02/4 IUTAM SYMPOSIUM on

Asymptotics, Singularities and Homogenisation in Problems of Mechanics,

University of Liverpool , Department of Mathematical Sciences, Liverpool, UK

8 - 11 JULY 2002

a) Scientific Committee

A. B. Movchan (UK, Chairman) , I. D. Abrahams (UK), A. G. Aslanyan (Russia),

D. Bigoni (Italy), H. Gao (Germany), K. Z. Markov (Bulgaria),

R. C. McPhedran (Australia), J. Salencon (France), W. Wendland (Germany)

b) Short summary of scientific progress achieved

The objective of the Symposium was to provide cross-linking of research activities in intensively developing areas of applied mathematics, continuum mechanics and theoretical physics involving asymptotic analysis and studies of singularities near non-smooth boundaries. Asymptotic analysis has proved to be one of the most powerful tools in singularly perturbed problems of mechanics and during recent years there were some new exciting developments in high order homogenisation theory, models of dynamic fracture, propagation of waves in composites and lattice models in mechanics of defects. In many of these areas rigorous asymptotic techniques can be engaged to produce a substantial breakthrough in longstanding problems. Phenomena of very different physical nature can be described in many instances by mathematical models of similar type. Examples include elastic and electromagnetic waves, dislocation dynamics and fluid motion along interface boundaries. The idea of bringing international experts in these fields together worked very well and the Symposium proved to be a great success. It initiated interesting new developments on the interfaces between applied mathematics, mechanics and theoretical physics. The topics covered in the Symposium included:

· Perturbation problems for partial differential equations and their applications in mechanics

· Homogenisation theory in models of composite structures

· Fracture. Mathematical models of cracks in solids

· Wave propagation, scattering

· Models of photonic and phononic band gap composite materials

· Models of dislocations in lattice structures

· Asymptotic and numerical models of imperfect interfaces

Forty four oral presentations and two poster sessions were given during the four days of the Symposium. Judging by the response of the participants the Symposium was highly successful and all the objectives were achieved completely.

c) Countries represented and number of participants

The meeting attracted 72 participants from 12 countries:

Australia, Denmark, France, Germany, Italy, Japan, Mexico, The Netherlands, Poland, Russia, UK, USA.

d) Publication of Proceedings of the Symposium

The Proceedings will be published by Kluwer Academic Publishers in 2003 (editor: A. B. Movchan).

e) Financial support

The Symposium was sponsored by the following funding bodies:

· International Union of Theoretical and Applied Mechanics

· European Office of Aerospace Research and Development, Air Force Office of Scientific Research, United States Air Force Research Laboratory

· London Mathematical Society

· Kluwer Academic Publishers

· University of Liverpool

We wish to thank our sponsors for their contribution to the success of the Symposium.

f) Scientific Programme

Monday, 8 July

09:00 - 09:20	Welcome address by J.W. Bruce Pro-Vice-Chancellor of Liverpool University
9:20-10.00	J.R. Willis^1 Dynamic perturbation of a propagating crack: implications for crack stability ^1University of Cambridge, UK
10:00 - 10:40	H. Gao^1 Extending fracture mechanics concepts to biological nanocomposite materials ^1Max Planck Institute, Stuttgart, Germany
10:40 - 11:20	D. Bigoni^1, E. Radi^2, D. Capuani^3 Instabilities and near tip crack fields in elastic, incompressible solids ^1University of Trento, Italy,^2University of Modena and Reggio Emilia, Italy,^3University of Ferrara, Italy
11:20 - 11.40	Refreshments - Reading Room

Monday, 8 July (continued)

