Wednesday, 29 November 2017

Modelling the production of silicon in furnaces

How can solar panels become cheaper? Part of the cost is in the production of silicon, which is manufactured in electrode-heated furnaces through a reaction between carbon and naturally occurring quartz rock. Making these furnaces more efficient could lead to a reduction in the financial cost of silicon and everything made from it, including computer chips, textiles, and solar panels. Greater efficiency also means reduced pollution.

Oxford Mathematics' Ben Sloman is working with colleagues Colin Please, Robert Van Gorder, and collaborators at Norwegian silicon production company Elkem to better understand how the furnaces behave.

One problem in silicon production is the formation of a solid crust, which clogs up the furnace and prevents the raw materials from falling down the furnace to the hot region, where the necessary chemical reactions occur. Due to the high temperatures involved (around 2000 kelvin) it is difficult to observe how this clogging happens, so Elkem have carried out experiments. A mathematical model developed by Ben and colleagues captures the evolution of gas flow, temperature, and chemical reactions in these experimental furnaces. Numerical simulations demonstrate that the position of crust formation is largely driven by temperature, with the location moving upwards as the furnace becomes hotter. This effect is quantified in an asymptotic analysis of the model [1]. The furnace operators can change the type of raw materials used in the process and the energy input into the electrodes. Simulations of the model show that using more reactive carbon particles (for example charcoal) reduces the amount of silicon monoxide gas escaping from the furnaces, allowing more silicon to be produced from the quartz, and also reducing the build up of the furnace crust.

The image shows a sketch of a silicon furnace, reproduced from The Si Process Drawings, by Thorsteinn Hannesson.

[1] B. M. Sloman, C. P. Please, and R. A. Van Gorder. Asymptotic analysis of a silicon furnace model. Submitted. (2017).

The research is funded by the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling here in Oxford in collaboration with Elkem.

Wednesday, 22 November 2017

Oxford Mathematics London Public Lecture with Andrew Wiles and Hannah Fry - watch it live

Andrew Wiles will be giving our first Oxford Mathematics London Public Lecture on Tuesday 28 November at 6.30pm in the Science Museum in London. Andrew will be talking about his current work and after the lecture he will be in conversation with mathematician and broadcaster Hannah Fry.

The event is now full but you can watch it live. It will also be streamed on the Oxford University Facebook page.

Tuesday, 21 November 2017

Four more universities join the Alan Turing Institute

The Alan Turing Institute is the national institute for data science, headquartered at the British Library. Five founding universities – Cambridge, Edinburgh, Oxford, UCL and Warwick – and the UK Engineering and Physical Sciences Research Council created The Institute in 2015. Now we are delighted to announce that four universities - Leeds, Manchester, Newcastle and Queen Mary University of London - are also set to join the Institute as university partners. The new universities will work with our growing network of partners in industry and government to advance the world-changing potential of data science.

Alan Wilson, CEO of the Institute, commented: “We are extending our university network in recognition of our role as a national institute and because we believe that increasing collaboration between researchers and private, public and third sector organisations will enable the UK to undertake the most ambitious, impactful research possible."

Peter Grindrod, Oxford Mathematics' nominee on the Turing board, said: “We are rightly proud to have launched the Alan Turing Institute in 2015, together with the other founding partners. The Turing is now on a journey to becoming a truly national endeavour, drawing in more universities and researchers and strengthening its international competitiveness. Data science and artificial intelligence will underpin many 21st century industry sectors; and, working with its partner universities, Turing is well placed to take a leading role in support of the Government’s Industrial Strategy.”


Tuesday, 21 November 2017

From Primes to Networks via Russia and ODEs - a sample of the latest books from Oxford Mathematics Faculty

When they aren't in their offices doing Maths our Faculty can be found in their offices writing books about doing Maths. Here is a recent sample of their labours. 

Richard Earl's 'Towards Higher Mathematics: A Companion' aims, as its title suggests, to bridge the gap between school and University, giving sixth-formers an insight into and preparation for the mathematics they will be studying at University.

By contrast Vicky Neale's 'Closing the Gap: the Quest to Understand Prime Numbers' is a mathematical thriller, a story of individual effort and innovative collaboration as the mathematical community tries to understand one of mathematics' great mysteries: Prime Numbers.

David Acheson's books aim to tell the world about the sheer excitement and pleasures of mathematics. His latest, 'the Calculus Story' does just that, giving the reader a tour of the mathematics of change via imaginary numbers, Isaac Newton and the electric guitar (amongst other mathematical things). You may even find yourself doing calculus.

Nick Trefethen is an expert in Numerical Analysis and one of the founders of the MATLAB-based Chebfun software project. Chebfun is at the heart of his latest book 'Exploring ODEs', an examination of the ubiquitous Ordinary Differential Equation.  

Christopher Hollings is an historian of mathematics and especially of Soviet Mathematics. His latest work 'Wagner’s Theory of Generalised Heaps' looks at the theories of the Russian mathematician V. V. Wagner (1908-1981). The book contains the first translation from Russian into English of a selection of Wagner’s papers.

Cornelia Drutu is an expert in geometric group theory and her forthcoming book on the subject (entitled 'Geometric Group Theory') attempts to make the subject accessible to students and researchers via proofs of many of its central tenets.

Renaud Lambiotte's 'A Guide to Temporal Networks' explores the fascinating world of networks and their profound and growing importance across the sciences, both physical and social. From the brain to Facebook, networks are at the heart of our interpretation of our world.

A full list of Faculty books is available.

