IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics: proceedings of the IUTAM symposium held in Liverpool, United Kingdom, 8-11 July 2002

This volume contains the Proceedings of the IUTAM Symposium held in Liverpool in 2002. It includes the articles presenting the results of recent work in mathematical modelling that covers the following areas of continuum mechanics and theoretical physics: * -Perturbation problems for partial differential equations and their applications in mechanics; * Analysis of singular fields; * Homogenisation theory in models of composite structures; * Mathematical models of cracks in solids; * Wave propagation, scattering; * Models of photonic and phononic band gap composite structures; * Advanced numerical techniques. Front Matter....Pages 3-3 Asymptotic Analysis of Higher Order Peripheral Modes in Acoustic Wave Scattering by an Elastic Cylinder or Sphere....Pages 5-14 Embedding Formulas and Singularities in Acoustic Scattering....Pages 15-22 Numerical Investigation of Photonic Crystal Fibers by Spectral and Multipole Methods....Pages 23-32 Method of Hyperelliptic Surfaces for Vector Functional-Difference Equations....Pages 33-42 Dynamics of Charge Rotators and Lattice Waves in a Plasma Environment....Pages 43-52 Propagation of Elastic Waves along Interfaces in Layered Beams....Pages 53-61 Low Frequency Band Gaps and Localised Modes for Arrays of Coated Inclusions....Pages 63-71 Phononic Band Gap Structures as Optimal Designs....Pages 73-83 A Parametric Investigation of the Acoustic Power in a Two-Dimensional Waveguide with Membrane Bounded Cavity....Pages 85-94 Vibrations of a Circular Cylinder in Oblique Incidence Revisited....Pages 95-104 Asymptotic Analysis of a “Crack” in a Layer of Finite Thickness....Pages 105-112 Summation of Gaussian Beams in 3D Problems of Radiation and Scattering of Elastic Waves....Pages 113-123 Front Matter....Pages 125-125 Asymptotics for the First Six Eigenfrequencies of a 1D-3D Multi-Structure....Pages 127-135 The Two-Term Interior Asymptotic Expansion in the Case of Low-frequency Longitudinal Vibrations of an Elongated Elastic Rectangle....Pages 137-145 Transverse Propagating Waves in Perturbed Periodic Structures....Pages 147-157 Anti-plane Harmonic Problems for a Class of Elastic Materials with Functional Inhomogeneity....Pages 159-167 On Analysing the Performance of a Dissipative Silencer: A Mode-Matching Approach....Pages 169-178 Front Matter....Pages 179-179 Localized Green’s Functions for a Two-Dimensional Periodic Material....Pages 181-190 Boundary Algebraic Equations for Lattice Problems....Pages 191-198 Front Matter....Pages 199-199 Dynamic Perturbation of A Propagating Crack: Implications for Crack Stability....Pages 201-210 Front Matter....Pages 199-199 Dynamic Crack Stability....Pages 211-220 A Thermoelasticity Problem in a Domain with an Edge Crack: Asymptotic Analysis....Pages 221-228 Methods of Assessment of Thermal Striping Fatigue Damage....Pages 229-239 Near-Tip Fields of Mode III Steady-State Crack Propagation in Elastic-Plastic Strain Gradient Solids....Pages 241-249 Mode III Interface Crack Lying at Thin Nonhomogeneous Anisotropic Interface. Asymptotics Near the Crack Tip....Pages 251-260 Fracture Criterion for Cracks with Bridged Zone....Pages 261-270 Front Matter....Pages 271-271 Dynamics of Damage in Two-Dimensional Structures With Waiting Links....Pages 273-283 Local and Non-Local Approaches to Fatigue Crack Initiation and Propagation....Pages 285-294 A Variational Approach to Modelling Initiation of Fracture in NonLinear Elasticity....Pages 295-306 Modeling Fracture in Nano Materials....Pages 307-316 Boundary Elements and Shear Bands in Incremental Elasticity....Pages 317-327 Front Matter....Pages 329-329 Spectral Coupling of Effective Properties of a Random Mixture....Pages 331-340 Homogenization Techniques Applied to Earthquake Problems....Pages 341-350 Stochastic Homogenisation of Fluid Flows in Heterogeneous Porous Media....Pages 351-361 On Micromechanics-Based Nonlocal Modeling of Elastic Matrices Containing Non-Spherical Heterogeneities....Pages 363-373 Artificial Ferro-Magnetic Anisotropy: Homogenization of 3D Finite Photonic Crystals....Pages 375-384 Homogenized Stiffnesses of Periodic Fibre-Reinforced Composites....Pages 385-392 Asymptotic Homogenisation in Strength and Fatigue Durability Analysis of Composites....Pages 393-403 Front Matter....Pages 405-405 On a Kind of Singular Perturbations for Transmission Problems....Pages 407-416 Asymptotics of Laminated Shells. Membrane — Bending Coupling and Numerical Implementation....Pages 417-429 Front Matter....Pages 405-405 Exact Singular Solutions for an Inhomogeneous Thick Elastic Plate....Pages 431-443 Stretch, Flexure and Twist in Finite Elasticity....Pages 445-454 Asymptotic Analysis of Heat Transfer in a System of Channels Connected by Thin Conducting Walls....Pages 455-464 Front Matter....Pages 465-465 Effect of a Thin Coating on the Stress Singularity at the Vertex of a Thin Conical Inclusion....Pages 467-476 3D Singularities with Applications to Fatigue Crack Growth....Pages 477-486 Front Matter....Pages 487-487 A Diffusing Vortex Circle in a Viscous Fluid....Pages 489-500 Low Axial Reynolds Number, High Swirl Ratio, Vortex Breakdown in a Slowly Varying Tube....Pages 501-511 Supersonic Leading-Edge Noise....Pages 513-521 Front Matter....Pages 523-523 Envelope Equations for Modulated Non-Conservative Waves....Pages 525-535 Nonlinear Waves in a Bi-Layer and Coupled Klein-Gordon Equations....Pages 537-546 Front Matter....Pages 547-547 Nonmodal Instability as the Mechanism of Acceleration of Cellular Flames....Pages 549-556 Catalytic Combustion: Making the Connection between the Physical/Chemical Processes and the Mathematical Model of the Reactor....Pages 557-568 Front Matter....Pages 569-569 The use of Lie Series Generating Functions to Derive Asymptotic Series Expressions for Orbital Perturbations....Pages 571-581 Front Matter....Pages 583-583 Inverse Iteration for Nonlinear Eigenvalue Problems in Electromagnetic Scattering....Pages 585-594 Fast Iterative Solution of Coupled 3-Dimensional Fluid-Structure Interaction Problems....Pages 595-604 Preconditioning for Finger Pattern Matrices Arising from Wavelet Discretisations of Boundary Integral Equations....Pages 605-613

This volume contains the Proceedings of the IUTAM Symposium held in Liverpool in 2002. It includes the articles presenting the results of recent work in mathematical modelling that covers the following areas of continuum mechanics and theoretical physics:

• -Perturbation problems for partial differential equations and their applications in mechanics;


• Analysis of singular fields;


• Homogenisation theory in models of composite structures;


• Mathematical models of cracks in solids;


• Wave propagation, scattering;


• Models of photonic and phononic band gap composite structures;


• Advanced numerical techniques.

Proceedings of the IUTAM Symposium held in Liverpool, UK, 8-11 July 2002