Eintrag weiter verarbeiten

Resonant Scattering and Generation of Waves: Cubically Polarizable Layers

Gespeichert in:

Personen und Körperschaften: Angermann, Lutz (VerfasserIn), Yatsyk, Vasyl V. (VerfasserIn)
Titel: Resonant Scattering and Generation of Waves: Cubically Polarizable Layers/ by Lutz Angermann, Vasyl V. Yatsyk
Format: E-Book
Sprache: Englisch
veröffentlicht:
Cham Springer International Publishing 2019

Gesamtaufnahme: Mathematical Engineering
Springer eBook Collection
SpringerLink
Schlagwörter:
Quelle: Verbunddaten SWB
LEADER 06918cam a22009972 4500
001 0-1028032390
003 DE-627
005 20220726184812.0
007 cr uuu---uuuuu
008 180801s2019 gw |||||o 00| ||eng c
020 |a 9783319963013  |9 978-3-319-96301-3 
024 7 |a 10.1007/978-3-319-96301-3  |2 doi 
035 |a (DE-627)1028032390 
035 |a (DE-576)508132088 
035 |a (DE-599)GBV1028032390 
035 |a (DE-He213)978-3-319-96301-3 
035 |a (EBP)040378845 
035 |a (ZBM)1414.78001 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
044 |c XA-DE 
050 0 |a QC1-999 
082 0 |a 530.1 
084 |a PHU  |2 bicssc 
084 |a SCI040000  |2 bisacsh 
084 |a *78-02  |2 MSC 
084 |a 78A40  |2 MSC 
084 |a 78A45  |2 MSC 
084 |a 78M10  |2 MSC 
084 |a 35B34  |2 MSC 
084 |a 35Q61  |2 MSC 
084 |a 35Q60  |2 MSC 
084 |a 78M22  |2 MSC 
084 |a 65R20  |2 MSC 
100 1 |a Angermann, Lutz  |e VerfasserIn  |4 aut 
245 1 0 |a Resonant Scattering and Generation of Waves  |b Cubically Polarizable Layers  |c by Lutz Angermann, Vasyl V. Yatsyk 
264 1 |a Cham  |b Springer International Publishing  |c 2019 
300 |a Online-Ressource (XX, 208 p. 72 illus., 68 illus. in color, online resource) 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
490 0 |a Mathematical Engineering 
490 0 |a Springer eBook Collection 
490 0 |a SpringerLink  |a Bücher 
520 |a 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 Maxwell’s 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 
520 |a The mathematical model -- Maxwell’s equations and wave propagation in media with nonlinear polarizability -- The reduced frequency-domain model -- The condition of phase synchronism -- Packets of plane waves -- Energy conservation laws -- Existence and uniqueness of a weak solution -- Weak formulation -- Existence and uniqueness of a weak solution -- The equivalent system of nonlinear integral equations -- The operator equation -- A sufficient condition for the existence of a continuous solution -- A sufficient condition for the existence of a unique continuous solution -- Relation to the system of nonlinear Sturm-Liouville boundary value problems -- Spectral analysis -- Motivation -- Eigen-modes of the linearized problems -- Spectral energy relationships and the quality factor of eigen-fields -- Numerical solution of the nonlinear boundary value problem -- The finite element method -- Existence and uniqueness of a finite element solution -- Error estimate -- Numerical treatment of the system of integral equations -- Numerical quadrature -- Iterative solution -- Numerical spectral analysis -- Numerical experiments -- Quantitative characteristics of the fields -- Description of the model problems -- The problem with the Kerr nonlinearity -- The self-consistent approach -- A single layer with negative cubic susceptibility -- A single layer with positive cubic susceptibility -- A three-layered structure -- Conclusion and outlook -- A Cubic polarization -- A.1 The case without any static field -- A.2 The case of a nontrivial static field -- B Tools from Functional Analysis -- B.1 Poincar´e-Friedrichs inequality -- B.2 Trace inequality -- B.3 Interpolation error estimates -- Notation -- References -- Index 
533 |f Springer eBook Collection. Engineering 
650 0 |a Physics 
650 0 |a Computer science  |x Mathematics 
650 0 |a Computer mathematics 
650 0 |a Solid state physics 
650 0 |a Optical materials 
650 0 |a Electronic materials 
650 0 |a Computer science  |x Mathematics 
650 0 |a Computer mathematics 
650 0 |a Solid state physics 
650 0 |a Optical materials 
650 0 |a Electronic materials 
650 0 |a Physics 
650 0 |a Engineering mathematics. 
