Holdings: The method of the Generalized Eikonal

$The method of the Generalized Eikonal new approaches in the Diffraction Theory$

The method of the Generalized Eikonal: new approaches in the Diffraction Theory

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Bibliographic Details
Main Author:	Vesnik, Michael V. (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] De Gruyter 2015
Series:	De Gruyter studies in mathematical physics 29
Subjects:	Beugungstheorie Eikonal
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 201 S. graph. Darst.
ISBN:	9783110311129 9783110311303

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adam_text	CONTENTS PREFACE VII INTRODUCTION 1 1 METHOD OF GENERALIZED EIKONAL 15 1.1 INTEGRAL REPRESENTATION OF SOLUTION 15 1.1.1 STATEMENT OF THE PROBLEM 15 1.1.2 CONSTRUCTION OF AUXILIARY DOMAIN AND GENERALIZED GEOMETRICAL OPTICS FUNCTION 16 1.1.3 BOUNDARY CONDITIONS 20 1.1.4 FEATURES OF THE SOLUTION 23 1.2 ASYMPTOTIC CALCULATION OF CONTOUR INTEGRALS BY METHOD OF STATIONARY PHASE 24 1.2.1 GENERAL SOLUTION 25 1.2.2 SOLUTION OF DIFFRACTION PROBLEM FOR PLANE AND CYLINDRICAL WAVES BY THE METHOD OF GENERALIZED EIKONAL 27 2 SOLUTION OF TWO-DIMENSIONAL PROBLEMS BY THE METHOD OF GENERALIZED EIKONAL 35 2.1 INTRODUCTION 35 2.2 DIFFRACTION BY HALF-PLATE 36 2.2.1 SOLUTION ON THE GIVEN CURVE R J 0 40 2.2.2 POWER NORMALIZATION 42 2.2.3 SOLUTION BY METHOD OF SUCCESSIVE DIFFRACTIONS (MSD) 46 2.2.4 RESULTS OF CALCULATIONS 48 2.3 DIFFRACTION BY A TRUNCATED WEDGE 56 2.3.1 SCHWARZ-CHRISTOFFEL INTEGRAL 59 2.3.2 FEATURES OF SOLUTION FOR HALF-PLATE 60 2.3.3 SOLUTION BY METHOD OF SUCCESSIVE DIFFRACTIONS 62 2.3.4 PRINCIPLES FOR THE CONSTRUCTION OF HEURISTIC SOLUTIONS FOR DIFFRACTION BY TRUNCATED WEDGE 63 2.3.5 SOLUTION WITH GENERALIZED FRESNEL INTEGRAL 64 2.3.6 NUMERICAL RESULTS 67 2.3.7 ANALYSIS OF SOLUTIONS 67 3 APPLICATION OF TWO-DIMENSIONAL SOLUTIONS TO THREE-DIMENSIONAL PROBLEMS 73 3.1 INTEGRALS OVER ELEMENTARY STRIPS 73 3.1.1 STATEMENT OF THE DIFFRACTION PROBLEM 73 HTTP://D-NB.INFO/105913098X X CONTENTS 3.1.2 INFINITE CYLINDER 75 3.1.3 FAR ZONE CONDITION 76 3.1.4 FRAGMENT OF CYLINDRICAL SURFACE 78 3.1.5 POLYGONAL EDGE 79 3.2 APPLICATION OF TWO-DIMENSIONAL SOLUTIONS TO THREE-DIMENSIONAL PROBLEMS 81 3.2.1 PHYSICAL OPTICS SOLUTION FOR DIFFRACTION BY A PLANE SCATTERER. PROPERTIES OF CONTOUR INTEGRAL 81 3.2.2 RIGOROUS 3D FORMULAS 82 3.2.3 COMPARISON WITH 2D CASE 84 3.2.4 TOTAL CURRENT DIFFRACTION COEFFICIENTS 84 4 DIFFRACTION BY A PLANE PERFECTLY CONDUCTING ANGULAR SECTOR (HEURISTIC APPROACH) 85 4.1 STATEMENT OF THE PROBLEM 85 4.2 SOLUTION IN PHYSICAL OPTICS APPROXIMATION 87 4.2.1 CONTOUR INTEGRAL WITH ENFORCED FAR ZONE CONDITION 89 4.2.2 INPUTS OF EDGES AND VERTICES 90 4.3 SOLUTION IN EECM APPROXIMATION 96 4.3.1 RIGOROUS SOLUTION FOR OBLIQUE INCIDENT WAVE 96 4.3.2 SUBSTITUTION OF POLARIZATION COMPONENTS OF DIFFRACTION COEFFICIENTS 98 4.4 MODIFIED EECM 101 4.5 APPLICABILITY LIMITS OF HEURISTIC APPROACHES 106 4.5.1 SOLUTION ALGORITHM 106 4.5.2 APPLICABILITY LIMITS OF HEURISTIC SOLUTIONS 108 5 PROPAGATION OF RADIO WAVES IN URBAN ENVIRONMENT (DETERMINISTIC APPROACH) 109 5.1 RELEVANCE OF THE PROBLEM 109 5.2 SPECIFICS OF RADIO WAVE PROPAGATION IN URBAN ENVIRONMENT 111 5.3 DESIGN FORMULAS 112 5.3.1 ZONE SIGNIFICANT FOR RADIO WAVE PROPAGATION 112 5.3.2 REFERENCE SOLUTIONS 114 5.3.3 MUTUAL COUPLING BETWEEN TWO ANTENNAS 115 5.3.4 ENERGY RELATIONSHIPS 117 5.3.5 FRESNELZONE 119 5.3.6 DERIVATION OF HEURISTIC FORMULAS 121 5.3.7 