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CONTRIBUTIONS TO THE THEORY OF NONLINEAR OSCILLATIONS, vol. 2. / CODDINGTON. CARTWRIGHT.
Titre : CONTRIBUTIONS TO THE THEORY OF NONLINEAR OSCILLATIONS, vol. 2. Type de document : document imprimé Auteurs : CODDINGTON. CARTWRIGHT., Auteur Editeur : Princeton University Press Année de publication : 1952 Importance : 116,00 Note générale : Paperback
Langues : Français (fre) Mots-clés : ASYMPTOTIC EXPANSIONS LINEAR SYSTEMS POL'S EQUATION Index. décimale : 05.45 Nonlinear dynamics and nonlinear dynamical systems, chaos, fractals CONTRIBUTIONS TO THE THEORY OF NONLINEAR OSCILLATIONS, vol. 2. [document imprimé] / CODDINGTON. CARTWRIGHT., Auteur . - [S.l.] : Princeton University Press, 1952 . - 116,00.
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Mots-clés : ASYMPTOTIC EXPANSIONS LINEAR SYSTEMS POL'S EQUATION Index. décimale : 05.45 Nonlinear dynamics and nonlinear dynamical systems, chaos, fractals Réservation
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Code-barres Cote Support Localisation Section Disponibilité FA0002 05.45 CAR Document imprimé IRPHE Bibliothèque de l'IRPHE Disponible A treatise on the theory of bessel functions / G. N. Watson
Titre : A treatise on the theory of bessel functions Type de document : document imprimé Auteurs : G. N. Watson, Auteur Mention d'édition : 2n ed. Editeur : Cambridge, GB : Cambridge University Press Année de publication : 1952 Importance : 804,00 Langues : Français (fre) Mots-clés : ASYMPTOTIC EXPANSIONS ASYMPTOTIC EXPANSIONSA TREATISE ON THE THEORY OF BESSEL FUNCTIONS BESSEL FUNCTIONS DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS vol. 2. BESSEL FUNCTIONS Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions A treatise on the theory of bessel functions [document imprimé] / G. N. Watson, Auteur . - 2n ed. . - Cambridge, GB : Cambridge University Press, 1952 . - 804,00.
Langues : Français (fre)
Mots-clés : ASYMPTOTIC EXPANSIONS ASYMPTOTIC EXPANSIONSA TREATISE ON THE THEORY OF BESSEL FUNCTIONS BESSEL FUNCTIONS DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS vol. 2. BESSEL FUNCTIONS Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions Réservation
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Code-barres Cote Support Localisation Section Disponibilité CB0078 02.30 WAT Document imprimé IRPHE Bibliothèque de l'IRPHE Sorti jusqu'au 14/04/2007 Advanced mathematical methods for scientists and engineers / C. M. Bender
Titre : Advanced mathematical methods for scientists and engineers Type de document : document imprimé Auteurs : C. M. Bender, Auteur ; S. A. Orszag, Auteur Editeur : New York : McGraw-Hill Année de publication : 1978 Collection : International series in pure and applied mathematics Importance : XIV-593 p ; 25 cm ISBN/ISSN/EAN : 0-07-004452-X Note générale : Hardback
Langues : Français (fre) Mots-clés : ASYMPTOTIC EXPANSION ASYMPTOTIC EXPANSIONADVANCED MATHEMATICAL METHODS FOR SCIENTIST AND ENGINEERS. MATHEMATICAL METHODS MATHEMATICAL METHODS ORDINARY ORDINARY PERTURBATION METHODS PERTURBATION METHODS WKB THEORY WKB THEORY Index. décimale : 02 Mathematical methods in physics, theoretical physics Note de contenu : References, p. 577-579 Index, p. 581-593
Advanced mathematical methods for scientists and engineers [document imprimé] / C. M. Bender, Auteur ; S. A. Orszag, Auteur . - McGraw-Hill, 1978 . - XIV-593 p ; 25 cm. - (International series in pure and applied mathematics) .
