Browsing Applied Mathematics by Title
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Generalized travelling wave solutions for a microscopic chemotaxis model.
(2014)In biology cell migration is one of the most critical processes, for it is decisive in the mechanisms leading to the beginning of life. The collective migration of cells via wave motion plays a key role in understanding ... 
Group analysis of equations arising in embedding theory.
(2010)Embedding theories are concerned with the embedding of a lower dimensional manifold (dim = n, say) into a higher dimensional one (usually dim = n+1, but not necessarily so). We are concerned with the particular case of ... 
Group theoretic approach to heat conducting gravitating systems.
(20150107)We study shearfree heat conducting spherically symmetric gravitating fluids defined in four and higher dimensional spacetimes. We analyse models that are both uncharged and charged via the pressure isotropy condition ... 
Identifying and modeling the dynamics of a core cancer subnetwork.
(2011)Many recent studies have shown that the initiation of human cancer is due to the malfunction of some genes at the Rcheckpoint during the G1toS transition of the cell cycle. Identifying and modeling the dynamics of ... 
Impact of exogenous reinfection on TB infection in a genetically susceptible population.
(20131217)In this study we investigated the impact of exogenous reinfection on genetically resistant and genetically sensitive sub populations. We qualitatively analysed the dynamics of TB by assuming that TB is transmitted in two ... 
Initial conditions of the universe : signatures in the cosmic microwave background and baryon acoustic oscillations.
(2012)In this thesis, we investigate the signatures of isocurvature initial conditions in the cosmic microwave background (CMB) through the temperature and polarization anisotropies, and in the largescale structure distribution ... 
Interative approaches to convex feasibility problems.
(2001)Solutions to convex feasibility problems are generally found by iteratively constructing sequences that converge strongly or weakly to it. In this study, four types of iteration schemes are considered in an attempt to ... 
Mathematical modeling of cancer treatments and the role of the immune system response to tumor invasion.
(2015)Despite the success of traditional cancer treatments, a definite cure to several cancers does not exist. Further, the traditional cancer treatments are highly toxic and have a relatively low efficacy. Current research ... 
Matrices of graphs and designs with emphasis on their integral eigenpair balance characteristic.
(20150105)The interplay between graphs and designs is well researched. In this dissertation we connect designs and graphs entirely through their associated matrices – the incidence matrix for designs and the adjacency matrix for ... 
Matrix models of population theory.
(20140512)Nonnegative matrices arise naturally in population models. In this thesis, we first study Perron Frobenius theory of nonnegative irreducible matrices. We use this theory to investigate the asymptotic behaviour ... 
A modelling approach for determining the freshwater requirements of estuarine macrophytes.
(1998)Increased abstraction of water in the catchment results in a reduced or altered pattern of river flow and this holds serious consequences for the downstream estuarine ecosystem. In South Africa this is a serious concern ... 
Modelling the response of cytotoxic tlymphocytes in controlling solid tumour invasion.
(20131220)We present mathematical models to study the mechanism of interaction of tumour infiltrating cytotoxic lymphocytes (TICLs) with tumour cells. We focus on the phase spaces of the systems and the nature of the solutions for ... 
Modelling waterborne diseases.
(20150320)Waterborne diseases are among the major health problems threatening the life of individuals globally. This thesis investigates the dynamics of waterborne disease under different conditions and consequently determines ... 
Models in isotropic coordinates with equation of state.
(20150904)In this thesis we consider spacetimes which are static and spherically symmetric related to the Einstein and EinsteinMaxwell system of equations in isotropic coordinates. We study both neutral and charged matter ... 
New classes of exact solutions for charged perfect fluids.
(20140328)We investigate techniques to generate new classes of exact solutions to the Einstein Maxwell field equations which represent the gravitational field of charged perfect fluid spherically symmetric distributions of ... 
New models for quark stars with charge and anisotropy.
(2014)We find new classes of exact solutions for the EinsteinMaxwell field equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field ... 
New realistic solutions for charged matter with an equation of state.
The purpose of this thesis is to provide new exact solutions to the EinsteinMaxwell system which are physically reasonable. We assume that the spacetime is static and spherically symmetric with a charged anisotropic ... 
Noncircularity of beams in the CMB polarization power spectrum estimation.
(20150105)Precise measurements of the Cosmic Microwave Background (CMB) anisotropies have been one of the foremost concerns in modern cosmology as it provides valuable information on the cosmology of the Universe. However, an ... 
Nonclassical solutions of hyperbolic conservation laws.
This dissertation studies the nonclassical shock waves which appears as limits of certain type diffusivedispersive regularisation to hyperbolic of conservation laws. Such shocks occur very often when the ux function ... 
On new and improved seminumerical techniques for solving nonlinear fluid flow problems.
(2012)Most real world phenomena is modeled by ordinary and/or partial differential equations. Most of these equations are highly nonlinear and exact solutions are not always possible. Exact solutions always give a good account ...