Graduate Student Workshop Problems
Problem 1: Management of rhino removals to maximise the reproductive potential of the rhino population
Presenter: Professor Norman Owen-Smith, School of Animal, Plant and Environmental Sciences, University of the Witwatersrand, Johannesburg
Problem statement
Especially for black rhinos, the objective for managers of extensive populations in wildlife reserves is to maximize the productive potential of the rhino population, so that surplus animals can be sold to restock intensively managed properties and extensive areas where populations have been depressed by illegal offtakes. Theoretically, this implies that populations should be held somewhat below the maximum stocking density (or “carrying capacity”) that can be sustained, to alleviate food shortfalls and thereby stimulate reproduction. However, this has not worked in practice because rhinos living in a home range in one place do not directly experience any benefit from rhinos that have been removed somewhere else. However, in the longer term the vacancies generated by removals could be recolonised by young rhinos dispersing from their natal areas to find somewhere less crowded to settle. The complication is that settlement may depend on finding signs that other rhinos are already living there, especially for females. This may be less of an inhibition for males forced to move because of territorial exclusions. But these young males are commonly removed as “surplus” to the reproductive potential of the population, and are in danger of being killed by territory-holding males if they are left. Areas that are left vacant may also deteriorate in their capacity to support rhinos, or become occupied by other competing herbivores. The problem to be addressed is, how best should rhino removals be conducted, in space and time and with regard to sex, to maximize the reproductive potential of the population?
Download:
EmsliePachyderm2001.pdf, Richard H. Emslie
HrabarAnimCons2005.pdf: Pilanesberg National Park, South Africa, Halszka Hrabar† and Johan T. du Toit
LinklaterSAJWR2010.pdf, Wayne L. Linklater & Ian R. Hutcheson
ReidOryx2007.pdf,South Africa, for Critically Endangered black rhinoceros Diceros bicornis, Caroline Reid, Rob Slotow, Owen Howison and Dave Balfour
Brodie et al BRhinoAnimCons2011.pdf, J. F. Brodie, J. Muntifering, M. Hearn, B. Loutit, R. Loutit, B. Brell, S. Uri-Khob, N. Leader-Williams & P. du Preez
Rhino Model Conservation.pdf
Presentation of problem statement
Rhino Model Conservation.pdf
Presentation of problem solution
finalpresentharvestingrhino.pdf
Problem 2: Reverse flow reactor for greenhouse gas conversion
Presenter: Professor Neville Fowkes, School of Mathematics and Statistics, University of Western Australia, Perth, Australia
Problem statement
Methane is produced by decaying organic material; landfills, wetlands, waste treatment plants are sources. Also forest fires and animals produce large quantities. As a greenhouse gas methane has a warming potential twenty five times greater than carbon dioxide, so removing it from the atmosphere is important for greenhouse reasons. Furthermore methane is a valuable energy source, so that an efficient conversion of methane to carbon dioxide would be doubly advantageous and this can be achieved by feeding oxygen or (air) and methane into a reactor. A catalyst is required to accelerate the conversion and normally preheating would be required to reach the required reaction temperature. However by reversing the flow of reacting gases one can avoid this preheating. Our aim is to model the reactor and thus determine an optimal design.
Presentation of problem statement
RCRbMISG2012.pdf
Presentation of problem solution
ReverseflowreactorMISG2013.pdf
Problem 3: Design of an ultrafiltration unit
Presenter: Professor Neville Fowkes, School of Mathematics and Statistics, University of Western Australia, Perth, Australia
Problem statement
We are concerned with the design of a novel filter for the purification of water, the treatment of wastes, the separation of oil from water etc. The heart of the filtration system is a bundle of about 3000 very small (radius 330 m) hollow fibres made of plastic foam. The fibres have millions of tiny holes (radius 0.1 m) in their walls which allow the pure water through (for example) but filter out small particles. The fibres are contained in a cartridge (15-50 cm long, diameter 7 cm) and the impure water is circulated around the fibres at low pressure (100 kPa) and the permeate moves almost radially through the fibres and then axially along the insides of the fibres (or the lumen) to be gathered at the cartridge ends. The filtration unit is novel in that the filtration surface is the outside of the tubes not the inside as one would expect.
Periodically the fibres have to be cleaned and this is done by exposing the ends of the lumen to a high pressure, short duration air pulse.
The issues are: What length and radius fibres? What pore size? How to optimize the operation of the filter cycle?
Download:
ultrafiltrationMISG2013.pdf, Neville Fowkes
Presentation of problem statement
ultrafiltrationbMISG2012.pdf
Presentation of problem solution
Design of an ultrafiltration unit MISG2013.pdf - presentation
Problem 4: The quadratic assignment problem
Presenter: Professor Montaz Ali, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg
Problem statement
The quadratic assignment problem is one of the most difficult combinatorial optimization problems. It has many applications including computer manufacturing, scheduling, building layout design, process communications and forest management. Due to the complex nature of the problem many mathematical formulations have been suggested. However the exact solution is still a challenge, and heuristics solution methods are generally used. Various formulations of the problem will be considered. Appropriate heuristics will be applied for the solution of a number of problem instances.
Download:
Quadratic Assignment Problem MISG2013.pdf - presentation