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Looking back - and forwards

1/11/2022

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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.
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Elena
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Daniel
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Marie
​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.
​On the subject of judging panels, Anastasia Kisil was one of five judges for the Royal Society Insight Investment Science Book Prize in 2021.  The panel was chaired by leading immunologist, presenter and writer, Professor Luke O’Neill FRS, and the winning book, announced in November, was Entangled Life: How Fungi Make Our Worlds, Change Our Minds and Shape Our Futures (Bodley Head), by biologist and writer Merlin Sheldrake.  You can read about the Sheldrake's book here.
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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.
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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.
PictureEleanor engages with young visitors at Bradford Science Festival
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.
[1] M.E. Curd, N.F. Morrison, M.J.A. Smith, P. Gajjar, Z. Yousaf, W.J. Parnell (2021) Geometrical and mechanical characterisation of hollow thermoplastic microspheres for syntactic foam applications Composites Part B: Engineering 223 108952
[2] R.C. Assier and A.V. Shanin (2021) Vertex Green’s functions of a quarter-plan e. Links between the functional equation, additive crossing and Lamé functions. Q.J. Mech. Appl. Math., 74(3):251-295
[3] A.V. Kisil, I. David Abrahams, G. Mishuris and S.V. Rogosin (2021) The Wiener–Hopf technique, its generalizations and applications: constructive and approximate methods
Proc. R. Soc. A 477(2254):20210533, DOI: 10.1098/rspa.2021.0533
[4] W. J. Parnell, W. Rowley and N. Curati N (2021) Tackling Noise Pollution With Slow Sound. Front. Young Minds. 9:703592. DOI: 10.3389/frym.2021.703592
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Stepping Into 2021

2/10/2021

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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.
Many congratulations to Marianthi Moschou who passed her PhD viva in December, and took up a post as teaching fellow in Mathematics!  Mary’s thesis is dedicated to diffraction theory, in particular to space varying impedance boundary conditions.

Online seminars
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​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".
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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.
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William Parnell’s EPSRC award for “The Princess and the Pea: Mathematical Design of Neutral Inclusions and their Fabrication” began this month.  This project will explore neutral inclusions (NIs): material inclusions with coatings designed to ensure that stress fields in the host material are unperturbed upon loading, as if the inclusion were absent. NIs have the potential to reduce material failures due to stress concentration, and enable lighter, stronger materials.

Online Engagement. 
In-person events are likely to be further postponed for the several months, and we are continuing to find ways to engage online.  Our Virtual Postcards offer visual snapshots of our research themes, and our ongoing series, the A-Z of the Mathematics of Waves and Materials, takes an alphabetical journey through some of the key concepts behind our work.  This week we reached the letter I, with a piece on inclusions, written by Neil Morrison, so there are plenty more updates to come! 
PhD students Eleanor Russell and Tom White recently featured in the New Scientist Jobs "A Day in the Life" series, where they describe a typical day as a Mathematics PhD student, and discuss the best and worst parts of PhD life.  Students interested in a career in Applied Mathematics can explore our Meet a Mathematician series, or visit our YouTube channel.

March brings British Science week, and we are looking forward to engaging with local high school pupils with our virtual workshop “The Great Maths Hunt”, which will take a look at everyday life and challenge students to answer: “Where is the maths?”  Students will uncover the hidden mathematical research behind everyday things, and find out who mathematicians work with, how they solve problems, and where a career in maths may take them.
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From March, we look forward to working with the Metamaterials Network’s Outreach and Education forum, led by Anja Roeding (University of Exeter), and Raphael Assier.  The group will coordinate outreach activities in the field of metamaterials across several UK institutions.

​Finally, during this extended 
International Year of Sound, the journal Frontiers for Young minds is preparing a special collection entitled “A World of Sound”.  Frontiers for Young Minds is an open access scientific journal written for and reviewed by children.  Naomi Curati is one of the collection editors, along with other members of the UK Acoustics Network.  We look forward to reading the collection!

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Into the New Academic Year

10/7/2020

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As we move into a new academic year we reflect on the difficulties and achievements of recent months and look forward to the challenges and opportunities ahead.
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.
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Also in February, PhD student, Marianthi Moschou, was a runner up in the Smith Institute TakeAim competition with her entry, "Noise Pollution: Our Enemy Against Green Aviation".

After lockdown, conferences moved online, and on the 25th of May, Postdoc Matt Nethercote spoke online at Days on Diffraction 2020.  The title of his talk was "High Contrast Approximation for Penetrable Wedge Diffraction".

