We wish you a Happy New Year!  ​2021 was a challenging but productive year for the Mathematics of Waves and Materials group.  Here is a summary of some of our news and activities.

People
​We welcomed three new group members this October.  Elena Medvedeva joined us as a first year PhD student, supervised by Anastasia Kisil and co-supervised by Raphael Assier.  Elena is working on the investigation of discrete diffraction problems, and understanding the links with their continuous counterparts.  We also have two new PDRAs working with Will Parnell: Dr Daniel Sy-Ngoc Nguyen and Dr Marie Touboul.  Daniel is working on the mathematical modelling of nanoreinforced syntactic foams, and Marie on novel resonant microstructures for elastodynamic metamaterials.

​Congratulations to Dr Marianthi Moschou, who was formally awarded her PhD in 2021, and well done to Erik Garcia-Neefjes and Cheuk-Him Yeung, who have submitted their theses and are awaiting their viva examinations.

Raphael Assier was promoted to Reader in August:  Many congratulations Raphael!  This year, Raphael was a member of the jury selecting the finalists of the IMA Lighthill-Thwaites prize in Applied Mathematics.  Raphael was the first winner of the biennial prize, in 2011.

Awards and Publications
Anastasia’s European Commission H2020 MCSA-RISE award, EffectFact: Effective Factorisation techniques for matrix-functions began in September, and Anastasia and Raphael were successful in securing an EPSRC Mathematical Sciences Small Grant, Developing Mathematics of New Composites of Metamaterials, beginning in February 2022.

There were several new publications from the group in 2021.  Highlights include work on Geometrical and mechanical characterisation of hollow thermoplastic microspheres for syntactic foam applications, by Matthew Curd, Neil Morrison, Zeshan Yousaf and Will Parnell along with with Michael Smith from the University of Cambridge and Parmesh Gajjar from the Henry Royce Institute here at Manchester [1].
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​In May, work by Raphael Assier with Andrey Shanin from Moscow State University: Vertex Green’s Functions of a Quarter-Plane: Links Between the Functional Equation, Additive Crossing and Lamé Functions, appeared in The Quarterly Journal of Mechanics and Applied Mathematics [2]. More recently, in October a review article on the Wiener-Hopf technique by Anastasia Kisil with I. David Abrahams, Gennady Mishuris and Sergei V. Rogosin, was published in Proceedings of the Royal Society A [3].  More publications from 2021 can be found in our ongoing list of academic publications.

Online Seminars
In June, Matt Nethercote spoke online at Days on Diffraction 2021.  Days on Diffraction is an annual conference organised jointly by St. Petersburg Department of V.A., Steklov Institute of Mathematics, Russian Academy of Sciences, Euler International Mathematical Institute, and St. Petersburg State University.  Matt’s talk was entitled Edge Diffraction of Acoustic Waves by Periodic Composite Metamaterials: The Hollow Wedge.  You can watch a recording of Matt’s talk here.

Raphael Assier gave a 3 lectures series: An applied perspective on multidimensional complex analysis, to an American Mathematical Society (AMS) Mathematics Research Community (MRC) hosted by Harvard University; and a talk at the Cambridge University Waves Group Seminar: A note on double Fourier Integrals with applications to diffraction theory.  He also gave an online talk, Analytical continuation of two-dimensional wave fields, at the ICMS Waves in Complex Continua (Wavinar) series, organised by Anastasia Kisil.  Raphael’s seminar will soon be available to watch online, along with the rest of the Wavinar series.

Engagement Activities
As in 2020, our engagement outputs were almost entirely online in 2021.  Despite this, we enjoyed a varied programme of activities. 166 secondary pupils took part in our online workshop 'The Great Maths Hunt', which looks at the hidden maths behind everyday situations.  We loved hearing the pupils’ ideas!  We created Slinky Science activities and experiment guides for Glasgow Science Festival, and Waves and Sound experiments for the University of Manchester’s online community festival.  In October, PhD student Eleanor Russell created some fun online games for Science X, the Science and Engineering Faculty’s annual engagement event.  Eleanor’s games explore the science and maths behind Smarter Materials for Greener Devices.  You can play them here.

Also in October we attended our first in-person event since the beginning of the pandemic.  PhD students Tom White and Eleanor Russell, and PE Manager Naomi Curati attended Bradford Science Festival, and used everyday objects to explore the question “how big is sound?”  More than 500 visitors joined us over two days, and feedback was extremely positive.
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We completed our A to Z of the Maths of Waves and Materials blog series in August, with Tom White contributing our final entry, Z is for Acoustic Impedance! Our A to Z is a great introduction to the concepts behind the research in the group, and features contributions from several group members.  Read them all here.

