Callophris Rubi
Holger Averdunk consultant
This is one frame from a 3D animation extracted from electron tomography images of photonic crystal structures found in the wings of the butterfly Callophris Rubi. 

Anna Carnerup, Ankie Larsson, Andy Christie, Nick Welham, Julie Anne Dougherty, and Stephen Hyde
Fossil or fake? The origin of life is hotly debated and many believe that “life- like” morphology is sufficient proof that billion year old remnants found in the Pilbara are our earliest ancestors. This delicate trumpet, as seen under a polarising microscope, might well be a simple organism, such as “Stentor” - but it isn’t. Using the chemistry found in rocks alone the group has been able to elucidate a menagerie of “biogenic” forms. While these forms are abiotic and cast doubt on bold statements about early life they do raise an interesting question. If life was not the template for these mineral forms, were these minerals templates for life?

two parallel sets, blue ball, blue doughnut, ‘Isotope C’ line drawing green ball, green doughnut, ‘Isotope B’ line drawing
Toen Castles PhD candidate
Solid shapes are often thought of as being angular blobs. If we let the surface smooth out though, the shapes become bubbles, with patterns - the old edges and corners - drawn on them. The cube and the octahedron are shown this way.
Another way to draw the same structures is to draw the edges and corners on another smooth surface, the doughnut. In the example of the octahedron, the ‘triangles’ ABCA and DEFD pass though each other, as do ADEA and BCFB. The cycle ABCFEDA is a loop tied into a trefoil knot. Compare these loops with the same loops drawn on the bubble. The cube example is also tangled.
If you cut the doughnut, so that it becomes a tube, and then cut the tube so it becomes a square, the planar ‘crystals’ result. Reversing the process, any repeating square pattern can be rolled up onto a doughnut. The dashed lines show where the cuts on the torus might appear in the crystal. The dots show the planar points of rotation. When the symmetry of these dots is just right, the patterns on the doughnut become symmetric. 

Reverse imaging
Assoc Professor Vincent Craig Australian Research Fellow
These are high magnification multilple images of a single particle using an Atomic Force Microscope. Multiple images of the same particle are obtained using a technique we developed called “reverse imaging”. 

Irregular 3-connected Trees
Myfanwy Evans PhD Candidate
The three images show three distinct arrangements of Irregular 3-connected trees on 2-dimensional Hyperbolic Space. The circle is a representation of 2-dimensional Hyperbolic space, where the space approaches infinity as it approaches the boundary of the circle. The arrangement of triangles is the *246 symmetry group, which is the underlying symmetry associated with the trees. The underlying symmetry group of all three arrangements is the same, where the images only differ by the arbitrary choice of vertex locations and edge locations. The classification of such trees will be an integral part of the classification of 3-dimensional networks. 

(images from left to right) 1. Roughened glass slide in air. 2. Roughened glass slide in 58% sucrose solution. 3. Roughened glass slide in 58% sucrose solution, higher magnification. 4.Smooth glass slide in 58% sucrose solution, higher magnification.
Christine Henry PhD candidate
Evanescent Wave Scattering Images from EW-Atomic Force Microscope.
When a laser beam is internally reflected at a glass surface, an ‘evanescent wave’ is created. These images show the light pattern resulting when an evanescent wave is scattered by an object in its path - in this case, a 20micron diameter silica sphere attached to a V-shaped cantilever spring. Analysis of scattered light intensity can show the sphere position; however these images were captured just to show that the technique could be used with a roughened surface. 

Optical reflectometer
Shaun Howard PhD candidate
Adsorption: the binding of molecules or particles to a surface.
The optical reflectometer utilizes small differences in the way light is reflected from a surface to measure the adsorption of molecules from solution. With this instrument we can measure molecules in quantities as small as 1 milligram (1/1000th of a gram) per square meter, and determine useful information such as the speed with which they do it. 

Friction apparatus
Anthony Hyde
This instrument measures the interfacial friction and wear forces between ultra-smooth surfaces at molecular levels in the field of nanotribology.
Two mica surfaces coated with solution are brought together under controlled conditions at nanometer separations. One surface is fixed and the other slides across. Any shear force that results from friction is measured with a strain gauge bridge, with output voltage detected with a lock-in amplifier.
A number have been sold to overseas reseach units. 

