Wilcox, Calvin H. (Calvin Hayden)
Overview
Works:  74 works in 227 publications in 4 languages and 2,837 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA3, 530.123 
Publication Timeline
.
Most widely held works by
Calvin H Wilcox
Scattering theory for the d'Alembert equation in exterior domains by
Calvin H Wilcox(
Book
)
22 editions published between 1975 and 2008 in 3 languages and held by 593 WorldCat member libraries worldwide
22 editions published between 1975 and 2008 in 3 languages and held by 593 WorldCat member libraries worldwide
Sound propagation in stratified fluids by
Calvin H Wilcox(
Book
)
14 editions published in 1984 in English and Undetermined and held by 413 WorldCat member libraries worldwide
Stratified fluids whose densities, sound speeds and other parameters are functions of a single depth coordinate occur widely in nature. Indeed, the earth's gravitational field imposes a stratification on its atmosphere, oceans and lakes. It is well known that their stratification has a profound effect on the propagation of sound in these fluids. The most striking effect is probably the occurrence of acoustic ducts, due to minima of the sound speed, that can trap sound waves and cause them to propagate hori zontally. The reflection, transmission and distortion of sonar signals by acoustic ducts is important in interpreting sonar echoes. Signal scattering by layers of microscopic marine organisms is important to both sonar engi neers and marine biologists. Again, reflection of signals from bottom sediment layers overlying a penetrable bottom are of interest both as sources of unwanted echoes and in the acoustic probing of such layers. Many other examples could be given. The purpose of this monograph is to develop from first principles a theory of sound propagation in stratified fluids whose densities and sound speeds are essentially arbitrary functions of the depth. In physical terms, the propagation of both timeharmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for a scalar wave equation whose coefficients contain the pre scribed density and sound speed functions
14 editions published in 1984 in English and Undetermined and held by 413 WorldCat member libraries worldwide
Stratified fluids whose densities, sound speeds and other parameters are functions of a single depth coordinate occur widely in nature. Indeed, the earth's gravitational field imposes a stratification on its atmosphere, oceans and lakes. It is well known that their stratification has a profound effect on the propagation of sound in these fluids. The most striking effect is probably the occurrence of acoustic ducts, due to minima of the sound speed, that can trap sound waves and cause them to propagate hori zontally. The reflection, transmission and distortion of sonar signals by acoustic ducts is important in interpreting sonar echoes. Signal scattering by layers of microscopic marine organisms is important to both sonar engi neers and marine biologists. Again, reflection of signals from bottom sediment layers overlying a penetrable bottom are of interest both as sources of unwanted echoes and in the acoustic probing of such layers. Many other examples could be given. The purpose of this monograph is to develop from first principles a theory of sound propagation in stratified fluids whose densities and sound speeds are essentially arbitrary functions of the depth. In physical terms, the propagation of both timeharmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for a scalar wave equation whose coefficients contain the pre scribed density and sound speed functions
Asymptotic solutions of differential equations and their applications; proceedings of a symposium conducted by the Mathematics
Research Center, United States Army, at the University of Wisconsin, Madison, May 46, 1964 by
Calvin H Wilcox(
Book
)
35 editions published in 1964 in English and Italian and held by 387 WorldCat member libraries worldwide
35 editions published in 1964 in English and Italian and held by 387 WorldCat member libraries worldwide
Scattering theory for diffraction gratings by
Calvin H Wilcox(
Book
)
15 editions published between 1980 and 1984 in English and held by 382 WorldCat member libraries worldwide
Scattering theory is developed for plane diffraction gratings. The author's theory of RayleighBloch wave expansions is used to construct wave operators and a scattering operator for such gratings. For gratings that admit no surface waves, transient wave fields near the gratings are shown to behave for large times like free waves and corresponding asymptotic wave functions are calculated. These results are applied to analyze the echoes from gratings of signals due to localized sources. Finally, the echoes of sources remote from the grating are estimated and shown to be completely characterized by the Smatrix and the signal waveform. (Author)
