Electrospinning is a technique, which can be used to produce nanofibrous materials by introducing electrostatic fields into the polymer solution. Due to their intrinsic properties, such as small fiber diameter, small pore size and large surface area, nanofibres are suitable for use in a variety of applications including wound dressing, filtration, composites and tissue engineering. The study demonstrates the successful and optimised production of Poly(ethylene oxide) (PEO) and chitosan nanofibres by electrospinning. The biocidal effects of chitosan, chitosan-silver nanofibres and silver nanoparticles were successfully investigated. To set up a functional electrospinning apparatus, the PEO solution parameters (concentration, molecular weight, solvent, and addition of polyelectrolyte) and applied potential voltage on the structural morphology and diameter of PEO nanofibres were studied. At lower PEO concentrations, the fibres had morphology with a large variation in fibre diameter, whereas at the higher concentrations, the nanofibres exhibited ordinary morphology with uniform but larger fibre diameters. Higher molecular weight showed larger average diameters when compared to that obtained with the same polymer but of a lower molecular weight. The addition of polyelectrolyte to the polymer solution had an influence on the structural morphology of the PEO. Flow simulation studies of an electrically charged polymer solution showed that an increase in the flow rate was associated with an increase in poly(allylamine hydrochloride) (PAH) concentration for the low molecular weight polymer, the shape and size of the Taylor cone increasing with an increase in PAH concentration for the low molecular weight polymer. During optimization of the PEO nanofibres, based on statistical modelling and using the Box and Behnken factorial design, the interaction effect between PAH concentration and the tip-to-collector distance played the most significant role in obtaining uniform diameter of nanofibres, followed by the interaction between the tip-to-collector distance and the applied voltage and lastly by the applied voltage. The production and optimization of chitosan nanofibres indicated that the interactions between electric field strength and the ratio of trifluoroacetic acid (TFA) and dichloromethane (DCM), TFA/DCM solvents as well as between electric field strength and chitosan concentration had the most significant effect, followed by the concentration of chitosan in terms of producing nanofibres with uniform diameters. Chitosan and chitosan-silver nanofibres could be successfully electrospun by controlling the solution properties, such as surface tension and electrical conductivity with the silver nanoparticles in the chitosan solutions affecting the electrospinnability. The silver nanoparticles in the chitosan solution modified the morphological characteristics of the electrospun nanofibres, while the conductivity and the surface tension were elevated. The fibre diameter of the chitosan and chitosan-silver nanoparticles decreased with an increase in the silver content. The electrospun chitosan nanofibres had a smooth surface and round shape as compared to the silver-chitosan nanofibres with a distorted morphology. The chitosan and chitosan-silver nanofibres as well as the silver nanoparticles exhibited antimicrobial or inhibition activity against S. aureus than against E. coli. S. aureus bacterial culture showed good cell adhesion and spreading inwards into the chitosan nanofibrous membrane. The chitosan-silver nanofibres exhibited a greater minimum inhibitory concentration (MIC), followed by silver nanoparticles and then chitosan nanofibres; suggesting a synergistic effect between the chitosan and silver nanoparticles.

The IL’s used in this study were either synthesized or commercially available. Preparation of the IL’s involved 2 step processes: firstly the heating of distilled 1-methylimidazole with distilled 1-chlorobutane under reflux to obtain 1-butyl-3- methylimidazolium chloride; secondly, the metathesis reaction of sodium tetrafluoroborate with 1-butyl-3-methylimidazolium chloride to obtain 1-butyl-3- methylimidazolium tetrafluoroborate. The addition of sodium tetrafluoroborate, sodium hexafluorophosphate and lithium trifluoromethane sulfonamide with 1-butyl-3-methylimidazolium chloride produced good yields of 1-butyl-3-methylimidazolium tetrafluoroborate, 1-butyl-3-methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide respectively. The IL’s are hygroscopic and must be stored under a nitrogen atmosphere. The IL’s were analyzed using 1H and 13C NMR analysis with CDCl3 as solvent. The physical and chemical properties of these IL’s were compared to commercial products. The physical and chemical properties compared well to reference values from the literature. The physical properties measured include the density, conductivity and electrochemical window. The electrochemical window is dependant primarily on the resistance of the cation to reduction and the resistance of the anion to oxidation. The electrochemical windows of the IL’s were very similar to the reference windows obtained from literature and it can be seen that some IL’s have a slightly lower window which can be due to water present. Water content in the IL’s was determined with the use of a Karl Fischer titrator, with Hydranal 5 Composite as titrant and HPLC grade methanol as the base. The concentration of halide in the IL’s was determined with a Perkin-Elmer ICP-MS.

