytical model was relatively crude, and the assumptions made appear unrealistic. Accordingly, in this thesis, an improved analyticalmodel is developed. To describe the dual excitation and phase detection problem more comprehensively, principles of classical dynamics are used herein to investigate the dual excitation of a two degree of freedom spring-mass-damper system subjected to an applied rotation rate. In doing so, an analytical formulation including mechanical coupling effects is extended into a generalized form, after which the amplitude and phase responses of the mechanically uncoupled system are interpreted. The differences between the amplitude and phase measurement techniques are illustrated. Finally, the system is modelled numerically, and the scale factor of a hypothetical device based on the phase-based detection method is optimized, subject to constraints on the nonlinearity of the device, using constrained mathematical optimization techniques.

Heterogeneous photocatalysis is an advanced oxidation technology widely applied in environmental remediation processes. It is a relatively safe and affordable technology with a low impact on the environment and has found applications in a number of fields from chemical engineering, construction and microbiology to medicine. It is not catalysis in the real sense of the word as the photons which initiate the desired photocatalytic reaction are consumed in the process. The cost of these photons is by far the limiting economic factor in its application. From a technical standpoint, the inefficient use of the aforementioned photons during the photocatalytic reaction is responsible for the limited adoption of its application in industry. This inefficiency is characterised by low quantum yields or photonic efficiencies during its application. The mechanism of the technique of controlled periodic illumination which was previously proposed as a way of enhancing the low photonic efficiency of TiO2 photocatalysis has been investigated using a novel controlled experimental approach; the results showed no advantage of periodic illumination over continuous illumination at equivalent photon flux. When the technique of controlled periodic illumination is applied in a photocatalytic reaction where attraction between substrate molecules and catalyst surface is maximum and photo-oxidation by surface-trapped holes, {TiIVOH•}+ ads is predominant, photonic efficiency is significantly improved. For immobilized reactors which usually have a lower illuminated surface area per unit volume compared to suspended catalyst and mass transfer limitations, the photonic efficiency is even lower. A novel photocatalytic impeller reactor was designed to investigate photonic efficiency in gas–solid photocatalysis of aromatic volatile organic compounds. The results indicate photonic efficiency is a function of mass transfer and catalyst deactivation rate. The development of future reactors which can optimise the use of photons and maximize photonic efficiency is important for the widespread adoption of heterogeneous photocatalysis by industry.

Thesis (MSc)--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: We investigate the nuclei 20Ne, 44Ti, 94Mo, 136Te and 212Po using a model of an α-cluster orbiting a closed shell core. A purely phenomenological cluster-core potential is found to provide a successful description of the spectra, B(E2↓) transition strengths, and α-decay rates of the low-lying positive parity states of these nuclei. We then use the same potential as the real part of an optical model potential to describe the α elastic scattering by 16O, 40Ca, 90Zr and 208Pb. The experimental differential cross-section data are reasonably well reproduced with the imaginary potential depth as the only free parameter. The special case of the 8Be system is also analysed. / AFRIKAANSE OPSOMMING: Ons ondersoek die kerne 20Ne, 44Ti, 94Mo, 136Te en 212Po deur gebruik te maak van ’n model waar ’n α-bondel om ’n kern met ’n geslote skil wentel. ’n Suiwer fenomenologiese bondelkern potentiaal is gevind wat die energie spektra, B(E2 ↓) oorgangs sterktes, en α-verval tempo vir laagliggende positiewe pariteitstoestande vir hierdie kerne beskryf. Ons gebruik dieselfde potentiaal as die reele deel van die optiese potentiaal om die alpha elastiese verstrooiing deur die kerne 16O, 40Ca, 90Zr en 208Pb te beskryf. Die eksperimentele differensiele kansvlak data word redelik goed gereprodukseer met slegs die imaginere potensiaal diepte as die enigste vrye parameter. Die spesiale geval van 8Be is ook ondersoek.

