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
matthew.gwynne@postgrad.manchester.ac.uk. The abstract should not exceed
500 words, and the submission deadline is **28 April**.

Mathematics of Black Holes and the Big Bang

Quantum Gravity, Black Holes and the Big Bang are topics at the
frontier of current theoretical physics research. They are related
to challenging conceptual questions, but also involve very advanced
mathematics. The main difficulty is the fact that all these
phenomena require to take into account both quantum theory and
Einstein's general relativity. In this talk I will give a
pedagogical overview of current mathematical physics research into
these questions.

The Perilous Practice of Flying and Applying

Early aeronautical research in Britain was advanced by a decision to
allow a number of the nation’s finest mathematicians to train as
pilots and conduct airborne experiments using full-scale aircraft.
Given that many would subsequently perish in flying accidents, what
justified the risk?

Navier-Stokes-Fokker-Planck systems:

modelling, analysis, approximation and computation

Statistical physics is a fertile source of high-dimensional partial
differential equations. We shall survey recent developments
concerning a system of nonlinear partial differential equations,
which involves the Navier--Stokes system coupled with a
high-dimensional parabolic Fokker--Planck equation describing the
motion of polymer molecules in a viscous fluid occupying a bounded
spatial domain. The model arises in the kinetic theory of dilute
solutions of nonhomogeneous polymeric liquids, where the polymer
molecules are idealized as bead-spring chains with finitely or
infinitely extensible nonlinear elastic spring potentials, and has
been the subject of active research over the past decade. We shall
review recent results concerning the existence of large-data global
weak solutions to this high-dimensional system. We shall also
highlight a number of nontrivial open questions concerning the
mathematical analysis, approximation and numerical analysis of
high-dimensional Navier--Stokes--Fokker--Planck systems.

A Brief History of Numerical Libraries

(and a few other historical titbits)

A numerical library is a consistent, documented collection of
quality software. The first published program was for computing the
Bernoulli numbers, on Charles Babbage's analytical engine, by Ada
Lovelace in 1842. The first published collection was in 1954 by
Wilkes, Wheeler and Gill, primarily for the EDSAC computer at
Cambridge University. This talk is essentially about the history of
the development of quality numerical software, particularly
numerical linear algebra software which has had a big influence on
development in other areas. We shall look at the early influences
and challenges and what I believe should be the attributes of
quality software.

Predicting the Results of Tennis & Volleyball Matches Using Regression Models, and Applications to Gambling Strategies

Predicting the outcomes of sports matches, based on information
available in advance of the match, is of interest to a variety of
parties – players, coaches, fans, bookmakers and gamblers. Some
previous approaches have used computer simulations and/or stochastic
models based on player statistics to predict such outcomes. In this
paper, we instead investigate the use of regression models, using
player or team rankings, previous performance in the same
tournament, continent of origin and of the tournament, in predicting
such outcomes of matches in the major “Grand Slam” tennis
tournaments and international volleyball tournaments. We compare the
use of “official” rankings of teams and players with ranking
produced by a variant of a “page ranking” algorithm for internet web
pages in these models, and study the success rate of each in
predicting the results of matches not used for training the
parameters of the models. We compare our results with those based on
predicting that the higher ranked player/team, or the bookmaker’s
favourite, would always win. Our models show a modest advantage over
both simpler schemes. We then apply our models to both simple (fixed
stake) and Kelly “odds overlay” betting strategies, placing virtual
bets on each match. Our models were trained on “Grand Slam” results
up to and including Wimbledon 2014 and the Volleyball 2014, and
tested on the 2014 US Tennis Open and the 2014 Volleyball World
Championships, neither of which was used in training the models. We
find that in most cases, a Kelly betting strategy based on our model
performs better than simpler approaches, and on average gives a
positive return (unlike some of the other 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

Synaptic vesicles are storage units for neurotransmitters that are
released at the synapse. This release depends on an ion-induced Ca
2+ voltage gradient which regulates the rate of release of the
neurotransmitters (the neuron fires a signal). If the quantity of
released neurotransmitters is too small we get unusual nerve
signals. Understanding the transport of synaptic vesicles is thus
important in designing treatment for disorders such as ALS or
Parkin- son’s disease. A particularly puzzling question in the field
is how the high frequency of neuron firing can be achieved when the
synaptic vesicles must traverse a very crowded environment to reach
the cell membrane and release their cargo. In this talk I will
introduce a mathematical model for the life cycle of synap- tic
vesicles and discuss the role of the crowded environments on
large-scale transport. The crowding effects can be reconciled with
experimental obser- vations by introducing a zone of active
transport or facilitated diffusion.

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

Uncertainty quantification (UQ) is rapidly gaining traction in the
physical modelling and engineering communities and stochastic
Galerkin finite element methods (SGFEMs) are now commonplace when
approximating solutions to PDEs with random or parameter-dependent
inputs. However, due to the tensor product structure of the
approximation space, it is well known that SGFEMs quickly exhaust
desktop computer memory. One technique to reduce the dimension of
the approximation space is to initially construct a low-dimensional
space, and use a posteriori error estimators to drive its
incremental enrichment adaptively. For the enrichment strategy to be
effective, the estimators must be accurate. We begin our talk by
reviewing a classical a posteriori error estimation technique for
weak problems. Following [A. Bespalov, C.E. Powell, and D.
Silvester, Energy norm a posteriori error estimation for parametric
operator equations, *SIAM J. Sci. Comput.*, 36(2), 2014] we
demonstrate that the weak parametric reformulation of the stochastic
diffusion problem elegantly fits the classical framework. The
effectivity of that estimator depends on a (deterministic) finite
element space of our choosing. We investigate various spaces with
the aim of designing an accurate error estimator (i.e., with
effectivity indices close to one). For a model stochastic diffusion
problem we demonstrate that very accurate *and*
cheap-to-compute estimators are achievable.

Scattering of acoustic waves by obstacles with simple geometries

We will introduce three mathematical approaches to investigate a
number of problems of acoustic scattering by obstacles with simple
geometries.
Firstly, the simple method of separation of variables will be used
to solve the problem of scattering by a cylinder subject to either a
plane-wave or a point-source incidence.
The half-plane problem will then be tackled with the more
sophisticated Wiener--Hopf technique. Finally, we will give an
outline of a probably less well known procedure used for the
representation of the far-field of a solution: the embedding
formula.

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 |

Jonathan Deakin

Massimiliano Fasi

Matthew Gwynne

Georgia Lynott

Mante Zemaityte

If you have any further questions, please send us an email at matthew.gwynnenonsense@nonsensepostgrad.manchesternonsense.ac.uk