Resonant Scattering and Generation of Waves: Cubically Polarizable Layers - Couverture souple

Angermann, Lutz; Yatsyk, Vasyl V.

Couverture souple

ISBN 10 : 3030071723 ISBN 13 : 9783030071721

Editeur : Springer, 2018

Synopsis

This monograph deals with theoretical aspects and numerical simulations of the interaction of electromagnetic fields with nonlinear materials. It focuses in particular on media with nonlinear polarization properties. It addresses the direct problem of nonlinear Electrodynamics, that is to understand the nonlinear behavior in the induced polarization and to analyze or even to control its impact on the propagation of electromagnetic fields in the matter. 

The book gives a comprehensive presentation of the results obtained by the authors during the last decade and put those findings in a broader, unified context and extends them in several directions.

It is divided into eight chapters and three appendices. Chapter 1 starts from the Maxwells equations and develops a wave propagation theory in plate-like media with nonlinear polarizability. In chapter 2 a theoretical framework in terms of weak solutions is given in order to prove the existence and uniqueness of a solution of the semilinear boundary-value problem derived in the first chapter. Chapter 3 presents a different approach to the solvability theory of the reduced frequency-domain model. Here the boundary-value problem is reduced to finding solutions of a system of one-dimensional nonlinear Hammerstein integral equations. Chapter 4 describes an approach to the spectral analysis of the linearized system of integral equations. Chapters 5 and 6 are devoted to the numerical approximation of the solutions of the corresponding mathematical models. Chapter 7 contains detailed descriptions, discussions and evaluations of the numerical experiments. Finally, chapter 8 gives a summary of the results and an outlook for future work.

A propos du livre

À propos de l'auteur

Peter Knabner is Professor emeritus at the University of Erlangen-Nürnberg, where he has led the chair Applied Mathematics I from 1994 to 2020, and also guest professor at the cluster of excellence SimTech of the University of Stuttgart. Knabner'research is focussed on the derivation, analysis and numerical approximation of mathematical models for flow and transport in porous media. with applications in science and technology, in particular in hydrogeology.

After the study of Mathematics and Computer Science at the Freie Universität Berlin (diploma in 1972) he earned a PhD from the University of Augsburg in 1983, where he also received a higher doctoral degree (habilitation) in 1988.

Peter Knabner is author of more than 180 peer-reviewed publications in applied analysis, numerical mathematics and geohydrology. He is author and co-author of 13 research monographs and textbooks in German and English.

Lutz Angermann is Professor of Numerical Mathematics at the Department of Mathematics of the Clausthal University of Technology since 2001. His research is concerned with the development and mathematical analysis of numerical methods for solving partial differential equations with special interests in finite volume and finite element methods and their application to problems in Physics and Engineering.

After the study of Mathematics at the State University of Kharkov (now V.N. Karazin Kharkiv National University, Ukraine) he earned a PhD from the University of Technology at Dresden in 1987. The University of Erlangen-Nürnberg awarded him a higher doctoral degree (habilitation) in 1995. From 1998 to 2001, he held the post of an Associate Professor of Numerical Mathematics at the University of Magdeburg.

He has authored or co-authored about 100 scientific papers, among them four books as co-author, and he edited two books.

À propos de la quatrième de couverture

This monograph deals with theoretical aspects and numerical simulations of the interaction of electromagnetic fields with nonlinear materials. It focuses in particular on media with nonlinear polarization properties. It addresses the direct problem of nonlinear Electrodynamics, that is to understand the nonlinear behavior in the induced polarization and to analyze or even to control its impact on the propagation of electromagnetic fields in the matter. 

The book gives a comprehensive presentation of the results obtained by the authors during the last decade and put those findings in a broader, unified context and extends them in several directions.

It is divided into eight chapters and three appendices. Chapter 1 starts from the Maxwells equations and develops a wave propagation theory in plate-like media with nonlinear polarizability. In chapter 2 a theoretical framework in terms of weak solutions is given in order to prove the existence and uniqueness of a solution of the semilinear boundary-value problem derived in the first chapter. Chapter 3 presents a different approach to the solvability theory of the reduced frequency-domain model. Here the boundary-value problem is reduced to finding solutions of a system of one-dimensional nonlinear Hammerstein integral equations. Chapter 4 describes an approach to the spectral analysis of the linearized system of integral equations. Chapters 5 and 6 are devoted to the numerical approximation of the solutions of the corresponding mathematical models. Chapter 7 contains detailed descriptions, discussions and evaluations of the numerical experiments. Finally, chapter 8 gives a summary of the results and an outlook for future work.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 3030071723
• ISBN 13: 9783030071721
• Reliure: Broché
• Nombre de pages: 208
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne