ICMS

Jun 23, 2008 - Jun 27, 2008

Heriot Watt University, Edinburgh

Scientific Organiser
Jack Carr

Scientific Committee
Professor Jerry Bona, Co-Chair (University of Illinois)
Professor Jack Carr, Heriot-Watt University
Professor Dick James (University of Minnesota)
Professor Jerry Marsden, Co-Chair (California Institute of Technology)
Professor Stefan Müller (Max Planck Institute for Mathematics, Leipzig)
Dr François Murat (Université Pierre et Marie Curie, Paris VI)
Professor Marshall Slemrod (University of Wisconsin)

Local Organising Committee
Professor Tony Carbery (University of Edinburgh)
Professor Jack Carr (Heriot-Watt University)
Professor Chris Eilbeck (Heriot-Watt University)
Professor Robin Knops (Heriot-Watt University)
Professor John Toland (University of Bath)

2008 sees the 60th birthday of Sir John Ball, FRS, FRSE, and we will be celebrating this occasion during the workshop. Lecture notes and photographs from the workshop are now available on a page maintained by Professor Eilbeck.

Nonlinear Partial Differential Equations (PDE) are of fundamental importance in mathematics and although major progress in their study has recently been achieved, many profound challenges remain. Developments are motivated not only by advances in pure and applied mathematics but also by new issues in the physical and biological sciences, mathematical finance and risk theory and many other applied disciplines.

Analytical, dynamical systems, as well as geometric methods continue to play a critical role in both fundamental investigations as well as numerical methods in solid and fluid mechanics, including complex materials, such as material microstructures and liquid crystals. It is clear that this subject is in a period of exciting growth and development. The principal aim of the workshop is to promote international exchange of recent developments in the analysis and geometry of PDE and their applications.

Specific objectives include:

1. mapping new frontiers of research
2. building bridges between the most recent developments in the general mathematical theory and the areas of applications that have developed most actively in the last few years,
3. identifying new applications of PDE

Specific themes of the workshop include:

• Nonlinear elasticity and liquid crystals
• Material science; microstructure, minimizer in the presence of symmetry, relation with experiment
• Calculus of variations
• Systems of conservation laws
• Transport equations
• Biomaterials Dynamical systems methods and the PDEs of mechanics

Supporting Institutions
EPSRC
Maxwell Institute for Mathematical Sciences (Centre for Analysis and Nonlinear PDE)
University of Oxford
LMS
Edinburgh Mathematical Society

 

Arrangements

Participation
You may apply to attend this meeting by completing the application form which is available at the top of this page. (Please note that the application form will close on 23 May, or when we have reached the maximum number for the meeting, 150.) You will then receive an e-mail confirming your place. Speakers and committee members will receive a separate invitation via e-mail.

If you do not receive an e-mail please contact Morag Burton.

Venue
The Workshop will be held at Heriot-Watt University. The campus is on the western edge of the city, near the airport, with excellent public transport to and from Edinburgh city centre. Click here for instructions on how to reach the university by various forms of transport.

Registration
There will be a combined Registration and Welcome Buffet on Sunday 22 June, at Heriot-Watt University. Those who cannot register on Sunday evening may do so on Monday 23 June prior to the start of the lectures or during the first coffee break. There will be a Registration Fee of 60.00 GBP. For those of you who want to pay by credit card, the credit card form can be found here. You may post or fax (+44 (0)131 220 1053) this to us in advance or bring it with you, already filled in, to registration. Please note that there is a 1.75% charge for use of credit cards

Poster Sessions
Contributed presentations in poster format are invited in all areas consistent with the conference themes. If you wish to submit a poster please submit a title and abstract (maximum 75 words) to J. Carr (at) ma.hw.ac.uk and a prompt decision will be made on its acceptability. Information on the format of the poster sessions will be available in March 2008.

Audio/Visual Facilities
A data projector, overhead projector, PC, laptopconnection and blackboards will be available.