Frontiers for Young Minds is hosting a special collection: A World of Sound, to mark the International Year of Sound 2020/2021. Frontiers for Young Minds is a science journal for children, where the articles are reviewed by 8-15 year olds under the guidance of a science mentor.  Our article, Tackling Noise Pollution with Slow Sound was published in December, after helpful discussions with young reviewer Ginny.

We continued our collaboration with local illustrator John Cooper to create another explainer video in 2021, this time about the concept of Neutral Inclusions.  The Princess and the Neutral Inclusion has John’s trademark humour.  You can watch it below – no peas were harmed in its creation!

Looking forward to 2022
We look forward to another busy year in 2022.  You can find a list of upcoming events that group members are involved in here, and various external conferences taking place in 2022 here.  Teaching fellow Marianthi Moschou is organising an interdisciplinary conference for STEM undergraduates: Manchester Interdisciplinary Mathematics Undergraduate Conference, which will ​take place 31st March-1st April.​  Contact www.mimuc@gmail.com for details.  Follow @MWMmaths on social media for news and upcoming events.

2021 has perhaps not had the start we would have hoped for.  It will be a while yet before we are back together again in the Alan Turing building.  Nevertheless, we are continuing meet online, and to balance research and online teaching with homeschooling and other family commitments, and we have had a busy few months since the last update in October.

​Several MWM group members have delivered online talks since the last update.  In November, Matt Nethercote contributed to the ICMS virtual seminar series on Waves in Complex Continua, with his talk, “Edge Diffraction of Acoustic Waves by Periodic Composite Metamaterials: The Hollow Wedge”.  You can find a recording of Matt’s seminar with all the other "Wavinars" here.  You will also find a talk given in the summer by PhD student Erik Garcia-Neefjes, "Thermo-Visco-Elastic effects in Wave Propagation".

Anastasia Kisil spoke in the RCMM Wave Scattering and Solid Mechanics online seminar series in December. Her talk, entitled “Edges and Point Scatterers: a simple model for a metamaterial with edges” covered collaborative work with Raphael Assier and Matt Nethercote, and is available to view here.  Also in December, Will Parnell spoke about “Elastostatic cloaking, low frequency elastic wave transparency and neutral inclusions” at the ICMS Continuum Mechanics virtual seminar series in December, and online at the Laboratoire de Mécanique et d’Acoustique (Marseille) in October.  You can watch the ICMS talk here. 

In January, Raphael Assier gave a 3 lecture series to an American Mathematical Society (AMS) Mathematics Research Community (MRC) entitled “An applied perspective on multidimensional complex analysis”, hosted by Harvard University.

Click here to find a list of virtual seminar series.

Awards and publications

Papers from academic year 2019-2020 were discussed in October’s update, but some new publications have been released since then.  Most recently in January, several examples from Raphael Assier appeared, including "A Surprising Observation in the Quarter-Plane Diffraction Problem", with I. D. Abrahams in SIAM J. Appl. Math, and "Analytical continuation of two-dimensional wave fields" with Andrey Shanin in Proc. R. Soc. A.  An ongoing list can be found here.

Anastasia Kisil was part of a multi-institutional group that were successful in securing funding from European Commission H2020 MCSA-RISE for "EffectFact: Effective Factorisation techniques for matrix-functions".  This is a joint venture between several European Institutions in the area of factorisation techniques, Wiener-Hopf and Riemann-Hilbert problems and related numerical techniques, beginning in September 2021.  Anastasia, along with Anna Zemlyanova (Kansas State University), Gennady Mishuris (Aberystwyth University) and Xun Huang (Peking University) made a successful application to the BIRS Scientific Board to host a conference in the Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China.  "Cross-Fertilisation of ideas from the Riemann–Hilbert Technique and the Wiener–Hopf Method" will be held in September 2022.

Like many, we have had an eventful and challenging second semester and summer in 2019.  The lockdown which began in March has meant adapting to online teaching and home working, with some group members also balancing work commitments with the demands of home schooling.

Here is some of the news from our group during this most unusual time.

Moving on
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Congratulations to Georgia Lynott, who successfully completed her PhD this year! Georgia's viva was conducted online in June, and the group got together virtually to celebrate.  We hope that we can celebrate in person in the near future!  Final year PhD student Marianthi Moschou has also recently submitted her thesis and is awaiting her viva.