SOLUTION ALGORITHM 121 CONTENTS * XI 6 ANALYTICAL HEURISTIC SOLUTION FOR WAVE DIFFRACTION BY A PLANE POLYGONAL SCATTERER 125 6.1 INTRODUCTION 125 6.2 PROBLEM FORMULATION FOR ELASTIC WAVE DIFFRACTION 126 6.3 APPROACH TO DERIVATION OF FORMULAS 130 6.4 GENERAL FORM OF THE SOLUTION 134 7 CONCLUSION 135 A APPLICATION OF STOKES THEOREM TO DIFFRACTION PROBLEMS 139 A.L STOKES THEOREM. RELATIONSHIP BETWEEN THE SURFACE AND CONTOUR INTEGRALS 139 A.2 INTEGRAL OVER THE SURFACE OF A FINITE-SIZE POLYGON 141 A.3 INTEGRAL OVER THE SURFACE OF A PLANE ANGULAR SECTOR 143 A.4 VERTEX WAVES FOR A FINITE-SIZE POLYGON 144 A.5 PHASE FUNCTION AND FAR ZONE CONDITION 147 B RIGOROUS TWO-DIMENSIONAL SOLUTION FOR DIFFRACTION BY HALF-PLANE 149 C APPLICATION OF IMAGINARY EDGE IN DIFFRACTION PROBLEMS 157 D SUMMARY OF FORMULAS FOR DIFFRACTION BY PLANE ANGULAR SECTOR 163 E FRESNEL INTEGRAL AND ITS PROPERTIES 169 F GENERALIZED FRESNEL INTEGRAL AND ITS PROPERTIES 173 G ELECTROMAGNETIC WAVE DIFFRACTION BY SEMI-TRANSPARENT PLATE 177 H GENERALIZED DIFFRACTION COEFFICIENT AND ITS APPLICATION TO DIFFRACTION PROBLEMS 181 BIBLIOGRAPHY 193 INDEX 199
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spelling	Vesnik, Michael V. Verfasser (DE-588)1075180090 aut The method of the Generalized Eikonal new approaches in the Diffraction Theory Michael V. Vesnik The method of the Generalised Eikonal Berlin [u.a.] De Gruyter 2015 XI, 201 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematical physics 29 Beugungstheorie (DE-588)4268180-7 gnd rswk-swf Eikonal (DE-588)4151213-3 gnd rswk-swf Beugungstheorie (DE-588)4268180-7 s Eikonal (DE-588)4151213-3 s DE-604 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-038301-0 Erscheint auch als Online-Ausgabe, PDF 978-3-11-031129-7 De Gruyter studies in mathematical physics 29 (DE-604)BV040141722 29 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028181809&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Vesnik, Michael V. The method of the Generalized Eikonal new approaches in the Diffraction Theory De Gruyter studies in mathematical physics Beugungstheorie (DE-588)4268180-7 gnd Eikonal (DE-588)4151213-3 gnd
subject_GND	(DE-588)4268180-7 (DE-588)4151213-3
title	The method of the Generalized Eikonal new approaches in the Diffraction Theory
title_alt	The method of the Generalised Eikonal
title_auth	The method of the Generalized Eikonal new approaches in the Diffraction Theory
title_exact_search	The method of the Generalized Eikonal new approaches in the Diffraction Theory
title_full	The method of the Generalized Eikonal new approaches in the Diffraction Theory Michael V. Vesnik
title_fullStr	The method of the Generalized Eikonal new approaches in the Diffraction Theory Michael V. Vesnik
title_full_unstemmed	The method of the Generalized Eikonal new approaches in the Diffraction Theory Michael V. Vesnik
title_short	The method of the Generalized Eikonal
title_sort	the method of the generalized eikonal new approaches in the diffraction theory
title_sub	new approaches in the Diffraction Theory
topic	Beugungstheorie (DE-588)4268180-7 gnd Eikonal (DE-588)4151213-3 gnd
topic_facet	Beugungstheorie Eikonal
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028181809&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV040141722
work_keys_str_mv	AT vesnikmichaelv themethodofthegeneralizedeikonalnewapproachesinthediffractiontheory AT vesnikmichaelv themethodofthegeneralisedeikonal

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