Author: Alexander Komech
Publisher: Springer Nature
ISBN: 3030266990
Category : Mathematics
Languages : en
Pages : 167
Book Description
This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann–Hilbert problem. The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.
Stationary Diffraction by Wedges
Author: Alexander Komech
Publisher: Springer Nature
ISBN: 3030266990
Category : Mathematics
Languages : en
Pages : 167
Book Description
This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann–Hilbert problem. The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.
Publisher: Springer Nature
ISBN: 3030266990
Category : Mathematics
Languages : en
Pages : 167
Book Description
This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann–Hilbert problem. The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.
Diffraction by an Immersed Elastic Wedge
Author: Jean-Pierre Croisille
Publisher: Springer
ISBN: 3540466983
Category : Mathematics
Languages : en
Pages : 138
Book Description
This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.
Publisher: Springer
ISBN: 3540466983
Category : Mathematics
Languages : en
Pages : 138
Book Description
This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers.
Scattering and Diffraction by Wedges 2
Author: Vito G. Daniele
Publisher: John Wiley & Sons
ISBN: 1119779448
Category : Technology & Engineering
Languages : en
Pages : 240
Book Description
The book has a dual purpose. The first is to expose a general methodology to solve problems of electromagnetism in geometries constituted of angular regions. The second is to bring the solutions of some canonical problems of fundamental importance in modern electromagnetic engineering with the use of the Wiener-Hopf technique. In particular, the general mathematical methodology is very ingenious and original. It is based on sophisticated and attractive procedures exploiting simple and advanced properties of analytical functions. Once the reader has acquired the methodology, she/he can easily obtain the solution of the canonical problems reported in the book. The book can be appealing also to readers who are not directly interested in the detailed mathematical methodology and/ or in electromagnetics. In fact the same methodology can be extended to acoustics and elasticity problems. Moreover, the proposed practical problems with their solutions constitute a list of reference solutions and can be of interests in engineering production in the field of radio propagations, electromagnetic compatibility and radar technologies.
Publisher: John Wiley & Sons
ISBN: 1119779448
Category : Technology & Engineering
Languages : en
Pages : 240
Book Description
The book has a dual purpose. The first is to expose a general methodology to solve problems of electromagnetism in geometries constituted of angular regions. The second is to bring the solutions of some canonical problems of fundamental importance in modern electromagnetic engineering with the use of the Wiener-Hopf technique. In particular, the general mathematical methodology is very ingenious and original. It is based on sophisticated and attractive procedures exploiting simple and advanced properties of analytical functions. Once the reader has acquired the methodology, she/he can easily obtain the solution of the canonical problems reported in the book. The book can be appealing also to readers who are not directly interested in the detailed mathematical methodology and/ or in electromagnetics. In fact the same methodology can be extended to acoustics and elasticity problems. Moreover, the proposed practical problems with their solutions constitute a list of reference solutions and can be of interests in engineering production in the field of radio propagations, electromagnetic compatibility and radar technologies.
Scattering and Diffraction by Wedges 1
Author: Vito G. Daniele
Publisher: John Wiley & Sons
ISBN: 1119780055
Category : Science
Languages : en
Pages : 240
Book Description
The book has a dual purpose. The first is to expose a general methodology to solve problems of electromagnetism in geometries constituted of angular regions. The second is to bring the solutions of some canonical problems of fundamental importance in modern electromagnetic engineering with the use of the Wiener-Hopf technique. In particular, the general mathematical methodology is very ingenious and original. It is based on sophisticated and attractive procedures exploiting simple and advanced properties of analytical functions. Once the reader has acquired the methodology, they can easily obtain the solution of the canonical problems reported in the book. The book can be appealing also to readers who are not directly interested in the detailed mathematical methodology and/ or in electromagnetics. In fact the same methodology can be extended to acoustics and elasticity problems. Moreover, the proposed practical problems with their solutions constitute a list of reference solutions and can be of interest in engineering production in the field of radio propagations, electromagnetic compatibility and radar technologies.
Publisher: John Wiley & Sons
ISBN: 1119780055
Category : Science
Languages : en
Pages : 240
Book Description
The book has a dual purpose. The first is to expose a general methodology to solve problems of electromagnetism in geometries constituted of angular regions. The second is to bring the solutions of some canonical problems of fundamental importance in modern electromagnetic engineering with the use of the Wiener-Hopf technique. In particular, the general mathematical methodology is very ingenious and original. It is based on sophisticated and attractive procedures exploiting simple and advanced properties of analytical functions. Once the reader has acquired the methodology, they can easily obtain the solution of the canonical problems reported in the book. The book can be appealing also to readers who are not directly interested in the detailed mathematical methodology and/ or in electromagnetics. In fact the same methodology can be extended to acoustics and elasticity problems. Moreover, the proposed practical problems with their solutions constitute a list of reference solutions and can be of interest in engineering production in the field of radio propagations, electromagnetic compatibility and radar technologies.
