Scalar wave theory: Green's functions and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona
Springer
1992
|
| Schriftenreihe: | Springer series on wave phenomena
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 193 S. graph. Darst. |
| ISBN: | 3540552634 0387552634 |
Internformat
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| 100 | 1 | |a DeSanto, John A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Scalar wave theory |b Green's functions and applications |c J. DeSanto |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona |b Springer |c 1992 | |
| 300 | |a XIII, 193 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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CONTENTS
1. SCALAR WAVE THEORY . 1
1.1 FLUID EQUATIONS. 1
1.2 SOUND. 3
1.3 WAVE EQUATIONS. 5
1.4 SPATIALLY VARIABLE DENSITY. 6
1.5 HELMHOLTZ EQUATION AND SEPARABLE SOLUTIONS. 7
1.6 ONE-DIMENSIONAL PROBLEMS AND STURM-LIOUVILLE THEORY 14
1.7 CALCULATION OF EIGENVALUES FROM EIGENFUNCTIONS . 21
1.8 INTERFACE BOUNDARY CONDITIONS. 23
LA ENERGY AND MOMENTUM. 24
APPENDICES. 27
L.A WAVE EQUATION DERIVATION
FOR SPATIALLY VARYING DENSITY . 27
1 .B WAVE EQUATION DERIVATION FOR SPATIALLY AND TEMPORALLY
VARIABLE DENSITY WITH QUADRATIC VELOCITY TERMS
. 28
2. GREEN'S FUNCTIONS. 33
2.1 BASIC DEFINITION. 33
2.2 EIGENFUNCTION EXPANSION. 34
2.3 ONE-DIMENSIONAL EXAMPLES . 36
2.4 ELEMENTARY SOURCE. 41
2.5 GREEN'S FUNCTIONS FOR THE WAVE EQUATION. 42
2.6 GREEN'S FUNCTIONS FOR THE WAVE EQUATION
IN TWO DIMENSIONS. 50
2.7 GREEN'S FUNCTIONS FOR THE WAVE EQUATION
IN ONE DIMENSION. 51
2.8 GREEN'S FUNCTIONS FOR THE HELMHOLTZ EQUATION. 52
2.8.1 THREE DIMENSIONS. 52
2.8.2 TWO DIMENSIONS. 54
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/920767281
XII CONTENTS
2.8.3 ONE DIMENSION. 55
2.9 INTEGRAL REPRESENTATIONS: HELMHOLTZ GREEN'S FUNCTIONS 56
2.9.1 WEYL REPRESENTATION. 56
2.9.2 SOMMERFELD REPRESENTATION . 59
2.9.3 EXPLICIT EVALUATION OF G
(3). 60
2.9.4 WEYRICH REPRESENTATION . 61
2.9.5 PLANE-WAVE DECOMPOSITION OF G(2) . 63
2.9.6 EXPLICIT EVALUATION OF G(2). 64
2.9.7 EXPLICIT RELATION BETWEEN G(3) AND G(2) . 64
2.10 DELTA FUNCTIONS IN DIFFERENT COORDINATE SYSTEMS . 65
2.10.1 CYLINDRICAL COORDINATES . 65
2.10.2 SPHERICAL COORDINATES . 67
2.11 OTHER EXAMPLES OF GREEN'S FUNCTIONS. 69
APPENDIX . 75
2.A DIRAC-PLEMELJ RELATIONS. 75
3
.
SCALAR PLANE WAVE SCATTERING
.