700 1 |a Yatsyk, Vasyl V.  |e VerfasserIn  |4 aut 
776 1 |z 9783319963006 
776 0 8 |i Erscheint auch als  |n Druck-Ausgabe  |z 978-3-319-96300-6 
776 0 8 |i Printed edition  |z 9783319963006 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-96301-3  |x Verlag  |3 Volltext 
856 4 0 |u https://doi.org/10.1007/978-3-319-96301-3  |m X:SPRINGER  |x Resolving-System  |z lizenzpflichtig 
856 4 2 |u https://swbplus.bsz-bw.de/bsz508132088cov.jpg  |m V:DE-576  |m X:Springer  |q image/jpeg  |v 20180802141106  |3 Cover 
856 4 2 |u https://zbmath.org/?q=an:1414.78001  |m B:ZBM  |v 2021-04-12  |x Verlag  |y Zentralblatt MATH  |3 Inhaltstext 
912 |a ZDB-2-ENG  |b 2019 
912 |a ZDB-2-SEB 
912 |a ZDB-2-SXE  |b 2019 
935 |i Blocktest 
951 |a BO 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-96301-3  |9 DE-14 
852 |a DE-14  |x epn:3588575782  |z 2020-02-06T11:11:32Z 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-96301-3  |9 DE-Ch1 
852 |a DE-Ch1  |x epn:337664179X  |z 2018-11-30T16:17:09Z 
912 |9 DE-105  |a ZDB-2-ENG 
972 |k Campuslizenz 
972 |c EBOOK 
852 |a DE-105  |x epn:3376641897  |z 2018-12-10T12:24:33Z 
975 |o Springer E-Book 
975 |k Elektronischer Volltext - Campuslizenz 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-96301-3  |9 DE-Zwi2 
852 |a DE-Zwi2  |x epn:3376642052  |z 2018-11-08T17:30:15Z 
980 |a 1028032390  |b 0  |k 1028032390  |o 508132088 
openURL url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fvufind.svn.sourceforge.net%3Agenerator&rft.title=Resonant+Scattering+and+Generation+of+Waves%3A+Cubically+Polarizable+Layers&rft.date=2019&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Resonant+Scattering+and+Generation+of+Waves%3A+Cubically+Polarizable+Layers&rft.series=Mathematical+Engineering&rft.au=Angermann%2C+Lutz&rft.pub=Springer+International+Publishing&rft.edition=&rft.isbn=3319963015
SOLR
_version_ 1796700521926492160
author Angermann, Lutz, Yatsyk, Vasyl V.
author_facet Angermann, Lutz, Yatsyk, Vasyl V.
author_role aut, aut
author_sort Angermann, Lutz
author_variant l a la, v v y vv vvy
callnumber-first Q - Science
callnumber-label QC1-999
callnumber-raw QC1-999
callnumber-search QC1-999
callnumber-sort QC 11 3999
callnumber-subject QC - Physics
collection ZDB-2-ENG, ZDB-2-SEB, ZDB-2-SXE
contents 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 Maxwell’s 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, The mathematical model -- Maxwell’s equations and wave propagation in media with nonlinear polarizability -- The reduced frequency-domain model -- The condition of phase synchronism -- Packets of plane waves -- Energy conservation laws -- Existence and uniqueness of a weak solution -- Weak formulation -- Existence and uniqueness of a weak solution -- The equivalent system of nonlinear integral equations -- The operator equation -- A sufficient condition for the existence of a continuous solution -- A sufficient condition for the existence of a unique continuous solution -- Relation to the system of nonlinear Sturm-Liouville boundary value problems -- Spectral analysis -- Motivation -- Eigen-modes of the linearized problems -- Spectral energy relationships and the quality factor of eigen-fields -- Numerical solution of the nonlinear boundary value problem -- The finite element method -- Existence and uniqueness of a finite element solution -- Error estimate -- Numerical treatment of the system of integral equations -- Numerical quadrature -- Iterative solution -- Numerical spectral analysis -- Numerical experiments -- Quantitative characteristics of the fields -- Description of the model problems -- The problem with the Kerr nonlinearity -- The self-consistent approach -- A single layer with negative cubic susceptibility -- A single layer with positive cubic susceptibility -- A three-layered structure -- Conclusion and outlook -- A Cubic polarization -- A.1 The case without any static field -- A.2 The case of a nontrivial static field -- B Tools from Functional Analysis -- B.1 Poincar´e-Friedrichs inequality -- B.2 Trace inequality -- B.3 Interpolation error estimates -- Notation -- References -- Index
ctrlnum (DE-627)1028032390, (DE-576)508132088, (DE-599)GBV1028032390, (DE-He213)978-3-319-96301-3, (EBP)040378845, (ZBM)1414.78001
de105_date 2018-12-10T12:24:33Z
dech1_date 2018-11-30T16:17:09Z