Three forms
Stephen Hyde Professor and Federation Fellow
We are physicists looking at broadening our catalogue of form, in order to recognise forms in nature, from simple molecular liquid crystals to folded membranes in living cells.
We need a broader catalogue than currently available, as nature dreams up far more complex shapes than standard geometry books can offer. Nature plays with sphere, cylinders, planes, etc. But it also knows about topologically complicated forms, including complex three-dimensional weavings and knots.
To enrich out catalogue of shapes and form in three-dimensional euclidean space, we take a novel route, passing through previously unvisited places. That route involves two-dimensional non-euclidean, or hyperbolic geometry.
The pictures show the steps we take in going from hyperbolic space (the flat disc), to euclidean space (the pointy saddle) via the three-handled donut. 

Hip72R_Xn Hip3 Hip72R_300_Xp
Anthony Jones PhD candidate
Network representation of the two human proximal femur specimens with differing porosity. The network representations retain the topology of the bone elements and illustrate the anisotropy within the femoral neck. 

Some different bubble shapes naturally formed. The images were made using Drishti, from tomographic data produced by the X-ray micro-CT system developed in-house at the ANU, Research School of Physical Sciences and Engineering, Department of Applied Mathematics. The resolution of these images is approximately 10 microns/voxel.
Munish Kumar  PhD candidate
Wettability is an interesting research question which has far-reaching applications in bioengineering and petroleum industries. Hydrophobic interactions play an important role in interface processes for self-assembly of molecules, and in micelle agglomeration. In petroleum science, understanding the wettability of rocks allows one to predict reservoir performance, conduct forecasts and estimate reserves, and aids in secondary and tertiary oil recovery processes.
Pore spaces within a reservoir rock contain various fluids (water, oil, contaminants, natural gas or air). It was determined that a non-wetting fluid would evolve on hydrophobic surfaces because this is thermodynamically favorable. Since water forms hydrogen bonds with other molecules of water, it ignores any non-polar molecules that exist in aqueous solution. Hence, gas, which is mostly covalent non-polar bonds, only evolves on a hydrophobic surface [1].
In these images, large bubbles of CO2 form on silanated surfaces of Ottawa sand. Interestingly, the large bubbles also tell us that Ostwald ripening took place. This process refers to when gas pressure is greater than the surrounding fluid initially. Thus, in order to minimize energy, small gas bubbles re-dissolve into the aqueous solution, and combine to form larger bubbles to reduce the overall Laplace pressure.
1. J. N. Israelachvili. Intermolecular and Surface Forces. Academic Press, London, 1991. 

Empty triangles in 3D
Dr Vanessa Robbins Research Fellow
Topological measures of shape are finding increasing use in the study of point or coverage processes and the characterisation of complex three- dimensional structures. This is because topology is independent of geometry, and so both types of information are necessary to fully characterise spatial structure. The most commonly studied topological invariants are the number of connected components (the zeroth order Betti number, β0) and the Euler characteristic (χ, the zero-dimensional Minkowski measure from integral geometry). This paper also investigates β1 and β2, the higher-order Betti numbers that count the number of independent handles (non-contractible loops) and enclosed voids.
The section 4.3 Empty triangles in 3D presents a mathematical derivation of the expected number of loops in a purely random arrangement of balls in space, in the limit of small radius and low density.
This work is an edited extract from the paper Betti number signatures of homogeneous Poisson point processes, Physical Review E 74 061107 (2006). 

X-ray micro-CT system
Tim Sawkins
This instrument for 3D computed tomography is capable of imaging materials with a wide variety of densities and sizes. From 5cm cores of rock, imaged at 20 micron resolution, down to samples less than 5mm across, imaged with a voxel size of less than 2 microns. The facility is undergoing continuous refinement and improvement, and will soon be upgraded to improve resolution and decrease acquisition time.
Photo: Tim Wetherell

Associate Professor Tim Senden and Dr John Long (Museum Victoria)
By the time fish crawled up on land most of the big evolutionary steps towards humans had been made - some 350 million years ago and a good 100 million years before dinosaurs. ‘Gogonasus’ is one of the pivotal fish in this evolutionary picture. Discovered in the Kimberleys in June 2005 the complete, articulated and three dimensionally preserved skeleton gives us a remarkably detailed insight into how forelimbs and air breathing developed. It challenges the view that a single species made the transition to land and shifts the focus to Gondwanaland as another source of the necessary biodiversity to support tetrapod (all animals with four limbs) development.
Three dimensional X-ray microscopy (X-ray CT) is also helping to probe the way the sensory system was arranged and the complete set of facio-cranal nerves have been mapped with this technique, and completely mirrors that in human skull. Indeed the pectoral fin is comprised of the same set of bones we have in our arms.
The discovery of this specimen is significant in that builds a greater understanding of why some fish have remained fish and others started to sniff air. 

