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News & Events - 0 views

  • Here are upcoming and recent Meetings, Workshops, Programmes etc. organized or co-organized
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  • by members of the School.
  • 2013 16th - 20th September 2013 Classifying Structures for Operator Algebras and Dynamical Systems Location: Institute of Mathematics and Physics, Aberystwyth University, UK Organizers: Gwion Evans (Aberystwyth), Otgonbayar Uuye (Cardiff), Wilhelm Winter (Muenster) 12th - 13th April 2013 WIMCS Operator Algebras Workshop Location: Swansea University, UK Organizer : David Evans 20th May - 22nd May 2013 Wales Mathematics Colloquium 2013 - Gregynog 25-27 March 2013 The Kavli Royal Society International Centre at Chicheley Hall : Advances in Non-Newtonian Fluid Mechanics (Including a minisymposium on Theoretical Rheology)  
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  • 2012 3 - 7 September 2012 Complex patterns in wave functions - drums, graphs, and disorder The Kavli Royal Society International Centre at Chicheley Hall Organized by Sven Gnutzmann (Nottingham)  and Uzy Smilansky (WIS Israel and Cardiff) LMS Regional Meeting and Workshop: Quantum Probabilistic Symmetries Aberystwyth University Scientific Advisory Committee David Evans (Cardiff), Martin Lindsay (Lancaster), Gilles Pisier (Paris and Texas A&M) and  Dan Voiculescu  (Berkeley) 23 July - 17th August 2012 Spectral Theory of Relativistic Operators Isaac Newton Institute for Mathematical Sciences, Cambridge Organized by B.M. Brown (Cardiff), M.J. Esteban (CEREMADE), K-M. Schmidt (Cardiff), H. Siedentop (Munich) 18 - 22 - July 2012 XXth Oporto Meeting on Geometry, Topology and Physics Noncommutative Geometry and Conformal Field Theory, Oporto University, Portugal Organized by C Herdeiro (CFP and Univ. of Aveiro), D. E. Evans (Cardiff) - Chairman, J.N. Tavares (CMUP and Univ. of Porto), J. Mourao (CAMGSD and IST Instituto Superior Tecnico, Lisbon), M. Mackaay (CAMGSD and Univ. of the Algarvel), M. Costa (CFP and Univ. of Porto), P. Pinto (CAMGSD and IST), R. Picken (CAMGSD and IST) 2 - 3 April 2012 6th MOPNet Meeting : University Of Bath
  • 2013 17-19 December 2013 Workshop on Combinatorial Physics Organized by Dr. Roger Behrend. 16-18 December 2013 Optimal Decisions in Statistics and Data Analysis Organized by Prof. Anatoly Zhigljavsky and Dr. Jonathan Gillard 18 October 2013 Categorically Cardiff: Derived Categories and Algebraic Geometry Organized by Timothy Logvinenko 17 October 2013 COW Seminar Organized by Timothy Logvinenko 1-2 July 2013 Spectral Analysis and Differential Equations 13 - 15 May 2013 LANCS International Workshop on Discrete and Nonlinear Optimisation 16 April 2013 LSW Frontiers Distinguished Lecture Sir Vaughan Jones FRS (Vanderbilt) 15th March 2013 COW Algebraic Geometry Seminar Organized by Timothy Logvinenko 15th February 2013 Modern Trends in Markov Processes and Queueing Theory Organized by Jeff Griffiths and Nikolai Leonenko 21 January 2013 SIAM Chapter Day 7 - 10 January 2013 Dissipative Spectral Theory Organized by Marco Marletta and  Kirill Cherednichenko  
  • 2011 20 September - 1 October 2011 Rigorous Quantum Field Theory in the LHC era Erwin Schrödinger International Institute for Mathematical Physics (ESI) Organized by C. Jäkel (Cardiff), C. Kopper (Ecole Polytechnique), G. Lechner (Vienna) 12 - 13 September 2011 5th Mopnet Meeting : University College, London 11 - 14 September 2011 Bath-Berlin Workshop "Phase boundaries and random polymers" Organisers: Nicolas Dirr (Cardiff), Peter Mörters (Bath) and Max von Renesse (TU Berlin) 27 - 28 April 2011 4th MOPNet Meeting : Manchester Institute for the Mathematical Sciences 25 - 30 April 2011 EU-NCG 4th Annual Meeting Simion Stoilow Institute of Mathematics of the Romanian Academy (IMAR) Bucharest, Romania Organized by D.E. Evans (Cardiff), R. Nest (Copenhagen), R Purice (IMAR), S Stratila (IMAR) 2-3 May 2011 WIMCS workshop on Representations of Braid and Symmetric Groups - New Approaches  Aberystwyth University  Organized by David Evans (Cardiff), Rolf Gohm (Aberystwyth) and Claus Köstler (Aberystwyth) See Also: http://users.aber.ac.uk/cck/wicms_may2011_aber/index.html  