Monday, 20 November 2017 Women in Technology Scholarships

Supporting female students is a priority for Oxford Mathematics, particularly on courses where women have historically been underrepresented.  We are delighted that, due to the support of, Oxford University can offer 10 scholarships to female Home/EU students studying MScs in mathematics, statistics and computer science in 2018-19. The scholarships will cover both fees and a stipend at the level of the national minimum doctoral stipend as set by the research councils. Scholarships are available to female applicants for the following MScs:

MSc Mathematical Sciences (OMMS)
MSc Statistical Science
MSc Mathematics and the Foundations of Computer Science
MSc Mathematical Modelling and Scientific Computing
MSc Mathematical and Theoretical Physics
MSc Computer Science
MSc Software Engineering
MSc Software and Systems Security

There is no separate application process for this scholarship. To be considered, submit your application for graduate study by Friday 19th January 2018. Selection is expected to take place by the end of April 2018. If you fulfil the eligibility criteria, you will be automatically considered for these scholarships.


Monday, 20 November 2017

West Nile Virus and understanding the spread of infection

West Nile virus (WNV) is responsible for viral encephalitis in humans, a condition that causes inflammation of the brain and can have longer-lasting physical effects. WNV is also related to similar viruses such as Dengue and Zika that are also of significant public health concern. Faced with the challenge of understanding how the virus reproduces within the host and its potential for epidemic, Oxford Mathematician Soumya Banerjee and colleagues have developed a computational method to determine characteristics of WNV infection even in the face of limited experimental data, an approach that could be applicable to other emerging diseases like the Zika virus for which there is little data.

Diseases that jump the species barrier from animals to humans affect millions worldwide. An understanding of how disease progression and immune response vary from species to species could have important public health benefits. In their work the team attempt to understand how immune function scales with body size, work which is a foundation for understanding scaling of immune response to other pathogens or in other animals. 

The team’s computational framework for infectious disease modelling at the within-host level leverages data from multiple species. This is likely to be of interest to modellers of infectious diseases that jump species barriers and infect multiple species – the method can be used to determine computationally the competency of a host to infect mosquitoes that will sustain West Nile virus infection. The models show that smaller Passerine species are more competent in spreading the disease than larger non-Passerine species. This suggests the role of host phylogeny as an important determinant of within-host pathogen replication.

Ultimately the team believes their work could be an important step in linking within-host viral dynamics models to the between-host models that predict spread of infectious disease between different hosts. 

Thursday, 16 November 2017

The Seduction of Curves: The Lines of Beauty That Connect Mathematics, Art and The Nude. Allan McRobie's Oxford Mathematics Public Lecture now online

There is a deep connection between the stability of oil rigs, the bending of light during gravitational lensing and the act of life drawing. To understand each, we must understand how we view curved surfaces. We are familiar with the language of straight-line geometry – of squares, rectangles, hexagons - but curves also have a language - of folds, cusps and swallowtails - that few of us know.

Allan explains how the key to understanding the language of curves is René Thom’s Catastrophe Theory, and how - remarkably - the best place to learn that language is perhaps in the life drawing class. Sharing its title with Allan's new book, the talk wanders gently across mathematics, physics, engineering, biology and art, but always with a focus on curves.

Warning: this talk contains nudity.

Allan McRobie is Reader in Engineering, University of Cambridge






Tuesday, 14 November 2017

Andrew Dancer elected to the Council of the LMS

Oxford Mathematician Andrew Dancer has been elected to the Council of the London Mathematical Society (LMS).  The Society publishes books and periodicals, organises mathematical conferences, provides funding to promote mathematical research and education and awards a number of prizes and fellowships for excellence in mathematical research.

Andrew Dancer's research focuses on Differential Geometry, especially the study of Einstein spaces. His recent work on Ricci flows features in our latest case-studies series.

Andrew is a Fellow of Jesus College here in Oxford.



Monday, 13 November 2017

Mathematics tracks the flu. Julia Gog Oxford Mathematics Public Lecture now online

Can mathematics really help us in our fight against infectious disease? Join Julia Gog as she explores some exciting current research areas where mathematics is being used to study pandemics, viruses and everything in between, with a particular focus on influenza.

Julia Gog is Professor of Mathematical Biology, University of Cambridge and David N Moore Fellow at Queens’ College, Cambridge.






Friday, 10 November 2017

James Maynard appointed Research Professor and receives a Wolfson Merit Award from the Royal Society

Oxford Mathematician James Maynard has been appointed Research Professor and receives a Wolfson Merit Award from the Royal Society. The Royal Society Wolfson Merit Award is a prestigious award intended to attract or retain respected scientists of outstanding achievement and potential.

Professor Maynard's project, 'Structure in the primes, with applications', aims to develop techniques to understand the statistical properties of the distribution of prime numbers - a central problem in number theory. The project consists of three large projects to be investigated over a five-year period. The projects follow the common theme of studying classical problems in analytic number theory by attempting to classify counter-examples, should they exist. This approach has been remarkably successful in analytic arguments, and is an example of a common connection between analysis, combinatorics and algebra. The underlying techniques also provide flexible and universal means of answering rigorously many real-world questions about primes.

James Maynard is one of the brightest young stars in world mathematics at the moment, having made dramatic advances in analytic number theory in the years immediately following his 2013 doctorate. These advances have brought him worldwide attention in mathematics and beyond. Just 30, he has already gained many markers of distinction, including the European Mathematical Society Prize, the Ramanujan Prize and the Whitehead Prize. He will be an invited speaker at the quadrennial International Congress of Mathematicians in 2018. He also holds a Clay Research Fellowship (2013-18), the most prestigious early career position in world mathematics.