Thesis (MSc)--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: We construct and study a simple model for an active gel of exible polymer filaments crosslinked by a molecular motor cluster that perform reversible work while translating along the filaments. The filament end points are crosslinked to an elastic background. In this sense we employ a simplified model for motor clusters that act as slipping links that exert force while moving along the strands. Using the framework of replica theory, quenched averages are taken over the disorder which originates from permanent random crosslinking of network end points to the background. We investigate how a small motor force contributes to the elastic properties of the network. We learn that in addition to the normal elastic response for the network there is an extra contribution to the network elasticity from the motor activity. This depends on the ratio of the entropic spring constant for the linked bio-polymerchain to the spring constant of the tether of the motor. / AFRIKAANSE OPSOMMING: Ons konstrueer en bestudeer 'n eenvoudige model vir 'n aktiewe netwerk van eksieble polimeerfilamente wat deur grosse van molekulere motors aan mekaar verbind word wat omkeerbare werk doen terwyl dit langs die filamente transleer. Die eindpunte van die filamente is aan 'n elastiese agtergrond verbind. In hierdie sin benut ons 'n eenvoudige model vir motorclusters wat as verskuifbare verbindings krag op die filamente tydens beweging kan uitoefen. Nie-termiese wanorde gemiddeldes word geneem oor die wanorde wat deur die lukrake permanente verbindings van netwerk eindpunte aan die agtergrond veroorsaak word. Ons ondersoek hoe 'n klein motorkrag tot die elastiese eienskappe van die netwerk bydra. Ons leer dat daar bo en behalwe die gewone elastiese respons vir die netwerk 'n elastiese bydrae as gevolg van die motors se aktiwiteit voorkom. Dit hang af van die verhouding van die entropiese veerkonstante van die biopolimerketting tot die veerkonstante van die anker van die motor.

Thesis (MScEng (Civil Engineering)--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: A study of the state of reservoir sedimentation in South Africa based on reservoir sediment deposit data, has shown that a considerable number of reservoirs have serious sedimentation problems. The analysis of the reservoir sediment deposit data showed that almost 25% of the total number of reservoirs have lost between 10 to 30% of their original storage capacity. The average storage loss due to sedimentation in South African reservoirs is approximately 0.3% per year while the average annual storage loss for all the reservoirs in the world is 0.8%. The aim of this research was to develop sediment yield prediction methods based on analytical approaches and mathematical modelling. The sediment yield prediction methods can be used in planning and management of water resources particularly in reservoir sedimentation control. The catchment erosion and sediment yield modelling methods can be applied in temporal and spatial analysis of sediment yields which results are essential for detailed design of water resources, particularly in the identification of critical erosion areas, sediment sources and formulation of catchment management strategies. Current analytical methods for the prediction of sediment yield have been reviewed. Nine sediment yield regions have been demarcated based on the observed sediment yields and catchment characteristics. Empirical and probabilistic approaches were investigated. The probabilistic approach is based on analysis of the observed sediment yields that were calculated from reservoir sediment deposit, river suspended sediment sampling data and soil erodibility data. The empirical equations have been derived from regression analysis of the variables that were envisaged to have a significant effect on erosion and sediment yields in South Africa. Empirical equations have been developed and shown to have accurate and reliable predictive capability in six of the nine regions. The probabilistic approach has been recommended for the prediction of sediment yields in the remaining three regions where reliable regression equations could not be derived. The predictive accuracy of both the probabilistic and empirical approaches was checked and verified using the discrepancy ratio and graphs of the observed and calculated data. While the analytical methods are needed