Diffraction theory: the Sommerfeld-Malyuzhinets technique
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Alpha Science Internat.
2008
|
| Schriftenreihe: | Alpha Science series on wave phenomena
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 215 S. Ill., graph. Darst. |
| ISBN: | 9781842653104 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035110609 | ||
| 003 | DE-604 | ||
| 005 | 20090304 | ||
| 007 | t | ||
| 008 | 081021s2008 ad|| |||| 00||| eng d | ||
| 020 | |a 9781842653104 |c (hbk.) : £59.95 |9 978-1-84265-310-4 | ||
| 035 | |a (OCoLC)441760333 | ||
| 035 | |a (DE-599)HBZHT015602480 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 | ||
| 080 | |a 537 | ||
| 084 | |a UH 5200 |0 (DE-625)145655: |2 rvk | ||
| 100 | 1 | |a Babič, Vasilij M. |d 1930- |e Verfasser |0 (DE-588)109303229 |4 aut | |
| 245 | 1 | 0 | |a Diffraction theory |b the Sommerfeld-Malyuzhinets technique |c Vasilii M. Babich ; Mikail A. Lyalinov ; Valery E. Girkurov |
| 264 | 1 | |a Oxford |b Alpha Science Internat. |c 2008 | |
| 300 | |a X, 215 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Alpha Science series on wave phenomena | |
| 650 | 4 | |a matematična fizika - valovanje - sipanje valovanja - teorija loma žarkov - metoda Sommerfeld-Malyu-Zhinetsa - generalizacije - nove aplikacije | |
| 700 | 1 | |a Ljalinov, Michail A. |e Verfasser |4 aut | |
| 700 | 1 | |a Girkurov, Valerij E. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016778437 | ||
Datensatz im Suchindex
| _version_ | 1804138083065528320 |
|---|---|
| adam_text | Contents
Foreword
...................................................
V
Introduction and Historic Remarks
........................ 1
1.1
Outline of the Book
...................................... 1
1.2
Historical Remarks
...................................... 4
1.3
Biographies of A.
Sommerfeld
and G. Malyuzhinets
.......... 6
1.3.1
Arnold Johannes William
Sommerfeld (1868-1951) .,.. 6
1.3.2
Georgy Danilovich Malyuzhinets
(1910-1969) ........ 8
The Diffraction Problem in Angular Domains
.............. 11
2.1
The Helmholtz Equation and Boundary Conditions
.......... 11
2.2
Vicinity of the Edge and Meixner Conditions
................ 13
2.2.1
On the Behaviour of Solutions to the Helmholtz
Equation in the Angular Domain as
r
—> 0............ 15
2.3
Plane-Wave Incidence and the Geometrical-Optic Part of the
Solution
................................................ 19
2.3.1
Waves Reflected by a Wedge
........................ 20
2.3.2
Plane Waves Inside the Domain
φ < Φ
<
f
.......... 21
2.4
Radiation Conditions and Completion of the Formulation of
the Problem
............................................ 22
2.5
Uniqueness of the Solution to the Impedance-Wedge
Diffraction Problem
...................................... 24
2.6
Uniqueness of the Solution to the Perfect-Wedge Diffraction
Problem
................................................ 27
2.7
Uniqueness Theorem and the Limiting-Absorption Principle
.. 29
Solution of the Helmholtz Equation by the
Sommerfeld
Integral
.................................................... 33
3.1
The
Sommerfeld
Integral
................................. 33
3.2
The Laplace Transform
................................... 35
3.3
Representation by Means of Integrals along {/-shaped
Contours
.............................................. 36
3.4
The Malyuzhinets Theorem
............................... 39
3.5
Further Properties of the Function
Ξ(ζ, φ) .................
