. Advances in Applied Mathematics and Mechanics School of Mathematics Alan Turing Building University of Manchester Manchester, UK 5th-7th June 2013 Introduction I am very pleased to welcome you all to the School of Mathematics in the Alan Turing Building at the University of Manchester for this workshop entitled Advances in Applied Mathematics and Mechanics. The workshop will host a number of talks focusing on rather theoretical and more applied aspects of mechanics. Applications range from the prediction of composite material behaviour to aspects of biological materials. In order to ensure variety there is no prescription of the type of mechanics discussed at the workshop although the stress is on the development of the theory and applications of continuum mechanics. Although we have plenty of talks I have benefitted significantly in recent years from the French style of conferences which strives for good break-out time and time for lunch - this ensures good interaction! Although I cannot provide lunch-time wine unfortunately! As you may be aware, the School of Mathematics at the University of Manchester has a rich history. Many famous mathematicians have worked here including Horace Lamb, Lewis Fry Richardson, Sydney Goldstein, Paul Erdos, Max Newman, Frank Adams, James Lighthill and Alan Turing. In 2007 the department moved into the purpose built Alan Turing Building which provides a superb environment in which to teach and do research. The Manchester Institute for Mathematical Sciences (MIMS) hosts numerous visitors throughout the year with dedicated office space. More broadly the University of Manchester has given rise to numerous momentous advances, including the discovery of the nuclear nature of the atom at Manchester by Rutherford and the world’s first stored-program computer coming into being at the university. In total the university counts 25 Nobel Prize winners amongst its current and former staff and students, with its most recent coming in 2010 with the award of two Nobel prizes to Andre Geim and Konstantin Novoselov, for groundbreaking experiments regarding the two-dimensional material graphene. We are assured of a wonderful three days of talks at this workshop. I’d like to thank all of the speakers for their contributions. I sent out a large number of invites and almost all were accepted within a short time frame which made for difficult timetabling but an excellent programme. I’d like to thank the Engineering and Physical Sciences Research Council (EPSRC) for their financial support of this workshop via grant EP/H050779/1. I’d also like to thank Riccardo De Pascalis for his help in producing this short booklet, Dave Abrahams for general discussion and Sue Tizini, Jenny Gradwell and Sebastian Rees for their admin support. The poster session will be on Thursday lunch time. Since many participants of this are PhD students I would urge you to attend and ask questions. Enjoy the meeting and (sunny) Manchester, Regards, William Parnell Schedule WEDNESDAY 5th JUNE, 2013 10.00-10.40 Arrivals and coffee 10.40-10.45 Introduction and opening (Will Parnell) 10.45-11.15 Richard Craster (Imperial College, UK): “High frequency homogenization” 11.45-12.15 Sasha Movchan (University of Liverpool, UK): “Trapped flexural modes and transmission resonances in structured plates” 12.15-12.45 Vincent Pagneux (University of Maine, France): “Multimodal admittance method in waveguides with improved convergence” 12.45-14.15 Buffet lunch 14.15-14.45 Paul Martin (Colorado School of Mines, USA): “N masses on a string” 14.45-15.15 Karima Khusnutdinova (Loughborough University, UK): “On Boussinesq and Kadomtsev-Petviashvili type models and applications” 15.15-16.00 Coffee, tea and biscuits 16.00-16.30 Ray Ogden (University of Glasgow, UK): “Residual stress and its effect on elastic response” 16.30-17.00 Jacopo Ciambella (University of Bristol, UK): “Large strain viscoelastic effects in short fibre composites” 17.00-17.30 Luigi Vergori (National University of Galway, Ireland): “On the finite element implementation of anisotropic elasticity” 17.30 onwards Wine and nibbles THURSDAY 6th JUNE, 2013 09.30-10.00 Yibin Fu (University of Keele, UK): “Bifurcation and stability of pressurized ellipsoidal membrane shells” 10.00-10.30 Eliot Fried (McGill University, Canada): “Stability and bifurcation in a simple model for shape changes in discoidal high-density lipoproteins” 10.30-11.15 Coffee, tea and biscuits 11.15-11.45 Alain Goriely (University of Oxford, UK): “Magnetic chains: from self-buckling to self-assembly” 11.45-12.15 Oscar Lopez-Paimes (University of Illinois at Urbana Champaign, USA): “The nonlinear elastic response of suspensions of rigid inclusions in rubber” 12.15-12.45 John Berger (Colorado School of