15 editions published between 1980 and 1984 in English and held by 382 WorldCat member libraries worldwide
Scattering theory is developed for plane diffraction gratings. The author's theory of RayleighBloch wave expansions is used to construct wave operators and a scattering operator for such gratings. For gratings that admit no surface waves, transient wave fields near the gratings are shown to behave for large times like free waves and corresponding asymptotic wave functions are calculated. These results are applied to analyze the echoes from gratings of signals due to localized sources. Finally, the echoes of sources remote from the grating are estimated and shown to be completely characterized by the Smatrix and the signal waveform. (Author)
Perturbation theory and its applications in quantum mechanics; proceedings of an advanced seminar by
Calvin H Wilcox(
Book
)
3 editions published in 1966 in English and held by 355 WorldCat member libraries worldwide
3 editions published in 1966 in English and held by 355 WorldCat member libraries worldwide
Analytical and computational methods of advanced engineering mathematics by
Grant B Gustafson(
Book
)
11 editions published in 1998 in English and held by 306 WorldCat member libraries worldwide
(NOTES)This text focuses on the topics which are an essential part of the engineering mathematics course:ordinary differential equations, vector calculus, linear algebra and partial differential equations. Advantages over competing texts: 1. The text has a large number of examples and problems  a typical section having 25 quality problems directly related to the text. 2. The authors use a practical engineering approach based upon solving equations. All ideas and definitions are introduced from this basic viewpoint, which allows engineers in their second year to understand concepts that would otherwise be impossibly abstract. Partial differential equations are introduced in an engineering and science context based upon modelling of physical problems. A strength of the manuscript is the vast number of applications to realworld problems, each treated completely and in sufficient depth to be selfcontained. 3. Numerical analysis is introduced in the manuscript at a completely elementary calculus level. In fact, numerics are advertised as just an extension of the calculus and used generally as enrichment, to help communicate the role of mathematics in engineering applications. 4. The authors have used and updated the book as a course text over a 10 year period. 5. Modern outline, as contrasted to the outdated outline by Kreysig and Wylie. 6. This is now a one year course. The text is shorter and more readable than the current reference type manuals published all at around 13001500 pages
11 editions published in 1998 in English and held by 306 WorldCat member libraries worldwide
(NOTES)This text focuses on the topics which are an essential part of the engineering mathematics course:ordinary differential equations, vector calculus, linear algebra and partial differential equations. Advantages over competing texts: 1. The text has a large number of examples and problems  a typical section having 25 quality problems directly related to the text. 2. The authors use a practical engineering approach based upon solving equations. All ideas and definitions are introduced from this basic viewpoint, which allows engineers in their second year to understand concepts that would otherwise be impossibly abstract. Partial differential equations are introduced in an engineering and science context based upon modelling of physical problems. A strength of the manuscript is the vast number of applications to realworld problems, each treated completely and in sufficient depth to be selfcontained. 3. Numerical analysis is introduced in the manuscript at a completely elementary calculus level. In fact, numerics are advertised as just an extension of the calculus and used generally as enrichment, to help communicate the role of mathematics in engineering applications. 4. The authors have used and updated the book as a course text over a 10 year period. 5. Modern outline, as contrasted to the outdated outline by Kreysig and Wylie. 6. This is now a one year course. The text is shorter and more readable than the current reference type manuals published all at around 13001500 pages
Radar and sonar by
Richard E Blahut(
Book
)
14 editions published between 1991 and 1992 in English and held by 225 WorldCat member libraries worldwide
14 editions published between 1991 and 1992 in English and held by 225 WorldCat member libraries worldwide
Perturbation theory and its applications in quantum mechanics : proceedings of an advanced seminar conducted by the Mathematics