  • 2012 5 - 7 September 2012 Stochastic Methods and Nonlinear PDEs Conference 4 September 2012 South West PDE Day Confirmed Speakers: Issac Vikram Chenchiah (Bristol), Roger Moser (Bath), Matteo Novaga (Padova), Kewei Zhang 28 June 2012 Institute of Non-Newtonian Fluid Mechanics Annual Public Lecture Speaker: Roland Keunings (UCL, Belgium) 8 - 11 May 2012 WIMCS-Leverhulme Conference on Spectral Theory 24 April 2012 Inverse Problems In Neuroimaging Conference 18 April 2012 LSW Frontiers Distinguished Lecture Isaac Newton Institute 20th Anniversary Lecture Alain Connes (College de France, IHES and Vanderbilt). Click here for more information. 17 April 2012 LSW Frontiers Distinguished Lecture Lyn Evans (CERN). Click here for more information. 16 - 20 April 2012 INI-WIMCS Meeting on Noncommutative Geometry  
  • 20 - 22 September 2010 3rd MOPNet Meeting : Edinburgh Conference Centre at Heriot-Watt University29 - 30 March 2010 2nd MOPnet Meeting : Department of Mechanical Materials and Manufacturing Engineering at Nottingham University 1 March - 30 April 2010 Quantum field theory on curved space-times and curved target-spaces Erwin Schrödinger International Institute for Mathematical Physics (ESI) Organized by M. Gaberdiel (ETH Zurich), S. Hollands (Cardiff), V. Schomerus (Hamburg) J. Yngvason (ESI Vienna) Included a workshop (March 22 - 26) 26 February 2010 WIMCS Mathematical Physics Colloquium Swansea University Organized by David Evans (Cardiff) Speakers: Marcos Marino (Geneva) and Richard Thomas (Imperial)
  • 2008 16 – 20 June 2008 EU-NCG 1st Annual Meeting School of Theoretical Physics, Dublin Institute for Advanced Studies (DIAS) Scientific Advisory Committee: R. Dijkgraaf (Amsterdam), D.E. Evans (Cardiff), A. Jaffe (Harvard), R. Nest (Copenhagen), W. Nahm (DIAS Dublin), D. O'Connor, Dublin.     2007 8 January - 29 June 2007 Analysis on Graphs and its Applications Isaac Newton Institute for Mathematical Sciences, Cambridge Organised by :  B..M Brown (Cardiff),  P. Exner (Czech Academy of Sciences),  P. Kuchment (Texas), T Sunada (Meiji)
  • 2009 28 September - 2 October 2009 EU-NCG 2nd Annual Meeting and Mid-Term Review Mathematics Institute, Copenhagen University Organized by E. Christensen (Copenhagen), S. Eilers (Copenhagen), D. E. Evans (Cardiff), R Nest (Copenhagen) 14 - 15 September 2009 1st MOPnet Meeting : Department of Mathematics at Reading University  
  • 2011 24 – 19 July 2011 ORAHS 2011 OR Informing National Health Policy 1 July 2011 WIMCS Mathematical Physics Colloquium Speakers: Susanne Danz (Oxford), Terry Gannon (Edmonton), Grigory Garkusha (Swansea) 9 - 10 May 2011 EU-NCG WIMCS workshop on Higher Gauge Theory, TQFT's and Categorification. Speakers include: Aristide Baratin (Orsay, Paris), Benjamin Bahr (Cambridge), Alexander Kahle (Göttingen), Jeffrey Morton (Lisbon), Urs Schreiber (Utrecht), Jamie Vicary (Oxford), Konrad Waldorf (Regensburg), Christoph Wockel (Hamburg) 20 - 21 April 2011 EU-NCG WIMCS workshop on Quantum Field Theory Speakers: Henning Bostelmann (York), Romeo Brunetti (Trento), Detlev Buchholz (Göttingen), Christian Jäkel (Cardiff), Gandalf Lechner (Vienna), Florian Robl (Cardiff) 4-8 April 2011 European Study Group with Industry 80 17 January 2011 LSW Frontiers Distinguished LectureSpeaker: Sir Michael Atiyah (Edinburgh)  
