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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

Water research aids decision making on national level
2015-05-25

Photo: Leonie Bolleurs

With water being a valuable and scarce resource in the central regions of South Africa, it is no wonder that the UFS has large interdisciplinary research projects focusing on the conservation of water, as well as the sustainable use of this essential element.

The hydropedology research of Prof Pieter le Roux from the Department of Soil, Crop and Climate Sciences and his team at the UFS focuses on Blue water. Blue water is of critical importance to global health as it is cleared by the soil and stored underground for slow release in marshes, rivers, and deep groundwater. The release of this water bridges the droughts between showers and rain seasons and can stretch over several months and even years. The principles established by Prof Le Roux, now finds application in ecohydrology, urban hydrology, forestry hydrology, and hydrological modelling.

The Department of Agricultural Economics is busy with three research projects for the Water Research Commission of South Africa, with an estimated total budget of R7 million. Prof Henry Jordaan from this department is conducting research on the water footprint of selected field and forage crops, and the food products derived from these crops. The aim is to assess the impact of producing the food products on the scarce freshwater resource to inform policy makers, water managers and water users towards the sustainable use of freshwater for food production.

With his research, Prof Bennie Grové, also from this department, focuses on economically optimising water and electricity use in irrigated agriculture. The first project aims to optimise the adoption of technology for irrigation practices and irrigation system should water allocations to farmers were to be decreased in a catchment because of insufficient freshwater supplies to meet the increasing demand due to the requirements of population growth, economic development and the environment.

In another project, Prof Grové aims to economically evaluate alternative electricity management strategies such as optimally designed irrigation systems and the adoption of new technology to mitigate the substantial increase in electricity costs that puts the profitability of irrigation farming under severe pressure.

Marinda Avenant and her team in the Centre for Environmental Management (CEM), has been involved in the biomonitoring of the Free State rivers, including the Caledon, Modder Riet and part of the Orange River, since 1999. Researchers from the CEM regularly measures the present state of the water quality, algae, riparian vegetation, macro-invertebrates and fish communities in these rivers in order to detect degradation in ecosystem integrity (health).

The CEM has recently completed a project where an interactive vulnerability map and screening-level monitoring protocol for assessing the potential environmental impact of unconventional gas mining by means of hydraulic fracturing was developed. These tools will aid decision making at national level by providing information on the environment’s vulnerability to unconventional gas mining.

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