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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.

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Well-established root system important for sustainable production in semi-arid grasslands
2015-02-24

Plot layout where production and root studies were done
Photo: Supplied

The importance of a well-established root system for sustainable production in the semi-arid grasslands cannot be over-emphasised.

A study of Prof Hennie Snyman from the Department of Animal and Wildlife and Grassland Sciences at the University of the Free State is of the few studies in which soil-water instead of rainfall has been used to estimate above- and below-ground production of semi-arid grasslands. “In the past, plant ecological studies have concentrated largely on above-ground parts of the grassland ecosystem with less emphasis on root growth. This study is, therefore, one of the few done on root dynamics in drier areas,” said Prof Snyman.

The longevity of grass seeds in the soil seed bank is another aspect that is being investigated at present. This information could provide guidelines in grassland restoration.

“Understanding changes in the hydrological characteristics of grassland ecosystems with degradation is essential when making grassland management decisions in arid and semi-arid areas to ensure sustainable animal production. The impact of grassland degradation on productivity, root production, root/shoot ratios, and water-use efficiency has been quantified for the semi-arid grasslands over the last 35 years. Because of the great impact of sustainable management guidelines on land users, this study will be continuing for many years,” said Prof Snyman.

Water-use efficiency (WUE) is defined as the quantity of above- and/or below-ground plant produced over a given period of time per unit of water evapotranspired. Sampling is done from grassland artificially maintained in three different grassland conditions: good, moderate, and poor.

As much as 86, 89 and 94% of the roots for grasslands in good, moderate and poor conditions respectively occur at a depth of less than 300 mm. Root mass is strongly seasonal with the most active growth taking place during March and April. Root mass appears to be greater than above-ground production for these semi-arid areas, with an increase in roots in relation to above-ground production with grassland degradation. The mean monthly root/shoot ratios for grasslands in good, moderate, and poor conditions are 1.16, 1.11, and 1.37 respectively. Grassland degradation lowered above- and below-ground plant production significantly as well as water-use efficiency. The mean WUE (root production included) was 4.79, 3.54 and 2.47 kg ha -1 mm -1 for grasslands in good, moderate, and poor conditions respectively.

These water-use efficiency observations are among the few that also include root production in their calculations.

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