  • 2010 20 – 22 December WIMCS Annual Meeting 18 - 20 December New Trends in Spectral Theory and Applications 28 June LSW Frontiers Distinguished Lecture Speaker: Dan-Virgil Voiculescu (Berkeley) 28 June - 2 July EU-NCG 3rd Annual Meeting Speakers include: Iakovos Androulidakis (Göttingen), Dorothea Bahns (Göttingen), Moulay-Tahar Benameur (Metz), Sebastiano Carpi (Rome), Kenny De Commer (Rome), Bergfinnur Durhuus (Copenhagen), Robin Hillier (Rome), Stefan Hollands (Cardiff), Tommaso Isola (Rome), Yasuyuki Kawahigashi (Tokyo), Amin Malik (Oslo), Jouko Mickelsson (Helsinki), Denjoe O'Connor (DIAS), Thomas Schucker (Provence), Wojciech Szymanski (Odense), Otgonbayar Uuye (Copenhagen), André Verbeure (K.U. Leuven), Dan Voiculescu (Berkeley), Mihaly Weiner (Rome), Jakob Yngvason (ESI, Vienna), Laszlo Zsido (Rome). 21-25 June
  • LMS Regional Meeting and Workshop on Operator Algebras and Physics Principal Speaker: Constantin Teleman (Berkeley) who is giving a series of talks on Two Dimensional Topological Quantum Field Theories and Gauge Theories. The first talk by Constantin Teleman will be in the LMS regional meeting on the first afternoon, Monday 21 June which is embedded in the five-day workshop. The other speaker in the regional meeting on the Monday afternoon will be Werner Nahm (Dublin). Speakers include Terry Gannon (Alberta), Johannes Kellendonk (Lyon), Michael Müger (Nijmegen), Andreas Recknagel (King's), Karl-Henning Rehren (Göttingen), Richard Szabo (Heriot-Watt), Jean-Louis Tu (Metz), Gerard Watts (King's) 17-21 May Nigel Higson Lectures The Baum-Connes Conjecture and Group Representations. This includes a Spitalfields Day on 17 May with speakers Terry Gannon (Alberta) and Nigel Higson. Speaker: Nigel Higson (Penn State) 5 May Multifractionality and Multifractality and Their Applications TThe Workshop was sponsored by a grant form European Commu
  • nities PIRSES-GA-2008-230804 (Marie Curie) "Multi-parameter Multi-fractional Brownian Motion" for collaboration between Cardiff University and CNRS, Nancy (France), Kyiv National Taras Shevchenko University (Ukraine) and Bar Ilan University (Israel). Speakers: Prof. Y. Mishura (Kyiv University), Prof. N. Leonenko (Cardiff University), Dr.L.Sakhno (Kyiv University), Dr.G.Shevchenko (Kyiv University), Mr A.Ralchenko (Kyiv University).   15 April COW Seminar Speakers: Katrin Wendland (Augsburg) and Sven Meinhardt (Oxford) 15 February - 5 March Period on Planar Algebras and Physics Speakers: JulienBichon (Clermont), Stephen Bigelow (UCSB), Richard Burstein (Vanderbilt), Ben Davison (Oxford), Jürgen Fuchs (Karlstad), Shamindra Ghosh (KU Leuven), Pinhas Grossman (Cardiff), Ved Gupta (Leuven), Amihay Hanany (Imperial), Yang-Hui He (Oxford), PawelKasprzak (Copenhagen), Alastair King (Bath), Mathew Pugh (Cardiff), Alex Quintero-Velez (Glasgow), Sven Raum (Leuven), Peter West (King's College, London) 13-14 January 2010 LANCS Workshop on Heuristic Understanding  
  • 2009 3 – 4 September Lattice Boltzmann Method Workshop 29 June– 1 July Spectral Theory, Quantum Chaos and Random Matrices Organized by: Michael Levitin (Cardiff) and Uzy Smilansky (WIS Israel and Cardiff). 15 – 17 April AERC 2009 5th Annual European Rheology Conference 30-31 March Inaugural Meeting of MOPNET 19 March 125th Anniversary Cardiff Distinguished Lecture Speaker: Percy Deift (Courant Institute) 11 February Analysis Cluster Workshop 22 January Operator Algebras Seminar Speakers: Simon Wassermann (Glasgow), Wilhelm Winter (Nottingham), Rolf Gohm (Aberystwyth). 13 and 14 January WIMCS Mathematical Physics Lectures Speaker: Professor Tim Porter (Bangor, Wales). Title: Categorification and bundles
  • 2008 26 – 27 August Non-classical, boundary and localisation phenomena in mathematical homogenisation, sponsored by LMS and WIMCS 12 – 18 July Workshop on Computation and Analytic Problems in Spectral Theory Gregynog 30 April Workshop on Mathematical Analysis and Modern Applications, Spaces and Operators on Bad Domains in Rn 30 January Workshop on Mathematical Analysis and Modern Applications   2007 25 – 26 September Perturbed periodic PDEs, problems with singular boundaries, and their numerical aspects, sponsored by LMS.