We look forward to a full programme of online conferences and seminars this semester.  Regular fixtures include the ICMS Virtual Seminar Series: Waves in Complex Continua (Wavinar), which is organised by Anastasia Kisil.  You can find a list of regular seminar series here, and upcoming conferences 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].
Zeshan Yousaf and Will Parnell collaborated with Prasad Potluri from the Department of Materials here at the University of Manchester, and Michael Smith from the Department of Applied Mathematics and Theoretical Physics, University of Cambridge.  Their paper examining the properties of polymer filled syntactic foams was published in April [3].  You can read a 3-minute précis of their work here.

Recent work from Matt Nethercote and Raphael Assier with David Abrahams, 
High-contrast approximation for penetrable wedge diffraction, appeared in the IMA Journal of Applied Mathematics [4].
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Engagement

Before lockdown we took our Making Music With Maths KS1&2 workshop to IntoUniversity Manchester North.  IntoUniversity is an organisation that supports young people from disadvantaged backgrounds to attain either a university place or another chosen aspiration.  We had great fun learning about sound and vibration, and making noisy kazoos!  We also brought our Seeing Sounds KS3 workshop to several local high Schools, where students got hands-on using musical instruments to work out the speed of sound.  Information on schools outreach can be found here.
We had several live events planned for the summer, including Big Bang Fair, Glasgow Science festival and more locally, BlueDot festival.  In celebration of the International Year of Sound 2020, our hands-on exhibit would have asked the question “how big is sound?” and offered visitors the chance to explore the scale of sound waves, and find out why this matters to noise reduction.  Sadly of course, in-person events were cancelled due to the Covid-19 coronavirus.  However, we have enjoyed taking part in online engagement events, including CocoMAD 2020 and Glasgow Science Festival’s Hands-On(line).  The International Year of Sound has been extended into 2021, and you can find the event calendar here.
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During lockdown, we have created many online learning resources about materials and waves, including several experiments with household objects that we recorded at home on a mobile phone!  You can find them here, and on our YouTube channel, newly launched this year.  Also on our YouTube channel you can find short clips of our excellent PhD students talking about their research.
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.
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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. 
[1] I D Abrahams, X Huang, A Kisil, G Mishuris, M Nieves, S Rogosin, I Spitkovsky, Reinvigorating the Wiener-Hopf technique in the pursuit to understand processes and materials, National Science Review, 2020, nwaa225, https://doi.org/10.1093/nsr/nwaa225

[2] M. J. Colbrook. and A. V. Kisi, A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics, Proc. R. Soc. A., 2020, 47620200184, https://doi.org/10.1098/rspa.2020.0184

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[3 ]Z. Yousaf, M. Smith, P. Potluri, W. Parnell, Compression properties of polymeric syntactic foam composites under cyclic loading, Composites Part B: Engineering, 2020, 186, 107764, 
 https://doi.org/10.1016/j.compositesb.2020.107764

​[4]​ M A Nethercote, R C Assier, I D Abrahams, High-contrast approximation for penetrable wedge diffraction, IMA Journal of Applied Mathematics, 2020, 85, 3, 421-466,   https://doi.org/10.1093/imamat/hxaa011
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Illustrating the Research

6/3/2020

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We worked with Illustrator John Cooper to create a short video about metamaterials for noise reduction.
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Still image from the video. Credit: John Cooper.
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.
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Sketches from the initial storyboard proposal. Credit: John Cooper, reproduced with kind permission from the artist
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!
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A Fruitful Visit to Australia

3/20/2020

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Erik Garcia Neefjes

3rd Year PhD Student

​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.
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​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!
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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". 
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​We also discussed some interesting problems involving the interaction of waves in ice-ocean systems together with Prof. Malte Peter, who was also visiting Luke. They showed me around Adelaide where the Fringe festival was, coincidentally, also taking place. Thanks again Luke and Malte!

​After this, I headed up to Sydney and visited Prof. Nicole Kessissoglou and her research group at the University of New South Wales with whom I spent a great day and was shown some of their fantastic work in the field of acoustic metamaterials. I went for a small trip down to the stunning South Coast and got to see first hand the impact that the fires had on the small communities, it was devastating to see how so many homes have been completely burned down as well hectares of land.
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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.
I would like to thank the MWM group and my supervisors for giving me this opportunity and look forward to the next few months.
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    The Mathematics of Waves and Materials group are are a research group in the Department of Mathematics at the University of Manchester.  We work on the theoretical, numerical and experimental aspects of both materials and waves. See our research page for more information and details.

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