Accommodation and Facilities
Single study-bedrooms are available at Heriot-Watt University. To book contact the Edinburgh Conference Centre directly on +44 (0)131 451 3669 or e-mail info@edinburgh-conference.com .
Invited participants should refer to their personal invitation letter for accommodation arrangements.

All rooms have a private shower and toilet and a telephone. The telephone will access incoming calls. You need to buy a telephone card from Reception in order to make outgoing calls. Each room also has an internet point should you wish to bring your laptop, although there is a charge for this service. Free email and internet access will be arranged in the central computer labs, the Library and to the university wireless network.

Meals and Refreshments
Breakfast will be provided for Heriot-Watt University residents for the period of their stay in the Middle Floor Dining Room.

Refreshments will be available during workshop breaks.

There will be a buffet supper (free of charge to participants) on the evening of Sunday 22 June between 19.00 and 20.30. Participants may register for the workshop during this buffet.

The Workshop Dinner will be on Thursday 26 June. Non-invitees are welcome to come to this on payment of £30.00, which will cover the dinner and wine. Payment for the dinner may be added to the amount being paid for the Registration Fee (see above).

Programme

Provisional Timetable

Monday 23 June

09:00-09:30	John Toland: Welcome
Chair:	Jack Carr
09:30-10:30	Constantine Dafermos (Brown University) Elastodynamics and John Ball
10:30-11:00	Refreshments
11:00-12:00	Stuart Antman (University of Maryland) Asymptotics of small inertias and large times in nonlinear continuum mechanics
12:00-13:00	Carme Calderer (University of Minnesota) Nonlinear elasticity and liquid crystals in biological and biomedical application
13:00-14:30	Lunch
Chair:	Tony Carbery
14:30-15:30	Maria J. Esteban (CEREMADE) Critical magnetic field for the Dirac-Coulomb model
15:30-16:00	Refreshments
16:00-17:00	Vladimir Sverak (University of Minnesota) Liouville theorems for the Navier-Stokes equations
17:00-18:00	Poster Viewing

Tuesday 24 June

Chair:	Robin Knops
09:30-10:30	Stefan Müller (Max Planck Institute for Mathematics, Leipzig) Some thoughts about crystals and the Cauchy-Born rule at positive temperature
10:30-11:00	Refreshments
11:00-12:00	Sergio Conti (Universität Bonn) Patterns in thin elastic sheets
12:00-13:00	Philippe Ciarlet (City University of Hong Kong) Intrinsic elasticity
13:00-14:30	Lunch and Poster Viewing
Chair:	Dick James
14:30-15:30	Nick Schryvers (University of Antwerp) Nano- and microstructures charaterized by transmission electron microscopy
15:30-16:00	Refreshments
16:00-17:00	Kaushik Bhattacharya (California Institute of Technology) Electronic structure and macroscopic properties of solids
17:00-18:00	Poster Viewing

Wednesday 25 June

Chair:	Chris Eilbeck
09:30-10:30	Bob Kohn (New York University) Cloaking by change of variables
10:30-11:00	Refreshments
11:00-12:00	Gero Friesecke (University of Warwick) A mathematical picture of basic aspects of the periodic table
12:00-13:00	Oliver Penrose (Heriot-Watt University) Statisical mechanics of nonlinear elasticity in the system of hard disks
13:00-14:30	Lunch
14:30-19:00	Afternoon Free

Thursday 26 June

Chair:	Stefan Müller
09:30-10:30	François Murat (Université Pierre et Marie Curie (Paris VI)) A priori estimate and existence for elliptic problems with subquadratic gradient dependent terms
10:30-11:00	Refreshments
11:00-12:00	Laszlo Szekelyhidi (Max Planck Institute, Leipzig) The h-principle in fluid mechanics
12:00-13:00	Michael Ortiz (California Institute of Technology) Minimum principles for characterizing the trajectories and microstructural evolution of dissipative systems
13:00-14:30	Lunch
Chair:	François Murat
14:30-15:30	Bernard Dacorogna (École Polytechnique Fédérale de Lausanne) On the pullback equation
15:30-16:00	Refreshments
16:00-17:00	Gilles Francfort (Université Paris-Nord) Evolution and approximation in brittle fracture
17:00-18:00	Discussions
Host:	Robin Knops
19:00-22:30	Evening Banquet

