<p>Coherent, large-scale shapes and patterns are evident in many landscapes, and evolve according to climate and hydrological forces. For large-scale, sandy coastlines, these shapes depend on wave climate forcing. The wave climate is influenced by storm patterns, which are expected to change with the warming climate, and the associated changes in coastline shape are likely to increase rates of shoreline change in many places. Humans have historically responded to coastline change by manipulating various coastal processes, consequently affecting long-term, large-scale coastline shape change. Especially in the context of changing climate forcing and increasing human presence on the coast, the interaction of the human and climate-driven components of large-scale coastline evolution are becoming increasingly intertwined. </p><p>This dissertation explores how climate shapes coastlines, and how the effects of humans altering the landscape interact with the effects of a changing climate. Because the coastline is a spatially extended, nonlinear system, I use a simple numerical modeling approach to gain a basic theoretical understanding of its dynamics, incorporating simplified representations of the human components of coastline change in a previously developed model for the physical system. </p><p>Chapter 1 addresses how local shoreline stabilization affects the large scale morphology of a cuspate-cape type of coastline, and associated large-scale patterns of shoreline change, in the context of changing wave climate, comparing two fundamentally different approaches to shoreline stabilization: beach nourishment (in which sediment is added to a coastline at a long-term rate that counteracts the background erosion), and hard structures (including seawalls and groynes). The results show that although both approaches have surprisingly long-range effects with spatially heterogeneous distributions, the pattern of shoreline changes attributable to a single local stabilization effort contrast greatly, with nourishment producing less erosion when the stabilization-related shoreline change is summed alongshore. </p><p>Chapter 2 presents new basic understanding of the dynamics that produce a contrasting coastline type: convex headland-spit systems. Results show that the coastline shapes and spatially-uniform erosion rates emerge from two way influences between the headland and spit components, and how these interactions are mediated by wave climate, and the alongshore scale of the system. Chapter 2 also shows that one type of wave-climate change (altering the proportion of `high-angle' waves) leads to changes in coastline shape, while another type (altering wave-climate asymmetry) tends to reorient a coastline while preserving its shape. </p><p>Chapter 3 builds on chapter 2, by adding the effects of human shoreline stabilization along such a convex coastline. Results show that in the context of increasing costs for stabilization, abandonment of shoreline stabilization at one location triggers a cascade of abandonments and associated coastline-shape changes, and that both the qualitative spatial patterns and alongshore speed of the propagating cascades depends on the relationship between patterns of economic heterogeneity and the asymmetry of the wave-climate change--although alterations to the proportion of high-angle waves in the climate only affects the time scales for coupled morphologic/economic cascades.</p> / Dissertation

Statistical mechanics has been applied to a wide range of systems in physics, biology, medicine and even anthropology. This theory has been recently used to model the complex biochemical processes of gene expression and regulation. In particular, genetic networks offer a large number of interesting phenomena, such as multistability and oscillatory behaviour, that can be modelled with statistical mechanics tools. In the first part of this thesis we introduce gene regulation, genetic switches, and the colonization of a spatially structured media. We also introduce statistical mechanics and some of its useful tools, such as the master equation and mean- field theories. We present simple examples that are both pedagogical and also set the basis for the study of more complicated scenarios. In the second part we consider the exclusive genetic switch, a fundamental example of genetic networks. In this system, two proteins compete to regulate each other's dynamics. We characterize the switch by solving the stationary state in different limits of the protein binding and unbinding rates. We perform a study of the bistability of the system by examining its probability distribution, and by applying information theory techniques. We then present several versions of a mean field theory that offers further information about the switch. Finally, we compute the stationary probability distribution with an exact perturbative approach in the unbinding parameter, obtaining a valid result for a wide range of parameters values. The techniques used for this calculation are successfully applied to other switches. The topic studied in the third part of the thesis is the propagation of a trait inside an expanding population. This trait may represent resistance to an antibiotic or being infected with a certain virus. Although our model accounts for different examples in the genetic context, it is also very useful for the general study of a trait propagating in a population. We compute the speed of expansion and the stationary population densities for the invasion of an established and an expanding population, finding non-trivial criteria for speed selection and interesting speed transitions. The obtained formulae for the different wave speeds show excellent agreement with the results provided by simulations. Moreover, we are able to obtain the value of the speeds through a detailed analysis of the populations, and establish the requirements for our equations to present speed transitions. We finally apply our model to the propagation in a position-dependent fitness landscape. In this situation, the growth rate or the maximum concentration depends on the position. The amplitudes and speeds of the waves are again successfully predicted in every case.

