The flow of water through soil is a crucial aspect of agriculture, and a research collaboration between La Trobe University and Kyushu University in Japan has been studying the theoretical mathematical framework of the process.
The research is headed by Professor Philip Broadbridge from La Trobe University’s Department of Mathematics and Statistics and Professor Kenji Kajiwara from the Institute of Mathematics for Industry (IMI) at Kyushu University in Japan. They formed a strong working relationship after meeting five years ago at an international conference.
“We both found we had an interest in the application of discrete integrable systems to boundary value problems,” says Professor Kajiwara. “Professor Broadbridge is interested in continuum aspects, while my focus is discrete. We’ve found a common ground for mathematical modelling and It has led to a productive collaboration for us.”
Their joint research has resulted in the publication of a paper in the journal Studies in Applied Mathematics with more in development.
"There is a lot of potential for practical applications when approximating the conservation laws in nature, in particular for water volume,” says Professor Broadbridge. “Integrable discrete systems can model water flow through unsaturated soil, which is very important in fields such as agriculture and civil engineering.
“For example, a classic boundary value problem would be to predict the water distribution beneath the soil surface that has a prescribed irrigation schedule. External factors such as water absorption by roots during the supply to plants could help to establish fundamental discrete model practical applications.”
This is just one of a number of collaborations between La Trobe University and Kyushu University, with further projects in agriculture, education and political sciences. The hope is that these will lead to a closer formal working relationship between the two universities.
La Trobe University also hosts the Australia Branch of the Institute of Mathematics for Industry, a Joint Use Institute funded by the Japanese Government. A current visitor from Kyushu is Dr Daniel Gaina who works on the logical foundations of computer science.
“Kyushu University has the reputation as one of the foremost institutions for mathematical sciences in the Asia Pacific, and there is much we can gain from working with each other,” says Professor Broadbridge. “It’s a crucial part of maintaining a strong regional scientific community.”