Diffraction by an Immersed Elastic Wedge
Author: Jean-Pierre Croisille
Publisher:
ISBN: 9783662168318
Category :
Languages : en
Pages : 150
Book Description
Publisher:
ISBN: 9783662168318
Category :
Languages : en
Pages : 150
Book Description
Diffraction by Wedges
Author: Bair Budaev
Publisher: Longman Sc & Tech
ISBN: 9780470235041
Category : Diffraction
Languages : en
Pages : 141
Book Description
The problem of wave diffraction by wedge-shaped structures is important in many applications, including electromagnetics, acoustics, and geophysics. Numerous attempts to solve these problems have been made during the last 70 years using both analytical and numerical methods, but this has proved to be very difficu
Publisher: Longman Sc & Tech
ISBN: 9780470235041
Category : Diffraction
Languages : en
Pages : 141
Book Description
The problem of wave diffraction by wedge-shaped structures is important in many applications, including electromagnetics, acoustics, and geophysics. Numerous attempts to solve these problems have been made during the last 70 years using both analytical and numerical methods, but this has proved to be very difficu
Geometrical Theory of Diffraction
Author: Vladimir Andreevich Borovikov
Publisher: IET
ISBN: 9780852968307
Category : Mathematics
Languages : en
Pages : 408
Book Description
This book details the ideas underlying geometrical theory of diffraction (GTD) along with its relationships with other EM theories.
Publisher: IET
ISBN: 9780852968307
Category : Mathematics
Languages : en
Pages : 408
Book Description
This book details the ideas underlying geometrical theory of diffraction (GTD) along with its relationships with other EM theories.
Application of Wedge Diffraction to Antenna Theory
Author: R. C. Rudduck
Publisher:
ISBN:
Category : Diffraction
Languages : en
Pages : 76
Book Description
Publisher:
ISBN:
Category : Diffraction
Languages : en
Pages : 76
Book Description
Fundamentals of the Physical Theory of Diffraction
Author: Pyotr Ya. Ufimtsev
Publisher: John Wiley & Sons
ISBN: 1118753666
Category : Science
Languages : en
Pages : 496
Book Description
The book is a complete, comprehensive description of the modern Physical Theory of Diffraction (PTD) based upon the concept of elementary edge waves. The theory is demonstrated with examples of the diffraction of acoustic and electromagnetic waves at perfectly reflecting objects. Readers develop the skills to apply PTD to solve various scattering problems. The derived analytic expressions clearly illustrate the physical structure of the scattered field. They additionally describe all of the reflected and diffracted rays and beams, as well as the fields in the vicinity of caustics and foci. Shadow radiation, a fundamental component of PTD, is introduced and proven to contain half the total scattered power. The equivalence relationships between acoustic and electromagnetic diffracted waves are established and emphasized. Throughout the book, the author enables readers to master both the theory and its practical applications. Plotted numeric results supplement the theory and facilitate the visualization of individual contributions of distinct parts of the scattering objects to the total diffracted field Detailed comments help readers understand and implement all the critical steps of the analytic and numeric calculations Problem sets in each chapter give readers an opportunity to analyse and investigate the diffraction phenomena
Publisher: John Wiley & Sons
ISBN: 1118753666
Category : Science
Languages : en
Pages : 496
Book Description
The book is a complete, comprehensive description of the modern Physical Theory of Diffraction (PTD) based upon the concept of elementary edge waves. The theory is demonstrated with examples of the diffraction of acoustic and electromagnetic waves at perfectly reflecting objects. Readers develop the skills to apply PTD to solve various scattering problems. The derived analytic expressions clearly illustrate the physical structure of the scattered field. They additionally describe all of the reflected and diffracted rays and beams, as well as the fields in the vicinity of caustics and foci. Shadow radiation, a fundamental component of PTD, is introduced and proven to contain half the total scattered power. The equivalence relationships between acoustic and electromagnetic diffracted waves are established and emphasized. Throughout the book, the author enables readers to master both the theory and its practical applications. Plotted numeric results supplement the theory and facilitate the visualization of individual contributions of distinct parts of the scattering objects to the total diffracted field Detailed comments help readers understand and implement all the critical steps of the analytic and numeric calculations Problem sets in each chapter give readers an opportunity to analyse and investigate the diffraction phenomena
Advanced Theory of Diffraction by a Semi-infinite Impedance Cone
Author: J.M.L Bernard
Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED
ISBN: 1783320281
Category : Mathematics
Languages : en
Pages : 170
Book Description
The mathematical problem concerning the diffraction by a semi-infinite cone with circular cross section for the Helmholtz equation, which has well-known solutions for Dirichlet and Neumann boundary conditions, is here considered for the more general boundary condition of constant impedance type. As previously stated by D.S. Jones, the problem then changes in complexity, beginning with the difficulty of obtaining the uniqueness of the solution. An exact analytical method is developed to reduce this problem to the determination of the solution of a well-posed non-oscillatory integral equation, of which the solution can be directly used to express the field in an integral form. Some generalization, in particular to the electromagnetic case, are also given.
Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED
ISBN: 1783320281
Category : Mathematics
Languages : en
Pages : 170
Book Description
The mathematical problem concerning the diffraction by a semi-infinite cone with circular cross section for the Helmholtz equation, which has well-known solutions for Dirichlet and Neumann boundary conditions, is here considered for the more general boundary condition of constant impedance type. As previously stated by D.S. Jones, the problem then changes in complexity, beginning with the difficulty of obtaining the uniqueness of the solution. An exact analytical method is developed to reduce this problem to the determination of the solution of a well-posed non-oscillatory integral equation, of which the solution can be directly used to express the field in an integral form. Some generalization, in particular to the electromagnetic case, are also given.