to predict the sediment yield for the whole catchment, mathematical modelling to predict sediment yields is applied for more detailed analysis of sediment yield within the catchment. An evaluation of available catchment sediment yield mathematical modelling systems was carried out. The main criteria for the choice of a numerical model to be adopted for detailed evaluation was based on the following considerations: the model’s capabilities, user requirements and its application. The SHETRAN model (Ewen et al., 2000) was therefore specifically chosen because of its ability to simulate relatively larger catchment areas (it can handle catchment scales from less than 1km2 to 2500km2), its ability to simulate erosion in channels, gullies and landslides, its applicability to a wide range of land-use types and ability to simulate land use changes. Another model, ACRU (Smithers et al., 2002) was also reviewed. The aim of the model evaluation was to provide a conceptual understanding of catchment sediment yield modelling processes comprising model set up, calibration, validation and simulation. The detailed evaluation of the SHETRAN model was done through a case study of Glenmaggie Dam in Australia. The flow was calibrated and validated using data from 1975 to 1984, and 1996 to 2006 respectively. The results for both the calibration and validation were reasonable and reliable. The sediment load was validated against turbidity derived sediment load data from 1996 to 2006. The model was used to identify sources of sediment and areas of higher sediment yield. The land use of a selected sub-catchment was altered to analyse the impact of land use and vegetative cover on the sediment yield. Based on the results, the SHETRAN model was confirmed to be a reliable model for catchment sediment yield modelling including simulation of different land uses. / AFRIKAANSE OPSOMMING: ‘n Studie van die stand van damtoeslikking in Suid-Afrika toon dat daar ernstige toeslikkingsprobleme by baie reservoirs bestaan. ’n Ontleding van die toeslikkingsyfers gegrond op damkomopmetings toon dat omtrent 25% van die totale getal reservoirs tussen 10 en 30% van hulle oorspronklike opgaarvermoë verloor het. Die gemiddelde tempo van damtoeslikking in Suid-Afrika is 0.3%/jaar, wat laer is as die wêreld gemiddeld van 0.8%/jaar. Die oogmerk met hierdie navorsing was om sedimentlewering voorspellingsmetodes te ontwikkel deur gebruik te maak van analitiese metodes en wiskundige modellering. Die sedimentlewering voorspellingsmetodes kan gebruik word vir die beplanning en bestuur van waterbronne en veral vir damtoeslikking beheer. Die opvangsgebied erosie en die sedimentlewering modelleringsmetodes kan toegepas word in tydveranderlike en ruimtelike ontleding van sedimentlewering. Hierdie inligting word benodig vir die detail ontwerp van waterhulpbronne en veral vir die identifisering van kritiese erosiegebiede, bronne van sediment en die formulering van opvangsgebied-bestuur strategië. ‘n Literatuuroorsig oor die huidige metodes vir die voorspelling van erosie en sedimentlewering is gedoen. Nege sedimentasie streke is afgebaken in Suid-Afrika, gegrond op waargenome damtoeslikkingsdata en opvangsgebied-eienskappe. Proefondervindelike en waarskynlikheidsbenaderinge is ondersoek. Die waarskynlikheidsbenadering is gegrond op die ontleding van waargenome damtoeslikking wat bereken is uit reservoir opmeting data en rivier gesuspendeerde sediment data, asook data oor gronderosie. Die proefondervindelike metode se vergelykings is afgelei vanuit regressie ontleding van die veranderlikes wat ‘n belangrike invloed het op die erosie en sedimentlewering in Suid-Afrika. Daar is bevestig dat die ontwikkelde proefondervindelike (empiriese) vergelykings ‘n akkurate en betroubare voorspellingsvermoë in ses van die nege streke het. Die waarskynlikheidsbenadering is aanbeveel vir die voorspelling van sedimentlewering in die ander drie streke, waar betroubare regressie vergelykings nie afgelei kon word nie. Die voorspellingsakkuraatheid van albei metodes is nagegaan en bevestig deur gebruik te maak van die teenstrydigheidsverhouding en grafieke van die waargenome en berekende data. Analitiese metodes van sedimentleweringsvoorspelling is nodig vir ‘n volle opvangsgebied, terwyl wiskundige modellering om sedimentlewerings te voorspel gebruik kan word om ‘n meer in diepte ontleding van die sedimentlewering binne ‘n opvanggebied te doen. ‘n Evaluasie