Thousands of years ago, early Mesopotamian people discovered that a mixture of mud and straw creates strong durable buildings, what we call today a composite material. Composites are far better than the sum of their parts, for example they can be stronger and cheaper. Hundreds of years of experimentation has led to similar discoveries when mixing fluids and gases, what we now call complex fluids/media.
Today composite materials and complex fluids have enabled amazing advances in areas including: aerospace, automobile, food science, communications technology, biotechnology.
Click on images above. Metal matrix foams and fibre composites are examples of composites, while emulsions, suspensions, complex gases, and polymers are complex fluids.
My research focuses on waves (like sound, radio, light, and vibrations) interacting with these complex materials. Developing mathematical models of this interaction has two exciting goals:
Controlling waves by designing the next generation of materials. These new materials can then improve telecommunications by controlling light and elastic waves, and mechanical engineering by controlling vibrations and even earthquakes.
Sensing materials with waves. We sense the world around us by using waves. Light and sound are reflected from all materials, and when they reach us, our brains can decode them to understand what objects are around us. In a similar way, waves are used to sense the microstructure materials. One use is to automate manufacturing, where we need to develop sensors that can detect changes in microstructure from reflected waves. Keeping track of the microstructure is essential to determine when the material has reached its optimally flexibility, strength, or capacity to transmit information.
Mathematical models
In all these complex materials, it is impossible to know the exact position and shapes of all the microstructure. But the reflected wave does depend on the configuration of the microstructure.
Caption: one reflected wave from a complex material. What can we learn about this material from measuring the wave at the receiver?
Caption: the wave reflected from the same complex material can be different each time if its microstructure moves, or if the position of the receiver moves. For example the grey curves above are all different reflected waves from the same material. To make sense of these curves, we investigate the average (mean: black curve) reflected wave, and the variation of the reflected waves (std: green region).
Our goal is to develop mathematical models which predict the average reflected wave and its variance (or standard deviation), as these do not depend on the configuration of the microstructure. One of our discoveries [paper 1,paper 2] is that there exists many waves, with different speeds and characteristics, that can propagate
(in an ensemble averaged sense) inside these complex materials.
Once we have accurate mathematical models, and software, we can generate a large quantity of (average) reflected waves from different material, such as shown below. This large quantity of data is essential to learn how to sense materials and design materials to control waves.
The average and variation of waves reflected from a variety of complex materials. With only reflected signal (one sensor) we can clearly the affect of the different particulate microstructure.
Art Gower is a lecturer at the University of Sheffield and part of the Dynamics group. He uses maths to understand waves (sound and light) in materials. Sometimes computers show him that his maths is wrong.