elliothowells

Postgraduate Seminars 2014 - 2015 - 0 views

  • Postgraduate Seminars 2014-2015 Programme All seminars will be held at 3:15pm in M/2.06 on Wednesdays unless otherwise stated. If there is a colloquium being held that week then no seminar will be held. Please direct any enquiries to the organizer James Evans (EvansJA8@Cardiff.ac.uk) 15 October 2014 Speaker: James Evans. Title: An Overview of Vector Calculus. Abstract: Vector calculus is an essential tool in most of applied mathematics and concerns itself with the differentiation and integration of vector fields mostly in 3D. The talk will build up to two key theorems; Gauss’ Divergence Theorem and Stokes’ Theorem. Applications in fluid mechanics and electromagnetic theory will be discussed.
  • 22 October 2014 Speaker: Waleed Ali. Title: Introduction to Statistical Mechanics. Abstract:Ever since James Clerk Maxwell put forward the first-ever statistical law in physics, the idea of “probabilistic mechanics” became a topic of great interest for many disciplines. This seminar will merely introduce the main concepts and the revolutionary ideas that helped shape mechanics and mathematical physics as it is known today. The talk will deal with questions raised in mechanics, statistics, physics, philosophy, history and how they are all tied together. Examples of statistical mechanics will also be briefly discussed, including applications in thermodynamics, quantum mechanics and biology.
  • 19 November 2014 Speaker: Edd Lewis. Title: On Solving Linear Systems Efficiently. Abstract: Here we discuss the ways in which one can efficiently solve large linear systems of equations, the Ax=b problem. We will start by outlining the nature of the problem, discussing factorization techniques such as QR and Cholesky decomposition before moving on to some iterative solvers. 3 December 2014 Speaker: Brad Hardy. Title: Introduction to Heuristic Methods. Abstract: Heuristic methods are used when an optimal solution would require an excessive, if not infinite, amount of time to obtain. Although not guaranteeing optimality, heuristic methods find “good” solutions in much shorter periods of time. In this talk I will briefly outline why we use heuristic methods and introduce several, different approaches. Throughout, I will use the graph colouring problem (GCP) to illustrate examples and highlight my particular interest in these methods..
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  • 29 October 2014 Speaker: Gareth Davies. Title: Introduction to Survey Sampling. Abstract: Sampling theory is concerned with the problem of selecting samples that, when given a characteristic of interest, is representative of a “target’’ population. Survey sampling specifically considers sampling theory in the case where surveys or questionnaires are used to retrieve data from the sample. Various survey sampling techniques will be introduced, including simple random sampling, stratified sampling and cluster sampling. Application of these techniques in practice shall also be considered. 12 November 2014 Speaker: Xander Ramage. Title: Introduction to Fluid Dynamics. Abstract: The Navier-Stokes equations, which describe the motion of fluid, will be solved in some cases for which analytic solutions exist (such as flow through a pipe or channel). The Reynolds number will be introduced and its significance discussed. If time permits, the Blasius Boundary layer describing flow over a flat plate will be discussed as an example of a flow configuration without analytic solution.
  • 10 December 2014 Speaker: Stephen Moore. Title: An Introduction to Group Theory Abstract: Group theory has been a major area of research in pure mathematics for nearly 200 years, and has been used in a wide range of areas from Galois' proof that there is no quintic equation, to invariants for topological spaces and forming the standard model of particle physics. The talk will introduce the basic definitions and properties of groups, then briefly cover major areas such as the classification of finite groups, group actions, representations and Lie groups.