van beskikbare wiskundige modelle wat opvangsgebied sedimentlewering kan voorspel, is gedoen. Die hoofkriteria vir die keuse van ‘n model vir gebruik by gedetailleerde ontleding is gegrond op die volgende: die vermoëns van die model, wat verbruikers benodig en die aanwending van die model. Die SHETRAN model (Ewen et al., 2000) is spesifiek gekies weens sy vermoë om relatief groter opvangsgebiede te simuleer (dit kan opvangsgebiede van 1km2 tot 2500km2 wees) asook om erosie in kanale, dongas en grondverskuiwing simuleer. Dit kan toegepas word op ‘n wye reeks grondtipes en kan ook die gevolge simuleer as die gebruik van die grond verander. ‘n Ander model, ACRU (Smithers et al., 2002) is ook ondersoek. Die doel van die modelevaluering was om ‘n konseptuele begrip te kry van sedimentlewering modelleringsprosesse wat die opstelling, kalibrasie, toetsing en simulasies insluit. Die volledige evaluasie van SHETRAN is gedoen deur middel van ‘n gevalle-studie van die Glenmaggiedam in Australia. Die riviervloei is gekalibreer en getoets deur gebruik te maak van data wat strek van 1975 tot 1984, en van 1996 tot 2006 onderskeidelik. Die resultate van beide die kalibrasie en die toetswas redelik en betroubaar. Die sedimentlading is gekalibreer teen velddata van 1996 tot 2006. Die model is gebruik om bronne van sediment te identifiseer, asook gebiede met ‘n hoër sedimentlewering. Die gebruik van die grond op ‘n gekose sub-opvangsgebied is verander om die impak van grondgebruik en plantbedekking op sedimentlewering te ontleed. Die resultate bewys dat die SHETRAN model ‘n betroubare model is vir groot opvangsgebied sedimentlewering modellering, asook vir die simulasie van verskillende grondgebruike.

Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The scour process of unlined spillways is an important research topic of value in engineering practice. In South Africa numerous unlined spillway dams have experienced severe erosion. This led, in some cases, to the costly concrete lining of spillways for erosion protection. On the other hand, the erosion of unlined spillways can lead to damage to, and even failure of dams and consequently can affect public safety, properties, infrastructure and the environment. In this regard, methods to predict erosion of unlined spillways are therefore needed as tools in the risk management and design of existing unlined spillways as well as future spillway structures. The prediction of the rock scouring process is challenging and empirical formulas have been established to predict incipient conditions for scour. These empirical methods however do not predict the rate of scour or the ultimate equilibrium rock scour. The key objective in this study was to investigate the applicability of a non-cohesive two-dimensional (2D) sediment transport hydrodynamic mathematical model to simulate unlined spillway scour. A physical model flume test was set up to simulate rock scour represented by uniformly sized polyethylene cubes. The flume slope and discharge were varied in the different test scenarios. The 2D mathematical model correctly predicted the extent and location of scour as observed in the laboratory tests. Temporal changes in the scour formation were also predicted with reliability. This was achieved by only calibrating the hydraulic roughness of the 2D model, and by specifying the ”rock ” particle settling velocity and material density. The simulation results were satisfactory, providing an accurate and detailed erosion prediction. From this, the mathematical modelling was validated by using a field case study. The results obtained with the mathematical model were promising for non-cohesive cases and could be applied to field prototype cases if the rock joint structure is known. This would typically apply in fault zones, where the joints would give an idea of the rock size to be used in the mathematical model. In general, where jointed rock is more massive and acts ”cohesive ”, rock parameters describing critical scour conditions for the rock in terms of stream power are required to be built into the mathematical models. / AFRIKAANSE OPSOMMING: Die uitskuringsproses van onbelynde oorlope is ’n belangrike navorsingsonderwerp in die ingenieurspraktyk. In Suid-Afrika word ernstige erosie in baie onbelynde oorlope van damme ondervind. In sommige gevalle het dit gelei tot die duur belyning van oorlope met beton, om die oorlope te beskerm. Aan die anderkant kan die