Applied Mathematics
Differential Equations, Theoretical PhysicsDr JM Manale Tel: +27 12 429 8732 My research interests include the interplay of discrete and continuous variables and functions. Their applications to mechanics, symmetry, finite elements, and differential equations in general. Fluid MechanicsDr R Maritz Tel: +27 12 429 8015 The application of Fluid Mechanics to the physiology of the cardiovascular system has been explored by many scientists in the last couple of years. The main function of blood is to supply nutrients to the tissues and to remove waste products. Blood is a circulating substance composed of plasma, red blood cells, white blood cells and platelets. Blood also enables cells and different substances (like lipids, hormone, amino acids) to be transported between tissues and organs. The researcher in this area has plenty possibilities of modelling the flow of blood through arteries, through capillaries, permeable boundaries in the formation of the cerebrospinal fluids, in the lymphatic system ext. Blood can be modelled as a Navier Stokes Fluid or as a mixture or as a viscous elastic fluid, it all depends on the focus of the research. These partial differential equations, with applicable boundary conditions can then be solved or studied in various ways. I prefer to use the Finite Element method to investigate the existence and uniqueness of a numerical solution. The environment is Sobolev Spaces, which is a research area on its own. Fluid MechanicsDr GM Moremedi Tel: +27 12 429 6601 Slow viscous fluids past bodies are investigated. The fluids are immiscible, incompressible and viscous Newtonian fluids. The research is conducted both analytically and numerically. The initial work is on slow steady problems and subsequently unsteady flows will be considered. Fluid Mechanics, Fibres Suspension and Blood FlowsDr JMW Munganga Tel: +27 12 429 6576 The use of fibre composite compounds has grown in commercial importance in recent years due to desirable cost and performance characteristics, especially in relation to mechanical and thermal properties. Fibre composites are generally formed by automated methods such as injection The properties of fibre suspension composite parts depend highly on the way the part is manufactured. If such a material is formed, the flow changes the orientation of the fibres. As the resin or moulding compound deforms to achieve the desired shape, the orientation of fibres is changing. Fibre orientation changes stop when the matrix solidifies, and the orientation pattern becomes part of the microstructure of the finished article. The fibre orientation pattern is the dominant structural feature of a fibre composite. The composite is stiffer and stronger in the direction of greatest orientation, and weaker and more compliant in the Our research is interested to answer the following questions, no matter which
We investigate the circumstances under which the constitutive equations are consistent with the Another aspect of our research is to apply the knowledge of the orientation of fibres to study the effect of suspended particles in Blood. Relastivistic CosmologyProf WM Lesame Tel: +27 12 429 6266 His research interest is in relativistic cosmology. This involves developing cosmological models using Einstein's theory of general relativity. His main focus is in the analysis of consistency conditions of various cosmological models. Stochastic Differential EquationsDr E Rapoo Tel: +27 12 429 6087 Her research field is the theory and applications of stochastic processes, in particular stochastic differential equations. Stochastic differential equations provide a mathematically rigorous way of introducing random fluctuations into mathematical models, and accordingly the theory has many applications in various disciplines. The theory is based on relatively recent developments of martingale theory and stochastic integration, and many areas still remain uncharted. She is currently focusing on approximation and numerical analysis of stochastic differential equations, as well as the more theoretical problem of extending the scope of permitted noise processes in stochastic differential equations.
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