Low Frequency Scattering

by Dassios, George; Kleinman, Ralph

• ISBN13: 9780198536789
• ISBN10: 019853678X
• Format: Hardcover
• Copyright: 2000-03-02
• Publisher: Oxford University Press

Summary

This is the first book to unify the theories of acoustic, electromagnetic, and elastic waves and discuss the many physical and geometric aspects of their interactions with obstacles. It offers a complete introduction to scattering theory, and discusses low frequency scattering in particular. A significant number of results are previously unpublished, and this book fills many gaps in the existing literature. Included is an extended bibliography covering the whole existing literature on low frequency scattering, making this an invaluable reference for researchers.

Table of Contents

Notation	xiii
Basic theory	1	(40)
The basic theory of acoustic waves	1	(16)
Field equations	1	(5)
Boundary conditions	6	(2)
Transmission conditions	8	(3)
Radiation condition	11	(1)
Incident fields and the fundamental solution	11	(1)
Basic scattering problems	12	(2)
Energy functionals	14	(2)
Problems in acoustics	16	(1)
The basic theory of electromagnetic waves	17	(11)
Field equations	17	(3)
Boundary conditions	20	(1)
Transmission conditions	21	(1)
Radiation conditions	22	(1)
Incident fields and the fundamental solution	22	(2)
Basic scattering problems	24	(1)
Energy functionals	25	(1)
Problems in electromagnetics	26	(2)
The basic theory of elastic waves	28	(13)
Field equations	28	(5)
Boundary conditions	33	(1)
Transmission conditions	33	(1)
Radiation conditions	34	(1)
Incident fields and the fundamental solution	34	(2)
Basic scattering problems	36	(1)
Energy functionals	37	(2)
Problems in elasticity	39	(2)
Integral representations and scattering theorems	41	(38)
Acoustics	41	(11)
Integral representations in acoustics	41	(2)
The far field	43	(1)
The far field expansion theorem	44	(1)
Cross sections	45	(3)
Basic scattering theorems	48	(3)
Problems in acoustics	51	(1)
Electromagnetics	52	(17)
Integral representations in electromagnetics	52	(5)
The far field	57	(3)
The far field expansion theorem	60	(1)
Cross sections	61	(2)
The basic scattering theorems	63	(4)
Problems in electromagnetics	67	(2)
Elasticity	69	(10)
Integral representations in elasticity	69	(1)
The far field	70	(2)
The far field expansion theorem	72	(1)
Cross sections	73	(3)
The basic scattering theorems	76	(2)
Problems in elasticity	78	(1)
Low frequency expansions	79	(59)
Acoustics	79	(22)
General low frequency expansions in acoustics	79	(5)
The Dirichlet problem	84	(3)
The Neumann problem	87	(3)
The Robin problem	90	(3)
The transmission problem	93	(7)
Problems in acoustics	100	(1)
Electromagnetics	101	(20)
General low frequency expansions in electromagnetics	101	(5)
The perfect conductor problem	106	(6)
The impedance problem	112	(1)
The transmission problem	112	(8)
Problems in electromagnetics	120	(1)
Elasticity	121	(17)
General low frequency expansions in elasticity	121	(6)
The rigid problem	127	(3)
The cavity problem	130	(3)
The transmission problem	133	(3)
Problems in elasticity	136	(2)
The transmission problem revisited	138	(25)
Acoustics	138	(6)
The volume integral formulation	138	(6)
Problems in acoustics	144	(1)
Electromagnetics	144	(13)
The volume integral formation	144	(13)
Problems in electromagnetics	157	(1)
Elasticity	157	(6)
The volume integral formulation	157	(5)
Problems in elasticity	162	(1)
Rayleigh scattering	163	(38)
Basic potential problems	163	(6)
Acoustics	169	(16)
The Dirichlet problem	169	(7)
The Neumann problem	176	(2)
The Robin problem	178	(2)
The transmission problem	180	(4)
Problems in potentials and acoustics	184	(1)
Electromagnetics	185	(8)
The perfect conductor problem	185	(3)
The transmission problem	188	(5)
Problems in electromagnetics	193	(1)
Elasticity	193	(8)
The rigid problem	193	(1)
The cavity problem	194	(2)
The transmission problem	196	(4)
Problems in elasticity	200	(1)
Integral equations	201	(20)
Fundamental relations	201	(3)
Acoustics	204	(7)
Basic equations in acoustics	204	(1)
The Dirichlet problem	205	(2)
The Neumann problem	207	(1)
The Robin problem	207	(1)
The transmission problem	208	(2)
Problems in acoustics	210	(1)
Electromagnetics	211	(4)
Basic equations in electromagnetics	211	(1)
The perfect conductor problem	212	(1)
The transmission problem	213	(2)
Problems in electromagnetics	215	(1)
Elasticity	215	(6)
Basic equations in elasticity	215	(1)
The rigid problem	216	(1)
The cavity problem	217	(1)
The transmission problem	217	(3)
Problems in elasticity	220	(1)
The sphere	221	(28)
Basics	221	(3)
Acoustics	224	(8)
The Dirichlet problem	224	(1)
The Neumann problem	225	(1)
The Robin problem	226	(2)
The lossless transmission problem	228	(1)
The lossy transmission problem	229	(3)
Electromagnetics	232	(3)
The perfect conductor problem	232	(1)
The impedance problem	233	(1)
The lossless transmission problem	233	(1)
The lossy transmission problem	234	(1)
Elasticity	235	(6)
The rigid problem	235	(2)
The cavity problem	237	(1)
The transmission problem	238	(3)
Point sources in acoustics	241	(8)
The Dirichlet problem	242	(1)
The Neumann problem	243	(1)
The Robin problem	244	(2)
The transmission problem	246	(3)
The ellipsoid	249	(25)
Basics	249	(6)
Acoustics	255	(5)
The Dirichlet problem	255	(1)
The Neumann problem	256	(1)
The Robin problem	257	(1)
The lossless transmission problem	257	(1)
The lossy transmission problem	258	(2)
Electromagnetics	260	(4)
The perfect conductor problem	260	(1)
The impedance problem	261	(1)
The lossless transmission problem	261	(2)
The lossy transmission problem	263	(1)
Elasticity	264	(10)
The rigid problem	264	(3)
The cavity problem	267	(3)
The transmission problem	270	(4)
Bibliography	274	(21)
Index	295