dewey-full 530.1
dewey-hundreds 500 - Natural sciences and mathematics
dewey-ones 530 - Physics
dewey-raw 530.1
dewey-search 530.1
dewey-sort 3530.1
dewey-tens 530 - Physics
doi_str_mv 10.1007/978-3-319-96301-3
facet_912a ZDB-2-ENG, ZDB-2-SEB, ZDB-2-SXE
facet_avail Online
finc_class_facet Physik
finc_id_str 0021360541
fincclass_txtF_mv science-physics
format eBook
format_access_txtF_mv Book, E-Book
format_de105 Ebook
format_de14 Book, E-Book
format_de15 Book, E-Book
format_del152 Buch
format_detail_txtF_mv text-online-monograph-independent
format_dezi4 e-Book
format_finc Book, E-Book
format_legacy ElectronicBook
format_legacy_nrw Book, E-Book
format_nrw Book, E-Book
format_strict_txtF_mv E-Book
geogr_code not assigned
geogr_code_person not assigned
id 0-1028032390
illustrated Not Illustrated
imprint Cham, Springer International Publishing, 2019
imprint_str_mv Cham: Springer International Publishing, 2019
institution DE-14, DE-105, DE-Zwi2, DE-Ch1
is_hierarchy_id
is_hierarchy_title
isbn 9783319963013
isbn_isn_mv 9783319963006, 978-3-319-96300-6
kxp_id_str 1028032390
language English
last_indexed 2024-04-18T19:05:39.677Z
local_heading_facet_dezwi2 Physics, Computer science, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics., Mathematics
marc024a_ct_mv 10.1007/978-3-319-96301-3
marc_error [geogr_code]Unable to make public java.lang.AbstractStringBuilder java.lang.AbstractStringBuilder.append(java.lang.String) accessible: module java.base does not "opens java.lang" to unnamed module @d9403fb
match_str angermann2019resonantscatteringandgenerationofwavescubicallypolarizablelayers
mega_collection Verbunddaten SWB
misc_de105 EBOOK
physical Online-Ressource (XX, 208 p. 72 illus., 68 illus. in color, online resource)
publishDate 2019
publishDateSort 2019
publishPlace Cham
publisher Springer International Publishing
record_format marcfinc
record_id 508132088
recordtype marcfinc
rvk_facet No subject assigned
series2 Mathematical Engineering, Springer eBook Collection, SpringerLink ; Bücher
source_id 0
spelling Angermann, Lutz VerfasserIn aut, Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk, Cham Springer International Publishing 2019, Online-Ressource (XX, 208 p. 72 illus., 68 illus. in color, online resource), Text txt rdacontent, Computermedien c rdamedia, Online-Ressource cr rdacarrier, Mathematical Engineering, Springer eBook Collection, SpringerLink Bücher, 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 Maxwell’s 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, The mathematical model -- Maxwell’s equations and wave propagation in media with nonlinear polarizability -- The reduced frequency-domain model -- The condition of phase synchronism -- Packets of plane waves -- Energy conservation laws -- Existence and uniqueness of a weak solution -- Weak formulation -- Existence and uniqueness of a weak solution -- The equivalent system of nonlinear integral equations -- The operator equation -- A sufficient condition for the existence of a continuous solution -- A sufficient condition for the existence of a unique continuous solution -- Relation to the system of nonlinear Sturm-Liouville boundary value problems -- Spectral analysis -- Motivation -- Eigen-modes of the linearized problems -- Spectral energy relationships and the quality factor of eigen-fields -- Numerical solution of the nonlinear boundary value problem -- The finite element method -- Existence and uniqueness of a finite element solution -- Error estimate -- Numerical treatment of the system of integral equations -- Numerical quadrature -- Iterative solution -- Numerical spectral analysis -- Numerical experiments -- Quantitative characteristics of the fields -- Description of the model problems -- The problem with the Kerr nonlinearity -- The self-consistent approach -- A single layer with negative cubic susceptibility -- A single layer with positive cubic susceptibility -- A three-layered structure -- Conclusion and outlook -- A Cubic polarization -- A.1 The case without any static field -- A.2 The case of a nontrivial static field -- B Tools from Functional Analysis -- B.1 Poincar´e-Friedrichs inequality -- B.2 Trace inequality -- B.3 Interpolation error estimates -- Notation -- References -- Index, Springer eBook Collection. Engineering, Physics, Computer