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A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to - . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some...

About asymptotic approximations in thin waveguides

Nicole Turbe, Louis Ratier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the propagation of electromagnetic waves in a guide the section of which is a thin annulus. Owing to the presence of a small parameter, explicit approximations of the TM and TE eigenmodes are obtained. The cases of smooth and non smooth boundaries are presented.

About asymptotic approximations in thin waveguides

Nicole Turbe, Louis Ratier (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the propagation of electromagnetic waves in a guide the section of which is a thin annulus. Owing to the presence of a small parameter, explicit approximations of the TM and TE eigenmodes are obtained. The cases of smooth and non smooth boundaries are presented.

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification is such that...

Matching of asymptotic expansions for waves propagation in media with thin slots II: The error estimates

Patrick Joly, Sébastien Tordeux (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We are concerned with a 2D time harmonic wave propagation problem in a medium including a thin slot whose thickness ε is small with respect to the wavelength. In a previous article, we derived formally an asymptotic expansion of the solution with respect to ε using the method of matched asymptotic expansions. We also proved the existence and uniqueness of the terms of the asymptotics. In this paper, we complete the mathematical justification of our work by deriving optimal error estimates between...

Meta-optimization of bio-inspired algorithms for antenna array design

Virgilio Zúñiga-Grajeda, Alberto Coronado-Mendoza, Kelly Joel Gurubel-Tun (2018)

Kybernetika

In this article, a technique called Meta-Optimization is used to enhance the effectiveness of bio-inspired algorithms that solve antenna array synthesis problems. This technique consists on a second optimization layer that finds the best behavioral parameters for a given algorithm, which allows to achieve better results. Bio-inspired computational methods are useful to solve complex multidimensional problems such as the design of antenna arrays. However, their performance depends heavily on the...

On the curvature and torsion effects in one dimensional waveguides

Guy Bouchitté, M. Luísa Mascarenhas, Luís Trabucho (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the Laplace operator in a thin tube of 3 with a Dirichlet condition on its boundary. We study asymptotically the spectrum of such an operator as the thickness of the tube's cross section goes to zero. In particular we analyse how the energy levels depend simultaneously on the curvature of the tube's central axis and on the rotation of the cross section with respect to the Frenet frame. The main argument is a Γ-convergence theorem for a suitable sequence of quadratic energies.

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