ISBN : 0-07-004452-X
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Langues : Français (fre)
Mots-clés : ASYMPTOTIC EXPANSION ASYMPTOTIC EXPANSIONADVANCED MATHEMATICAL METHODS FOR SCIENTIST AND ENGINEERS. MATHEMATICAL METHODS MATHEMATICAL METHODS ORDINARY ORDINARY PERTURBATION METHODS PERTURBATION METHODS WKB THEORY WKB THEORY Index. décimale : 02 Mathematical methods in physics, theoretical physics Note de contenu : References, p. 577-579 Index, p. 581-593
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Code-barres Cote Support Localisation Section Disponibilité C0006 02 BEN Document imprimé IRPHE Bibliothèque de l'IRPHE Sorti jusqu'au 29/09/2007 Asymptotic and numerical methods for partial differential equations with critical parameters. / Garbey Marc, Pieper Gail W. Kaper Hans G.
Titre : Asymptotic and numerical methods for partial differential equations with critical parameters. Type de document : document imprimé Auteurs : Garbey Marc, Pieper Gail W. Kaper Hans G., Auteur Editeur : Dordrecht, : Kluwer Academic Publishers, Année de publication : 1993 Collection : (NATO ASI Series, Series C, vol. 384). ISBN/ISSN/EAN : 0-7923-2061-1 Langues : Français (fre) Mots-clés : asymptotic theory critical parameters domain decomposition numerical methods partial differential equations Note de contenu : 0200 - mathematical methods in physics
Asymptotic and numerical methods for partial differential equations with critical parameters. [document imprimé] / Garbey Marc, Pieper Gail W. Kaper Hans G., Auteur . - Kluwer Academic Publishers,, 1993. - ((NATO ASI Series, Series C, vol. 384).) .
ISBN : 0-7923-2061-1
Langues : Français (fre)
Mots-clés : asymptotic theory critical parameters domain decomposition numerical methods partial differential equations Note de contenu : 0200 - mathematical methods in physics
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Code-barres Cote Support Localisation Section Disponibilité MA5667 Document imprimé Bureau chercheur Indéterminé Disponible ASYMPTOTIC APPROXIMATIONS OF INTEGRALS. / WONG R.
Titre : ASYMPTOTIC APPROXIMATIONS OF INTEGRALS. Type de document : document imprimé Auteurs : WONG R., Auteur Editeur : Academic Press Année de publication : 32509 Collection : (Computer Science and Scientific Computing). Importance : 544,00 Langues : Français (fre) Mots-clés : APPROXIMATIONS OF INTEGRALS ASYMPTOTICS METHODS Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions Note de contenu : emprunté par Mr LE DIZES
ASYMPTOTIC APPROXIMATIONS OF INTEGRALS. [document imprimé] / WONG R., Auteur . - Academic Press, 32509 . - 544,00. - ((Computer Science and Scientific Computing).) .
Langues : Français (fre)
Mots-clés : APPROXIMATIONS OF INTEGRALS ASYMPTOTICS METHODS Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions Note de contenu : emprunté par Mr LE DIZES
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Code-barres Cote Support Localisation Section Disponibilité MA2169 02.30 WON Document imprimé Bureau chercheur Indéterminé Disponible Asymptotic expansions / ERDELYI A.
Titre : Asymptotic expansions Type de document : document imprimé Auteurs : ERDELYI A., Auteur Editeur : New York : Dover Publications Année de publication : 1956 Importance : 108,00 Langues : Français (fre) Mots-clés : ASYMPTOTIC SERIES DIFFERENTIAL EQUATIONS WITH A LARGE PARAMETER INTEGRALS SINGULARITIES OF DIFFERENTIAL EQUATIONS Index. décimale : 02.60 Numerical differentiation and analysis Asymptotic expansions [document imprimé] / ERDELYI A., Auteur . - New York : Dover Publications, 1956 . - 108,00.
Langues : Français (fre)
Mots-clés : ASYMPTOTIC SERIES DIFFERENTIAL EQUATIONS WITH A LARGE PARAMETER INTEGRALS SINGULARITIES OF DIFFERENTIAL EQUATIONS Index. décimale : 02.60 Numerical differentiation and analysis Réservation
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Code-barres Cote Support Localisation Section Disponibilité MA0659 02.60 ERD Document imprimé Bureau chercheur Indéterminé Sorti jusqu'au 03/06/2007 Difference equations : an introduction with applications / W. G. Kelley
Titre : Difference equations : an introduction with applications Type de document : document imprimé Auteurs : W. G. Kelley, Auteur ; A. C. Peterson, Auteur Editeur : Boston, MA : Academic Press Année de publication : 1991 Importance : 455,00 ISBN/ISSN/EAN : 0-12-403325-3 Note générale : Hardback
Langues : Français (fre) Mots-clés : asymptotic methods difference equations stability theory Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions Note de contenu : 0200 - mathematical methods in physics
Difference equations : an introduction with applications [document imprimé] / W. G. Kelley, Auteur ; A. C. Peterson, Auteur . - Boston, MA : Academic Press, 1991 . - 455,00.