42
3.6
On Plane and Surface Waves
.............................. 44
VIII Contents
3.7
Far-Field Asymptotic Analysis of the
Sommerfeld
Integral
(Nonuniform
Formulae)
.................................. 46
3.8
On the Behaviour of the
Sommerfeld
Integrals Near the Edge
. 49
4 Sommerfeld
Integral in the Problem of the Plane-Wave
Diffraction by a Perfect Wedge
............................ 51
4.1
Dirichlet Boundary Conditions
............................ 51
4.2
Neumann Boundary Conditions
........................... 53
4.3
Wave Field Radiated by a Vibrating Wedge s Face
........... 54
4.3.1
Representation of the Solution by Means of
Sommerfeld
Integral
............................... 55
4.3.2
Construction of the Function s(z)
................... 57
4.3.3
Verification of
(4.35)............................... 58
4.3.4
Numerical Illustrations
............................. 59
5 Sommerfeld
Diffraction Problem on a Riemann Surface
and the Uniform Ear-Field Asymptotics
................... 61
5.1
The
Sommerfeld
Problem
.............. ................... 61
5.2
Plane-Wave Diffraction by
a
Halfplane..................... 63
5.3
Representation of the Solution by Means of the Fresnel
Integrals
............................................... 63
5.4
Riemann Surface in the Wedge-Diffraction Problem
.......... 66
5.5
The Elimination of Singularities and the Uniform Formulae
in the Penumbra
........................................ 67
5.6
Numerical Examples and Discussion
....................... 69
5.6.1
The Accuracy of the Asymptotic Formulae
........... 71
5.7
GTD and the Matching Procedure
......................... 73
6
Diffraction by a Wedge with Impedance-Boundary
Conditions (the Malyuzhinets Problem)
................... 75
6.1
Functional Equations for the Malyuzhinets Problem
......... 75
6.1.1
The Multiplication Principle, and the Auxiliary
Solution
φο(ζ)
of the Functional Equations
(6.6) ...... 77
6.2
The Malyuzhinets Function
ψφ(ζ)
and its Basic Properties
... 79
6.2.1
Examination of
¿
ίηψΦ{ζ).........................
80
6.2.2
The Function
φΦ (ζ) ...............................
82
6.3
Completion of the Construction of
!Ѓ0(г)
and of s(z)
......... 85
6.4
Far-Field Analysis of the Exact Solution
.................... 87
6.4.1
Contribution of the Surface Waves to the Total Field
.. 90
7
General Theory of the Malyuzhinets-Type Equations
with One Unknown Function
.............................. 95
7.1
The General Malyuzhinets Equations
...................... 95
7.2
Solution to the Homogeneous Malyuzhinets Equations
....... 95
Contents
IX
7.3
Solution
to the Inhomogeneous Equations of the Malyuzhinets
Type
.................................................. 96
7.3.1
Modified Fourier Transform and «S-integrals
........... 98
7.3.2
Direct Application of 5-mtegrals
.................... 99
8
Green Function for an Angular Domain (Cylindrical-Wave
Diffraction)
................................................103
8.1
Statement of the Problem
................................103
8.2
Integral Representation of the Solution
.....................104
8.3
Far-Field Analysis of the Green Function
...................107
8.3.1
On the Far-Field Asymptotics of Green Function
......107
8.3.2
Fresnel Part of the Far Field: Perfect Boundary
Conditions
.......................................108
8.3.3
Impedance Boundary Conditions: Fresnel Part of a
Far Field
.........................................114
8.3.4
Impedance Boundary Conditions: Uniform Directivity
Diagram
.........................................116
8.3.5
On Surface Waves Excited by a Filamentary Source
... 117
9
Diffraction of a Plane Wave by a Wedge with Thin
Dielectric Coatings
........................................119
9.1
Simulation of a Wedge with Thin Material Coatings:
Formulation of the Diffraction Problem
.....................119
9.2
Construction of the Explicit Solution
.......................123
9.3
The Far-Field Analysis
...................................130
9.3.1
Nonuniform
Asymptotics
...........................130
9.3.2
The Uniform Formulae
.............................131
10
Wave Diffraction in the Wedge s Exterior Bisected by a
Thin Semi-Transparent Layer
..............................135
10.1
Statement of the Problem and Reduction to a Functional
Difference Equations
.....................................135
10.2
Reduction to a Second-Order Difference Equation
...........138
10.3
Reduction to
a Fredholm
Integral Equation of the Second Kind
139
10.4
Uniform Asymptotics and the Diffraction Coefficients
........142
10.4.1
Calculation of the Poles and the Residues
............142
10.4.2
Uniform Asymptotics of the Far Field
................145
10.5
Numerical Implementation of the Solution
..................146
10.5.1
Computation of the Spectral Functions
...............146
10.5.2
An Example of the Far-Field Computation
...........148
11
Diffraction of a Skew-Incident Plane Electromagnetic
Wave by an Impedance Wedge
............................151
