By Rajai S. Alassar (auth.), Carmelo Clavero, José Luis Gracia, Francisco J. Lisbona (eds.)
This quantity will comprise chosen papers from the lectures held on the BAIL 2010 convention, which came about from July fifth to ninth, 2010 in Zaragoza (Spain). The papers current major advances within the modeling, research and development of effective numerical the right way to remedy boundary and inside layers showing in singular perturbation difficulties. targeted emphasis is wear the mathematical foundations of such equipment and their software to actual versions. issues in clinical fields equivalent to fluid dynamics, quantum mechanics, semiconductor modeling, keep an eye on concept, elasticity, chemical reactor idea, and porous media are tested in detail.
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Extra resources for BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods
Z/ cos '. Different novel expansions, taking account of the cut in complex plane are given in . We then give the absolute value of J as ' varies for kR D 1 (Fig. 3) and kR D 3 (Fig. 4), for different choices of g with Reg D :3 and Img varying from :5 to C:5:, as we go through the cut. i k cos Âi / D 0 with g D sin Âi , in the region Reg < 0. 5 Conclusion The high order impedance boundary conditions on metamaterials with negative permittivity and permeability imply exceptional new behaviour as we go through the branch cut in the expression of the field.
Bernard 1 Introduction In electromagnetism, a surface composed of a homogeneous planar substrate on a perfectly reflecting plane can be modelled by boundary layer method as a plane which satisfies surface boundary conditions with high order normal derivatives of the field (Fig. 1): N Y @ . (1) i kgj /ut ot jzD0 D 0 @z j D1 where u is some components of the fields. It can be shown that, in case of a metamaterial substrate having both a permittivity and a permeability with negative real parts, the roots of the characteristic equation have exceptional positions in the complex plane, which implies particular properties of the field for point source (dipole) illumination.
P/ D 0, p 2 ! as n ! 1, therefore, the sequence converges to u1 . n/ fu 1 g converges to u 1 . Now by linearity of the operator L and the continuity of f , we conclude that u1 and u 1 are solutions to (3). By the maximum principle in Lemma 1, under assumption (2) the nonlinear difference (3) has a unique solution u , hence, u1 D u 1 D u . p/g p2! p/g; p2! p/, respectively, are calculated in (7). The following theorem gives the quadratic convergence of the monotone method (7)–(9). Theorem 2. Let the assumptions in Theorem 1 be satisfied.