11:40 - 12:20	A.J.M. Spencer^1 Exact singular solutions for an inhomogeneous thick elastic plate ^1University of Nottingham, UK
12:20 - 13:00	Yu.A. Antipov^1, V.V. Silvestrov^2 Method of hyperelliptic surfaces for vector functional-difference equations ^1University of Bath, UK^2Chuvash State University, Russia
13:00 - 13:40	Sandwich Lunch - Dining Room
13:40 - 14:20	F.J. Sabina^1, J. Bravo-Castillero^2, R. Rodriguez-Ramos^2, R. Guinovart-Diaz^2, Analysis of fibre-reinforced materials via the asymptotic homogenization method ^1Universidad Nacional Autonoma de Mexico, Mexico,^2Universidad de la Habana, Cuba
14:20 - 15:00	M. Gei^1, E. Radi^1 Near-Tip fields of mode III steady-state crack propagation in elastic-plastic strain gradient solids ^1University of Modena and Reggio Emilia, Italy
15:00 - 15:40	A. Cherkaev^1 Damageable structures of waiting links ^1University of Utah, USA
15:40 - 16:20	I.S. Jones^1 Methods of assessment of thermal striping fatigue damage ^1John Moores University, UK
16:20 - 17:00	O. Obrezanova^1, A.B. Movchan^2, J.R. Willis^1 Dynamic crack stability ^1University of Cambridge, UK, ^2Univerity of Liverpool, UK
17:00 - 17:40	I. Monetto^1, W.J. Drugan^2 On micromechanics-based non-local modeling of elastic matrices containing non-spherical heterogeneities ^1University of Genova, Italy, ^2University of Wisconsin-Madison, USA
17:40 - 18:00	Refreshments - Reading Room

Monday, 8 July (continued) Poster Session I: 18:00 - 19:00

M.D. Hughes^1, K. Chen^1 Fast iterative solution of coupled 3-dimensional fluid-structure interaction problems ^1University of Liverpool, UK	G.T. Piliposian^1, P.G. Appleby^1 A simple model of the origin and transport of ^222Rn and ^210Pb in the atmosphere ^1 University of Liverpool, UK
S.B. Platts^1, N.V. Movchan^1 Filtering and polarisation of elastic waves by 2D phononic crystals ^1University of Liverpool, UK	P.G. Appleby^1, A. Ploger^1, L. Camarero^2 The transport of fallout radionuclides in a high mountain lake ^1University of Liverpool, UK, ^2Universitat de Barcelona, Spain
A. Selsil^1, A.B. Movchan^1, N.V. Movchan^1 Asymptotic analysis of heat transfer in a system of channels connected by thin conducting walls ^1University of Liverpool, UK	G.S. Mishuris^1, K. Kolk^2, G. Kuhn^2 3D Singularities and its application to fatigue crack growth simulation ^1Rzeszow University of Technology, Poland, ^2 University of Erlangen, Nurnberg, Germany
S.E. Mikhailov^1, J. Orlik^2 Asymptotic homogenisation in strength and durability analysis of composites ^1Glasgow Caledonian University, UK, ^2 ITWM, Kaiserslautern, Germany	M.L. Shendeleva^1 Wave analogies in thermal wave reflection and refraction at an interface ^1South Bank University, UK
V.N. Biktashev^1 Envelope equations for modulated non-conservative waves ^1University of Liverpool, UK	M. Brun^1, D. Bigoni^1, D. Capuani^2 Boundary elements for non-linear elasticity ^1University of Trento, Italy^2University of Ferrara, Italy
E. Babenkova^1, J. Kaplunov^1 The two-term asymptotic expansion in the case of low-frequency vibrations of elongated elastic rectangular ^1University of Manchester, UK	C.G. Poulton^1, S. Guenneau^1, A. Nicolet^2, A.B. Movchan^1 Investigation of the coupling between light and sound waves in periodic structures with finite element and Rayleigh methods ^1University of Liverpool, UK, ^2Fresnel Institute, Marseille, France
R. Suckley^1, V.N. Biktashev^1 Geometry of the slow manifold in the Hodgkin-Huxley system of equations ^1University of Liverpool, UK	C.J. Powles^1 Supersonic leading-edge noise ^1Keele University, UK
J.B. Lawrie^1, R. Kirby^1 Analysing the performance of a dissipative silencer: a mode-matching approach ^1Brunel University, UK	I.M. Mohamed^1, J.B. Lawrie^1 A parametric investigation of the acoustic power in a two dimensional waveguide with membrane bounded cavity ^1Brunel University, UK
M. Perelmuter^1 Fracture criterion for cracks with bridged zone ^1IPM, Moscow, Russia