  • 4 February 2015 Speaker: Ross MacKenzie. Title: Modelling large physical systems via Modelica Abstract: The talk will give an introduction to component based modelling and the Modelica language. There will be many physical examples shown and challenges that face the approach will be highlighted.
  • 18 February 2015 Speaker: Scott Morgan. Title: An Introduction to Hydrodynamic Stability Theory Abstract: Hydrodynamic stability theory aims to understand the evolution of small disturbances in fluid flows over time. An unstable flow when subjected to a small perturbation will develop into an undesirable turbulent state. Turbulence arises in many engineering applications with the most obvious being air travel. Even a small delay in laminar to turbulent transition can have major positive effects on fuel efficiency and cost. Here we will cover basic ideas of what it means for a flow to be stable or unstable and introduce the defining equation for instability - the Orr-Sommerfeld equation. Some well-established results will be presented and some ideas about how turbulence may be delayed in practice will be discussed. Time permitting, we will briefly discuss some numerical techniques used to solve the eigenvalue problem associated with the Orr-Sommerfeld equation
  • 25 February 2015 Speaker: Peter Embacher. Title: Elementary Properties of Gamma-Convergence Abstract: Gamma-convergence is a tool particularly useful to derive meaningful limit problems in the context of calculus of variations. The goal of the talk is to introduce the basic concept of Gamma-convergence, giving the abstract definition as well as examples to illustrate the main properties and sketch the scope of applications. The most characteristic features are formulated as theorems and proved. 4 March 2015 Speaker: Jason Young. Title: Simulating a Queue in Python Abstract: Simulation is useful in a wide range of fields in Mathematics. This talk will give a brief overview into the algorithms behind simulations and how they can be applied specifically to a single server queueing problem. The talk will conclude with an overview of the code which will simulate a simple queue (in Python) and a quick demonstration of the software verifying theoretical results. 11 March 2015 Speaker: Matthew Lewis. Title: Introduction to Crytography Abstract: TBC
  • 18 March 2015 Speaker: Alex Mackay. Title: An introduction to Special Relativity Abstract: What would the world look like if you were riding alongside a light beam? The simple thought experiment that lead to one of the most important advancements in human history. Einstein's revolutionary papers in 1905 unlocked a whole ocean of knowledge that we now take for granted including the famous special theory of relativity. The concept of relativity i.e. the absence of absolute motion has been understood since the days of Galileo. However this concept, when formulated by Newtonian classical mechanics clashes with other fundamental principles in physics, namely Maxwell's Theory of electromagnetism. Who was wrong: Newton or Maxwell? Einstein set out to correct the issue in his special theory, and in doing so has changed the way we perceive space and time forever. 25 March 2015 Speaker: Freddy Symons. Title: TBC Abstract: TBC 29 April 2015 Speaker: James Evans. Title: What is Homogenisation? Abstract: Abstract: Homogenisation is a theory which has been developing in a number of directions for well over four decades and captures well the behaviour of a class of problems in elasticity, electromagnetism and fluid mechanics. In this talk, I will discuss briefly the need for homogenisation methods in the analysis of partial differential equations with coefficients which depend on a small parameter. A simple illustrative example will be given to try and motivate the theory as well as an overview of the variety of problems for which this theory can be applied.
elliothowells

Holly Robinson - Lloyds Banking Group - 0 views

  • Holly Robinson - Lloyds Banking Group June 2009 to June 2010 In June 2009, after passing a one day assessment centre and a follow up interview, I started my Industrial Placement with Lloyds Banking Group based in Bristol. Having banked with and researched the organisation, I was excited to know I would be joining the UK's largest retail bank at a critical time following the acquisition of HBOS just 6 months prior. I was initially nervous with starting, but over the 14 months I spent in the Business Analysis team, I feel I really grew as a person and became an integral part of the team. My role involved using my newly learnt data mining and analyst skills to answer real business questions from all different areas. I worked primarily on supporting the Savings business, although I was given many opportunities outside my normal role to project manage, lead a team, network and deliver some high profile work for senior managers. Overall for my placement I achieved a 'Strong Performer' rating and won a Gold Award for "outstanding behaviour". Some of the feedback I received includes being described as "invaluable member of the team, comfortably exceeding (my) expectations for an Industrial Placement" having done a "fantastic job this year!" The main benefits I will take away include motivation for my final year, guidance on future jobs, relevant experience and business understanding that will aid me interviews, both technical and soft skills training and most of all confidence in my own ability. During my placement I feel that I not only made real contribution but gained a lot that will hopefully make me a more attractive candidate for graduate jobs. I think what sums up my time most at Lloyds Banking Group is having cried during my leaving speech. The only thing I was able to manage to say, was that "I never thought I would enjoy working so much."