MSc / Thesis (MSc (Physics))--University of Stellenbosch, 2009. / The propagation of electromagnetic radiation in homogeneous or periodically modulated media can be described by the coupled mode equations. The aim of this study was to derive analytical expressions modeling the solutions of the coupled-mode equations, as alternative to the generally used numerical and transfer-matrix methods. The path integral formalism was applied to the coupled-mode equations. This approach involved deriving a path integral from which a generating functional was obtained. From the generating functional a Green’s function, or propagator, describing the nature of mode propagation was extracted. Initially a Green’s function was derived for the propagation of modes having position independent coupling coefficients. This corresponds to modes propagating in a homogeneous medium or in a uniform grating formed by a periodic variation of the index of refraction along the direction of propagation. This was followed by the derivation of a Green’s function for the propagation of modes having position dependent coupling coefficients with the aid of perturbation theory. This models propagation through a nonuniform inhomogeneous medium, specifically a modulated grating. The propagator method was initially tested for the case of propagation in an arbitrary homogeneous medium. In doing so three separate cases were considered namely the copropagation of two modes in the forward and backward directions followed by the counter propagation of the two modes. These more trivial cases were used as examples to develop a rigorous mathematical formalism for this approach. The results were favourable in that the propagator’s results compared well with analytical and numerical solutions. The propagator method was then tested for mode propagation in a periodically perturbed waveguide. This corresponds to the relevant application of mode propagation in uniform gratings in optical fibres. Here two case were investigated. The first scenario was that of the copropagation of two modes in a long period transmission grating. The results achieved compared well with numerical results and analytical solutions. The second scenario was the counter propagation of two modes in a short period reflection grating, specifically a Bragg grating. The results compared well with numerical results and analytical solutions. In both cases it was shown that the propagator accurately predicts many of the spectral properties of these uniform gratings. Finally the propagator method was applied to a nonuniform grating, that is a grating for which the uniform periodicity is modulated - in this case by a raised-cosine function. The result of this modulation is position dependent coupling coefficients necessitating the use of the Green’s function derived using perturbation theory. The results, although physically sensible and qualitatively correct, did not compare well to the numerical solution or the well established transfer-matrix method on a quantitative level at wavelengths approaching the design wavelength of the grating. This can be explained by the breakdown of the assumptions of first order perturbation theory under these conditions.