Friday 27 June

Chair:	Marshall Slemrod
09:30-10:30	Robert Pego (Carnegie Mellon University) How to compute the pressure in incompressible viscous flow with no-slip boundary
10:30-11:00	Refreshments
11:00-12:00	Antonio DeSimone (SISSA, Trieste) Excellent swimmers
12:00-13:00	Carsten Carstensen (Humboldt-Universität zu Berlin) Computational challenges in the calculus of variations
13:00-14:30	Lunch
Chair:	Jan Kristensen
14:30-15:30	Yann Brenier (Université de Nice-Sophia-Antipolis) Convection, magnetic relaxation and optimal transport
15:30-16:00	Refreshments
16:00-17:00	Terry Tao (University of California at Los Angeles) Global regularity of wave maps via harmonic map heat flow
17:00-18:00	Jack Carr: Close of Meeting

 

 

Presentations:

Presentation Details
Antman, Stuart
Asymptotics of small inertias and large times in nonlinear continuum mechanics
View Abstract Hide Abstract
There are numerous dynamical problems in mechanics in which some inertias are very small, their smallness signalled by a small parameter. For such problems it is customary to discard the small terms, in which case some or all the variables evolve quasistatically, i.e., through a sequence of equilibrium states parametrized by time. Formal asymptotic expansions in the small parameter might exhibit the detailed effects of the parameter. Rigorous asymptotic justifications, which provide error estimates and are typically far harder to carry out, are used by those compulsive about mathematical hygiene. They are valuable, however, when the formal theory exhibits surprising results. The purpose of this lecture is to illuminate the material behavior supporting the asymptotic justification of quasistatic response and to examine some strange and surprising large-time dynamical behavior when such justification is not available. These results will be described in the context of a couple of conceptually simple problems from particle and continuum mechanics.
Bhattacharya, Kaushik
Electronic structure and macroscopic properties of solids
View Abstract Hide Abstract
Defects play a critical role in determining the properties of solids. They do so even though they are present at extremely small concentrations because the long-range elastic fields they generate enables them to respond to macroscopic stresses and to interact with other distant defects. At the same time, the strength of the elastic field and other critical aspects of the defect core are determined by quantum mechanical interactions. This direct coupling between electronic and macroscopic scales makes defects both interesting and challenging to understand. We present a computational method for studying the electronic structure at macroscopic scales. We explain the mathematical framework that enables a systematic means of adaptive coarse-graining retaining full resolution where it is necessary and coarsening with no patches, assumptions or structure. We demonstrate its accuracy under modest computational cost and the physical insights it offers using various examples.
Brenier, Yann
Convection, magnetic relaxation and optimal transport.
View Abstract Hide Abstract
We establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport problems by a gradient flow approach. We interpret this geometric equation as a generalization of the Darcy-Boussinesq equations for use in Convection Theory. This suggests that the Navier-Stokes-Boussinesq equations, the basic model in Convection Theory, provide a good framework for Optimal Transport related problems, such as Hoskins' Semigeostrophic equations and some fully nonlinear version of some Chemotaxis equations. In a different direction, we introduce a "stringy" generalization of the Angenent Haker Tannenbaum model. This model is closely related to the Magnetic Relaxation model investigated by Arnold and Moffatt. It is a gradient flow for which the equilibrium states are just the (variational) solutions of the Euler equations for incompressible flows. We also discuss a vectorial version of the Burgers equation, the 'cross-Burgers' equation.
Calderer, Carme
Nonlinear elasticity and liquid crystals in biological and biomedical application
View Abstract Hide Abstract
