Time-domain scattering:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge ; New York, NY ; Port Melbourne ; New Delhi ; Singapore
Cambridge University Press
2021
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
180 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032860126&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xi, 250 Seiten Diagramme |
| ISBN: | 9781108835596 |
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| 245 | 1 | 0 | |a Time-domain scattering |c P.A. Martin ; Colorado School of Mines |
| 264 | 1 | |a Cambridge ; New York, NY ; Port Melbourne ; New Delhi ; Singapore |b Cambridge University Press |c 2021 | |
| 264 | 4 | |c © 2021 | |
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| 653 | 0 | |a Time-domain analysis | |
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Datensatz im Suchindex
| _version_ | 1819285674980802560 |
|---|---|
| adam_text | ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS
Time-Domain Scattering
P A MARTIN
Colorado School of Mines
Contents
Preface page xiii
1 Acoustics and the Wave Equation 1
1 1 Governing Equations 1
111 Linearisation: Ambient Flows 2
112 Linearisation: Acoustics 3
113 Zero Ambient Velocity: Bergmann’s Equation 4
114 Zero Ambient Velocity and Constant Ambient Density 4
115 Zero Ambient Velocity and Homogeneous Fluid 5
116 Non-Zero Ambient Velocity and Homogeneous Fluid 5
117 Non-Uniform Ambient Flows and Dynamic Materials 6
118 Nonlinear Acoustics 10
1 2 Acoustic Scattering 10
1 3 Waves on a String il
131 An Initial-Value Problem 13
132A Bead on an Infinite String: Solution for All t 13
133A Bead on an Infinite String: Initial- Value Problem 15
134A Simple Initial-Boundary Value Problem 16
135A Bead on an Infinite String: Use of Laplace
Transforms 17
136 Discussion and Summary 18
137 Damping, Dissipation, Absorption and Losses 18
138 The Forced Wave Equation 20
1 4 Laplace Transforms: Formal Properties 21
1 5 Causality 22
1 6 Electromagnetics, Elastodynamics and Hydrodynamics 24
161 Electromagnetics 24
162 Elastodynamics 25
163 Hydrodynamics 26
1 7 Overview of the Book 27
viii
Contents
Wavefunctions
2 Simple Solutions
3 1 Plane Waves
Chara
Initial,
2,12 Spherical Polar Coordinates
2 13 Spherically Symmetric Wavefunctions
The Time-Domain Far-Field Pattern
Use of Spherical Harmonics
23 1 Separated Solutions
232 Similarity Solutions
733 Smirnov’s Representation
134 A Bateman-Like Wavefunction
935 Multipole Representation
23 6 Lamb, Grote and Keller
23 7 Changing the Independent Variables
Harry Bateman and the Wave Equation
24 1 Integral Representations
2,42 Transformations Similar to Kelvin Inversion
2 43 Some Two-Dimensional Wavefunctions
744 Further Transformations
Spheroidal Wavefunctions
251 Spheroidal Wave Equation
252 Angular Spheroidal Wavefunctions
253 Radial Spheroidal Wavefunctions
254 Summary
Moving Sources
cteristics and Discontinuities
Characteristics
The Eikonal Equations
Discontinuous Solutions
Weak Solutions and Discontinuities
341 Green s Formula
342 Weak Solutions of the Wave Equation
343 Discontinuous Weak Solutions
Jump Relations in Continuum Mechanics
“Boundary Value Problems
Formulation of IBVPs
Acoustic Energy
#21 Energy Conservation
422 Energy Inequality
4 23 Energy Decay
Incident Sound Pulses
Compatibility Conditions
n
4 5
Contents
Bateman’s IBVP for a Sphere
Further Problems and Boundary Conditions
461 Locally Reacting Surfaces
462 Transmission Problems
463 Membrane Problems
464 Elastic Shells
465 Hydrodynamic Problems
The Forced Wave Equation
471 Forward Problem
472 The Limiting Amplitude Principle
4 713 Aerodynamic Sound
474 Inverse Source Problems
Existence and Uniqueness Results
481 Function Spaces and Notation
4 82 Problem Dig
4 83 Problem Nip
484 Summary
Use of Laplace Transforms
Formal Treatment
Laplace Transform of Discontinuous Functions
Laplace Transform of Wavefunctions
Laplace Transform of Boundary Conditions
Synthesis
Fourier Transforms
561 Basic Definitions and Strategy
562A Time-Domain Radiation Condition
563 Further Remarks
Laguerre Transforms
Problems with Spherical Symmetry
6 1 Use of Simple Sources
611 Dirichlet Boundary Condition
612 Pressure Boundary Condition
613 Neumann Boundary Condition
614 Discussion and Special Cases
6 2 Use of Laplace Transforms
621 Dirichlet Boundary Condition
622 Pressure Boundary Condition
623 Neumann Boundary Condition
Scattering by a Sphere
7 1 Preliminaries
7 2 Use of Laplace Transforms
7 21 Dirichlet Boundary Condition