A number of experimental implementations of the multigrid algorithm for the solution of systems of partial differential equations have been produced. One program is applicable to simple nonlinear scalar equations, the others to linear equations, scalar and systems, which may be mildly stiff. All use nested grids and residual extrapolation techniques to compute solution and error estimates very economically. One version implements list based adaptive grids to further decrease both computation and storage needed for comparable problems. Each experiment was demonstrated using a set of problems with known solutions and the program performance or nonperformance discussed. Several techniques were examined to ensure that the system of difference equations representing a given problem would be convergent. The use of artificial viscosity was found to be practical in the general case, though for linear problems the use of one-sided differencing may be superior. / Science, Faculty of / Computer Science, Department of / Graduate

No description available.

In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.

The evaluation of infinite series plays an important part in numerical calculation. In hand calculation whenever a transcendental function is involved, one usually consults a table. Not only do the construction of the tables require the evaluation of transcendental functions, but with the advent of the electronic computer it is usually more convenient to have such evaluation carried out by the computer than to try to store a table of the necessary values to carry out the intended calculation. / Advisor: H. C. Griffith, Professor Directing Study. / Typescript. / "August 1960." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 37).

The theory of viscosity solutions was developed for certain types of nonlinear first-order and second-order partial differential equations. It has been particularly useful in describing the solutions of partial differential equations associated with deterministic and stochastic optimal control problems [16], [53]. In its classical formulation, see [16], the theory deals with solutions which are continuous functions. The concept of continuous viscosity solutions was further generalized in various ways to include discontinuous solutions with the definition of Ishii given in [71] playing a pivotal role. In this thesis we propose a new approach for the treatment of discontinuous solutions of first-order Hamilton-Jacobi equations, namely, by involving Hausdorff continuous interval valued functions. The advantages of the proposed approach are justified by demonstrating that the main ideas within the classical theory of continuous viscosity solutions can be extended almost unchanged to the wider space of Hausdorff continuous functions and the existing theory of discontinuous viscosity solutions is a particular case of that developed in this thesis in terms of Hausdorff continuous interval valued functions. Two approaches to numerical solutions for Hamilton-Jacobi equations are presented. The first one is a monotone scheme for Hamilton-Jacobi equations while the second is based on preserving total variation diminishing property for conservation laws. In the first approach, we couple the finite element method with the nonstandard finite difference method which is based on the Mickens’ rule of nonlocal approximation [9]. The scheme obtained in this way is unconditionally monotone. In the second approach, computationally simple implicit schemes are derived by using nonlocal approximation of nonlinear terms. Renormalization of the denominator of the discrete derivative is used for deriving explicit schemes of first or higher order. Unlike the standard explicit methods, the solutions of these schemes have diminishing total variation for any time step size. / Thesis (PhD (Mathematical Science))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