Research Center, United States Army, and the Theoretical Chemistry Institute at the University of Wisconsin, Madison, October
46, 1965 by
Calvin H Wilcox(
Book
)
29 editions published between 1965 and 1966 in English and held by 82 WorldCat member libraries worldwide
29 editions published between 1965 and 1966 in English and held by 82 WorldCat member libraries worldwide
The domain of dependence inequality and initialboundary value problems for symmetric hyperbolic systems by
Calvin H Wilcox(
Book
)
3 editions published in 1962 in English and held by 4 WorldCat member libraries worldwide
The usual systems of partial differential equations that govern wave propagation (equations of acoustics, electromagnetics, magnetohydrodynamics, elasticity, etc.) have an energy integral and corresponding Poynting vector which describes the flow of energy. The most general systems of this type were introduced by K.O. Friedrichs, who called them 'symmetric hyperbolic' systems. An a priori domain of dependence inequality is proved for solutions of such systems in cylindrical spacetime domains subject to local, dissipative boundary conditions. The inequality expresses the fact that energy propagates with a finite speed in such systems. It is used to derive existence, uniqueness and regularity theorems for solutions of initialboundary value problems for symmetric hyperbolic systems. These problems provide a mathematical model for the diffraction by obstacles of the waves described by such systems. (Author)
3 editions published in 1962 in English and held by 4 WorldCat member libraries worldwide
The usual systems of partial differential equations that govern wave propagation (equations of acoustics, electromagnetics, magnetohydrodynamics, elasticity, etc.) have an energy integral and corresponding Poynting vector which describes the flow of energy. The most general systems of this type were introduced by K.O. Friedrichs, who called them 'symmetric hyperbolic' systems. An a priori domain of dependence inequality is proved for solutions of such systems in cylindrical spacetime domains subject to local, dissipative boundary conditions. The inequality expresses the fact that energy propagates with a finite speed in such systems. It is used to derive existence, uniqueness and regularity theorems for solutions of initialboundary value problems for symmetric hyperbolic systems. These problems provide a mathematical model for the diffraction by obstacles of the waves described by such systems. (Author)
Mathematical foundations of diffraction theory by
Calvin H Wilcox(
Book
)
2 editions published in 1961 in English and held by 3 WorldCat member libraries worldwide
A mathematical study is made on the problem of the electromagnetic theory to determine the diffracted electromagnetic wave which is produced when a prescribed wave, propagating in a homogeneous isotropic dielectric medium, strikes a prescribed metallic obstacle. The foundations for a mathematical theory of this problem are developed together with theorems which demonstrate the existence and uniqueness of the solution and theorems which describe its functional properties. (Author)
2 editions published in 1961 in English and held by 3 WorldCat member libraries worldwide
A mathematical study is made on the problem of the electromagnetic theory to determine the diffracted electromagnetic wave which is produced when a prescribed wave, propagating in a homogeneous isotropic dielectric medium, strikes a prescribed metallic obstacle. The foundations for a mathematical theory of this problem are developed together with theorems which demonstrate the existence and uniqueness of the solution and theorems which describe its functional properties. (Author)
Multiparameter acoustic imaging in the Born approximation by
Calvin H Wilcox(
Book
)
3 editions published between 1982 and 1983 in English and held by 3 WorldCat member libraries worldwide
Computerbased acoustic imaging techniques have been studied intensively during the last decade. Typical techniques involve irradiating a sample with prescribed sound fields, measuring the resulting scattered fields and applying a computational algorithm to the scattering data to produce maps of such sample parameters as density, sound speeds and perhaps others. These techniques have important applications to medical ultrasonic imaging where the sample is a living organism, to nondestructive evaluation where the sample is a manufactured item such as a metal casting or ceramic object and to geophysical prospecting where the sample is a portion of the earth's crust. This paper treats a problem of medical ultrasonic imaging. The sample is modelled as an inhomogeneous fluid which is characterized by a variable density rho(x) and sound speed c(x). The use of a fluid model is motivated by the fact that in biological tissues, other than bone, acoustic shear waves are not observed. In acoustic imaging, the scale of the smallest structures that can be resolved is of the order of the smallest wavelength employed. A typical sound speed in biological tissue is c = 1500 m/sec
