Direct and inverse scattering from dispersive media

Fuks, Peter; Larson, Gunnar

doi:10.1088/0266-5611/10/3/005

Cited by 16 publications

(6 citation statements)

References 10 publications

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“…Note however that we are only considering a oneparameter inverse problem here, which means that we will not utilize the hard reflection from the far end in the present inverse method. The general solution for V ± (x, t) ∈ (0, l), in the case where the impedance at x = 0 is continuous, is given by [9] V…”

Section: Green's Functionsmentioning

confidence: 99%

Comparison between Frequency Domain and Time Domain Methods for Parameter Reconstruction on Nonuniform Dispersive Transmission Lines

Lundstedt¹,

Norgren²

2003

PIER

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In this paper, we present two methods for the inverse problem of reconstructing a parameter profile of a nonuniform and dispersive transmission line-one frequency domain and one time domain method. Both methods are based on the wave splitting technique, but apart from that the methods are mathematically very different. The time domain analysis leads to hyperbolic partial differential equations and an inverse method based on solving implicit equations. The frequency domain analysis leads instead to Riccati differential equations and an inverse method based on optimization. The two methods are compared numerically by simulating a reconstruction of a soil moisture profile along a flat band cable. A heuristic model of the dispersion characteristics of a flat band cable in moist sand is derived. We also simulate the effect parasitic capacitances at the cable ends has on the reconstructions. The comparison shows that neither method outperforms the other. The time domain method is numerically much faster whereas the frequency domain method is much faster to implement. An important conclusion is also that it is crucial to model the connector parasitic capacitances correctly-especially if there are impedance mismatches at the connectors.

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Section: Green's Functionsmentioning

confidence: 99%

Comparison between Frequency Domain and Time Domain Methods for Parameter Reconstruction on Nonuniform Dispersive Transmission Lines

Lundstedt¹,

Norgren²

2003

PIER

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“…At the boundary, the jumps in g ± are related to each other as 10) where the subscript +(−) indicates that the jump across L + (L − ) is referred to. The jumps in the x-derivatives of u ± across L ± , respectively, are of less interest, but can be computed by (2.3), once the jumps in the s-derivatives have been calculated.…”

Section: Theorem 22 If In the Foregoing Theorem A Is Differentiabmentioning

confidence: 99%

Existence, Uniqueness, and Causality Theorems for Wave Propagation in Stratified, Temporally Dispersive, Complex Media

Rikte¹

1997

SIAM J. Appl. Math.

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Abstract.A mixed initial-boundary value problem for a nonlocal, hyperbolic equation is analyzed with respect to unique solubility and causality. The regularity of the step response and impulse response (the Green functions) is investigated, and a wave front theorem is proved. The problem arises, e.g., at time-varying, electromagnetic, plane wave excitation of stratified, temporally dispersive, bi-isotropic or anisotropic slabs. Concluding, the problem is uniquely solvable, strict causality holds, and a well-defined wave front speed exists. This speed is independent of dispersion and excitation, and depends on the nondispersive properties of the medium only.

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“…The mverse algorithm which uses the recovered time-domain transmission kerne! to reconstruct the derivative of the creep compliance is described in detail elsewhere and is not repeated here [12) [5).…”

Section: Numerical Experiments Descriptionmentioning

confidence: 99%

“…Recent experiments in an electromagnetic coaxialline system utilizing wave splitting and invariant embedding signal processing teclmiques have demonstrated the proof of principle of material property reconstruction for linear, isotropic and spatially inhomogeneous dielectric material [4] as weil as for LHI dispersive material [5]. The mechanical analog to electromagnetic LHI dispersive media is LHI viscoelastic media.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown by Fuks [5] in an analogaus paper for dispersive electromagnetic media t hat the reflection and transmission kernels are related to dispersive material properties by time-domain Valterra integral equations of the second kind independent of space due to ~atial homogeneity of the medium. Although both approaches are analogous, it is the method of Fuks which is adopted here due to its simphcity and reduced computation time.…”

Section: Introductionmentioning

confidence: 99%

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