science Mathematics, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics., Yatsyk, Vasyl V. VerfasserIn aut, 9783319963006, Erscheint auch als Druck-Ausgabe 978-3-319-96300-6, Printed edition 9783319963006, http://dx.doi.org/10.1007/978-3-319-96301-3 Verlag Volltext, https://doi.org/10.1007/978-3-319-96301-3 X:SPRINGER Resolving-System lizenzpflichtig, https://swbplus.bsz-bw.de/bsz508132088cov.jpg V:DE-576 X:Springer image/jpeg 20180802141106 Cover, https://zbmath.org/?q=an:1414.78001 B:ZBM 2021-04-12 Verlag Zentralblatt MATH Inhaltstext, http://dx.doi.org/10.1007/978-3-319-96301-3 DE-14, DE-14 epn:3588575782 2020-02-06T11:11:32Z, http://dx.doi.org/10.1007/978-3-319-96301-3 DE-Ch1, DE-Ch1 epn:337664179X 2018-11-30T16:17:09Z, DE-105 epn:3376641897 2018-12-10T12:24:33Z, http://dx.doi.org/10.1007/978-3-319-96301-3 DE-Zwi2, DE-Zwi2 epn:3376642052 2018-11-08T17:30:15Z
spellingShingle Angermann, Lutz, Yatsyk, Vasyl V., Resonant Scattering and Generation of Waves: Cubically Polarizable Layers, 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 Maxwell’s 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, The mathematical model -- Maxwell’s equations and wave propagation in media with nonlinear polarizability -- The reduced frequency-domain model -- The condition of phase synchronism -- Packets of plane waves -- Energy conservation laws -- Existence and uniqueness of a weak solution -- Weak formulation -- Existence and uniqueness of a weak solution -- The equivalent system of nonlinear integral equations -- The operator equation -- A sufficient condition for the existence of a continuous solution -- A sufficient condition for the existence of a unique continuous solution -- Relation to the system of nonlinear Sturm-Liouville boundary value problems -- Spectral analysis -- Motivation -- Eigen-modes of the linearized problems -- Spectral energy relationships and the quality factor of eigen-fields -- Numerical solution of the nonlinear boundary value problem -- The finite element method -- Existence and uniqueness of a finite element solution -- Error estimate -- Numerical treatment of the system of integral equations -- Numerical quadrature -- Iterative solution -- Numerical spectral analysis -- Numerical experiments -- Quantitative characteristics of the fields -- Description of the model problems -- The problem with the Kerr nonlinearity -- The self-consistent approach -- A single layer with negative cubic susceptibility -- A single layer with positive cubic susceptibility -- A three-layered structure -- Conclusion and outlook -- A Cubic polarization -- A.1 The case without any static field -- A.2 The case of a nontrivial static field -- B Tools from Functional Analysis -- B.1 Poincar´e-Friedrichs inequality -- B.2 Trace inequality -- B.3 Interpolation error estimates -- Notation -- References -- Index, Physics, Computer science Mathematics, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics.
swb_id_str 508132088
title Resonant Scattering and Generation of Waves: Cubically Polarizable Layers
title_auth Resonant Scattering and Generation of Waves Cubically Polarizable Layers
title_full Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk
title_fullStr Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk
title_full_unstemmed Resonant Scattering and Generation of Waves Cubically Polarizable Layers by Lutz Angermann, Vasyl V. Yatsyk
title_short Resonant Scattering and Generation of Waves
title_sort resonant scattering and generation of waves cubically polarizable layers
title_sub Cubically Polarizable Layers
title_unstemmed Resonant Scattering and Generation of Waves: Cubically Polarizable Layers
topic Physics, Computer science Mathematics, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics.
topic_facet Physics, Computer science, Computer mathematics, Solid state physics, Optical materials, Electronic materials, Engineering mathematics., Mathematics
url http://dx.doi.org/10.1007/978-3-319-96301-3, https://doi.org/10.1007/978-3-319-96301-3, https://swbplus.bsz-bw.de/bsz508132088cov.jpg, https://zbmath.org/?q=an:1414.78001
work_keys_str_mv AT angermannlutz resonantscatteringandgenerationofwavescubicallypolarizablelayers, AT yatsykvasylv resonantscatteringandgenerationofwavescubicallypolarizablelayers