Nonlinear elasticity plays a prominent role in the mathematical modeling of gels from the point of view of continuum physics. The coexistence of materials such as synthetic polymers and biological fibers with fluid, naturally yields gel states characterized by macroscopic properties including elasticity, diffusion, transport and dissipation. The mathematical problems analyzed in this presentation are motivated by two types of modeling endeavors: cell motility in fiber matrices and elastic behavior of body-implantable biomedical devices. Some of these systems are also highly anisotropic and exhibit liquid crystal behavior. I formulate and analyze boundary value problems arising in the design and implanting of biomedical devices. I will also discuss time dependent regimes dominated by dissipation. One main difficulty is the fact that both formulations, Lagrangian and Eulerian are present in the governing systems of partial differential equations. Finally, I will address the early-dynamics regime where chemical potentials dominate over viscosity. The governing system in such case is hyperbolic with a source term.
Carstensen, Carsten
Computational challenges in the calculus of variations
View Abstract Hide Abstract
The difficulties in the numerical simulation of three classes of problems, namely convex, polyconvex, and quasiconvex minimisation problems, guide through the presentation. Simple benchmarks in computational microstructures with finer and finer oscillations allow for a convexified relaxation hull to model the macroscopic behaviour of measure-valued generalised solutions. This motivates a class of degenerate convex minimisation problems with local regularity of stresses and a seemingly optimal a priori error control. Despite some reliability-efficiency gap in the a posteriori error analysis, there exist some convergent adaptive mesh-refining algorithm. Polyconvex minimisation problems allow for the existence of global minimisers with unclear regularity. For arbitrarily small loads in hyperelasticity, global minimisers coincide with local smooth solutions based on the implicit function theorem. In this situation, finite element methods are convergent as well. For more realistic loads, however, even $Gamma$ convergence of finite element approximations is uncertain. Finite strain elastoplasticity is based on a multiplicative split of elastic and plastic deformations which results in a non-convex mathematical model. In fact, a typical time-step within some incremental description of the elastoplastic evolution results in a non-quasiconvex minimisation problem. Difficulties with the efficient numerical relaxation are discussed for some single-slip elastoplastic benchmark. Nonlinear minimisation problems allow exciting phenomena such as repelling singularities. The Lavrentiev phenomena is shown to be equivalent to the failure of finite element methods. This motivates non-conforming discrete spaces and/or modified energies. The presentations reviews some solution strategies and a $L^p$ penalisation scheme with some preliminary affirmative results. The presentation is based on recent joint work with S. Conti, R. Huth, A. Orlando, C. Ortner.
Ciarlet, Philippe G.
Intrinsic elasticity
View Abstract Hide Abstract
In the classical approach to elasticity problems, the deformation field is the primary unknown. In the "intrinsic" approach, new unknowns with more mechanical or geometrical meanings, such as a strain tensor field or a rotation field for instance, are instead taken as the primary unknowns. We survey here recent progress about the mathematical analysis of such methods.
Conti, Sergio
Patterns in thin elastic sheets
View Abstract Hide Abstract
Crumpling a sheet of paper leads to the formation of folding patterns over several length scales. This can be understood on the basis of the interplay of a nonconvex elastic energy, which favors locally isometric deformations, and a small singular perturbation, which penalizes high curvature. Based on three-dimensional nonlinear elasticity and by using a combination of explicit constructions and general results from differential geometry, we prove that, in agreement with previous heuristic results in the physics literature, the total energy per unit thickness of such folding patterns scales at most as the thickness of the sheet to the power $5/3$. We contrast this scaling with the linear scaling obtained in the case of Dirichlet boundary conditions.
Dacorogna, Bernard
On the pullback equation
View Abstract Hide Abstract
I discuss the existence of a diffeomorphism for the change of variables formula for differential forms
Dafermos, Constantine
Elastodynamics and John Ball
View Abstract Hide Abstract
The seminal ideas introduced by John Ball in elastostatics are also relevant to elastodynamics.