erosie van onbelynde oorlope lei tot groot skade en selfs tot die faling van ’n dam. Dit kan weer lei tot skade aan eiendom, infrastruktuur en die omgewing, en die publiek in die gevaar stel. Daarom is dit nodig dat daar besin word oor metodes om erosie in onbelynde oorlope te voorspel, sodat die risiko bestuur kan word en om te sorg vir die beter ontwerp van onbelynde oorlope in die toekoms. Dit is moeilik om die uitskuringsproses te voorspel, maar empiriese formules is bestaan om die aanvang van uitskuring te voorspel. Hierdie empiriese metodes voorspel egter nie die snelheid waarteen die uitskuring sal plaasvind of die uiteindelike mate waartoe dit sal gebeur nie. Die hoofdoelwit van hierdie studie was om die toepasbaarheid van ’n nie- kohesie, twee-dimensionele (2D) hidrodinamiese wiskundige model te ondersoek, om sodoende die uitskuring van onbelynde oorlope te simuleer. ’n Fisiese model om die uitskuring van rots te simuleer is ook gebou. Die rots is deur polietileen blokkies van dieselfde grootte gemodelleer. Verskillende kanaalhellings en deurstromings is in verskillende toetse gebruik. Die 2D wiskundige model het volgens die waarnemings in laboratorium toetse, die mate en ligging van die uitskuring korrek voorspel. Veranderinge wat met verloop van tyd in die uitskuring formasie plaasgevind het, is ook betroubaar voorspel. Dit is gedoen deur die hidrouliese ruheid van die 2D model te kalibreer en deur te spesifiseer hoe vinnig die ”rots ” deeljies afsak en wat die digtheid van die materiaal is. Die uitslag van die simulasie was bevredigend en het die erosie akkuraat en in detail voorspel. Die wiskundige modellering is gevalideer deur middel van ’n gevallestudie. Die uitslae wat met die wiskundige model verkry is, is belowend, en geld vir nie-kohesie gevalle. Dit kan op prototipe gevalle in die veld toegepas word as die rots se naatstruktuur bekend is. Dit kan toegepas word in foutsones waar die nate ’n aanduiding sal gee van die grootte van ”rotse ” wat in die wiskundige model gebruik moet word. Maar as die rots baie groot is en die kohesie goed is, is dit nodig om meer parameters betreffende uitskuringstoestande gekoppel aan stroomdrywing, in die wiskundige model te gebruik.

<p>This licentiate thesis describes development of modellingtools, experimental physical modelling and numerical modellingto simulate real combustion processes for advanced industrialutility boiler before and after retrofit.</p><p>The work presents extended study about formation,destruction and control of pollutants, especially NOx, whichoccur during combustion process.</p><p>The main aim of this work is to improve mixing process incombustion chamber. To do this, the optimization of placementand direction of additional air and fuel nozzles, the physicalmodelling technique is used. By using that method, it ispossible to obtain qualitative information about processes,which occur in the real boiler. The numerical simulationsverify the results from physical modelling, because duringmathematical modelling quantitative informations about flow andmixing patterns, temperature field, species concentration areobtained.</p><p>Two 3D cases, before and after retrofit, of pulverized fuelfired boiler at 125 MW output thermal power are simulated. Theunstructured mesh technique is also used to discretize theboiler. The number of grid was 427 656 before retrofit and 513362 after retrofit. The comparisons of results of numericalsimulation before and after retrofit are presented. The resultsfrom physical modelling and numerical simulation are alsoshown.</p><p>Results present that nozzles of additional air and fuel givea considerably better mixing process, uniform temperature fieldand CO2 mass fraction. The whole combustion chamber worksalmost as a "well stirred reactor", while upper part of boilerworks as a "plug flow reactor".</p><p>Differences between from measured of temperatures andpredicted temperatures are not too big, the maximum differenceis about 100 K. It seems, that calculated temperatures showgood agreement with measurement data.</p><p>The results illuminate the potential of physical andnumerical modelling methods as promising tools to deal with thecomplicated combustion processes, even for practicalapplication in the industry.</p><p><b>Keywords:</b>air staging, fuel staging, boiler, furnace,computational fluid dynamics, numerical simulation, pollutants,physical modeling, pulverized fuel combustion.</p>