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07 September 2018 Photo Stephen Collett
Mathematician makes popular contribution to science Prof Atangana
Prof Atangana is the first African under 40 years of age to be selected as African Academic of Science affiliated in Mathematics. He recently delivered his inaugural lecture and is pictured with Eelco Lukas, Director of the Institute for GroundwaterStudies at the UFS (middle) and Prof Hendri Kroukamp, Acting Vice-Rector: Academic

Prof Abdon Atangana, researcher in the Institute for Groundwater Studies at the University of the Free State (UFS), recently delivered his inaugural lecture on the topic: Understanding God’s Nature with Non-Local Operators.

His research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Prof Atangana is the founder of the fractional calculus with non-local and non-singular kernels popular in applied mathematics today. He has introduced more than 12 mathematical operators, most of which bear his name (such as the Atangana-Baleanu fractional integral).

He stated: “We will not stop until we change the classical view of doing mathematics. Mathematics is not a subject but a tool given to mankind by God to understand nature. One single mathematical operator cannot portray God’s nature accurately. Therefore the Atangana Baleanu was suggested.”

New weapons

Most physical problems can be expressed in terms of mathematical formulations called differential equations. According to him the differential equation’s aim is to analyse, understand, and predict the future of a physical problem. Prof Atangana introduced the Atangana-Baleanu fractional integral. This brought new weapons into applied mathematics to model complex real-world problems more accurately.

Prof Atangana explained: “The Atangana-Baleanu fractional derivative is able to describe real-world problems with different scales, or problems that change their properties during time and space for instance, the spread of cancer, the flow of water within heterogeneous aquifers, movement of pollution within fractured aquifers, and many others. This crossover behaviour is observed in many empirical systems.”

Sudden change

The Atangana-Baleanu fractional derivative is also able to describe physical or biological phenomena, such as a heart attack, the physiological progression from life to death, structural failure in an aeroplane, and many other physical occurrences with sudden change with no steady state.

The new differential and integral operators are nowadays in fashion and are being applied with great success in many fields to model complex natural phenomena. It is believed that the future of modelling complex real-world problems relies on these non-local operators.

News Archive

Fracking in the Karoo has advantages and disadvantages
2012-05-25

 

Dr Danie Vermeulen
Photo: Leatitia Pienaar
25 May 2012

Fracking for shale gas in the Karoo was laid bare during a public lecture by Dr Danie Vermeulen, Director of the Institute for Groundwater Studies (IGS). He shared facts, figures and research with his audience. No “yes” or “no” vote was cast. The audience was left to decide for itself.

The exploitation of shale gas in the pristine Karoo has probably been one of the most debated issues in South Africa since 2011.
 
Dr Vermeulen’s lecture, “The shale gas story in the Karoo: both sides of the coin”, was the first in a series presented by the Faculty of Natural and Agricultural Science under the theme “Sustainability”. Dr Vermeulen is a trained geo-hydrologist and geologist. He has been involved in fracking in South Africa since the debate started. He went on a study tour to the USA in 2011 to learn more about fracking and he visited the USA to further his investigation in May 2012.
 
Some of the information he shared, includes:

- It is estimated that South Africa has the fifth-largest shale-gas reserves in the world, following on China, the USA, Argentina and Mexico.
- Flow-back water is stored in sealed tanks and not in flow-back dams.
- Fracturing will not contaminate the water in an area, as the drilling of the wells will go far deeper than the groundwater aquifers. Every well has four steel casings – one within the other – with the gaps between them sealed with cement.
- More than a million hydraulic fracturing simulations took place in the USA without compromising fresh groundwater. The surface activities can cause problems because that is where man-made and managerial operations could cause pollution.
- Water use for shale-gas exploration is lower than for other kinds of energy, but the fact that the Karoo is an arid region makes the use of groundwater a sensitive issue. Dr Vermeulen highlighted this aspect as his major concern regarding shale-gas exploration.
- The cost to develop is a quarter of the cost for an oil well in the Gulf of Mexico.
- Dolerite intrusions in the Karoo are an unresearched concern. Dolerite is unique to the South African situation. Dolerite intrusion temperatures exceed 900 °C.

He also addressed the shale-gas footprint, well decommissioning and site reclamation, radio activity in the shale and the low possibility of seismic events.
 
Dr Vermeulen said South Africa is a net importer of energy. About 90% of its power supply is coal-based. For continued economic growth, South Africa needs a stable energy supply. It is also forecast that energy demand in South Africa is growing faster than the average global demand.
 
Unknowns to be addressed in research and exploration are the gas reserves and gas needs of South Africa. Do we have enough water? What will be the visual and social impact? Who must do the exploration?
 
“Only exploration will give us these answers,” Dr Vermeulen said.

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