11.1
Statement of the Problem
................................152
X
Contents
11.1.1
Formulation
of the Problem
........................152
11.1.2
Comments on the Limiting Absorption Principle
......154
11.2
Reduction to Functional Equations
........................155
11.2.1
Reduction to Decoupled Second-Order Functional
Equations
........................................155
11.3
Simplified FD Equation
and Reduction to an Integral Equation
.....................157
11.3.1
Integral Representation of
Д(а)
.....................159
11.3.2
Determination of the Constants Af
..................162
11.3.3
Fredholm
Integral Equation of the Second Kind
.......163
11.4
Uniform Asymptotic of the Solution
.......................164
11.4.1
Poles and Residues
................................164
11.4.2
First-Order Uniform Asymptotics
...................166
11.5
Numerical Aspects and Examples
..........................168
11.5.1
Numerical Computation of the Spectral Functions
.....168
11.5.2
Relations for /2(q)
................................170
11.5.3
Examples
........................................171
Concluding Remarks
......................................173
A On the Saddle-Point Technique
............................175
A.I The Saddle Point and the Contour of the Steepest Descent
... 175
A.2 Asymptotic Evaluation of Integrals
........................177
В
The Stationary-Phase Method
.............................183
B.I Asymptotic Contributions of End and Stationary Points
......183
B.I.I Asymptotic Contribution of the Non-Degenerate
Stationary Point
..................................185
B.2 Stationary Point Near the Integration End-Point
............186
С
The Fresnel Integral
.......................................191
D
The
Kirchhoff
and Physical-Optics Approximations
........195
D.I The
Kirchhoff
Approximation
.............................195
D.2 The Physical-Optics Approximation
.......................198
E
Computation of the Malyuzhinets Function
................203
References
.....................................................207
Index
..........................................................213
|
| adam_txt |
Contents
Foreword
.
V
Introduction and Historic Remarks
. 1
1.1
Outline of the Book
. 1
1.2
Historical Remarks
. 4
1.3
Biographies of A.
Sommerfeld
and G. Malyuzhinets
. 6
1.3.1
Arnold Johannes William
Sommerfeld (1868-1951) .,. 6
1.3.2
Georgy Danilovich Malyuzhinets
(1910-1969) . 8
The Diffraction Problem in Angular Domains
. 11
2.1
The Helmholtz Equation and Boundary Conditions
. 11
2.2
Vicinity of the Edge and Meixner Conditions
. 13
2.2.1
On the Behaviour of Solutions to the Helmholtz
Equation in the Angular Domain as
r
—> 0. 15
2.3
Plane-Wave Incidence and the Geometrical-Optic Part of the
Solution
. 19
2.3.1
Waves Reflected by a Wedge
. 20
2.3.2
Plane Waves Inside the Domain
\φ\ < Φ
<
f
. 21
2.4
Radiation Conditions and Completion of the Formulation of
the Problem
. 22
2.5
Uniqueness of the Solution to the Impedance-Wedge
Diffraction Problem
. 24
2.6
Uniqueness of the Solution to the Perfect-Wedge Diffraction
Problem
. 27
2.7
Uniqueness Theorem and the Limiting-Absorption Principle
. 29
Solution of the Helmholtz Equation by the
Sommerfeld
Integral
. 33
3.1
The
Sommerfeld
Integral
. 33
3.2
The Laplace Transform
. 35
3.3
Representation by Means of Integrals along {/-shaped
Contours
. 36
3.4
The Malyuzhinets Theorem
. 39
3.5
Further Properties of the Function
Ξ(ζ, φ) .
42
3.6
On Plane and Surface Waves
. 44
VIII Contents
3.7
Far-Field Asymptotic Analysis of the
Sommerfeld
Integral
(Nonuniform
Formulae)
. 46
3.8
On the Behaviour of the
Sommerfeld
Integrals Near the Edge
. 49
4 Sommerfeld
Integral in the Problem of the Plane-Wave
Diffraction by a Perfect Wedge
. 51
4.1
Dirichlet Boundary Conditions
. 51
4.2
Neumann Boundary Conditions
. 53
4.3
Wave Field Radiated by a Vibrating Wedge's Face
. 54
4.3.1
Representation of the Solution by Means of
Sommerfeld
Integral
. 55
4.3.2
Construction of the Function s(z)
. 57
4.3.3
Verification of
(4.35). 58
4.3.4
Numerical Illustrations
. 59
5 Sommerfeld
Diffraction Problem on a Riemann Surface
and the Uniform Ear-Field Asymptotics
. 61
5.1
The
Sommerfeld
Problem
.'. 61
5.2
Plane-Wave Diffraction by
a
Halfplane. 63
5.3
Representation of the Solution by Means of the Fresnel
Integrals
. 63
5.4
Riemann Surface in the Wedge-Diffraction Problem
. 66
5.5
The Elimination of Singularities and the Uniform Formulae
in the Penumbra
. 67
5.6
Numerical Examples and Discussion
. 69
5.6.1
The Accuracy of the Asymptotic Formulae
. 71
5.7
GTD and the Matching Procedure
. 73
6
Diffraction by a Wedge with Impedance-Boundary
Conditions (the Malyuzhinets Problem)
. 75
6.1
Functional Equations for the Malyuzhinets Problem
. 75
6.1.1
The Multiplication Principle, and the Auxiliary
Solution
φο(ζ)
of the Functional Equations
(6.6) . 77
6.2
The Malyuzhinets Function
ψφ(ζ)
and its Basic Properties
. 79
6.2.1
Examination of
¿
ίηψΦ{ζ).
