By A.B. Movchan

This quantity includes the lawsuits of the IUTAM Symposium held in Liverpool in 2002. It contains the articles providing the result of fresh paintings in mathematical modelling that covers the next parts of continuum mechanics and theoretical physics: -Perturbation difficulties for partial differential equations and their functions in mechanics; research of singular fields; Homogenisation concept in versions of composite constructions; Mathematical versions of cracks in solids; Wave propagation, scattering; types of photonic and phononic band hole composite constructions; complicated numerical suggestions.

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**Extra resources for IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics (Solid Mechanics and Its Applications)**

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T and satisfying the boundary condition Φ(σ) = G(σ)Φ(σ − h) + g(σ), σ ∈ Ω. e. as Im(s) → ±∞, Φ(s) = O(eb Im(s) ) with b± being real, ﬁnite and prescribed. The matrix G(σ) and the vector g(σ) satisfy the H¨ older condition on every ﬁnite segment of Ω. e. as σ → ω ± i∞, the components of the G(σ) and g(σ) may have a ﬁnite exponential growth not necessarily the same. The matrix G(σ) is also nonsingular on Ω. Vector functional-diﬀerence equations 35 Let λ1 (σ), λ2 (σ) be the eigenvalues of the matrix G(σ) and let λ1 (σ) = λ2 (σ).

Multipole method for microstructured optical ﬁbers II: implementation and results. J. Opt. Soc. Am. B, 19(10):2331-2340, 2002. [12] B. Kuhlmey, G. Renversez, D. Maystre, T. White, R. McPhedran, L. Botten and M. de Sterke. Multipole study of dispersion and losses of photonic crystal ﬁbres. SPIE Proceedings, Photonic Bandgap Materials and Devices, A. Adibi, A. Scherer and S. Lin editors, 4655, 2002. [13] B. Kuhlmey, G. Renversez and D. Maystre. Chromatic dispersion and losses of microstructured optical ﬁbers.

1. INTRODUCTION The most powerful and general technique for exact solution of model problems in acoustic and electromagnetic scattering is Maliuzhinets’ method [1]. 1) where Φ(σ) is an unknown vector analytic in the strip Π = {ω − h < Re(s) < ω}. The matrix G(σ) and the vector g(σ) are supposed to be known. e. B. ), IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, 33–42. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. 34 two factors: G(σ) = X(σ)[X(σ − h)]−1 , σ ∈ Ω.