Inventing the Sader Method

Most of us don’t get an opportunity to drive or operate an atomic force microscope, but if we did we could use the official ‘Sader method’ to calibrate this machine that reveals the atomic and molecular details of materials and biological specimens. The ‘Sader Method’ is named after University of Melbourne’s Professor John Sader from the Department of Mathematics and Statistics. While having anything named after you is a great lifetime achievement it’s the unofficial Sader method that is also worth acknowledging, and that is the daily passion to pursue the mathematical problems of the physical world with a sense of gleeful adventure. 

It’s not usual for professors to start their academic life in one field and end up mastering another. Professor Sader is one of these cross-disciplinary adventurers. He started out as an engineer but ‘extrapolated’ into a mathematician.

“I am actually an electrical engineer by training, and my PhD was in fibre optics. I essentially solved Maxwell’s equations on how light propagates along optical fibres. My very first research papers were in this area. 

“When I finished my PhD, I recognised my passion was in the mathematics and not so much in engineering. So I started looking around for positions in mathematics and luckily I landed a postdoctoral position in applied mathematics in the area of fluid mechanics. The academic who took a chance with me and employed me was Professor Lee White. He is retired now – he actually used to have this very office I now occupy. I remember he handed me a textbook on fluid and solid mechanics, something I had never studied before and said ‘here is the textbook – we are going to do some research on this,’ and we did, and I still do.” 

One of Professor Sader’s latest papers describes the mathematics of how liquids behave at the nano-level when pushed very quickly. 

“Using a combination of maths and experiment, we found that simple liquids like water can act like solids. In the nano-scale world classical fluid dynamics may no longer hold true.”

The predictive power of the mathematics behind this finding is vital as industry strives to enhance the performance of mechanical sensors through miniaturisation. 

“Measuring the mass of a biomolecule at such small scales can be very challenging. So you need to have the right approach mathematically for design and characterisation.”

Understanding how these nano-level sensors operate in a gas, like air, is also a big problem. 

“There’s a lot of trial-and-error design going on, because there is no practical maths available to design these sensors. So I thought back to my engineering days and wondered if I could develop a formula whereby people could make a big object in the micro world, which is relatively easy to do, and measure its behaviour to predict how a small nano-scale one works.” 

In the end, he discovered a beautifully elegant formula that took into account the differences in the micro and nano-worlds, but he had no idea if the formula worked in the real world of engineering design. 

“My colleagues at the California Institute of Technology offered to test it out; they made six sensor devices, shrunk them in all three dimensions and tested out my formula. It worked beautifully,” Professor Sader says with a gleeful smile, delighted that his curiosity, can-do and this-will-be-fun attitude had paid off.

“The beauty of mathematics is that it’s a universal language that can be used to understand our world, so mathematicians are able to work in many different disciplines and industries.”

For example, their expertise is useful in spacecraft design, communications technology, understanding the way materials behave, and even financial institutions like banks.

“A couple of my students have gone to work for banks developing financial products, as the banks need people with good quantitative skills. I had a coffee with one of them the other day. He seems to be having fun resolving the analytics. But its the mathematics that drives us, we love a mathematical adventure that delivers a useful solution.”

This is the unofficial Sader Method, which works for both its inventor, his diverse research group, and which infects the next generation of successful mathematicians.