ISBN : 0-12-403325-3
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Langues : Français (fre)
Mots-clés : asymptotic methods difference equations stability theory Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions Note de contenu : 0200 - mathematical methods in physics
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Code-barres Cote Support Localisation Section Disponibilité CG.0000.080 02.30 KEL Document imprimé IRPHE Bibliothèque de l'IRPHE Disponible MATHEMATICAL THEORY OF PROBABILITY AND STATISTICS. / Richard von Mises
Titre : MATHEMATICAL THEORY OF PROBABILITY AND STATISTICS. Type de document : document imprimé Auteurs : Richard von Mises (1883-1953), Auteur Editeur : Academic Press Année de publication : 1964 Importance : 694,00 Langues : Français (fre) Mots-clés : ASYMPTOTIC DISTRIBUTION BASIC ASSUMPTIONS BASIC PROPERTIES CHARACTERISTIC FUNCTION CORRELATION LABEL SPACE PROBABILITY INFERENCE Index. décimale : 02.50 Probability theory, stochastic processes, and statistics MATHEMATICAL THEORY OF PROBABILITY AND STATISTICS. [document imprimé] / Richard von Mises (1883-1953), Auteur . - [S.l.] : Academic Press, 1964 . - 694,00.
Langues : Français (fre)
Mots-clés : ASYMPTOTIC DISTRIBUTION BASIC ASSUMPTIONS BASIC PROPERTIES CHARACTERISTIC FUNCTION CORRELATION LABEL SPACE PROBABILITY INFERENCE Index. décimale : 02.50 Probability theory, stochastic processes, and statistics Réservation
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Code-barres Cote Support Localisation Section Disponibilité CD0054 02.50 VON Document imprimé IRPHE Indéterminé Disponible Multidimensional hyperbolic problems and computations. / J. Glimm
Titre : Multidimensional hyperbolic problems and computations. Type de document : document imprimé Auteurs : J. Glimm, Auteur ; A. J. Majda, Auteur Editeur : New York, : Springer-Verlag, Année de publication : 1991 Collection : (The IMA volumes in Mathematics and its Applications, vol. 29). Importance : 386,00 ISBN/ISSN/EAN : 0-387-97485-7 Langues : Français (fre) Mots-clés : asymptotic methods nonlinear partial differential equations numerical computation Note de contenu : 0200 - mathematical methods in physics
Multidimensional hyperbolic problems and computations. [document imprimé] / J. Glimm, Auteur ; A. J. Majda, Auteur . - Springer-Verlag,, 1991 . - 386,00. - ((The IMA volumes in Mathematics and its Applications, vol. 29).) .
ISBN : 0-387-97485-7
Langues : Français (fre)
Mots-clés : asymptotic methods nonlinear partial differential equations numerical computation Note de contenu : 0200 - mathematical methods in physics
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Code-barres Cote Support Localisation Section Disponibilité MA5616 Document imprimé Bureau chercheur Indéterminé Disponible OPERATIONAL CALCULUS BASED ON THE TWO-SIDED LAPLACE INTEGRAL. / BREMMER H. VAN DER POL B.
Titre : OPERATIONAL CALCULUS BASED ON THE TWO-SIDED LAPLACE INTEGRAL. Type de document : document imprimé Auteurs : BREMMER H. VAN DER POL B., Auteur Editeur : Cambridge University Press Année de publication : 1950 Importance : 415,00 Langues : Français (fre) Mots-clés : ASYMPTOTIC RELATIONS ASYMPTOTIC RELATIONS CONVERGENCE CONVERGENCE FOURIER INTEGRAL LINEAR DIFFERENTIAL LINEAR DIFFERENTIALOPERATIONAL CALCULUS BASED ON THE TWO-SIDED LAPLACE INTEGRAL. FOURIER INTEGRAL OPERATIONAL CALCULUS OPERATIONAL CALCULUS Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions OPERATIONAL CALCULUS BASED ON THE TWO-SIDED LAPLACE INTEGRAL. [document imprimé] / BREMMER H. VAN DER POL B., Auteur . - [S.l.] : Cambridge University Press, 1950 . - 415,00.