79
3.1 SCATTERING FROM A PLANE INTERFACE. 79
3.2 EXAMPLES. 65
3.3 INTERFACE VALUES AND IMPEDANCES . 84
3.4 IMPEDANCE BOUNDARY CONDITION. 86
3.5 WAVE FRONTS AND RAY PARAMETER . 88
3.6 TOTAL TRANSMISSION. 90
3.7 TOTAL INTERNAL REFLECTION. 93
3.8 EFFECT OF SURFACE ROUGHNESS. 97
4. SPHERICAL WAVES SCATTERING FROM PLANAR BOUNDARIES 101
4.1 WEYL AND SOMMERFELD REPRESENTATIONS.101
4.2 FIELD REPRESENTATIONS.103
4.3 SQUARE ROOT BRANCH POINTS .106
4.4 REFLECTED FIELD.110
4.5 CASE 1: CI
C
2
.115
4.6 CASE 2: CI C% .117
4.7 TRANSMITTED FIELD.127
APPENDIX .137
4.A STEEPEST DESCENT METHOD.137
5. TWO-LAYERED LIQUID HALF-SPACE (PEKERIS WAVEGUIDE) 143
5.1 GEOMETRY AND NOTATION .143
5.2 GREEN'S FUNCTION.144
CONTENTS XIII
5.3 ANALYTIC PROPERTIES OF G
2 .148
5.4 NORMAL MODE (NM) REPRESENTATION.157
5.5 FOURIER-BESSEL REPRESENTATION.160
5.6 PSEUDO-PROPER MODES.162
5.7 LEAKY WAVES .163
5.8 BRANCH LINE INTEGRAL (BLI).169
5.9 VIRTUAL MODES.171
5.10 MODAL ATTENUATION.180
APPENDIX .183
5.A PROOF OF THE CONTOUR REPRESENTATION.183
REFERENCES .187
INDEX .191 |
| any_adam_object | 1 |
| author | DeSanto, John A. |
| author_facet | DeSanto, John A. |
| author_role | aut |
| author_sort | DeSanto, John A. |
| author_variant | j a d ja jad |
| building | Verbundindex |
| bvnumber | BV025860210 |
| classification_rvk | SK 950 UF 5000 |
| ctrlnum | (OCoLC)246671173 (DE-599)BVBBV025860210 |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-10-09T16:24:41Z |
| institution | BVB |
| isbn | 3540552634 0387552634 |
| language | English |
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| physical | XIII, 193 S. graph. Darst. |
| publishDate | 1992 |
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| publishDateSort | 1992 |
| publisher | Springer |
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| series | Springer series on wave phenomena |
| series2 | Springer series on wave phenomena |
| spelling | DeSanto, John A. Verfasser aut Scalar wave theory Green's functions and applications J. DeSanto Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona Springer 1992 XIII, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series on wave phenomena 12 Schallausbreitung (DE-588)4179359-6 gnd rswk-swf Welle (DE-588)4065310-9 gnd rswk-swf Schallwelle (DE-588)4191490-9 gnd rswk-swf Green-Funktion (DE-588)4158123-4 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Streuung (DE-588)4058056-8 gnd rswk-swf Wellengleichung (DE-588)4065315-8 gnd rswk-swf Green-Funktion (DE-588)4158123-4 s DE-604 Schallausbreitung (DE-588)4179359-6 s Wellengleichung (DE-588)4065315-8 s Schallwelle (DE-588)4191490-9 s Streuung (DE-588)4058056-8 s Welle (DE-588)4065310-9 s Wellenausbreitung (DE-588)4121912-0 s Springer series on wave phenomena 12 (DE-604)BV000022763 12 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019107935&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | DeSanto, John A. Scalar wave theory Green's functions and applications Springer series on wave phenomena Schallausbreitung (DE-588)4179359-6 gnd Welle (DE-588)4065310-9 gnd Schallwelle (DE-588)4191490-9 gnd Green-Funktion (DE-588)4158123-4 gnd Wellenausbreitung (DE-588)4121912-0 gnd Streuung (DE-588)4058056-8 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4179359-6 (DE-588)4065310-9 (DE-588)4191490-9 (DE-588)4158123-4 (DE-588)4121912-0 (DE-588)4058056-8 (DE-588)4065315-8 |
| title | Scalar wave theory Green's functions and applications |
| title_auth | Scalar wave theory Green's functions and applications |
| title_exact_search | Scalar wave theory Green's functions and applications |
| title_full | Scalar wave theory Green's functions and applications J. DeSanto |
| title_fullStr | Scalar wave theory Green's functions and applications J. DeSanto |
| title_full_unstemmed | Scalar wave theory Green's functions and applications J. DeSanto |
| title_short | Scalar wave theory |
| title_sort | scalar wave theory green s functions and applications |
| title_sub | Green's functions and applications |
| topic | Schallausbreitung (DE-588)4179359-6 gnd Welle (DE-588)4065310-9 gnd Schallwelle (DE-588)4191490-9 gnd Green-Funktion (DE-588)4158123-4 gnd Wellenausbreitung (DE-588)4121912-0 gnd Streuung (DE-588)4058056-8 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Schallausbreitung Welle Schallwelle Green-Funktion Wellenausbreitung Streuung Wellengleichung |
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