Thinking small

Clever mathematicians use clever machines to delve into the structures of small, complex materials.

Crouched on the side of a hill at midnight, Dr Adrian Sheppard uses a thin torch beam to examine a map of the land around him. He consults with his team-mates about which checkpoint they should hit next and how many more they can reach before sunrise.

“It’s a really nice challenge, particularly in the middle of the night, to be sitting miles from the nearest track in a beautiful place, to be able to look at a map, to know where you are, and make sense of these complex contour lines,” he says.

Making sense of the contour lines has paid off for Sheppard. He has twice been part of the nation’s top team for rogaining, an extreme sport that combines endurance, orienteering and cross-country running. His tall, lean runner’s frame is only half the equation. The other is a mind with an appetite for spatial problem solving.

Sheppard’s skill at rogaining may be concerned with understanding space on a large scale, but his day job requires that he think much, much smaller. He works at ANU as part of the porous media group in the Department of Applied Mathematics to understand the structures of complex materials like rocks, organic shells and paper. The research has potential impacts for all endeavours involving porous matter, ranging from the kinds of materials used in nappies through to methods for extracting petroleum from the ground. These new understandings are made possible through some complex mathematical thinking and clever technology.

“Our X-ray computer tomography (CT) facility is one of the best in the world,” Sheppard says. “When it comes to mapping the fine structure of complex materials over length scales of microns to millimetres, there are few other facilities anywhere that can match our capacity. There may be a handful of third-generation synchrotrons out there that could capture finer detail, but those are billion dollar facilities. By contrast, our CT facility is smaller, cheaper and far more flexible to use.”

CT uses X-rays to take several thousand projection images of a sample of material, and then uses a computer to combine the information from these projections to build a 3D image of the material’s structure. The sample is rotated in tiny steps during the imaging so that each projection provides a slightly different perspective. These multiple perspectives are then processed to create the detailed image.

The information for each image can be enormous, typically containing tens of gigabytes of information and requiring hundreds of gigabytes of computer system memory to analyse. This is especially the case for the labyrinthine structure of some rocks, an area of special interest to Sheppard. Making sense of these vast amounts of data demands the grunt of Australia’s largest supercomputer, the Australian Partnership for Advanced Computing’s National Facility, based at ANU.

“Before CT, people could take the rocks they’d collected from core samples and they’d get a few data points, but they might not quite understand what had caused the behaviours that they’d seen in their experiments,” Sheppard says. “If you can take that piece of rock and make a big, detailed three-dimensional picture of it, and then apply some sophisticated techniques for understanding that image, then you’ve got a much better handle on understanding why it is like it is and what behaviour might be expected elsewhere in the strata.

“Having detailed 3D images of a sample is great, but it’s really only the first step towards understanding the structure, especially when it’s highly irregular like many rock types. One approach is to make sense of the objects by transforming them into networks based on the voids and connective passages embedded through their structure.

“Of course, with oil prices going through the roof this position is being reconsidered and now there’s strong interest in understanding how more of the oil might be brought up. Techniques involving the pumping of various gases down into the oil-bearing rock to force the oil up are being considered, but to really understand what’s possible you need to understand the porous network in the rock and how it interacts with oil, water and gas.

“Understanding these complex structures can be fiendishly difficult because you can’t reduce them down to a simple formula. However, our approach here at Applied Maths in visualising the three-dimensional structures and then modelling them as complex networks is proving very fruitful.

“We describe and ‘type’ the rock using an approach that’s both reductionist and holistic. By partitioning the structure into small components, we can analyse each piece in reductionist isolation, but also step back and study how all these pieces connect together to form a huge complex network.”

Another advantage of the CT facility is its ability to conduct dynamic experiments while capturing images. Most other X-ray CT machines are encased in small lead boxes in order to contain the potentially harmful X-rays. At ANU, an entire room has been fitted with the protective lining, meaning that the researchers can run more detailed experiments. For example, they can take CT projections of two different fluids moving through a porous material, allowing them to see how the liquids flow through the myriad channels and chambers within the structure.

Such sophisticated technology enables detailed analysis, but it is researchers like Sheppard who do the legwork and make the creative leaps that drive the field of study forward. He and his colleagues in Applied Maths have spent many hours developing robust algorithms, or mathematical solutions, which underpin the study of complex materials.

“The data sets involved are enormous, and processing and manipulating these models requires tremendous computer grunt and parallel processing capacity,” he explains. “One of the areas where Applied Maths is leading the way has been in the development of algorithms that can cope with the parallel processing required to work with these data sets.

“It’s not just about having good imaging technology. It’s just as much about having a suite of skills in image processing, program writing, network modelling and synthesis. Applied Maths possesses a diverse team of researchers skilled in a wide variety of fields. You need a transdisciplinary approach if you’re going to tackle complexity. All of the skills you need to extract a better understanding of complex structures are readily on tap here. It’s a great place to be if you want to push your understanding of complex materials to the next level.”

Sheppard is full of praise for his colleagues, saying none of his work would be possible without Tim Senden and Tim Sawkins. They designed the experimental CT facility at ANU from the ground up, sourcing the more standard components ‘off the shelf’ and having custom components built to sufficient precision. Sheppard also mentions Arthur Sakellariou for writing the code used to reconstruct the projection images, Christoph Arns for his modelling skills, and Mark Knackstedt for his support of the group’s long-term research.

Rocks are just one of many materials under the microscope at the department. By studying how ink interacts with paper, the researchers are helping to develop innovations for the printing industry. They’re also working with medical clinicians to increase understanding of bone conditions like osteoporosis. Other research into how plants create incredibly tough structures like macadamia shells could also lead to new developments in materials engineering, allowing man to mimic natural armours.

Underpinning all these efforts is a quest to make sense of structures and space, tracing the common lines of contour and connection. It’s a link in which Sheppard takes obvious pleasure. When asked about the challenges presented by complex spaces, he beams, his mind engaged in another race towards understanding. 

^^

ANU Reporter Spring 2006