We are proud to present the 7th 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. Registration is now closed.
We invite attendees to present posters and talks in all areas of applied and industrial mathematics and it's applications. To submit an abstract, send the pdf with the title, author(s) and affiliation to firstname.lastname@example.org. The abstract should not exceed 500 words, and the submission deadline is 28 April.
Mathematics of Black Holes and the Big Bang
The Perilous Practice of Flying and Applying
modelling, analysis, approximation and computation
A Brief History of Numerical Libraries
(and a few other historical titbits)
Predicting the Results of Tennis & Volleyball Matches Using Regression Models, and Applications to Gambling Strategies
Finding Missing Meteorites
Many meteorites are found on the surface of Antarctica. This is because Antarctica contains small regions called meteorite stranding zones where the upward flow of ice combines with a high level of ablation (ice loss) at the surface to enable large numbers of meteorites to be englacially transported to the surface.
In fact, up until December 2015, 34 927 meteorites had been recovered from the surface of Antarctica. This accounted for 66.3% of the world’s total number of collected specimens. Interestingly, of all the meteorites found in Antarctica only 0.7% of these were iron or stony iron meteorites. To put this into perspective 6.9% of finds throughout the rest of the word were iron based.
The hypothesis is that, due to their higher thermal conductivity, iron and stony iron meteorites heat up enough during the summer months to melt back down into the ice and offset the total annual upward transport of the ice.
To defend this hypothesis a simple 1D mathematical model of the movement of a meteorite through the ice will be presented. The use of the quasi-static heat equation will be defended and the attenuation of solar radiation within the ice will be discussed. I will then talk about the intriguing lack of meteorite finds in Greenland.
Anomalous Diffusion of Synaptic Vesicles - how a neuron fires
Spreading of Single/Multiple Droplets on Patterned Substrates
Inkjet printing based manufacturing of high-resolution p-OLED displays involves simultaneous printing of large arrays of pixels in close proximity. This requires the ability to control the spread of the deposited liquid within the desired pixel shape/region. It is usually achieved by patterning the substrates using a photo-lithography method. These patterns (referred to as pixels) are in the form of micron-sized topographical features or variations in the wettability of the substrate or a combination of both. Here we investigate how liquid deposited by sequential printing of partially overlapping droplets can be restrained within a stadium shaped pixel. We present a novel experimental system that can be used to study the dynamics of a single/multiple microdroplets deposited over patterned substrates. On substrates with only topographic variations, we find that the sloping side wall of the pixel can either locally enhance or hinder spreading depending on whether the topography gradient ahead of the contact line is positive or negative. Locally enhanced spreading occurs via the formation of thin pointed rivulets along the side walls of the pixel through a mechanism similar to capillary rise in sharp corners. However, the efficacy of sloped side-walls in restraining the spreading of deposited liquid in the desired region is critically dependent on the accurate positioning of droplets in a pixel. We demonstrate that this crucial dependence on the positioning of droplets can be evaded on the substrates with both topographical and wettability patterns.
Building on the experimental observations we demonstrate that a thin-film model combined with an experimentally measured spreading law, which relates the speed of the contact line to the contact angle, provides excellent predictions of the evolving liquid morphologies. We also show that the spreading can be adequately described by a Cox–Voinov law for the majority of the evolution. The model does not include viscous effects and hence, the timescales for the spreading of deposited liquid are not captured. Nonetheless, this simple model can be used very effectively to predict the areas covered by the liquid in a pixel and may serve as a useful design tool for systems that require precise control of liquid on substrates.
Electromagnetic Wave Diffraction of Perfect Electric Conducting Wedges with Arbitrary Polarization.
This talk will present a method to find the electromagnetic field and the Poynting vector resulting from a time-harmonic electromagnetic plane wave with no skew incidence and arbitrary polarization incident on an infinite perfect electric conducting wedge. Wedge diffraction is a widely explored area with numerous applications in acoustics, RADAR and ice crystal diffraction.
The aim is to reduce the electromagnetic problem to a scalar problem and find out how the polarization of this incident electromagnetic wave impacts the solution to diffraction by perfectly conducting wedges. I will use the third dimensional invariance of the scatterer and the boundary conditions to rewrite the electromagnetic field, governed by the source free Maxwell's equations, in terms of two uncoupled scalar potentials. These potentials depend on the polarization angle and can be shown to respectively solve the sound-soft and sound-hard scalar wedge problems. They can therefore be found using a variety of techniques including the Sommerfeld-Malyuzhinets technique and the Wiener-Hopf technique.
After this, I will compare multiple methods of evaluation or approximation of the electromagnetic field and the time-averaged Poynting vector for high frequency and plot the components of both quantities for different values of the polarization angle to determine its impact.
A posteriori error estimation for stochastic Galerkin finite element methods
Scattering of acoustic waves by obstacles with simple geometries
Using Surrogate Models to Accelerate Bayesian Inverse Uncertainty Quantification
In this talk we consider inverse uncertainty quantification for the laser flash experiment. We assume the change in temperature of a material is modelled by the transient heat equation, with the diffusion coefficient considered unknown. We take the Bayesian approach, utilising Markov chain Monte Carlo (MCMC) methods to sample from the posterior distribution of the unknowns given observations of the temperature made during experimentation.
MCMC algorithms require many calculations of the posterior density. Each evaluation of the posterior density requires an evaluation of the forward model, which in this setting is the numerical solution of a time--dependent PDE. This requirement results in a computationally intensive routine, often taking days to achieve a desired Monte Carlo error in the quantities of interest. Although computationally intensive, such a routine is preferable to cheaper optimisation approaches which provide no quantification of the uncertainty, only a fitted best value.
We analyse the validity of using a surrogate model within an MCMC routine to reduce the computational cost. Specifically, we evaluate a single stochastic Galerkin finite element solution to the PDE in place of repeatedly computing deterministic finite element solutions within an MCMC routine. Investigations into how both the speed and accuracy of the approximation of the posterior are affected by this replacement are presented.
|09:30 - 10:00||Registration and Coffee|
|10:00 - 10:10||Opening|
|10:10 - 10:55||Plenary Session I (Kasia Rejzner)|
|11:00 - 11:25||Student Session I (Edyta Dziedzic) and II (Amy Mallinson)|
|11:25 - 11:50||Student Session I (Helena Stage) and II (Pallav Kant)|
|11:50 - 12:00||Group Photo|
|12:00 - 13:00||Lunch and Posters|
|13:00 - 13:45||Plenary Session II (Tony Royle)|
|13:50 - 14:15||Student Session III (Adam Crowder) and IV (Matthew Nethercote)|
|14:15 - 14:40||Student Session III (James Rynn) and IV (Marianthi Moschou)|
|14:40 - 15:20||Poster Session and Coffee|
|15:20 - 16:05||NASC Plenary session (Endre Süli)|
|16:05 - 16:50||NAG Lecture (Sven Hammarling)|
|16:50 - 17:00||Presentation of Awards and Closing|
|17:00 -||Dinner and informal outing|
If you have any further questions, please send us an email at email@example.com