DeSimone, Antonio
Excellent swimmers
View Abstract Hide Abstract
We will discuss swimming strategies for microscopic swimmers and recipes to optimize their strokes.
Esteban, Maria J.
Critical magnetic field for the Dirac-Coulomb model
View Abstract Hide Abstract
In this talk I will present joint work with Jean Dolbeault and Michael Loss in which we investigate the threshold of electron-positron pair creation for the Dirac-Coulomb model, describing the bound states of a relativistic electron submitted to a nuclear electrostatic field and an external constant magnetic field. Mathematically we are interested in the critical magnetic field at which the lowest energy state gets into the continuum spectrum, describing a destabilizing effect. A scaling argument allows us to find a simple variational characterization for the critical magnetic field. We use it in order to compare the general critical magnetic field and the one found when taking into account only states which lie in the lowest Landau level. We do this both analytically and numerically. We find an important discrepancy between the two regimes.
Francfort, Gilles A.
Evolution and approximation in brittle fracture
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In recent years, quasi-static crack evolution in a brittle solid has been revisited in a variational light. At this time, the only completely predictive model is based on global minimization, together with a surface energy that is proportional to the created crack area (the Griffith model). We will briefly review the main mechanical and mathematical features of this model and discuss its shortcomings. Because the essential ingredient of the model is an unconstrained crack path, the variational model is formulated in a BV type space which does not provide an easy setting for numerical computations. Approximating schemes, which are based on Gamma-convergence, typically fail to follow globally minimizing paths and may only capture paths among critical points. We will describe one dimensional results on the connection between critical points of the approximating functionals and those of the initial one. Finally, we will examine other approximations that are popular in the mechanics community and discuss their relevance to fracture evolution.
Friesecke, Gero
A mathematical picture of basic aspects of the periodic table
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In textbooks, the striking chemical similarities and differences between the elements are discussed on a descriptive, semi-empirical level, based on the "hydrogen orbital configurations'' developed by Bohr, Hund and Slater. In the talk I will present a mathematical picture (for the first ten elements H, He, Li, Be, B, C, N, O, F, Ne), based on calculating the many-electron Schroedinger ground state explicitly in a natural scaling limit. In this limit, the nontrivial postulates of Bohr, Hund and Slater (electrons filling orbitals, shell and sub-shell formation, sub-shell ordering rules such as 2s < 2p, Hund's rules) are seen to emerge in a natural way. In fact, in a small minority of cases (such as ordering of the excited states of the Carbon atom) our mathematical results differ from the semi-empirical theory (and experiment confirms our predictions). Proofs involve hydrogen atom theory, careful use of the symmetry group SU(2) x SO(3) x Z_2 of the many-electron Schroedinger equation and its representation theory, Fourier analysis, and ideas from quantum chemistry. Joint work with Ben Goddard (Warwick).
Kohn, Robert V.
Cloaking by Change of Variables
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We say a region of space is "cloaked" with respect to electromagnetic measurements if its contents -- and even the existence of the cloak -- are inaccessible to such measurements. One recent proposal for achieving cloaking takes advantage of the coordinate-invariance of Maxwell's equations. I shall explain this scheme, including its mathematical basis and its apparent limitations.
Murat, François
A priori estimate and existence for elliptic problems with subquadratic gradient dependent terms
View Abstract Hide Abstract
