We are proud to present the 8th Manchester SIAM-IMA Student Chapter Conference. This series of conferences has played a key role for the FSE students at The University of Manchester to showcase their research and foster interdisciplinary collaboration. The conference provides a forum for communication among students from applied mathematics, computer science, and computational science and engineering. It is a one day conference and is open to anyone interested or working in applied or industrial mathematics, including undergraduates, postgraduates and staff.
We invite attendees to present posters and talks in all areas of applied and industrial mathematics and its applications. To submit an abstract, send the pdf with the title, author(s) and affiliation to siam@maths.manchester.ac.uk. The abstract should not exceed 500 words, and the submission deadline is 9 April.
Producing High Quality Numerical Software
Mathematical modelling to assist disease eradication efforts
As more diseases are targetted for eradication by the global community, the question arises of how best to target our efforts. Mathematical modelling can be an important tool in addressing these issues. I will present work on two case studies: household modelling in yaws eradication efforts; and the challenge of systematic non-adherence in mass drug administration. Yaws is a painful and disabling infectious disease, with a latent form of infection that complicates eradication efforts. We use mathematical modelling along with data from the Solomon Islands to analyse the efficacy of the new WHO guidelines for yaws eradication.
It is well understood that the success or failure of a disease eradication campaign critically depends on the level of coverage achieved. However, the quality of the coverage achieved also affects the efficacy of the campaign: in particular, if the same people miss treatment every year, they can represent a reservoir of infection, posing a barrier to eradication efforts. We demonstrate that the modelling description used and the level of systematic non-adherence can have a profound effect on the outcome of a treatment campaign.
Iterative Regularization of Large-Scale Inverse Problems.
Fast Direct Solvers for Elliptic PDEs
Optimal coordinate transformations for the perfectly matched layer method
The widely used perfectly matched layer (PML) method employs a complex coordinate transformation to impose non-reflecting boundary conditions in the finite element solution of wave equations. The coordinate transformation is ap- plied in a layer surrounding the region of interest (the bulk) and in its exact form completely absorbs waves leaving the bulk, eliminating spurious reflections from the outer boundary. However, when the problem is discretised, if the solution in the PML region is under-resolved, spurious reflections are created, limiting the achievable accuracy of the computed solution in the bulk. Conversely, if the solution in the PML region is over-resolved then computational effort is wasted. The optimal balance between bulk and PML refinement is problem dependent and difficult to find a priori.
To address this problem we propose a PML which is optimal in the sense that the coordinate transformation ensures the solution varies linearly through the PML, making it trivial to discretise. We present an algebraic method for find- ing this optimal transformation which utilises information about the solution. While this makes the problem non-linear, we show that we can converge to the exact solution by iterating, using information from the previous solution. This iteration is natural if we are already performing spatial mesh adaptation in the bulk. We show that with this optimal PML, the numerical error is completely controlled by the refinement in the bulk.
The Direct Computation of Time-Periodic Solutions of PDEs & Applications to Fluid Dynamics
Many PDEs have time-periodic solutions and it is often of interest to explore their dependence on problem parameters. The determination of such solutions by direct time-integration can be very inefficient as transients may take a long time to decay. Furthermore, this method cannot robustly find unstable solutions, which may be of interest. In this talk we present a finite-element based space-time approach that allows the direct computation of time-periodic solutions. We demonstrate the application of the methodology for the forced unsteady heat equation and the diffusive Van der Pol equation. Finally, we illustrate its application to the study of flow past an oscillating cylinder.
Solving PDEs with Random Data by Sparse Grid Stochastic Collocation Methods
Recidivism in Human Activity
In the past couple of years, we have experienced a significant number of pivotal events which continue to influence our current lives, such as the Syrian refugee crisis, Brexit and the presidential election of the U.S.A. Central to all the challenges following these events is the question of how polarisations between different groups occur, and if similar future events can be predicted. This inflexibility in voting or political behaviour has critical consequences when applied to criminal activity; how likely is a criminal to be rehabilitated or, conversely, more deeply entrenched in crime?