Tuesday, 9 July

09:00 - 09:40	I.D. Abrahams^1 On the approximate factorization of Wiener-Hopf kernels with applications in structural acoustics ^1University of Manchester, UK
09:40 - 10:20	R.C. McPhedran^1, N. Nicorovici^1 C.G. Poulton^2, L.C. Botten^3 Localized states in photonic crystals: A multipole method ^1University of Sydney, Australia, ^2University of Liverpool, UK, ^3University of Technology Sydney, Australia
10:20 - 11:00	J.S. Jensen^1, O. Sigmund^1 Periodic band gap structures as optimal designs ^1Technical University of Denmark, Denmark
11:00 - 11:40	F.Zolla^1, S. Guenneau^2 Artificial ferro-magnetic anisotropy: Homogenization of 3D finite photonic crystals ^1Fresnel Institute, Marseille, France, ^2University of Liverpool, UK
11:40 - 12:00	Refreshments - Reading Room
12:00 - 12:40	S.T. Kolaczkowski^1 Catalytic combustion:making the connection between the physical/chemical processes and the mathematical model of the reactor ^1University of Bath, UK
12:40 - 13:20	V. Karlin^1 Nonmodal instability as the mechanism of acceleration of cellular flames ^1University of Central Lancashire, UK
13:20 - 14:00	Sandwich lunch - Dining Room
14:00 - 14:40	C.G. Poulton^1, A. Spence^2 Numerical methods for the solution of non-linear eigenvalue problems arising in electromagnetism ^1University of Liverpool, UK ^2University of Bath, UK
14:40 - 15:20	M. Hori^1, T. Ichimura^1, H. Nakagawa^1 Application of homogenization techniques to two earthquake problems ^1University of Tokyo, Japan

Tuesday, 9 July (continued)

15:20 - 16:00	A. Fadili^1, J.R.A. Pearson^1, P.M.J. Tardy^1 Stochastic homogenisation of fluid flows in heterogeneous porous media ^1Schlumberger Cambridge Research, UK
16:00 - 16:20	Refreshments - Reading Room
16:20 - 17:00	E. Sanchez-Palencia^1 On a kind of singular perturbations for transmission problems ^1Universite Pierre et Marie Curie, Paris, France
17:00 - 17:40	S. Sorokin^1, O.A. Ershova^1, S.V. Grishina^1 Asymptotic analysis of vibrations and wave propagation in sandwich plates with parametric stiffness modulation ^1State Marine Technical University of St. Petersburg, Russia
17:40 - 18:20	P.G. Martinsson^1, G. Rodin^1 Boundary algebraic equations for lattice problems ^1University of Texas at Austin, USA
18:20 - 19:00	J. Sanchez-Hubert^1, H. Ranarivelo^1 Asymptotics of laminated shells. Membrane - bending coupling and numerical implementation ^1Universite Pierre et Marie Curie, Paris, France
19:30	Conference Dinner - Dining Room

Wednesday, 10 July

08:20 - 09:00	L. Berlyand^1 Discrete network approximation for effective properties of high contrast random highly packed solid and fluid composites ^1Pennsylvania State University, USA
09:00 - 09:40	L.E. Fraenkel^1 A diffusing vortex circle in a viscous fluid ^1University of Bath, UK
09:40 - 10:20	C.J. Chapman^1 The asymptotic theory of fluid-structure interaction with heavy fluid loading ^1Keele University, UK
10:20 - 10:40	Refreshments - Reading Room
10:40 - 11:20	J. Sivaloganathan^1 Singular minimisers, configurational forces and implications for fracture in nonlinear elasticity ^1University of Bath, UK

Wednesday, 10 July (continued)

11:20 - 12:00	E.Cherkaev^1 Coupled effective properties of a random mixture ^1University of Utah
12:00 - 12:40	S. Vladimirov^1 Dynamics of charged rotators and lattice waves in a plasma environment ^1University of Sydney, Australia
12:40 - 13:20	C.M.Linton^1 Embedding formulas and singularities in acoustic scattering ^1Loughborough University, UK
13:20 - 14:00	Sandwich lunch - Dining Room
14:00 onwards	Liverpool Tour, museums and art galleries of Liverpool

Thursday, 11 July

08:20 - 09:00	A. Lacey^1 Singular behaviour of solutions to some parabolic models of shear-band formation ^1Herriot-Watt University, UK
09:00 - 09:40	D.F. Parker^1 Stretch, flexure and twist in finite elasticity ^1University of Edinburgh, UK
09:40 - 10:20	Y. Fu^1, Y.P. Lin^2 A WKB analysis of the buckling of an everted neo-Hookean cylindrical tube ^1Keele University, UK, ^2Kunming Institute of Science and Technology, China
10:20 - 10:40	Refreshments - Reading Room
10:40 - 11:20	H. Ockendon^1 Models for the textile industry ^1University of Oxford, UK
11:20 - 12:00	R. Craster^1, Yu. V. Obsonov^2 Model multi-phase composites ^1Imperial College, UK, ^2Kazan State University, Russia
12:00 - 12:40	W.J. Drugan^1 Comparisons of exact and gradient-approximate nonlocal constitutive equations from a Hashin-Shtrikman-Willis variational principle for random elastic composite materials ^1University of Wisconsin-Madison, USA
12:40 - 13:20	Sandwich lunch - Dining Room