Langues : Français (fre)
Mots-clés : ASYMPTOTIC RELATIONS ASYMPTOTIC RELATIONS CONVERGENCE CONVERGENCE FOURIER INTEGRAL LINEAR DIFFERENTIAL LINEAR DIFFERENTIALOPERATIONAL CALCULUS BASED ON THE TWO-SIDED LAPLACE INTEGRAL. FOURIER INTEGRAL OPERATIONAL CALCULUS OPERATIONAL CALCULUS Index. décimale : 02.30 Function theory, analysis (differential equations), asymptotic analysis, integration, distributions Réservation
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Code-barres Cote Support Localisation Section Disponibilité CB0076 02.30 VAN Document imprimé IRPHE Bibliothèque de l'IRPHE Disponible SATISFACTION OF ASYMPTOTIC BOUNDARY CONDITIONS IN NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS OF BOUNDARY-LAYER TYPE. / SWIGERT P. NACHTSHEIM P.R.
Titre : SATISFACTION OF ASYMPTOTIC BOUNDARY CONDITIONS IN NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS OF BOUNDARY-LAYER TYPE. Type de document : document imprimé Auteurs : SWIGERT P. NACHTSHEIM P.R., Auteur Editeur : National Aeronautics and Space Administration, Lewis Research Center Année de publication : 1965 Collection : (NASA TN D-3004). Importance : 34,00 Langues : Français (fre) Mots-clés : ASYMPTOTIC BOUNDARY CONDITION BOUNDARY-LAYER TYPE NONLINEAR EQUATION Index. décimale : 02.70 Computational techniques, Matlab, Programing, Internet SATISFACTION OF ASYMPTOTIC BOUNDARY CONDITIONS IN NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS OF BOUNDARY-LAYER TYPE. [document imprimé] / SWIGERT P. NACHTSHEIM P.R., Auteur . - National Aeronautics and Space Administration, Lewis Research Center, 1965 . - 34,00. - ((NASA TN D-3004).) .
Langues : Français (fre)
Mots-clés : ASYMPTOTIC BOUNDARY CONDITION BOUNDARY-LAYER TYPE NONLINEAR EQUATION Index. décimale : 02.70 Computational techniques, Matlab, Programing, Internet Réservation
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Code-barres Cote Support Localisation Section Disponibilité CF0048 02.70 NAC Document imprimé IRPHE Indéterminé Disponible SHOCK AND DETONATION WAVES. / KIRKWOOD J.
Titre : SHOCK AND DETONATION WAVES. Type de document : document imprimé Auteurs : KIRKWOOD J., Auteur Editeur : Gordon and Breach Science Publishers Année de publication : 1967 Importance : 123,00 Langues : Français (fre) Mots-clés : ASYMPTOTIC BEHAVIOR PROPAGATION EQUATIONS UNDERWATER DAMAGE Index. décimale : 47.40 Compressible flows SHOCK AND DETONATION WAVES. [document imprimé] / KIRKWOOD J., Auteur . - [S.l.] : Gordon and Breach Science Publishers, 1967 . - 123,00.
Langues : Français (fre)
Mots-clés : ASYMPTOTIC BEHAVIOR PROPAGATION EQUATIONS UNDERWATER DAMAGE Index. décimale : 47.40 Compressible flows Réservation
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Code-barres Cote Support Localisation Section Disponibilité OC0063 47.40 KIR Document imprimé IRPHE Indéterminé Disponible Journal of engineering mathematics, Vol.40 No.3. The unsteady motion of two-dimensional flags with bending stiffness / A. D. Fitt
in Journal of engineering mathematics
Titre de série : Journal of engineering mathematics, Vol.40 No.3 Titre : The unsteady motion of two-dimensional flags with bending stiffness Type de document : articles et extraits Auteurs : A. D. Fitt, Auteur ; M. P. Pope, Auteur Année de publication : 2001 Importance : p.227-248 ISBN/ISSN/EAN : 0022-0833 Langues : Français (fre) Mots-clés : unsteady incompressible aerodynamics - singular integro-differential equations - asymptotics - numerics - stability. Résumé : The motion of a two-dimensional flag at a time-dependent angle of incidence to an irrotational flow of an inviscid, incompressible fluid is examined. The flag is modelled as a thin, flexible, impermeable membrane of finite mass with bending stiffness. The flag is fixed at the leading edge where it is assumed to be either freely hinged or clamped with zero gradient. The angle of incidence to the outer flow is assumed to be small and thin aerofoil theory and simple beam theory are employed to obtain a partial singular integro-differential equation for the flag shape. Steady solutions to the problem are calculated analytically for various limiting cases and numerically for order one values of a non-dimensional parameter that measures the relative importance of outer flow momentum flux and flexural rigidity. For the unsteady problem, the stability of steady solutions depends only upon two non-dimensional parameters. Stability analysis is performed in order to identify the regions of instability. The resulting quadratic eigenvalue problem is solved numerically and the marginal stability curves for both the hinged and the clamped flags are constructed. These curves show that both stable and unstable solutions may exist for various values of the mass and flexural rigidity of the membrane and for both methods of attachment at the leading edge. In order to confirm the results of the linear stability analysis, the full unsteady flag equation is solved numerically using an explicit method. The numerical solutions agree with the predictions of the linear stability analysis and also identify the shapes that the flag adopts according to the magnitude of the flexural rigidity and mass.
