| 21. |
- Kristensson, Gerhard
(författare)
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Transient Electromagnetic Wave Propagation in Waveguides
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper focuses on propagation of transient electromagnetic waves in waveguides of general cross section with perfectly conducting walls. The solution of the transient wave propagation problem relies on a wave splitting technique, which has been frequently used in direct and inverse scattering problems during the last decade. The field in the waveguide is represented as a time convolution of a Green function and the excitation. Some numerical computations illustrate the method. Anew way of calculating the first precursor in a Lorentz medium is presented. This method, which is not based upon the classical asymptotic methods, gives an expression of the first precursor at all depths in the medium. The excitation of the waveguide modes for time dependent sources is also addressed.
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| 22. |
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| 23. |
- Kristensson, Gerhard, et al.
(författare)
-
Transient wave propagation in reciprocal bi-isotropic media at oblique incidence
- 1993
-
Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 34:4, s. 1339-1359
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi-isotropic media. Two different methods to solve the scattering problem are analyzed: the invariant imbedding and the Green function approach. The medium is modeled by constitutive relations in the time domain (time convolutions) and the slab is assumed to be inhomogeneous with respect to the depth. It is shown that the cross-polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab. Moreover, the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case. Special attention is paid to normal incidence and to the homogeneous semi-infinite medium.
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| 24. |
- Kristensson, Gerhard, et al.
(författare)
-
Transient wave propagation in reciprocal bi-isotropic media at oblique incidence
- 1992
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi-isotropic media. Two different methods to solve the scattering problem are analyzed; the invariant imbedding and the Green function approach. The medium is modeled by constitutive relations in the time domain (time convolutions) and the slab is assumed to be inhomogeneous with respect to the depth. It is showed that the cross-polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab. Moreover, the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case. Special attention is paid to normal incidence and to the homogeneous semi-infinite medium.
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| 25. |
- Malmqvist, Lennart, et al.
(författare)
-
Electromagnetic fields in boreholes-measurements and theory in three dimensions
- 1990
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A comparison between experimental measurements of the electromagnetic field in boreholes and a mathematical model is made. The transmitting antenna is a rectangular wire loop on the ground and the three orthogonal components of the magnetic field are measured below the ground in the borehole. In the mathematical model the ground is assumed to be a stratified half space with a rectangular wire antenna on the ground. Excellent agreement was found between the experimental results and the theoretical ones in most cases and where deviations were found, the assumption of a stratified ground was inaccurate due to present conductive inhomogeneities. The method presented in this paper is capable of determining an ore body within a radius of 100 m from the borehole. The position (direction and distance) of the target can be estimated from the measurements in the borehole. The impact on the economical effectiveness of a drilling programme is considerable when a prediction of the location of additional boreholes can be made. In the case of reconnaissance drilling of a geological structure or trend the distance between adjacent boreholes can be considerably enlarged.
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| 26. |
- Olsson, Peter, et al.
(författare)
-
Wave splitting of the Timoshenko beam equation in the time domain
- 1994
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Ingår i: Zeitschrift für Angewandte Mathematik und Physik. - 1420-9039. ; 45:6, s. 866-881
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Tidskriftsartikel (refereegranskat)abstract
- In recent years, wave splitting in conjunction with invariant imbedding and Green's function techniques has been applied with great success to a number of interesting inverse and direct scattering problems. The aim of the present paper is to derive a wave splitting for the Timoshenko equation, a fourth order PDE of importance in beam theory. An analysis of the hyperbolicity of the Timoshenko equation and its, in a sense, less physical relatives - the Euler-Bernoulli and the Rayleigh equations - is also provided.
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| 27. |
- Olsson, Peter, et al.
(författare)
-
Wave splitting of the Timoshenko beam equation in the time domain
- 1993
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In recent years, wave splitting in conjunction with invariant imbedding and Green’s function techniques has been applied with great success to a number of interesting inverse and direct scattering problems. The aim of the present paper is to derive a wave splitting for the Timoshenko equation, a fourth order PDE of importance in beam theory. An analysis of the hyperbolicity of the Timoshenko equation and its, in a sense, less physical relatives—the Euler-Bernoulli and the Rayleigh equations—is also provided.
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| 28. |
- Åberg, Ingegerd, et al.
(författare)
-
Propagation of transient electromagnetic waves in time-varying media - Direct and inverse scattering problems
- 1994
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e., it is stratified. The constitutive relations of the medium is a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green functions approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms.
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| 29. |
- Åberg, Ingegerd, et al.
(författare)
-
Transient waves in non-stationary media
- 1994
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper treats propagation of transient waves in non-stationary media, which has many applications in e.g. electromagnetics and acoustics. The underlying hyperbolic equation is a general, homogeneous, linear, first order 2×2 system of equations. The coefficients in this system depend only on one spatial coordinate and time. Furthermore, memory effects are modeled by integral kernels, which, in addition to the spatial dependence, are functions of two different time coordinates. These integrals generalize the convolution integrals, frequently used as a model for memory effects in the medium. Specifically, the scattering problem for this system of equations is addressed. This problem is solved by a generalization of the wave splitting concept, originally developed for wave propagation in media which are invariant under time translations, and by an imbedding or a Green functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green functions (propagator kernels) equations are derived. Special attention is paid to the problem of non-stationary characteristics. A few numerical examples illustrate this problem.
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