Thursday, 11 July (continued)

13:20 - 14:00	A. Nicolet^1, S. Guenneau^2, F. Zolla^1, C. Geuzaine^3, B. Kulhmey^1, G. Renversez^1 Numerical investigation of photonic crystal fibres by means of finite elements and matrix of diffraction methods ^1Fresnel Institute, Marseille, France, ^2 University of Liverpool, UK, ^3CALTECH, USA
14:00 - 14:40	B. Gralak^1, A. Tip^1 Calculation of dispersion relation in absorptive photonic crystals ^1FOM-Institute (AMOLF), The Netherlands
14:40 - 15:20	S.E. Mikhailov^1, I.V. Namestnikova^1 Non-local approach to fatigue crack initiation and propagation ^1Glasgow Caledonian University, UK
15:20 - 16:00	G. Mishuris^1 Asymptotic behaviour of mode III interface crack for various thin nonhomogeneous anisotropic interfaces ^1Rzeszow University of Technoloy, Poland
16:00 - 16:20	Refreshments - Reading Room
16:20 - 17:00	A.G. Aslanyan^1, A.B. Movchan^2, O. Selsil^2 Estimates for the first six eigenfrequencies for a massive body supported by thin cylindrical rods ^1MIREA, Moscow,Russia^2University of Liverpool, UK
17:00 - 17:40	J. Kaplunov^1, V. Kovalev^2, M. Wilde^3 Asymptotic analysis of higher order peripheral modes in acoustic wave scattering by elastic cylinders and spheres ^1University of Manchester, UK, ^2Moscow State Academy of Instrumentation and Informatics, Russia, ^3Saratov State University, Russia
17:40 - 18:20	K. Khusnutdinova^1 Non-linear dynamics of bi-layer and coupled Klein-Gordon equations ^1Loughborough University, UK

Thursday, 11 July (continued) Poster Session II: 18:20 - 19:20

D.A.MacDonald^1 On linear vortex breakdown in a slowly-varying tube impulsively rotated about its axis with constant angular velocity ^1University of Liverpool, UK	P.J. Message^1 The use of asymptotic series for Lie series generating functions in deriving multiple Fourier series expressions for orbital perturbations ^1University of Liverpool, UK
O. Avila-Pozos^1 Propagation of elastic waves along interfaces in layered beams ^1University of Pachuca, Mexico	S. Guenneau^1, C.G. Poulton^1, A.B. Movchan^1 Oblique propagation of electromagnetic and elasic waves for an array of cylindrical fibres ^1University of Liverpool, UK
D.J. Hasanyan^1, G.T. Piliposyan^2, A.H. Kamalyan^3, M.I. Karakhanyan^3 Some dynamical problems for a functionally inhomogeneous elastic material, including anti-plane deformations ^1Virginia Polytechnical Institute and State University, USA, ^2 University of Liverpool, UK, ^3Yerevan State University, Armenia	V.V. Zalipaev^1 Summation of Gaussian beams in 3D problems of radiation and scattering of elastic waves ^1University of Southampton, UK
S. Haq^1 Models of dislocation in lattice structures ^1University of Liverpool, UK	D. Esparza^1, N.V. Movchan^1 Effect of interface bonding on the stress singularity at the vertex of a thin conical inclusion ^1University of Liverpool, UK
S.C. Hawkins^1, K. Chen^1 Preconditioning for finger pattern matrices arising from wavelet discretisations of boundary integral equations ^1University of Liverpool, UK	J.P. Bercial^1 Asymptotic analysis of wave equation in a 3D layer containing a dynamic crack ^1University of Liverpool, UK
J. Servant^1, S. Guenneau^1, A.B. Movchan^1, C.G. Poulton^1 Scattering by a single circular cylinder in oblique incidence ^1University of Liverpool, UK	I.S. Jones^1, O. Selsil^2, A.B. Movchan^2 A thermoelasticity problem in a domain with an edge crack: Asymptotic analysis ^1John Moores University, UK, ^2University of Liverpool, UK

Report composed by Alexander B. Movchan.