Thesis (MSc)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: The determination of the platinum group metals (PGMs), platinum, palladium, rhodium, iridium, ruthenium and osmium, remains a problem for the low-grade ore samples, and the analysis of these samples in a routine laboratory relies entirely on the fire assay technique. The use of large sample masses to overcome sub-sampling errors has been the greatest advantage of this technique. The increased economic value of PGMs and recent developments in instrumentation such as inductively coupled plasma-mass spectrometry (ICP-MS) which is capable of trace element detection as low as part per billion (Ppb) levels, have led to a search for complementary methods to ensure the accuracy of fire assay results. This work investigates the feasibility of direct dissolution of ore samples using microwave-assisted dissolution followed by ICP-MS as the measurement technique. Due to the limited sample mass that can be used, a thorough consideration had to be given to sampling errors and analytical errors to assess the overall precision achievable. Most PGM-bearing minerals occur as sulphides and these are highly resistant to acid dissolution. It was found that roasting the Merensky type samples in air, prior to dissolution gives quantitative recoveries for platinum. Recoveries up to 100% were obtained for platinum, palladium, rhodium and gold for a Merensky flotation concentrate with excellent precision (about 4%) except for gold which had poorer precision (16%). However, ore samples presented a problem due to their lower PGM content and smaller sample masses being used. Precision for all elements improved significantly (from about 20% to about 8%), with the use of l g-sample aliquot compared to that ofO.25 g-sample. Acid dissolution, even after roasting proved to be insufficient for the UG-2 chromitite samples. When roasting was followed with reduction under hydrogen flame the solubility of the UG-2 flotation concentrate improved remarkably. The recoveries obtained were approximately 95 ± 5% for platinum, 99 ± 5% palladium, 104 ± 12% gold and 102 ± 5% for rhodium with good precision (comparable to that of Merensky concentrate). The accuracy and precision of the results depended very much on the sample mass and air-flow in the furnace during the roasting procedure. For this method to be used successfully, the air flow is very critical, and should lead to a better furnace design which can rotate the crucibles to enable an even flow of air over all the samples during roasting. / AFRIKAANSE OPSOMMING: Die bepaling van platinumgroep metale (PGM'e), platinum, palladium, rhodium, iridium, ruthenium en osmium is 'n voortdurende probleem vir die lae-graad erts monsters. Die analise van hierdie monsters in 'n roetine laboratorium is geheel afhanklik van die klassieke "fire assay"-tegnieke. Die groot voordeel van hierdie tegniek is die voorkoming van monsternemingsfoute deur die gebruik van groter monster massas. Die ekonomiese waarde van PGM'e saam met die onlangse ontwikkeling van instrumentasie soos die induktief-gekoppelde plasma-massaspektrometrie (IGP-MS) wat in staat is om spoorelemente in konsentrasies so laag soos dele per biljoen (ppb) te meet, het daartoe gelei na soeke vir komplementêre metodes om die akkuraatheid van klassieke "fire assay" -tegnieke te verseker. Hierdie werk ondersoek die waarskynlikheid van direkte oplossing van ertsmonsters deur gebruik te maak van mikrogolf-ondersteunde oplossing gevolg deur IGP-MS as opmetingstegniek. As gevolg van die beperkte monster massa wat gebruik kan word, moes deeglike oorweging gegee word aan monsternemingsfoute en analitiese foute, om die oorkoepelende presiesheid te bepaal. Meeste PGM-draende minerale bestaan in die vorm van sulfiede en bied groot weerstand teen oplossing in 'n suur. Die gloei van Merensky-tipe monsters in lug voor oplossing gee kwantitatiewe herwinning van platinum Herwinning tot 100% is behaal vir platinum, palladium, rhodium en goud vir 'n Merensky-flotasie-konsentraat met uitstekende akkuraatheid (4%) behalwe vir goud met 'n swak (16%) akkuraatheid. Die erts monsters was problematies as gevolg van die laer PGM inhoud en kleiner monstermassas wat gebruik is. Presiesheid vir al die elemente het beduidend verbeter (van 20% tot 8%) met die gebruik van 1 g- monster massas vergelyk met 0.25 g-monsters. Ten spyte van die gloei van die monster is suur oplossing onvoldoende vir die UG-2 chromatiet-houdende monsters. Wanneer die monster gegloei is onder 'n waterstof vlam (reduksie) het die oplossbaarheid van UG-2 flotasie-konsentraat aansienlik verbeter. Die herwinbaarheid wat behaal is, is 95 +/- 5% vir platinum, 99 +/- 5% vir palladium, 104 +/- 12% vir goud en 102 +/- 5% rhodium met goeie relatiewe presiesheid vergeleke met Merensky-konsentrate. Die akkuraatheid en presiesheid van resultate hang meerendeels af van monster massa en lugvloei in die oond gedurende gloei. Die lugvloei is krities vir die sukses van hierdie metode en sal moet lei tot beter oond ontwerp wat kroesies kan roteer en 'n gelyke vloei van lug oor die monsters gedurende verbranding toelaat.