Thesis(M.Sc.(Chemistry)) -- University of Limpopo, 2020 / An extensive search for a highly efficient, reusable, and non-toxic adsorbent materials for the removal of organic dyes from wastewater continues to be of great importance to the world. Activated carbon is the most widely used adsorbent material for treating dye contaminants from water owing to its high removal capacity and large surface area. However, activated carbon is expensive and not easy to regenerate. Hence, the use of biodegradable, non-toxic, and cost-effective biopolymer-based hydrogel adsorbents has attracted great attention. These adsorbents have high swelling capacity and number of adsorptive functional groups to allow adsorption of methylene blue dye. Hence in this work, we present carboxymethyl cellulose crosslinked with poly (acrylic acid) incorporated with magnetic cloisite 30B clay (CMC-cl-pAA/Fe3O4-C30B) and sodium alginate crosslinked with poly (acrylic acid) incorporated with zinc oxide (SA-cl pAA/ZnO) hydrogel nanocomposites (HNCs) for the removal of methylene blue from aqueous solution. The hydrogel nanocomposites were synthesised through in situ free radical polymerisation. The structural properties of the prepared materials were studied using Fourier transform infrared (FTIR), X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), thermogravimetric analysis (TGA), and dynamic mechanical analysis (DMA). The FTIR and XRD confirmed the successful synthesis of the CMC-cl-pAA and SA-cl-pAA hydrogels, Fe3O4-C30B and ZnO nanoparticles (NPs) and their hydrogel nanocomposites. Furthermore, the co-existence of the metal oxide nanoparticles in the CMC-cl-pAA and SA-cl-pAA hydrogel matrices was confirmed by XRD. The SEM revealed that upon the incorporation of the Fe3O4- C30B NPs onto CMC-cl-pAA, the resulting material showed spherical particles of the magnetite nanoparticles on the irregular shaped hydrogel structure. As well as on the SA-cl-pAA after modification by ZnO nanoparticles, the spherical ZnO particles were embedded on the hydrogel surface. The successful modification with metal oxide nanoparticles was also confirmed by the presence of characteristic elements of the incorporated materials on the EDS. The TEM coupled with selected area electron diffraction (SAED) confirmed the presence of Fe3O4-C30B on the hydrogel structure, in which circular bright dotted lines were observed corresponding to light diffracted by the lattice planes of different energies on the Fe3O4 structure. The thermogravimetric analysis was conducted to study the thermal stability of the materials, the results showed that the incorporation of Fe3O4-C30B and ZnO nanoparticles on CMC-cl-pAA and SA-cl-pAA hydrogels, respectively improved their thermal stability. Furthermore, DMA was used to study the mechanical stability of the prepared hydrogels and their composites. In the case of CMC-cl-pAA hydrogel, the storage modulus of CMC-cl pAA/Fe3O4-C30B nanocomposite was higher than of the hydrogel, indicating improved mechanical stability, and on SA-cl-pAA hydrogel the storage modulus decreased, indicating a decrease in mechanical stability on the SA-cl-pAA/ZnO HNC. Consequently, the swelling studies revealed that the SA/AA/ZnO HNC was highly efficient for water uptake in comparison to SA/AA hydrogel. Whereas, CMC-cl pAA/Fe3O4-C30B had lower swelling capacity than CMC-cl-pAA hydrogel. Various factors influencing the adsorption of adsorbents were systematically investigated. The kinetics, isotherms, and thermodynamics of adsorption were examined, and results showed that equilibrium data fitted the Langmuir isotherm model, and the adsorption kinetics of MB followed pseudo-second-order model in both the CMC-based HNC and SA-based HNC. Maximum adsorption capacities of 1129 and 1529.6 mg/g were achieved for SA/AA hydrogel and SA/AA/ZnO HNC, respectively, in 0.25 g/L MB solution at pH 6.0 within 40 min. Whereas maximum capacities of 1165 mg/g (pH 5) and 806.51 mg/g (pH 7) for CMC-cl-pAA hydrogel and CMC-cl-pAA/Fe3O4- C30B HNC, respectively. Thermodynamic parameters for SA/AA and CMC-cl-pAA hydrogels exhibited exothermic adsorption processes and their nanocomposites SA/AA/ZnO and CMC-cl-pAA/Fe3O4-C30B exhibited endothermic nature of the adsorption processes, respectively. Moreover, the CMC-cl-pAA/Fe3O4-C30B NCH showed improved mechanical and thermal properties as compared to CMC-cl-pAA hydrogel. In contrast, the SA/AA/ZnO HNC presented outstanding reusability with relatively better adsorption efficiencies than SA/AA hydrogel. / Sasol bursary and National Research Foundation (NRF)

N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES) has been shown to cause changes in cultured endothelial cells and smooth muscle function at concentrations from 5 to 25 mM. To determine whether HEPES also affects vascular permeability, the effects of two buffers, HEPES and phosphate, were compared in isolated perfused rabbit lungs. Hemodynamic parameters and vascular protein permeability-surface area products (PS) were measured after perfusion with the buffers. Endothelial permeability was measured for an anionic and a cationic albumin to assess the charge effects of the zwitterion buffer. With HEPES, there were no changes in vascular pressure or resistance but permeability was affected. Cationic albumin permeability increased with 12 mM HEPES (8.7(phosphate) → 30(12 mM HEPES) x ml · min-1 · g dry lung-1 x 10-2) as did the anionic albumin PS (2.7(phosphate) → 3.52(12 mM HEPES). The cationic PS returned to baseline (8.1(60 mM HEPES)) at 60 mM HEPES, but the anionic PS did not change from the 12 mM HEPES (4.01(60 mM HEPES)). In summary, we find that HEPES is not innocuous. Although hemodynamic parameters did not change, endothelial permeability was increased when HEPES was used at normal concentrations. Therefore, HEPES should be used with caution as a physiological buffer in perfused organ systems.

No description available.