80
6.2.2
The Function
φΦ (ζ) .
82
6.3
Completion of the Construction of
!Ѓ0(г)
and of s(z)
. 85
6.4
Far-Field Analysis of the Exact Solution
. 87
6.4.1
Contribution of the Surface Waves to the Total Field
. 90
7
General Theory of the Malyuzhinets-Type Equations
with One Unknown Function
. 95
7.1
The General Malyuzhinets Equations
. 95
7.2
Solution to the Homogeneous Malyuzhinets Equations
. 95
Contents
IX
7.3
Solution
to the Inhomogeneous Equations of the Malyuzhinets
Type
. 96
7.3.1
Modified Fourier Transform and «S-integrals
. 98
7.3.2
Direct Application of 5-mtegrals
. 99
8
Green Function for an Angular Domain (Cylindrical-Wave
Diffraction)
.103
8.1
Statement of the Problem
.103
8.2
Integral Representation of the Solution
.104
8.3
Far-Field Analysis of the Green Function
.107
8.3.1
On the Far-Field Asymptotics of Green Function
.107
8.3.2
Fresnel Part of the Far Field: Perfect Boundary
Conditions
.108
8.3.3
Impedance Boundary Conditions: Fresnel Part of a
Far Field
.114
8.3.4
Impedance Boundary Conditions: Uniform Directivity
Diagram
.116
8.3.5
On Surface Waves Excited by a Filamentary Source
. 117
9
Diffraction of a Plane Wave by a Wedge with Thin
Dielectric Coatings
.119
9.1
Simulation of a Wedge with Thin Material Coatings:
Formulation of the Diffraction Problem
.119
9.2
Construction of the Explicit Solution
.123
9.3
The Far-Field Analysis
.130
9.3.1
Nonuniform
Asymptotics
.130
9.3.2
The Uniform Formulae
.131
10
Wave Diffraction in the Wedge's Exterior Bisected by a
Thin Semi-Transparent Layer
.135
10.1
Statement of the Problem and Reduction to a Functional
Difference Equations
.135
10.2
Reduction to a Second-Order Difference Equation
.138
10.3
Reduction to
a Fredholm
Integral Equation of the Second Kind
139
10.4
Uniform Asymptotics and the Diffraction Coefficients
.142
10.4.1
Calculation of the Poles and the Residues
.142
10.4.2
Uniform Asymptotics of the Far Field
.145
10.5
Numerical Implementation of the Solution
.146
10.5.1
Computation of the Spectral Functions
.146
10.5.2
An Example of the Far-Field Computation
.148
11
Diffraction of a Skew-Incident Plane Electromagnetic
Wave by an Impedance Wedge
.151
11.1
Statement of the Problem
.152
X
Contents
11.1.1
Formulation
of the Problem
.152
11.1.2
Comments on the Limiting Absorption Principle
.154
11.2
Reduction to Functional Equations
.155
11.2.1
Reduction to Decoupled Second-Order Functional
Equations
.155
11.3
Simplified FD Equation
and Reduction to an Integral Equation
.157
11.3.1
Integral Representation of
Д(а)
.159
11.3.2
Determination of the Constants Af
.162
11.3.3
Fredholm
Integral Equation of the Second Kind
.163
11.4
Uniform Asymptotic of the Solution
.164
11.4.1
Poles and Residues
.164
11.4.2
First-Order Uniform Asymptotics
.166
11.5
Numerical Aspects and Examples
.168
11.5.1
Numerical Computation of the Spectral Functions
.168
11.5.2
Relations for /2(q)
.170
11.5.3
Examples
.171
Concluding Remarks
.173
A On the Saddle-Point Technique
.175
A.I The Saddle Point and the Contour of the Steepest Descent
. 175
A.2 Asymptotic Evaluation of Integrals
.177
В
The Stationary-Phase Method
.183
B.I Asymptotic Contributions of End and Stationary Points
.183
B.I.I Asymptotic Contribution of the Non-Degenerate
Stationary Point
.185
B.2 Stationary Point Near the Integration End-Point
.186
С
The Fresnel Integral
.191
D
The
Kirchhoff
and Physical-Optics Approximations
.195
D.I The
Kirchhoff
Approximation
.195
D.2 The Physical-Optics Approximation