Contents
Boundary Condition
essure
2 7 Boundary Condition
72,3 Neumann
72,4 Literature
Residual Potential Methods, Nonreflecting Boundary Kernels
and Dirichlet-to-Neumann Mappings 7
Application of the Similarity Representation
7 41 Dirichlet Boundary Condition
74 2 Pressure Boundary Condition
7 43 Neumann Boundary Condition
Moving Spheres
1 Scattering by a Spheroid
Scattering Frequencies and the Singularity Expansion Method
8 1 Fourier Transforms
82 Scattering Frequencies
83 Boundary Integral Equations
8 4 Generalised Eigenfunctions; Quasinormal Modes
8 5 Moving the Inversion Contour
8 6 The Singularity Expansion Method (SEM)
8 7 The Eigenmode Expansion Method (EEM)
871 Self-Adjoint Operators and Normal Operators
8 72 The Time-Harmonic Single-Layer Operator
8 73 Singular Value Decomposition (SVD)
8 74 The Eigenmode Expansion Method (EEM)
Integral Representations
9 1 Kirchhoff’s Formula: Classical Derivations
911 Kirchhoff’s Formula for Bounded Domains
912 Kirchhoff’s Formula for Exterior Domains
913 Special Cases of Kirchhoff’s Formula
9 14 A Formula for the Pressure
915 Use of Laplace Transforms
916 Weakening the Smoothness Assumptions
917 Literature
3 Kaas Formula a Space-Time Derivation
931 nn ormula: Use of Generalised Functions
ae ixed Surface §
94 an ring Surface S(t)
entials
oo Single-Layer Potential
03 Double-Layer Potential
Notation and Definitions
944 Kirchhoff’s Formula
lig
lig
lig
12)
13]
10
Contents
Integral Equations
Integral Equations: Indirect Method
10 2 Integral Equations: Direct Method
10 3 Integral Equations: Numerical Methods
10 3 1 Basic Time-Stepping Method
10 3 2 Instabilities and Remedies
10 4 Convolution Quadrature Methods
10 41A Volterra Integral Equation
10 4 2 Application to Time-Domain Boundary Integral
Equations
10 4 3 Application to Scattering by a Sphere
10 4 4 An Alternative View of CQMs
10 5 Electromagnetics
10 6 Elastodynamics
10 7 Hydrodynamics
10 7 1 Clément’s Equation
10 8 Method of Fundamental Solutions (MFS, ESM)
10 9 Use of Fourier Transforms
10 10 Cracks, Screens and Other Thin Scatterers
10 10 1 Derivation of Integral Equations Using Fourier
Transforms
10 10 2 Derivation of Integral Equations Using Layer Potentials
10 10 3 Comments and Literature
References
Citation index
Index
|
| any_adam_object | 1 |
| author | Martin, Paul A. ca. 20./21. Jh |
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| author_facet | Martin, Paul A. ca. 20./21. Jh |
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| author_sort | Martin, Paul A. ca. 20./21. Jh |
| author_variant | p a m pa pam |
| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QA329 |
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| ctrlnum | (OCoLC)1260136185 (DE-599)KXP1750497832 |
| dewey-full | 515/.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.724 |
| dewey-search | 515/.724 |
| dewey-sort | 3515 3724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV047458293 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T19:20:07Z |
| institution | BVB |
| isbn | 9781108835596 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032860126 |
| oclc_num | 1260136185 |
| open_access_boolean | |
| owner | DE-384 DE-83 DE-11 |
| owner_facet | DE-384 DE-83 DE-11 |
| physical | xi, 250 Seiten Diagramme |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spellingShingle | Martin, Paul A. ca. 20./21. Jh Time-domain scattering Encyclopedia of mathematics and its applications Zeitreihenanalyse (DE-588)4067486-1 gnd Streutheorie (DE-588)4183697-2 gnd Wellengleichung (DE-588)4065315-8 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4183697-2 (DE-588)4065315-8 |
| title | Time-domain scattering |
| title_auth | Time-domain scattering |
| title_exact_search | Time-domain scattering |
| title_full | Time-domain scattering P.A. Martin ; Colorado School of Mines |
| title_fullStr | Time-domain scattering P.A. Martin ; Colorado School of Mines |
| title_full_unstemmed | Time-domain scattering P.A. Martin ; Colorado School of Mines |
| title_short | Time-domain scattering |
| title_sort | time domain scattering |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Streutheorie (DE-588)4183697-2 gnd Wellengleichung (DE-588)4065315-8 gnd |
| topic_facet | Zeitreihenanalyse Streutheorie Wellengleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032860126&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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