Optimizing Talbot's Contours for the Inversion of the Laplace Transform

Talbot's method for the numerical inversion of the Laplace Transform consists of numerically integrating the Bromwich integral on a special contour by means of the trapezoidal or midpoint rules. In this paper we address the issue of how to choose the parameters that define the contour, for the particular situation when parabolic PDEs are solved. In the process the well known subgeometric convergence rate O(e -c \sqrt N) of this method is improved to the geometric rate O(e -cN) with N the number of nodes in the integration rule. The value of the maximum decay rate c is explicitly determined. Numerical results involving two versions of the heat equation are presented. With the choice of parameters derived here, the rule-of-thumb is that to achieve an accuracy of 10 -l at any given time t, the associated elliptic problem has to be solved no more that l times.\ud \ud Supported by the National Research Foundation in South Africa under grant NRF528

Parabolic and Hyperbolic Contours for Computing the Bromwich Integral

Some of the most effective methods for the numerical inversion of the Laplace transform are based on the approximation of the Bromwich contour integral. The accuracy of these methods often hinges on a good choice of contour, and several such contours have been proposed in the literature. Here we analyze two recently proposed contours, namely a parabola and a hyperbola. Using a representative model problem, we determine estimates for the optimal parameters that define these contours. An application to a fractional diffusion equation is presented.\ud \ud JACW was supported by the National Research Foundation in South Africa under grant FA200503230001

Land reform, equity and growth in South Africa: A comparative analysis

PhD - Political StudiesIn this thesis, the following methods were used to assess the South African Land Reform Programme; historically important documents, policy papers, library research, qualitative interviews and a comparative analysis, which included a wide range of African, Asian and Latin American countries. The aim of the thesis was twofold. First, to assess whether an essentially market-based land reform programme might bring about equity and growth. Second, to draw lessons and make recommendations based on an analysis of land reform programmes in other countries, as well as on South African case studies. Emerging issues related to farm size, food security, poverty alleviation, appropriate credit policies, the limitations of market-based reform, the problems relating to bureaucratic reform programmes, the importance of beneficiary participation, the necessity to develop a gender sensitive programme and, finally, the undeniable relationship between violence and land reform. This thesis highlights the link between the omission of gender in policy development and subsequent policy failures. It highlights the relationship between land reform and violence and, it points to the varied nature of rural livelihoods. There is also a focus on how South African land reform policies developed and an analysis of the influence that the various actors, who participated in this process, had on subsequen

A Numerical Methodology for the Painlevé Equations

The six Painlevé transcendents PI – PVI have both applications and analytic properties that make them stand out from most other classes of special functions. Although they have been the subject of extensive theoretical investigations for about a century, they still have a reputation for being numerically challenging. In particular, their extensive pole fields in the complex plane have often been perceived as ‘numerical mine fields’. In the present work, we note that the Painlevé property in fact provides the opportunity for very fast and accurate numerical solutions throughout such fields. When combining a Taylor/Padé-based ODE initial value solver for the pole fields with a boundary value solver for smooth regions, numerical solutions become available across the full complex plane. We focus here on the numerical methodology, and illustrate it for the PI equation. In later studies, we will concentrate on mathematical aspects of both the PI and the higher Painlevé transcendents

User's guide to resin infusion simulation program in the FORTRAN language

RTMCL is a user friendly computer code which simulates the manufacture of fabric composites by the resin infusion process. The computer code is based on the process simulation model described in reference 1. Included in the user's guide is a detailed step by step description of how to run the program and enter and modify the input data set. Sample input and output files are included along with an explanation of the results. Finally, a complete listing of the program is provided

Towards understanding Regge trajectories in holographic QCD

We reassess a work done by Migdal on the spectrum of low-energy vector mesons in QCD in the light of the AdS-QCD correspondence. Recently, a tantalizing parallelism was suggested between Migdal's work and a family of holographic duals of QCD. Despite the intriguing similarities, both approaches face a major drawback: the spectrum is in conflict with well-tested Regge scaling. However, it has recently been shown that holographic duals can be modified to accomodate Regge behavior. Therefore, it is interesting to understand whether Regge behavior can also be achieved in Migdal's approach. In this paper we investigate this issue. We find that Migdal's approach, which is based on a modified Pade approximant, is closely related to the issue of quark-hadron duality breakdown in QCD.Comment: 17 pages, 1 figure. Typos fixed, references added, improved discussion. Minor changes to match the journal versio

An infiltration/cure model for manufacture of fabric composites by the resin infusion process

A 1-D infiltration/cure model was developed to simulate fabrication of advanced textile composites by the resin film infusion process. The simulation model relates the applied temperature and pressure processing cycles, along with the experimentally measured compaction and permeability characteristics of the fabric preforms, to the temperature distribution, the resin degree of cure and viscosity, and the infiltration flow front position as a function of time. The model also predicts the final panel thickness, fiber volume fraction, and resin mass for full saturation as a function of compaction pressure. Composite panels were fabricated using the RTM (Resin Transfer Molding) film infusion technique from knitted, knitted/stitched, and 2-D woven carbon preforms and Hercules 3501-6 resin. Fabric composites were fabricated at different compaction pressures and temperature cycles to determine the effects of the processing on the properties. The composites were C-scanned and micrographed to determine the quality of each panel. Advanced cure cycles, developed from the RTM simulation model, were used to reduce the total cure cycle times by a factor of 3 and the total infiltration times by a factor of 2