Macadamia nut shell
Dr Adrian P Sheppard Senior Research Fellow
This image of the shell of a macadamia nut is one of 2,048 2D frames in a 3D image taken on a unique high-resolution X-ray tomography beamline at Europe’s largest synchrotron. It covers a region of about 0.3mm across. The coloured blobs are disconnected air pockets; relics of cells that were alive while the nut was still growing. Macadamia nut shells are a fascinating biomaterial due to their very high strength, so the structure of the air gaps is of great interest to materials scientists.
This work was done in collaboration with Ulrike Wegst and Boris Breidenbach of the Max Plank Institute for Metallforschung in Stuttgart.

3 slices
Michael Turner PhD candidate
A 2D slice through the 3D image of a grain pack, a subsection of the grain partitioning and a subsection of the void phase partitioning.  

Alpha simplex
Dr Peter Wood Postdoctoral Fellow
In 3 dimensions, a simplex is a point, edge, triangle or tetrahedron. A simplicial complex K is a collection of simplices such that
      (1) Every face of a simplex in K is in K;
      (2) The intersection of any two simplices in K is a face of each of them.
A finite point set S defines a special simplicial complex known as the Delaunay triangulation D of S. Given a positive number alpha, we call a simplex in D alpha-exposed if there is a ball with radius alpha which does not contain any points in S , but whose boundary touches the vertices of the simplex. The alpha-shape of S is made up from the alpha-exposed simplices in S.
To generate our point sets we use the chaos game algorithm to generate subsets of fractals. These images are of alpha shapes corresponding to these point sets. Different coloured triangles correspond to different values of alpha. For each of these alpha shapes, it is possible to count the Betti numbers, which count the connected components, tunnels and voids. 

2007 - RAW: Science Week Exhibition

RAW: 15-25 August, 2007, at Photospace, upstairs in Photomedia. Faculty of the Arts, School of Art, Australian National University, Childers Street, ACTON, Canberra, ACT.

Science at the School of Art!

To celebrate Science Week in 2007, the ANU School of Art hosted an exhibition of work from Researchers in the Department of Applied Mathematics at the Research School of Physical Sciences and Engineering, ANU.

The exhibition showcased images of research ranging from pure equations describing new technologies, three-dimensional shapes, Microscopic CT images of tiny bubbles, configurations of isotopes, topographical maps of particles to the optical structure of butterfly wings.

While artists don’t necessarily have to use the latest technology to make art, many artists are inspired by scientific concepts that attempt to describe the material structure of the universe and life itself. Artists and scientists have informed each other for centuries and the relationship is well documented, particularly in the last century where concepts of atomic and molecular science can be identified in the work of key artists such as Marcel Duchamp, and Kazimir Malevich and who inspired change and radical thinking in the modern art movement.

The exhibition was organised by Canberra based artist Erica Seccombe, who had an opportunity to work with the researchers in Applied Maths with support from an ACT Government visual arts grant in 2006. Her residency is testament to the legitimate relationship between artists and scientists needing increased support from local and federal government funding for collaborative projects.

Rather than highlighting examples of art resulting from these relationships, Erica felt that this exhibition was an opportunity to showcase images and ideas that have resulted from raw research, which in turn she hopes, will possibly inspire fresh ideas and collaborations between the two disciplines.

‘All of the work in this show is visually and conceptually intriguing and it gives an insight into variety of research undertaken in the Department of Applied Maths at the ANU. These researchers work on a range of experimental and theoretical problems in order to describe or discover the properties, structures and processes of material, often at nano-scale. Advanced technology plays a big part in their research and many of the machines they use they have designed and built within the Department.’

Researchers included in this exhibition were (in alphabetical order):

Please note that the information on this web page was collated in 2007. Titles and research may have since changed. For more up-to-date information on the Department of Applied Mathematics visit