Conferences and collaborations
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In January, Raphael Assier spent a very productive week at the Laboratoire de Mécanique et d'Acoustique in Marseille, working on homogenisation with Bruno Lombard and Cédric Bellis.

In February PhD student Erik Garcia Neefjes travelled to Australia where he spoke on "Wave Propagation in Thermo-Visco-Elastic Continua" at KOZWaves and explored waves in other ways, too!  You can read his blog about the trip here.

Publications
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There have been several new publications from the group this year.  An ongoing list of publications can be found here.

A few recent highlights include a new review paper in National Science Review, co-authored by Professor I. David Abrahams, Anastasia Kisil and several others [1].   This review was sparked by discussions at the Isaac Newton Institute’s 2019 research programme, "Bringing pure and applied analysis together via the Wiener-Hopf technique, its generalisations and applications".  Another recent paper from Anastasia, with Matthew Colbrook (DAMPT Cambridge) recently appeared in  Proc. R. Soc. A.: A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics [2].

For another recent project, we teamed up with illustrator and comedian, John Cooper, to create short illustrated explainer videos about our research.  You can find them on our YouTube channel, and read about the creative process on our blog, and on John’s.

Looking Forward
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Earlier this year we welcomed Matt Nethercote back to the group! Matt completed his PhD with Raphael Assier last year, and returned for a PostDoc with Anastasia Kisil.  This month we welcomed two new PhD students to the group: Matthew Riding, who has started his PhD with Anastasia Kisil, and Mark Mesbur, who is jointly supervised by Will Parnell and Professor Paola Carbone in the Department of Chemical Engineering.  We look forward to a busy academic year 2020-2021, meeting the challenges of online teaching, and remote-working. 

One of the things researchers often wrestle with is creating clear and succinct explanations of their research for the non-specialist.  It can be extremely helpful to work with others; such as illustrators, teachers and performers, to eliminate jargon and create meaningful outputs that showcase the research.

When we wanted to make a short video about the design of metamaterials for noise reduction devices, we turned to illustrator and comedian John Cooper.

John has worked on projects for the University of Manchester before, creating work for the University’s School Governor Initiative and for the Children’s University of Manchester.  His humorous style lends clarity and informality to a topic.

We started from a blog post about the piece of research in question.  John used it to sketch out an initial storyboard proposal featuring noisy geese!  We then put together an initial script, from which John created a slideshow storyboard.

This project was completed during lockdown, so all our discussions were carried out over email or video conferencing.  Keeping the length of the script to a minimum was challenging, but after several iterations we arrived at the final version, which John narrates.

Here’s what John had to say, ‘I really enjoyed this project. The work the department does is fascinating, and it was an exciting challenge in generating visuals to complement their work on noise reduction.  It's good to learn new things while being creative.’
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Here’s the finished product.  Watch out for those geese!

​One of the most rewarding experiences of my PhD is being able to attend to conferences and the opportunity to introduce myself and present my research to a wide audience of professionals. After two and a half years of PhD studies, I have had the chance to visit some great places within the UK and Europe, and now Australia! KOZWaves is a biennial conference focused on the study wave science and is always held somewhere within Australia and New Zealand. I first heard of it in my PhD first year and thought how amazing it would be to get to know a new community and give a talk at this event. Two years later I was very happy to receive the news that my talk: "Wave Propagation in Thermo-Visco-Elastic Continua" had been accepted to KOZWaves 2020 which was held at the University of Melbourne from the 17-19th of February.
 
The conference exceeded my expectations with great speakers talking from gravitational waves to water waves as well as light, sound and vibrations (to name just a few!) They showcased - the well known fact of - how waves describe so many physical phenomena of the world that surrounds us.

​The next step of the journey was a visit to the University of Adelaide in South Australia which is an 80 minute flight from Melbourne's Tullamarine Airport. As a keen surfer myself, before taking the flight I paid a visit to URBNSURF, a new facility for surfing artificial waves (again waves!) in a big pool right by the airport which was super fun!

I spent three fantastic days at the University of Adelaide visiting Dr. Luke Bennetts. I gave a talk to the Mechanics group on "Modelling Thermo-Viscous Damping in Continua". 

Finally, I visited Dr. Stuart Hawkins at Macquarie University in Sydney and some of his colleagues including Dr. Elena Vynogradova and her PhD student Martin Sagradian. I gave an hour long talk similar to the one I presented in Adelaide and had some interesting conversations. Stuart showed me some very impressive numerical computations via the use of the T-matrix approach for multiple scattering problems.