elliothowells

Applied and Computational Mathematics Seminars 2014 - 2015 - 0 views

  • Applied and Computational Mathematics Seminars Programme These seminars take place on Tuesdays, in Room M/2.06, Senghennydd Road, Cardiff from 3pm, unless otherwise stated. When a seminar is not scheduled there is a collaborative workshop with other groups within the College of Physical Sciences & Engineering or a SIAM Chapter Meeting. Further details can be found on the School Diary. For more information or if you wish to give a talk, please contact the programme organiser Dr Angela Mihai. 7 October 2014 Speaker: Daniel Lesnic (University of Leeds). Title: Determination of a force function in the wave equation. Abstract: The determination of an unknown space- or time-dependent force function acting on a vibrating structure from boundary, interior or integral observations are investigated. Sufficient conditions for the uniqueness of solution are provided. These linear inverse force problems are ill-posed since small errors in the input data cause large errors in the output force solution. Consequently, when the input data is contaminated with noise, we use regularization methods, e.g. Tikhonov's regularization, or conjugate gradient method, in order to obtain a stable solution. Numerical results will be presented and discussed. 14 October 2014 Speaker: Timo Betcke (University College London). Title: A spectral view on convolution quadrature methods for the wave equation.
  • Abstract: Convolution Quadrature (CQ) methods are Laplace transform type methods for the solution of time-domain wave problems. They are particularly popular for the solution of exterior time-domain wave scattering problems using boundary integral equation formulations in the Laplace domain. In this talk we will take a spectral view on CQ methods and discuss the connection between scattering poles of the solution operator, the underlying time-stepping scheme and convergence of CQ methods. The presented numerical examples are computed with BEM++, an open-source boundary element library developed at UCL. We will give a brief overview of BEM++ and demonstrate its functionality for solving boundary integral equations. 28 October 2014 Speaker: John Pryce (Cardiff School of Mathematics). Title: The Forthcoming IEEE 1788 Standard for Interval Arithmetic. Abstract: Interval arithmetic (IA) is the most used way of producing rigorously proven results in problems of continuous mathematics, usually in the form of real intervals that (even in presence of rounding error) are guaranteed to enclose a value of interest, such as a solution of a differential equation at some point. The basics of IA are generally agreed e.g., to add two intervals xx, yy, find an interval containing all x + y for x in xx and y in yy.
  • Many versions of IA theory exist, individually consistent but mutually incompatible. They differ especially in how to handle operations not everywhere defined on their inputs, such as division by an interval containing zero. In this situation a standard is called for, which not all will love but which is usable and practical in most IA applications. The IEEE working group P1788, begun in 2008, has produced a draft standard for interval arithmetic, currently undergoing the IEEE approval process. The talk will concentrate on aspects of its architecture, especially: - the levels structure, with a mathematical, a datum and an implementation level; - the decoration system, which notes when a library operation is applied to input where it is discontinuous or undefined. Time permitting, I may outline the P1788 flavor concept, by which implementations based on other versions of IA theory may be included into the standard in a consistent way. 11 November 2014 Speaker: Natalia Kopteva (University of Limerick, Ireland). Title: Maximum norm a posteriori error estimates for parabolic partial differential equations. Abstract: Solutions of partial differential equations frequently exhibit corner singularities and/or sharp boundary and interior layers. To obtain reliable numerical approximations of such solutions in an efficient way, one may want to use meshes that are adapted to solution singularities. Such meshes can be constructed using a priori information on the solutions, however it is rarely available in real-life applications. Therefore the best hope for the future seems to be offered by the automated mesh construction by adaptive techniques. This approach requires no initial asymptotic understanding of the nature of the solutions and the solution singularity locations.