in Journal of engineering mathematics
Journal of engineering mathematics, Vol.40 No.3. The unsteady motion of two-dimensional flags with bending stiffness [articles et extraits] / A. D. Fitt, Auteur ; M. P. Pope, Auteur . - 2001 . - p.227-248.
ISSN : 0022-0833
Langues : Français (fre)
Mots-clés : unsteady incompressible aerodynamics - singular integro-differential equations - asymptotics - numerics - stability. Résumé : The motion of a two-dimensional flag at a time-dependent angle of incidence to an irrotational flow of an inviscid, incompressible fluid is examined. The flag is modelled as a thin, flexible, impermeable membrane of finite mass with bending stiffness. The flag is fixed at the leading edge where it is assumed to be either freely hinged or clamped with zero gradient. The angle of incidence to the outer flow is assumed to be small and thin aerofoil theory and simple beam theory are employed to obtain a partial singular integro-differential equation for the flag shape. Steady solutions to the problem are calculated analytically for various limiting cases and numerically for order one values of a non-dimensional parameter that measures the relative importance of outer flow momentum flux and flexural rigidity. For the unsteady problem, the stability of steady solutions depends only upon two non-dimensional parameters. Stability analysis is performed in order to identify the regions of instability. The resulting quadratic eigenvalue problem is solved numerically and the marginal stability curves for both the hinged and the clamped flags are constructed. These curves show that both stable and unstable solutions may exist for various values of the mass and flexural rigidity of the membrane and for both methods of attachment at the leading edge. In order to confirm the results of the linear stability analysis, the full unsteady flag equation is solved numerically using an explicit method. The numerical solutions agree with the predictions of the linear stability analysis and also identify the shapes that the flag adopts according to the magnitude of the flexural rigidity and mass.
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Code-barres Cote Support Localisation Section Disponibilité ART-9056-0 ART Document imprimé Bureau chercheur Bureau de SOUILLIEZ Claire Disponible Documents numériques
DOI: 10.1023/A:1017595632666URL Mathematical notes of the Academy of Sciences of the USSR, Vol.72 No.3-4. On the Spectrum Localization of the Orr--Sommerfeld Problem for Large Reynolds Numbers / A. A. Shkalikov
in Mathematical notes of the Academy of Sciences of the USSR
Titre de série : Mathematical notes of the Academy of Sciences of the USSR, Vol.72 No.3-4 Titre : On the Spectrum Localization of the Orr--Sommerfeld Problem for Large Reynolds Numbers Type de document : articles et extraits Auteurs : A. A. Shkalikov, Auteur ; S. N. Tumanov, Auteur Année de publication : 2002 Importance : p.519-526 ISBN/ISSN/EAN : 0001-4346 Langues : Français (fre) Mots-clés : Asymptotic formulas for eigenvalues Couette and Poiseuille flows Orr Sommerfeld problem Résumé : The paper deals with the Orr--Sommerfeld problem and the corresponding model problem -i\varepsilon^2y''-q(x)y=-\lambda y, \qquad y(-1)=y(1)=0. The functions q(x)= x and q(x)= x^2 in this model correspond to the Couette and the Poiseuille profiles, respectively. Small values of the parameter \varepsilon correspond to large Reynolds numbers. As \varepsilon tends to zero, the spectrum of the model problem is localized near certain critical curves in the complex plane, whose explicit form can be determined. Moreover, there are asymptotic formulas for the eigenvalue distribution along these curves as \varepsilon\to 0. The main result of the paper is the following: as the Reynolds number tends to infinity, the spectrum of the Orr--Sommerfeld problem for the Couette and the Poiseuille flows is localized to the critical curves, which are the same as in the model problem. Moreover, the main terms of the asymptotic formulas for the eigenvalue distribution are preserved.
