Landmine detection is a very slow process, largely due to the huge number of false positives with a metal detector, which for safety reasons must all be removed from the ground. Incorporating an additional sensor type such as ground-penetrating radar (GPR) has been shown to reduce the rate of false positives, speeding the clearance process. So far, these GPR detectors have only used very basic imaging methods (or none at all). We discuss implementing a more advanced method, namely Full-Wave Inversion, highlighting some of the difficulties in this nonlinear and ill-conditioned optimisation based method.
The anterior cruciate ligament (ACL) is the most frequently injured knee ligament, and is one of the structures most commonly injured in sport. Due to the fact that it does not heal naturally, the standard treatment for a ruptured ACL is surgical reconstruction, to which there are several approaches, the most common being patellar tendon (PT) and hamstring tendon autograft. There is currently no consensus with respect to the choice between these two grafts, however, the PT is the most commonly used. In this talk, I mathematically model the ACL and PT in order to compare their mechanical properties within the same framework.
Ligaments and tendons have an extremely hierarchical structure, their main subunit being the fascicle, which is made of fibrils arranged in a crimped pattern. We utilise a strain energy function that was proposed for the modelling of arteries but is equally applicable to tendons and ligaments, to show that the differing alignments of the fascicles within the ACL and PT have a significant effect on their stress-strain curves.
In this talk I'll give an introduction to Taylor dispersion, a canonical problem involving the enhanced mixing of a solute due to a shear flow. This has many applications including gas exchange in the lungs, blood circulation and engineering. I'll then go on to talk about how similar methods can be used to describe the increased propagation speed of a premixed flame propagating against a shear flow in a channel.
Fibre reinforced composites (FRCs) are commonly used in industry, and many techniques have been developed in an attempt to understand what their effective properties are on a macroscopic level. While techniques such as the method of asymptotic homogenisation (MAH) can be effective, there are issues with using such techniques when in non-dilute regimes (i.e. when there are lots of fibres in the composite) and the equations we solve in such techniques are often very complicated.
In this talk, using the example of firing antiplane (SH) waves into a composite to find its longitudial shear modulus, an alternatvie technique shall be shown which yields a simpler asymptotic scheme, featuring a nice segregation of terms, and which is more reliable in non-dilute regimes.
Two major considerations in X-ray Computed Tomography are the required acquisition time and X-ray dose for the scans. In helical scan CT, scans are taken by moving source and detector in one continuous helix relative to the object rather than taking several separate circular scans. This not only reduces the acquisition time and dosage, but also allows faster processes to be captured and artefacts to be reduced at large cone angles. One theoretically exact reconstruction method for helical cone beam micro-CT is the Katsevich reconstruction algorithm. In this paper we look at two implementations of the derivatives required for the Katsevich reconstruction algorithm on flat detectors, both the original implementation suggested by Noo and a formulation proposed by Katsevich.
Noise production from a mechanical system can be understood as a dissipation process by which the system loses a tiny part of its energy. The particularity of this acoustic dissipation is that it propagates at large distances as sound and is therefore received as a nuisance. Unsteady turbulent flows in free space or developing over the surface of moving bodies will appear as the source of what is called the aerodynamically generated noise. In this talk I will introduce the basic theory and some applications in the aeronautics industry.
I will describe the IFISS software package http://www.maths.manchester.ac.uk/~djs/ifiss/ and explain how it can be used to solve advection-diffusion problems. I will also talk about solving Boussinesq systems---the simplest PDE model for buoyancy-driven incompressible fluid flow.
Despite the recent successes of the granular mu(I)-rheology in simulating flow, we show inherent ill-posed behaviour in the governing equations. In this context, the ill-posed ness is manifested as an unbounded growth of short wavelength perturbations. The instability is explored analytically with a linear stability analysis and numerically using an implicit finite volume scheme.
I have just returned to Manchester after spending six months working in the aeroacoustic research team at Dyson as part of a shorter knowledge transfer partnership (sKTP). I would like to discuss what it was like working for such an inspirational British technology company as Dyson, what research is like within industry compared to academia, and give an overview of some of the research I did there. All Dyson products move air as part of their primary function. Getting air to move and then controlling it can be a noisy business. Dyson sought academic input from applied mathematicians to aid the investigation of solutions which allow maximum acoustic benefit within strict design constraints. I will discuss the process in which we determined the scope of the project and the desired outcomes, and give some details of the mathematical modelling and experimental validation involved. Dyson are holding a workshop in the department on the 17th December. So this talk will also act as a bit of an introduction.