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  • Reliable adaptive algorithms are based on a posteriori error estimates, i.e. estimates of the error in terms of values obtained in the computation process: computed solution and current mesh. Such a posteriori error estimates for parabolic partial differential equations will be the subject of this talk. For classical and singularly perturbed semilinear parabolic equations, we give computable a posteriori error estimates in the maximum norm, which, in the singularly perturbed regime, hold uniformly in the small perturbation parameter. The parabolic equations are discretized in time using the backward Euler, Crank-Nicolson and discontinuous Galerkin methods. Both semidiscrete (no spatial discretization) and fully discrete cases will be considered. The analysis invokes certain bounds for the Green's function of the parabolic operator. When dealing with the full discretizations, we also employ the elliptic reconstruction technique. Although parts of our analysis are quite technical, it will be demonstrated (using a first-order ODE example as a trivial case of a parabolic PDE) that some main ideas are quite elementary. 18 November 2014 Speaker: Robert Style (University of Oxford). Title: The mechanics of soft solids - breaking classical laws. Abstract: Soft solids make up the bulk of biological material, and are increasingly being used for new technology like wearable electronics, and soft robotics. However, despite their importance, experiments show that many classical laws fail to describe them. For example, I will show how classical theories of wetting, composite mechanics and contact mechanics significantly break down at a critical `elastocapillary' lengthscale -- because of solid surface tension. Furthermore, I will show how these phenomena highlight the existence of a swathe of new, small-scale behaviour in soft materials. Co-Host: Dr. Maurice Blount.
  • 25 November 2014 Speaker: Xuesong Wu (Imperial College London). Title: Nonlinear development of disturbances in transitional and turbulent free shear flows. Abstract: Free shear flows, such as mixing layers, jets and wakes, are inviscidly unstable due to their inflectional velocity profiles. Instability modes, which are usually excited by external perturbations, amplify on the shear floow, leading to vortex roll-up and randomization in the nonlinear stage. Interestingly, in turbulent state free shear flows exhibit a high degree of order, characterised by the prevalent presence of so-called coherent structures, the most striking of which are Brown-Roshko rollers . Both instability waves and coherent structures are known to be dynamically significant for entrainment and mixing, noise generation as well as for turbulence modelling. In this talk, I will present a nonlinear theory to describe first the development of instability modes on laminar free shear layers. The theory predicts vortex roll-up and randomisation through a generalized side-band instability mechanism. The theory will then be modified to describe formation and evolution of Brown-Roshko rollers on turbulent mixing layers. Co-Host: Dr. Chris Davies
  • 2 December 2014 Speaker: Matthias Heil (University of Manchester). Title: Wrinkly fingers: fluid-structure interaction in elastic-walled Hele-Shaw cells. Abstract: Viscous fingering in Hele-Shaw cells is a classical and widely studied fluid-mechanical instability: When air is injected into the narrow, liquid-filled gap between parallel rigid plates, the axisymmetrically expanding air-liquid interface tends to be unstable to non-axisymmetric perturbations when the capillary number -- the ratio of (destabilising) viscous to (stabilising) capillary forces acting at the air-liquid interface -- becomes sufficiently large. The introduction of wall elasticity (via the replacement of one of the bounding plates by an elastic membrane) can weaken or even suppress the fingering instability, but it also makes the system susceptible to additional solid-mechanical instabilities.