3 editions published between 1982 and 1983 in English and held by 3 WorldCat member libraries worldwide
Computerbased acoustic imaging techniques have been studied intensively during the last decade. Typical techniques involve irradiating a sample with prescribed sound fields, measuring the resulting scattered fields and applying a computational algorithm to the scattering data to produce maps of such sample parameters as density, sound speeds and perhaps others. These techniques have important applications to medical ultrasonic imaging where the sample is a living organism, to nondestructive evaluation where the sample is a manufactured item such as a metal casting or ceramic object and to geophysical prospecting where the sample is a portion of the earth's crust. This paper treats a problem of medical ultrasonic imaging. The sample is modelled as an inhomogeneous fluid which is characterized by a variable density rho(x) and sound speed c(x). The use of a fluid model is motivated by the fact that in biological tissues, other than bone, acoustic shear waves are not observed. In acoustic imaging, the scale of the smallest structures that can be resolved is of the order of the smallest wavelength employed. A typical sound speed in biological tissue is c = 1500 m/sec
The nearfield behavior of the Green's matrix in anisotropic wave motion by
Geraldo S. S Avila(
Book
)
2 editions published in 1966 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1966 in English and held by 3 WorldCat member libraries worldwide
Regularity theorems for solutions of initialboundary value problems for linear hyperbolic equations of the second order by
Calvin H Wilcox(
Book
)
3 editions published in 1964 in English and held by 3 WorldCat member libraries worldwide
Sufficient conditions are derived for solutions of initialboundary value problems for linear hyperbolic equations to have partial derivatives of prescribed orders. (Author)
3 editions published in 1964 in English and held by 3 WorldCat member libraries worldwide
Sufficient conditions are derived for solutions of initialboundary value problems for linear hyperbolic equations to have partial derivatives of prescribed orders. (Author)
RayleighBloch wave expansions for diffraction gratings by
Calvin H Wilcox(
Book
)
3 editions published in 1980 in English and German and held by 3 WorldCat member libraries worldwide
This report is the second part of a study of RayleighBloch (RB) wave expansions for plane diffraction gratings. The principal concepts and results of the study, including the definition and construction of the RB waves, the formulation of the corresponding RB wave expansion theorem and the main ideas for the proofs were given in part I. The present part II contains complete proofs of the results whose proofs were omitted or only sketched in part I. (Author)
3 editions published in 1980 in English and German and held by 3 WorldCat member libraries worldwide
This report is the second part of a study of RayleighBloch (RB) wave expansions for plane diffraction gratings. The principal concepts and results of the study, including the definition and construction of the RB waves, the formulation of the corresponding RB wave expansion theorem and the main ideas for the proofs were given in part I. The present part II contains complete proofs of the results whose proofs were omitted or only sketched in part I. (Author)
The SMatrix and Acoustic Signal Structure in Simple and Compound Waveguides by
Calvin H Wilcox(
Book
)
3 editions published between 1982 and 1983 in English and held by 3 WorldCat member libraries worldwide
This paper deals with the propagation of transient acoustic fields in waveguides that consist of a semiinfinite cylinder coupled to a resonant cavity or resonator. The walls of the waveguide are assumed to be rigid. The sources of the transient sound fields, or signals, are assumed to be localized in a bounded portion of the waveguide and to act for a finite interval of time. The goal of the work is to calculate such acoustic signals and to analyze how their structure depends on the sources and the geometry of the waveguide. Particular attention is given to the cases in which the signal sources or observation point, or both, lie in the cylinder and are far from the resonator. It is well known that in the cylindrical portion of the waveguide each signal can be decomposed into a series of modal waves. These waves are calculated and are shown to be asymptotically independent for large times