In this lecture I will consider the nonlinear elliptic model problem $$ u in H^1_0 (Omega), qquad - div , A(x) Du + alpha_0 u = gamma |Du|^q + f(x) ; ; hbox{in} ; {cal D}'(Omega),$$ with $A$ a coercive matrix with bounded coefficients, $alpha_0 geq 0$, $0 leq q leq 2$ and $fin L^m (Omega)$ for some suitable~$m$. This is a model problem, and there are many possible variants of it. In particular, I will consider the case where the right-hand side is only bounded by (but not equal to) $gamma |Du|^q + f(x)$. In the case where $0 leq q < 1$, existence is classical for $f in H^{-1} (Omega)$. When $gamma$ is large, the case where $q = 1$ and $f in H^{-1} (Omega)$ is difficult but has been solved by G. Bottaro and M.E. Marina in 1973. On the other hand, the case $q = 2$ has been treated by many authors, including in particular in a series of papers by L.~Boccardo, J.-P.~Puel and myself. In a more recent paper, V. Ferone and myself proved the existence of a solution $u$ which further satisfies $ e^{gamma u} -1 in H^1_0 (Omega)$, and an a priori estimate for such solutions, when %$fin L^{{N} over {2}} (Omega)$. In this lecture I will mainly report about recent joint work with Nathalie Grenon and Alessio Porretta, the announcement of which has been published in C. R. Acad. Sci. Paris, S'erie I 342 (2006), {23-28}. When $1 + (2 / N) leq q <2$ and $fin L^m(Omega)$ with $m = {{N (q-1)} / {q}}$ (we also solved the case where $1leq q < 1 + {{2}over{N}} $, but I will not discuss it since it uses the notion of renormalized solution), and when either $alpha_0 >0$ or $f$ is sufficiently small in $L^m(Omega)$, we prove the existence of a solution $u$ which enjoys the further regularity $|u|^sigma in H^1_0(Omega)$ with, $sigma = {{(N-2) (q - 1)} / {2(2 - q)}}$. Uniqueness results in this class have also been proved by G. Barles and A. Porretta under certain structure conditions. We moreover prove an a priori estimate for every solution in this class. One of the main interests of our work lies in this a priori estimate, the proof of which is non standard.
Ortiz, Michael
Minimum principles for characterizing the trajectories and microstructural evolution of dissipative systems
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This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i. e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of energy-dissipation functionals under consideration is derived by first defining a sequence of time-discretized minimum problems, stringing them together with weights that decay exponentially over times of order epsilon, and formally passing to the limit of continuous time. The Gamma-limit of these functionals as epsilon tends to zero is highly degenerate and provides limited information regarding the limiting trajectories of the system. Instead we seek to characterize the minimizing trajectories directly. The special class of problems characterized by a rate-independent dissipation functional is amenable to a particularly illuminating analysis. For these systems it is possible to derive a priori bounds that are independent of the regularizing parameter, whence it is possible to extract convergent subsequences and find the limiting trajectories. The relaxation of energy-dissipation functionals and optimal scaling can be rigorously derived in a number of examples of application. A first example concerns a one-dimensional bar characterized by a quadratic dissipation function and a bistable energy density. A second example concerns the coarsening kinetics of island growth in thin films exhibiting a preferred slope. In both cases, we present closed-form relaxations in the local limit of the problem and optimal scaling relations for the nonlocal problems. The relaxations rigorously characterize macroscopic properties of complex microstructural evolution by means of well-posed effective problems. The scaling relations rigorously characterize some average properties of the coarsening kinetics of the systems, and lead to predictions on the growth exponents. A third example of application concerns crack propagation. When dissipation is assumed to be concentrated at the crack front, the dissipation must be relaxed in general. We prove a general relaxation formula that gives the surprising result that the effective dissipation is always rate-independent.
Pego, Robert
How to compute the pressure in incompressible viscous flow with no-slip boundary
View Abstract Hide Abstract
We describe a formula for the pressure in the Navier-Stokes equations for incompressible flow with no-slip boundary conditions, that involves the commutator of the Laplacian and Leray-Helmholtz projection operators. An estimate for this commutator shows that it is strictly dominated by the viscous term at leading order. This leads to a number of new developments, including a well-posedness theorem for an extended Navier-Stokes dynamics unconstrained by the divergence-free condition, and a number of significant improvements concerning methods of numerical computation and numerical analysis for such flows. This is joint work with Jian-Guo Liu (Maryland) and Jie Liu (Irvine).