For a stress-sensitive or stress-dependent reservoir, the interactions between its seepage field and in situ stress field are complex and affect hydrocarbon recovery. A coupled geomechanics and fluid-flow model can capture these relations between the fluid and solid, thereby presenting more precise history matchings and predictions for better well planning and reservoir management decisions. A traditional reservoir simulator cannot adequately or fully represent the ongoing coupled fluid-solid interactions during the production because of using the simplified update-formulation for porosity and the static absolute permeability during simulations. Many researchers have studied multiphase fluid-flow models coupled with geomechanics models during the past fifteen years. The purpose of this research is to develop a coupled geomechanics and compositional model and apply it to problems in the oil recovery processes. An equation of state compositional simulator called the General Purpose Adaptive Simulator (GPAS) is developed at The University of Texas at Austin and uses finite difference / finite control volume methods for the solution of its governing partial differential equations (PDEs). GPAS was coupled with a geomechanics model developed in this research, which uses a finite element method for discretization of the associated PDEs. Both the iteratively coupled solution procedure and the fully coupled solution procedure were implemented to couple the geomechanics and reservoir simulation modules in this work. Parallelization, testing, and verification for the coupled model were performed on parallel clusters of high-performance workstations. MPI was used for the data exchange in the iteratively coupled procedure. Different constitutive models were coded into GPAS to describe complicated behaviors of linear or nonlinear deformation in the geomechanics model. In addition, the geomechanics module was coupled with the dual porosity model in GPAS to simulate naturally fractured reservoirs. The developed coupled reservoir and geomechanics simulator was verified using analytical solutions. Various reservoir simulation case studies were carried out using the coupled geomechanics and GPAS modules. / text

A vast majority of heart attacks occur due to rapid progression of plaque buildup in the coronary arteries that supply blood to the heart muscles. The diseased arteries can be treated with drugs delivered locally to vulnerable plaques—ones that may rupture and release emboli, resulting in the formation of thrombus, or blood clot that can cause blockage of the arterial lumen. In designing these local drug delivery devices, important issues regarding drug distribution and targeting need to be addressed to ensure device design optimization as physiological forces can cause the local concentration to be very different from mean drug tissue concentration estimated from in vitro experiments and animal studies. Therefore, the main objective of this work was to develop a computational tool-set to support the design of a catheter-based local drug delivery system that uses nanoparticles as drug carriers by simulating drug transport and quantifying local drug distribution in coronary artery walls. Toward this end, a three dimensional mathematical model of coupled transport of drug and drug-encapsulated nanoparticles was developed and solved numerically by applying finite element based isogeometric analysis that uses NURBS-based techniques to describe the artery wall geometry. To gain insight into the parametric sensitivity of drug distribution, a study of the effect of Damkohler number and Peclet number was carried out. The tool was then applied to a three-dimensional idealized multilayered model of the coronary artery wall under healthy and diseased condition. Preliminary results indicated that use of realistic geometry is essential in creating physiological flow features and transport forces necessary for developing catheter-based drug delivery design procedures. Hence, simulations were run on a patient-specific coronary artery wall segment with a typical atherosclerotic plaque characterized by a lipid pool encased by a thin fibrous cap. Results show that plaque heterogeneity and artery wall inhomogeneity have a considerable effect on drug distribution. The computational tool-set developed was able to successfully capture trends observed in local drug delivery by incorporating a multitude of relevant physiological phenomena, and thus demonstrated its potential utility in optimizing drug design parameters including delivery location, nanoparticle surface properties and drug release rate. / text