  • We show that in elastic-walled Hele-Shaw cells that are bounded by sufficiently thin elastic sheets, the (fluid-based) viscous fingering instability can arise concurrently with a (solid-based) wrinkling instability. We study the interaction between these distinct instabilities, using a theoretical model that couples the depth-averaged lubrication equations for the fluid flow to the Föppl--von Kármán equations, which describe the deformation of the thin elastic sheet. We employ a linear stability analysis to determine the growth rate of non-axisymmetric perturbations to the axisymmetrically expanding bubble, and perform direct numerical simulations to study the nonlinear interactions between the instabilities. We show that the system's behaviour may be characterised by a non-dimensional parameter that indicates the strength of the fluid-structure interaction. For small [large] values of this parameter the system's behaviour is dominated by viscous fingering [wrinkling], with strong interactions between the two instabilities arising in an intermediate regime. [Joint work with Draga Pihler-Puzovic and Anne Juel]. Co-Host: Dr. Chris Davies
  • 3 February 2015 Speaker: Helen Wilson (University College London). Title: Instabilities in viscoelastic fluids. Abstract: Non-Newtonian and viscoelastic fluids show many fascinating properties. One of the most surprising (and irritating, for those who process them in a manufacturing context) is their susceptibility to instabilities at flow rates where an "equivalent" Newtonian fluid would flow stably. I will use linear stability theory, and some asymptotic expansions, to discuss two distinct instability mechanisms which are unique to viscoelastic fluids. Co-Host: Professor Tim Phillips. 10 February 2015 Speaker: Dmitri Tseluiko (University of Loughborough). Title: Wave dynamics on a liquid film sheared by a turbulent gas
  • Abstract: The dynamics of a thin laminar liquid film flowing under gravity down the lower wall of an inclined channel when turbulent gas flows above the film will be discussed. The solution of the full system of equations describing the gas-liquid flow faces serious technical difficulties. However, a number of assumptions allow isolating the gas problem and solving it independently by treating the interface as a solid wall. This permits finding the perturbations to normal and tangential stresses at the interface imposed by the turbulent gas in closed form. Then the liquid film flow under the influence of these perturbations can be analysed by deriving and analysing a hierarchy of model equations describing the dynamics of the interface, i.e. boundary-layer equations, a long-wave model and a weakly nonlinear model, which turns out to be the Kuramoto-Sivashinsky equation with an additional term due to the presence of the turbulent gas. Also, by combining the long-wave approximation with a weighted-residual technique, an integral-boundary-layer approximation that is valid for moderately large values of the Reynolds number can be obtained. This model is then used for a systematic investigation of the flooding phenomenon observed in various experiments: as the gas flow rate is increased, the initially downward-falling film starts to travel upwards while just before the wave reversal the amplitude of the waves grows rapidly. Co-Host: Dr Nikos Savva.
  • 17 February 2015 Speaker: David Needham (University of Birmingham). Title: The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data. Abstract: This talk addresses the Cauchy Problem for a Non-Lipschitz Semi-Linear parabolic PDE with trivial initial data. The question of uniqueness is considered, in particular in relation to the existence of classes of spatially inhomogeneous solutions, and their relation to maximal and minimal solutions. Co-Host: Professor Tim Phillips. 17 March 2015 Speaker: Paul Milewski (University of Bath). Title: Modelling and computation of pilot wave-bouncing droplet dynamics in a Faraday problem. Abstract: Recent experiments by two groups, Yves Couder (Paris) and John Bush (MIT) have shown experimentally that droplets will bounce on the surface of a vertically vibrated bath (instead of coalescing with it), generating a damped Faraday wavefield at every bounce. As the forcing is increased, a pitchfork symmetry breaking bifurcation leads to a "walking" state whereby the bouncing droplet is guided by the self-generated wavefield: the droplet s pilot wave. Once this state is achieved a large array of interesting dynamics ensues with surprising analogies to quantum mechanical behaviour. The system appears to show that probabilistic quantum behaviour can arise from a physical deterministic system. We present a coupled particle-fluid model that can can be used simulate the fascinating dynamics of this problem. This is joint work with John Bush, Andre Nachbin (IMPA) and Carlos Galeano-Rios (IMPA). Co-Host: Dr Nikos Savva.
  • 12 May 2015 Speaker: Pierre Colinet (TIPs laboratory, Université Libre de Bruxelles) Title: Evaporation of droplets with moving contact lines Abstract: Despite many years of intensive research, the modeling of contact lines moving by spreading and/or evaporation still remains a subject of debate nowadays, even for the simplest case of a pure liquid on a smooth and homogeneous horizontal substrate. In addition to the inherent complexity of the topic (singularities, micro-macro matching, intricate coupling of many physical effects, ), this also stems from the relatively limited number of studies directly comparing theoretical and experimental results, with as few fitting parameters as possible. In this presentation, I will address various related questions, focusing on the physics invoked to regularize singularities at the microscale, and discussing the impact this has at the macroscale. Two opposite minimalist theories will be detailed: i) a classical paradigm, based on the disjoining pressure in combination with the spreading coefficient; ii) a new approach, invoking evaporation/condensation in combination with the Kelvin effect (dependence of saturation conditions upon interfacial curvature). Most notably, the latter effect enables resolving both viscous and thermal singularities altogether, without needing any other regularizing effects such as disjoining pressure, precursor films or slip length. Experimental results are also presented about evaporation-induced contact angles, to partly validate the first approach, although it is argued that reality might often lie in between these two extreme cases. Co-Host: Dr Nikos Savva
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