Penrose, Oliver
Statistical mechanics of nonlinear elasticity in a system of hard disks
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The model considered is a two-dimensional system of hard disks, with or without an attractive short-range interaction. A `constrained free energy' is defined, using the standard configurational integral of statistical mechanics subject to two constraints which relate the set of configurations we integrate over to a given close-packed reference configuration of the set of disks under consideration. These constraints are: (i) if two disks are nearest neighbours in the reference configuration, then their separation is constrained to be at most sqrt{2} times the disk diameter and (ii) each disk at the boundary of the reference configuration is constrained to stay within a specified distance from a specified ``anchor point". It is shown that, if the anchor points of the boundary particles are related to their reference positions by a constant deformation matrix A belonging to a certain open set (whose closure comprises all 2 x 2 matrices which, when applied to the reference configuration, produce a configuration that is compatible with the constraint (i) and also with the condition that disks must not overlap), then the free energy per particle, related to the partition function in the usual way, has a well-defined thermodynamic limit. It is also shown that the free energy per particle is a Lipschitz-continuous function of the matrix A and that it satisfies the integral inequality characterizing quasi-convex functions.
Schryvers, Dominique (Nick)
Nano- and microstructures characterized by transmission electron microscopy
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The present lecture will focus on some typical examples showing the strength and variety of different transmission electron microscopy modes for the characterization of nano- and microstructures that play an important role in the shape memory behaviour of materials undergoing martensitic phase transformations. A chronology of research will be followed, starting with early work on pretransitional modulations in Ni-Al observed by atomic resolution and a series of stress induced martensitic structures surrounding a micro-crack in the thin edge of a TEM sample. The nucleation and growth of the Ni5Al3 phase in the austenite as well as martensite matrix will be discussed after which the emphasis will shift to muliple microtwinned martensite structures as well as bending martensite needles in Ni-Al. In a second part the focus will be on the Ni-Ti system, in which the refinement of the atomic structure of the R-phase and the Ni4Ti3 precipitates will be documented, the determination of strain and concentration fields surrounding these precipitates will be shown as well as the measurement of the elastic constants of these precipitates. To finish some ideas for future work will be proposed.
Sverak, Vladimir
Liouville theorems for the Navier-Stokes equations
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It is well-known that every bounded solution of the heat equation defined in in all space and for all negative times is constant. Is a suitable version of this statement true for the Navier-Stokes equations? We will discuss what is known about this problem and its connections to other questions. The problem is open in the general 3d situation, but results can be obtained in some interesting special cases.
Szekelyhidi, Laszlo
The h-principle in fluid mechanics
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In the talk we discuss parallels between the Nash-Kuiper theory of isometric embeddings and the weak solutions of the Euler equations of ideal incompressible flows, that were constructed by Scheffer and Shnirelman. In particular the latter, when interpreted in the framework of the former, can be largely simplified and extended.
Tao, Terence
Global regularity of wave maps via harmonic map heat flow
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We discuss the use of harmonic map heat flow to renormalise the wave maps equation heat flow, and its ramifications for the global regularity problem.