Oocyte maturation (OM) in teleosts is under precise hormonal control by estrogens and progestins. We show here that estrogens activate an epidermal growth factor receptor (EGFR) signaling pathway through the G protein-coupled estrogen receptor (GPER) to maintain meiotic arrest of full-grown zebrafish (Danio rerio) oocytes in an in vitro germinal vesicle breakdown (GVBD) bioassay. A GPER- specific agonist decreased OM and a GPER-specific antagonist increased spontaneous OM, whereas specific nuclear estrogen receptor (ERα and ERβ) agonists did not affect OM, which suggests the inhibitory action of estrogens on OM are solely mediated through GPER. Furthermore, a peptide-bound estrogen, which cannot enter the oocyte, decreased GVBD, showing that these estrogen actions are mediated through a membrane receptor. Treatment of oocytes with actinomycin D, a transcription inhibitor, did not block the inhibitory effects of estrogens on OM, indicating that estrogens act via a nongenomic mechanism to maintain oocyte meiotic arrest. EGFR mRNA was detected in denuded zebrafish oocytes by reverse transcription polymerase chain reaction (RT-PCR). Therefore, the potential role of transactivation of EGFR in estrogen inhibition of OM was investigated. The matrix metalloproteinase inhibitor, ilomastat, which prevents the release of heparin-bound epidermal growth factor (HB-EGF), increased spontaneous OM. Moreover, specific EGFR1 (ErbB1) inhibitors and inhibitors of extracellular-related kinase 1 and 2 (ERK1/2) increased spontaneous OM. Previously, estrogens have been shown to increase 3’-5’-cyclic adenosine mono phosphate (cAMP) levels through GPER in zebrafish oocytes during meiotic arrest. Taken together these present results suggest that estrogens also act through GPER to maintain meiotic arrest through a second signaling pathway involving transactivation of EGFR and activation of ERK 1 and 2. / text

Lysophosphatidic acid (LPA) belongs to a class of extracellular lipid signaling molecules. In the vasculature, LPA may regulate platelet activation and modulate endothelial and smooth muscle cell function. LPA has therefore been proposed as a mediator of cardiovascular disease. The bulk of circulating LPA is produced from plasma lysophosphatidylcholine (LPC) by autotaxin (ATX), a secreted lysophospholipase D (lysoPLD). Early studies suggest that some of the production of circulating LPA is platelet-dependent. ATX possesses an N-terminal somatomedin B-like domain suggesting the hypothesis that ATX interacts with platelet integrins which may localize ATX to substrate in the membrane and/or alter the catalytic activity of ATX. Using static adhesion and soluble binding assays we found that ATX does indeed bind to platelets and cultured mammalian cells in an integrin-dependent manner which is blocked by integrin function-blocking peptides and antibodies. This binding increases both the activity of ATX and localization of its product, LPA, to the platelet/cell membrane. LPA is generally stimulatory to human platelets although platelets from a small population of donors are refractory to LPA stimulation. Likewise LPA is inhibitory to murine platelets. We previously found that LPA receptor pan-antagonists reduce agonist-induced platelet activation, and partial stimulation of LPA5 specifically increases platelet activation in humans. Since both LPA5 and LPA4 are present at significant levels in human platelets, we hypothesized that LPA4 is responsible for an inhibitory pathway and LPA5 is responsible for an inhibitory pathway. We used mice deficient in LPA4 to test this model. Isolated platelet function tests revealed no major difference between lpa4-/- mice compared with WT mice although lpa4-/- mice were more prone to FeCl3-induced thrombosis. Paradoxically, chimeric mice reconstituted with lpa4-/- deficient bone marrow derived cells were protected from thrombosis. These discrepancies may be explained by involvement of endothelial cells and the relative scarcity of LPA receptors in murine platelets compared with human platelets. Taken together, these results demonstrate two critical regulators of LPA signaling and open up new avenues to further our understanding of atherothrombosis.