.198
E
Computation of the Malyuzhinets Function
.203
References
.207
Index
.213 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Babič, Vasilij M. 1930- Ljalinov, Michail A. Girkurov, Valerij E. |
| author_GND | (DE-588)109303229 |
| author_facet | Babič, Vasilij M. 1930- Ljalinov, Michail A. Girkurov, Valerij E. |
| author_role | aut aut aut |
| author_sort | Babič, Vasilij M. 1930- |
| author_variant | v m b vm vmb m a l ma mal v e g ve veg |
| building | Verbundindex |
| bvnumber | BV035110609 |
| classification_rvk | UH 5200 |
| ctrlnum | (OCoLC)441760333 (DE-599)HBZHT015602480 |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV035110609 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:17:20Z |
| indexdate | 2024-07-09T21:22:33Z |
| institution | BVB |
| isbn | 9781842653104 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016778437 |
| oclc_num | 441760333 |
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| owner_facet | DE-703 |
| physical | X, 215 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Alpha Science Internat. |
| record_format | marc |
| series2 | Alpha Science series on wave phenomena |
| spelling | Babič, Vasilij M. 1930- Verfasser (DE-588)109303229 aut Diffraction theory the Sommerfeld-Malyuzhinets technique Vasilii M. Babich ; Mikail A. Lyalinov ; Valery E. Girkurov Oxford Alpha Science Internat. 2008 X, 215 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Alpha Science series on wave phenomena matematična fizika - valovanje - sipanje valovanja - teorija loma žarkov - metoda Sommerfeld-Malyu-Zhinetsa - generalizacije - nove aplikacije Ljalinov, Michail A. Verfasser aut Girkurov, Valerij E. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Babič, Vasilij M. 1930- Ljalinov, Michail A. Girkurov, Valerij E. Diffraction theory the Sommerfeld-Malyuzhinets technique matematična fizika - valovanje - sipanje valovanja - teorija loma žarkov - metoda Sommerfeld-Malyu-Zhinetsa - generalizacije - nove aplikacije |
| title | Diffraction theory the Sommerfeld-Malyuzhinets technique |
| title_auth | Diffraction theory the Sommerfeld-Malyuzhinets technique |
| title_exact_search | Diffraction theory the Sommerfeld-Malyuzhinets technique |
| title_exact_search_txtP | Diffraction theory the Sommerfeld-Malyuzhinets technique |
| title_full | Diffraction theory the Sommerfeld-Malyuzhinets technique Vasilii M. Babich ; Mikail A. Lyalinov ; Valery E. Girkurov |
| title_fullStr | Diffraction theory the Sommerfeld-Malyuzhinets technique Vasilii M. Babich ; Mikail A. Lyalinov ; Valery E. Girkurov |
| title_full_unstemmed | Diffraction theory the Sommerfeld-Malyuzhinets technique Vasilii M. Babich ; Mikail A. Lyalinov ; Valery E. Girkurov |
| title_short | Diffraction theory |
| title_sort | diffraction theory the sommerfeld malyuzhinets technique |
| title_sub | the Sommerfeld-Malyuzhinets technique |
| topic | matematična fizika - valovanje - sipanje valovanja - teorija loma žarkov - metoda Sommerfeld-Malyu-Zhinetsa - generalizacije - nove aplikacije |
| topic_facet | matematična fizika - valovanje - sipanje valovanja - teorija loma žarkov - metoda Sommerfeld-Malyu-Zhinetsa - generalizacije - nove aplikacije |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT babicvasilijm diffractiontheorythesommerfeldmalyuzhinetstechnique AT ljalinovmichaila diffractiontheorythesommerfeldmalyuzhinetstechnique AT girkurovvalerije diffractiontheorythesommerfeldmalyuzhinetstechnique |