Participants

Name	Institution
Adams, Stefan	University of Warwick
Antman, Stuart	University of Maryland
Ball, Sir John	University of Oxford
Bates, Peter	Michigan State University
Beck, Margaret	University of Surrey
Bhattacharya, Kaushik	California Institute of Technology
Bochkina, Natalia	University of Edinburgh
Bourne, David	Max Planck Institute
Brenier, Yann	CNRS Nice
Brown, Ken	Heriot-Watt University
Burns, Martin	University of Strathclyde
Calderer, Carme	University of Minnesota
Capdeboscq, Yves	University of Oxford
Carbery, Anthony	University of Edinburgh
Carr, Jack	Heriot Watt University
Carstensen, Carsten	Humboldt-Universität zu Berlin
Chenchiah, Isaac	University of Bristol
Cherednichenko, Kirill	University of Cardiff
Chlebik, Miroslav	University of Sussex
Chmaj, Adam	Warsaw University of Technology
Ciarlet, Philippe G.	City University of Hong Kong
Conti, Sergio	Universität Bonn
Coutand, Daniel	CANPDE, Maxwell Institute
Crooks, Elaine	University of Swansea
Dacorogna, Bernard	École Polytechnique Fédérale de Lausanne
Dafermos, Constantine	Brown University
Davidson, Fordyce	University of Dundee
Davies, Penny	University of Strathclyde
DeSimone, Antonio	Scuola Internazionale Superiore di Studi Avanzati
Domanski, Wlodzimierz	Polish Academy of Sciences
Dondl, Patrick	Max Planck Institute
Douglas, Robert	Aberystwyth University
Duncan, Dugald	Heriot-Watt University
Duran, Angel	University of Valladolid
Eilbeck, Chris	Heriot-Watt University
Esteban, Maria J.	CEREMADE
Farkas, Jozsef	University of Stirling
Francfort, Gilles A.	Université Paris-Nord
Friesecke, Gero	TU Munich
Grinfeld, Michael	University of Strathclyde
Haskins, Mark	Imperial College London
Henao, Duvan	University of Oxford
Hoang, Viet Ha	Nanyang Technological University
Hornig, Gunnar	University of Dundee
Hornung, Peter	Universität Bonn
Hsu, Cheng-Hsiung	National Central University,Taiwan
Hu, Wen-Guei	National Chiao Tung University
James, Richard	University of Minnesota
Kadem, Abdelouahab	University of Setif
Kalamajska, Agnieszka	University of Warsaw
Karmakar, Biswajit	Max Planck Institute
Khan, Abdul Rahim	King Fahd University of Petroleum and Minerals
Kirchheim, Bernd	University of Oxford
Knops, Robin	Heriot-Watt University
Koch, Gabriel	University of Chicago
Kohn, Robert V.	New York University
Kokarev, Gerasim	University of Edinburgh
Kontovourkis, Michalis	Max Planck Institute
Koumatos, Konstantinos	University of Oxford
Kristensen, Jan	University of Oxford
Lacey, Andrew	Heriot-Watt University (Marine and Tidal)
Leimkuhler, Ben	University of Edinburgh
Lord, Gabriel	Heriot-Watt University
Mahalov, Alex	Arizona State University
Maitre, Emmanuel	Université de Grenoble
Marohnic, Maroje	University of Zagreb
Matthies, Karsten	University of Bath
Melcher, Christof	University of Oxford
Moser, Roger	University of Bath
Muite, Benson	University of Oxford
Müller, Stefan	Max Planck Institute
Murat, François	Université Pierre et Marie Curie (Paris VI)
Nesenenko, Sergiy	Darmstadt University of Technology
Neukamm, Stefan	TU München
Neygebauer, Igor	National University of Rwanda
Niethammer, Barbara	University of Oxford
Ortiz, Michael	California Institute of Technology
Ortner, Christoph	University of Oxford
Otto, Felix	Universität Bonn
Pankratova, Iryna	Narvik University College
Pego, Robert	Carnegie Mellon University
Penrose, Oliver	Heriot-Watt University
Petrache, Mircea	Scuola Normale Superiore
Piatnitski, Andrey	Narvik University College
Rekalo, Andrey	Heriot-Watt University
Rule, David	University of Edinburgh
Rynne, Bryan	Heriot-Watt University
Sadowski, Witold	University of Warwick
Schryvers, Dominique (Nick)	University of Antwerp
Sengul, Yasemin	University of Oxford
Seregin, Gregory	University of Oxford
Serrano, Hélia	Universidad de Castilla-La Mancha
Shargorodsky, Eugene	King's College London
Shearer, Michael	North Carolina State University
Singer, Michael	University of Edinburgh
Sivaloganathan, Jeyabal	University of Bath
Slastikov, Valeriy	University of Bristol
Slemrod, Marshall	University of Wisconsin
Staubach, Wolfgang	Heriot-Watt University
Stelzig, Philipp Emanuel	TU München/Università di Trento
Strzelecki, Pawel	University of Warsaw
Suli, Endre	University of Oxford
Sverak, Vladimir	University of Minnesota
Szekelyhidi, Laszlo	Universität Bonn
Taheri, Ali	University of Sussex
Tambaca, Josip	University of Zagreb
Tambue, Antoine	Heriot-Watt University
Tao, Terence	University of California at Los Angeles
Toland, John	University of Bath
Tsering, Basang	University of Oxford
Velcic, Igor	University of Zagreb
Wagner, David	University of Houston
Watson, Stephen	University of Glasgow
Yang, Ting-Hui	Tamkang University
Yang, Tzi-Sheng	Tunghai University
Zarnescu, Arghir	University of Oxford
Zhang, Kewei	University of Swansea