Impaired mass transfer characteristics of blood borne vasoactive species such as ATP in regions such as an arterial bifurcation have been hypothesized as a prospective mechanism in the aetiology of atherosclerotic lesions. Arterial endothelial (EC) and smooth muscle cells (SMC) respond differentially to altered local hemodynamics and produce coordinated macro-scale responses via intercellular communication. Using a computationally designed arterial segment comprising large populations of mathematically modelled coupled ECs & SMCs, we investigate their response to spatial gradients of blood borne agonist concentrations and the effect of micro-scale driven perturbation on the macro-scale. Altering homocellular (between same cell type) and heterocellular (between different cell types) intercellular coupling we simulated four cases of normal and pathological arterial segments experiencing an identical gradient in the concentration of the agonist. Results show that the heterocellular calcium (Ca2+) coupling between ECs and SMCs is important in eliciting a rapid response when the vessel segment is stimulated by the agonist gradient. In the absence of heterocellular coupling, homocellular Ca2+ coupling between smooth muscle cells is necessary for propagation of Ca2+ waves from downstream to upstream cells axially. Desynchronized intracellular Ca2+ oscillations in coupled smooth muscle cells are mandatory for this propagation. Upon decoupling the heterocellular membrane potential, the arterial segment looses the inhibitory effect of endothelial cells on the Ca2+ dynamics of underlying smooth muscle cells. The full system comprising hundreds of thousands of coupled nonlinear ordinary differential equations simulated on the massively parallel Blue Gene architecture. The use of massively parallel computational architectures shows the capability of this approach to address macro-scale phenomena driven by elementary micro-scale components of the system.

Hypothalamic gonadotropin-releasing hormone (GnRH) (GnRH I) is the central regulator of the mammalian reproductive system. Most vertebrates studied also possess a second form of GnRH, GnRH II. GnRH I acts on its cognate G proteincoupled receptor (GPCR) on pituitary gonadotropes and activates Gq/11-mediated signalling pathways to stimulate the biosynthesis and the release of luteinising hormone (LH) and follicle-stimulating hormone (FSH). Both GnRHs have also been suggested to inhibit cellular proliferation, an action which has largely been proposed to be mediated by the coupling of the receptor to Gi/o. However, the range of G proteins activated by the GnRH receptor and the signalling cascades involved in inducing antiproliferation remain controversial. To delineate the G protein coupling selectivity of the mammalian GnRH receptor and to identify the signalling pathways involved in GnRH I-mediated cell growth inhibition, I examined the ability of the receptor to interact with Gq/11, Gi/o and Gs in Gαq/11 knockout MEF cells. My results indicate that the receptor is unable to interact with Gi/o but can signal through Gq/11. Additionally, my data do not support the suggestion of GnRH receptor-Gs interaction. Furthermore, I show that the GnRH Iinduced inhibition of cell growth is dependent on Gq/11, src and extracellular signal regulated kinase (ERK) but is independent of the activity of protein kinase C (PKC), Ca2+, jun-N-terminal kinase (JNK) or P38. Based on these findings and previous research within our group, I propose a mechanism whereby GnRH I may induce antiproliferation. Previous studies from our laboratory suggest that the GnRH receptor can adopt distinct active conformations in response to the binding of GnRH I and GnRH II. These data thus account for our hypothesis of ligand-induced selective signalling (LiSS). Given my previous results, I examined the ability of the GnRH receptor to couple to G12/13. My work indicates that the receptor can directly activate G12/13 and the downstream signalling cascades associated with this G protein family. Indeed, I provide evidence, in several cellular backgrounds, to suggest that GnRH receptor- G12/13-mediated signalling is involved in the regulation of GnRH-induced MAPK activity, SRE-driven gene transcription and cytoskeletal reorganisation. Furthermore, I propose a role for these G proteins in the transcriptional regulation of LHβ and FSHβ. Finally, I confirm previous results from our laboratory indicating that the GnRH receptor may interact with src Tyr kinase and show that GnRH I but not GnRH II may, independently of Gq/11, stimulate the Tyr phosphorylation and thus the activation of this protein. I propose that this differential signalling accounts for the distinct effects of GnRH I and GnRH II on cellular morphology and SREpromoted transcriptional activity. The research presented within this thesis provides evidence to refute published conclusions based on largely circumstantial experimental data, describes novel GnRH receptor signalling pathways and offers support for the concept of LiSS. It may assist in the development of new therapeutic compounds which selectively target one GnRH-mediated signalling pathway while bypassing others.