In this talk I will introduce a mathematical model for \textit{recidivism}, the tendency of a convicted criminal to re-offend. Supported by empirical data, a key element of criminal activity and recidivism will be discussed, the degree of rehabilitation. The model is capable of describing both likely re-offenders as well as expected durations of low criminal activity. These results inform the best punitive measures to ensure a minimal number of repeat offenders in the penal system, taking into account the nature and location of the crime.
Numerical Solution to the Navier-Stokes Equations in Primitive Variables.
Ionic Diffusion Model for the Oxidation of Uranium
Uranium reacts with oxygen in the air to form uranium oxide and/or uranium hydride, with the latter being formed only in the presence of moisture. The corrosion product ura- nium hydride, formed from the reaction of uranium with water vapour is undesirable as it is pyrophoric (i.e. self-ignites), hence prompting the current study. The kinetics of uranium oxidation in dry air to form uranium oxide is dominated by the diffusion of oxygen anions, formed when the adsorbed oxygen atoms on the surface accepts electrons from the underlying metal. There are several empirical models available in the literature for the oxidation of ura- nium in dry and moist air, but very few mathematical models exist.
In our current research, a suitable mathematical model, with unsteady diffusion to be the rate-determining step, has been formulated and numerically solved. A boundary-fixing transformation has been used to solve the governing equation in a fixed domain at the expense of a more-complicated nonlinear governing equation. The overall process is one of combined temperature and time-dependent chemical and ionic diffusion within a growing substrate. In this talk, I will discuss the results obtained for the dry-air oxidation problem.
A new microstructural strain energy function for the hyperelastic modelling of skin
In the hyperelastic modelling of fibrous soft tissues, such as skin, we construct strain energy functions to model the anisotropic and nonlinear stress-strain behaviour that they exhibit. Phenomenological models can fit experimental data well. Parameters in mi- crostructural models, however, are connected to the properties and arrangement of the tissue’s constituents that influence the macroscopic behaviour of the tissue. Microstruc- tural models thus enable us to understand how the tissue deforms and, potentially, to measure the values of the parameters directly in experiments [1].
We, therefore, introduce a new model that assumes that fibres of collagen, a strong fibrous protein, in the skin are crimped (i.e. wavy) according to a triangular distribution. Crimp is an important property because we assume that collagen fibres straighten as the skin is stretched, and only contribute mechanically once straightened. To test the new model, we compare its fit to four data sets of uniaxial loading on mammalian skin to those of a commonly used phenomenological model and a microstructural tendon model [1].
The new model achieves the closest relative fit to three data sets, and the phenomenolo- gical model to one. The new model achieves a closer fit than the tendon model for each data set. The tendon model also outperforms the phenomenological model for three data sets. The number of fit parameters in the new model is then reduced to that of the pheno- menological model. The new model still produces a better fit than the phenomenological model for three of the four data sets.
[1] T. Shearer, A new strain energy function for the hyperelastic modelling of ligaments and tendons based on fascicle microstructure. J. Biomech, Vol. 48, pp. 290–297, 2015.Scattering from periodic arrays
08:45 - 09:05 | Registration and Opening of the conference |
09:05 - 09:50 | Plenary Session I (Louise Dyson) |
09:50 - 10:30 | Student Session I |
10:30 - 10:50 | Coffee Break |
10:50 - 11:35 | Plenary Session II (Silvia Gazzola) |
11:35 - 12:15 | Student Session II |
12:15 - 13:15 | Lunch and Group Photo |
13:15 - 14:00 | NAG Lecture (Nick Dingle) |
14:00 - 14:40 | Student Session III |
14:40 - 15:00 | Coffee Break |
15:00 - 15:45 | Plenary Session III (Gunnar Martinsson) |
15:45 - 16:25 | Student Session IV |
16:25 - 16:45 | Presentation of Awards and Closing |
16:45 - | Informal outing |
Yuqing Zhangn
Gian Maria Negri Porzio
Massimiliano Fasi
Thomas McSweeney
Steven Elsworth
If you have any further questions, please send us an email at siamnonsense@nonsensemaths.manchesternonsense.ac.uk