3 editions published between 1982 and 1983 in English and held by 3 WorldCat member libraries worldwide
This paper deals with the propagation of transient acoustic fields in waveguides that consist of a semiinfinite cylinder coupled to a resonant cavity or resonator. The walls of the waveguide are assumed to be rigid. The sources of the transient sound fields, or signals, are assumed to be localized in a bounded portion of the waveguide and to act for a finite interval of time. The goal of the work is to calculate such acoustic signals and to analyze how their structure depends on the sources and the geometry of the waveguide. Particular attention is given to the cases in which the signal sources or observation point, or both, lie in the cylinder and are far from the resonator. It is well known that in the cylindrical portion of the waveguide each signal can be decomposed into a series of modal waves. These waves are calculated and are shown to be asymptotically independent for large times
RayleighBloch Wave Expansions for Diffraction Gratings I by
Calvin H Wilcox(
Book
)
3 editions published in 1980 in English and German and held by 3 WorldCat member libraries worldwide
Plane diffraction gratings with period 2 pi lying in a strip 0 <y <h in the x, yplane are studied. A Rayleigh Bloch (RB) wave for a grating is the response Psi sub + (x, y, p, q) to a plane wave 1/2 pi exp(i(pxqy)) incident from y> h (p eta R, q> 0). The paper presents a construction of RB waves and a proof that (psi sub + (x, y, p, q)/p eta R, q> 0) is a complete orthogonal family in L(2)(G) in the sense of the Plancherel theory
3 editions published in 1980 in English and German and held by 3 WorldCat member libraries worldwide
Plane diffraction gratings with period 2 pi lying in a strip 0 <y <h in the x, yplane are studied. A Rayleigh Bloch (RB) wave for a grating is the response Psi sub + (x, y, p, q) to a plane wave 1/2 pi exp(i(pxqy)) incident from y> h (p eta R, q> 0). The paper presents a construction of RB waves and a proof that (psi sub + (x, y, p, q)/p eta R, q> 0) is a complete orthogonal family in L(2)(G) in the sense of the Plancherel theory
Initialboundary value problems for linear hyperbolic partial differential equations of the second order by
Calvin H Wilcox(
Book
)
2 editions published in 1962 in English and held by 3 WorldCat member libraries worldwide
A complete and selfcontained treatment of the initialboundary value problem for a class of linear hyperbolic partial differential equations of the second order is presented. Many conceps and techniques are incorporated and extended. The most basic of the new results is the domain of dependence inequality, which is the keystone of the theory. (Author)
2 editions published in 1962 in English and held by 3 WorldCat member libraries worldwide
A complete and selfcontained treatment of the initialboundary value problem for a class of linear hyperbolic partial differential equations of the second order is presented. Many conceps and techniques are incorporated and extended. The most basic of the new results is the domain of dependence inequality, which is the keystone of the theory. (Author)
Radar and sonar : Summer school : Papers by
Richard E Blahut(
)
1 edition published in 1991 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 3 WorldCat member libraries worldwide
Advanced engineering mathematics : analytical and computational methods by G. B Gustafson(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
Multiparameter acoustic imaging in the born approximation by
Calvin H Wilcox(
Book
)
1 edition published in 1983 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 1983 in German and held by 2 WorldCat member libraries worldwide
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Related Identities
 Mathematics Research Center (United States. Army)
 University of Wisconsin Theoretical Chemistry Institute
 Gustafson, Grant B. Author
 University of Wisconsin
 Miller, Willard
 Blahut, Richard E. Author
 Grünbaum, F. Alberto
 Mathematics research center (Madison, Wis.).
 SpringerLink (Service en ligne)
 Langer, Rudolph E. Honoree Author Dedicatee
Associated Subjects
Anisotropy Asymptotes Boundary value problems Canada Computer scienceMathematics Differential equations Differential equations, Hyperbolic Differential equationsNumerical solutions Diffraction gratings Engineering mathematics FluidsAcoustic properties Lagrange equations Laplacian operator Mathematics Numerical analysis Perturbation (Mathematics) Perturbation (Quantum dynamics) Physics Quantum theory Radar RadarMathematical models Scattering (Mathematics) Scientists Sonar SonarMathematical models SoundTransmission SoundwavesScattering SoundwavesTransmission Stratified flow United States Wave equation Wavemotion, Theory of