in Mathematical notes of the Academy of Sciences of the USSR
Mathematical notes of the Academy of Sciences of the USSR, Vol.72 No.3-4. On the Spectrum Localization of the Orr--Sommerfeld Problem for Large Reynolds Numbers [articles et extraits] / A. A. Shkalikov, Auteur ; S. N. Tumanov, Auteur . - 2002 . - p.519-526.
ISSN : 0001-4346
Langues : Français (fre)
Mots-clés : Asymptotic formulas for eigenvalues Couette and Poiseuille flows Orr Sommerfeld problem Résumé : The paper deals with the Orr--Sommerfeld problem and the corresponding model problem -i\varepsilon^2y''-q(x)y=-\lambda y, \qquad y(-1)=y(1)=0. The functions q(x)= x and q(x)= x^2 in this model correspond to the Couette and the Poiseuille profiles, respectively. Small values of the parameter \varepsilon correspond to large Reynolds numbers. As \varepsilon tends to zero, the spectrum of the model problem is localized near certain critical curves in the complex plane, whose explicit form can be determined. Moreover, there are asymptotic formulas for the eigenvalue distribution along these curves as \varepsilon\to 0. The main result of the paper is the following: as the Reynolds number tends to infinity, the spectrum of the Orr--Sommerfeld problem for the Couette and the Poiseuille flows is localized to the critical curves, which are the same as in the model problem. Moreover, the main terms of the asymptotic formulas for the eigenvalue distribution are preserved.
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in SIAM review
Titre de série : SIAM review, Vol.41 No.3 Titre : On the Theory of Complex Rays Type de document : articles et extraits Auteurs : S. J. Chapman, Auteur ; J. M. H. Lawry, Auteur ; J. R. Ockendon, Auteur ; R. H. Tew, Auteur Année de publication : 1999 Importance : p.417-509 Langues : Français (fre) Mots-clés : Exponential asymptotics Geometrical optics Geometrical theory of diffraction Helmholtz equation Stokes' phenomenon Résumé : The article surveys the application of complex-ray theory to the scalar Helmholtz equation in two dimensions. The first objective is to motivate a framework within which complex rays may be used to make predictions about wavefields in a wide variety of geometrical configurations. A crucial ingredient in this framework is the role played by Sp{} in determining the regions of existence of complex rays. The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the many characterizations of Stokes surfaces, including the adaptation and application of recent developments in exponential asymptotics to the complex Wentzel--Kramers--Brilbuin expansion of these wavefields. Examples are given for several cases of physical importance.
in SIAM review
SIAM review, Vol.41 No.3. On the Theory of Complex Rays [articles et extraits] / S. J. Chapman, Auteur ; J. M. H. Lawry, Auteur ; J. R. Ockendon, Auteur ; R. H. Tew, Auteur . - 1999 . - p.417-509.
Langues : Français (fre)
Mots-clés : Exponential asymptotics Geometrical optics Geometrical theory of diffraction Helmholtz equation Stokes' phenomenon Résumé : The article surveys the application of complex-ray theory to the scalar Helmholtz equation in two dimensions. The first objective is to motivate a framework within which complex rays may be used to make predictions about wavefields in a wide variety of geometrical configurations. A crucial ingredient in this framework is the role played by Sp{} in determining the regions of existence of complex rays. The identification of the Stokes surfaces emerges as a key step in the approximation procedure, and this leads to the consideration of the many characterizations of Stokes surfaces, including the adaptation and application of recent developments in exponential asymptotics to the complex Wentzel--Kramers--Brilbuin expansion of these wavefields. Examples are given for several cases of physical importance.
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Code-barres Cote Support Localisation Section Disponibilité ART-6928-0 ART Document imprimé Bureau chercheur Bureau de LE DIZES, Stéphane Disponible Documents numériques
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