Mines, USA): “Stresses due to intercalation and phase transformation in lithium ion battery cathodes” 12.45-14.15 Buffet lunch and poster session 14.15-14.45 Andrew Norris (Rutgers University, USA): “The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces” 14.45-15.15 Daniel Colquitt (University of Liverpool, UK): “Non-singular cloaking of a square inclusion with a microstructured coating” 15.15-16.00 Coffee, tea and biscuits 16.00-16.30 Ian Thompson (University of Liverpool, UK): “Rayleigh wave scattering by a submerged cavity” 16.30-17.00 Diki Porter (University of Bristol, UK): “Trapped modes in simply-supported thin elastic plates” 17.00-17.30 Michele Brun (University of Cagliari, Italy): “Analysis of propagation of a transition flexural wave in a supported beam” 17.30 onwards Wine and nibbles 20.00 Workshop meal - Don Giovanni’s restaurant, Oxford Road FRIDAY 7th JUNE, 2013 09.30-10.00 Oliver Jensen (University of Manchester, UK): “Instabilities of flexible-channel flows” 10.00-10.30 Massimiliano Gei (University of Trento, Italy): “Asymptotic models for the buckling of thin films resting on soft, prestretched substrates” 10.30-11.00 Giuseppe Saccomandi (University of Perugia, Italy): “Weak coaxial transversely isotropic materials” 11.00-11.45 Coffee, tea and biscuits 11.45-12.15 Martine Ben Amar (ENS, France): “Morphogenesis and embryogenesis” 12.15-12.45 Georges Limbert (University of Southampton, UK): “A microstructurally-based anisotropic continuum model of skin” 12.45-14.15 Buffet lunch 14.00-14.30 Salvatore Federico (University of Calgary, Canada): “Porous Materials with Statistical Fibre-Reinforcement” 14.30-15.00 Dave Abrahams (University of Manchester, UK): “Wave propagation in quasi-periodic media” 15.00-16.00 Coffee, tea biscuits and close Participants David Abrahams University of Manchester, UK Azwani Alias Loughborough University, UK Jean Marc Allain Ecole Polytechnique, France Martine Ben Amar Ecole Normale Superieure, France John Berger Colorado School of Mines, USA Emilie Blanc Aix/Marseille University, France Michele Brun University of Cagliari, Italy Luigi Cabras University of Liverpool, UK Giorgio Carta University of Liverpool, UK John Chapman University of Keele, UK Igor Chernyavsky University of Nottingham, UK Jacopo Ciambella University of Bristol, UK Richard Clift Loughborough University, UK Daniel Colquitt University of Liverpool, UK Simon Cotter University of Manchester, UK Phil Cotterill Thales/University of Manchester, UK Jamie Cowley Strathclyde University, UK Richard Craster Imperial College, UK Riccardo De Pascalis University of Manchester, UK Salvatore Federico University of Calgary, Canada Eliot Fried McGill University, Canada Yibin Fu University of Keele, UK Massimiliano Gei University of Trento, Italy Alain Goriely University of Oxford, UK Art Gower National University of Galway, Ireland Stewart Haslinger Liverpool John Moores University, UK David Harris University of Manchester, UK Oliver Jensen University of Manchester, UK Ian Jones Liverpool John Moores University, UK Lina Joseph Imperial College, UK Savina Joseph University of Oxford, UK Duncan Joyce University of Manchester, UK Karima Khusnutdinova Loughborough University, UK Jane Lawrie Brunel University, UK Georges Limbert University of Southampton, UK Barbara Lynch Ecole polytechnique, France Oscar Lopez-Paimes University of Illinois at Urbana-Champaign Mehul Makwana Imperial College, UK Paul Martin Colorado School of Mines, USA Agnes Maurel ESPCI, France Maureen McIver Loughborough University, UK Kieron Moore Loughborough University, UK Natasha Movchan University of Liverpool, UK Sasha Movchan University of Liverpool, UK Michael Nieves University of Liverpool, UK David Nigro University of Manchester, UK Andrew Norris Rutgers University, USA Ray Ogden University of Glasgow, UK Zuonaki Ongodiebi University of Manchester, UK Jane O’Neill University of Liverpool, UK William Parnell University of Manchester, UK Vincent Pagneux University of Maine, France Phil Pearce University of Manchester, UK Draga Pihler-Puzovic University of Manchester, UK Diki Porter University of Bristol, UK Wassamon Phusakulkajorn University of Manchester, UK Giuseppe Saccomandi University of Perugia, Italy Tom Shearer University of Manchester, UK Rebecca Shipley UCL, UK Ian Thompson University of Liverpool, UK Luigi Vergori National University of Galway, Ireland Feng Xu University of Nottingham, UK Xizheng Zhang Loughborough University, UK WEDNESDAY 5th JUNE, 2013 Richard Craster - High frequency homogenization It is highly desirable to be able to create continuum equations that embed a known microstructure through effective or averaged quantities such as wavespeeds or shear moduli. The methodology for achieving this at low frequencies