# Electromagnetic material interrogation using conductive interfaces and acoustic wavefronts

##### Citations

61 citations

### Cites methods from "Electromagnetic material interrogat..."

...The treatment for finite element methods has been limited to scalar-potential formulations to model dielectric dispersion at low frequencies ([9]), scalar Helmholtz equation ([10]), and in some cases, hybrid methods ([11])....

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...We apply a finite element method using standard piecewise linear one dimensional basis elements to discretize the model (2.6) in space....

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...One can then turn to combinations of Debye, Lorentz, or even more general nth order mechanisms [25] as well as Cole-Cole type (fractional order derivative) models [32]....

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54 citations

### Cites background from "Electromagnetic material interrogat..."

...It is demonstrated computationally that this model captures transient e ects and shows the formation of Brillouin precursors inside the material [8]....

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...Since the material properties are assumed to be homogeneous in the x and y variables, it can be shown that the propagating waves in are also reduced to one nontrivial component [8]....

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...Existence, uniqueness and regularity of solutions is established in [8], and a comprehensive approximation framework is developed for the forward as well as the inverse problems....

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...In the following we will summarize a model developed in [8] for the propagation of windowed microwave (3-100 GHz) pulses in a dielectric medium....

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..., [0; 1]; as explained above and in [8]....

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46 citations

### Cites background or methods from "Electromagnetic material interrogat..."

...We illustrate the possibilities with N = T = { τ |τ ∈ [τa, τb]} for τ the relaxation parameter in, for example, a Debye or Lorentz mechanism....

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...We conclude that the inverse problem involving a Gaussian distribution of relaxation times for a Debye polarization model is computationally feasible for the sample parameters presented here....

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...(12) To describe the behavior of the electric polarization P , we may employ a general polarization kernel, or dielectric response function, g as follows: P (t, z) = ∫ t 0 g(t − s, z; τ)E(s, z)ds (13) where, for instance using a Debye polarization model, g(t; τ) = 0( s − ∞)/τ e−t/τ ....

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...Examples of often-used DRFs are the Debye [11, 24, 30] in a material region Ω defined in the time domain by g(t,x) = 0( s − ∞)/τ e−t/τ , the Lorentz [11, 24, 41] given by g(t,x) = 0ω 2 p/ν0e −t/2τsin(ν0t), and the Cole-Cole [24, 28, 33, 39, 47] defined by g(t,x) = L−1 { 0( s − ∞) 1 + (sτ)α } = 1 2πi ∫ ζ+i∞ ζ−i∞ 0( s − ∞) 1 + (sτ)α estds, where L is the Laplace transform....

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...3 The 1-D Problem Formulation For our initial numerical efforts, we turned to the 1-D example as explained in detail in [11]....

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43 citations

### Cites background from "Electromagnetic material interrogat..."

...We refer the reader to [3, 11] for details....

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...MODELS FOR POLARIZATION The constitutive law in (8) is sufficiently general to include models based on differential equations and systems of differential equations or delay differential equations whose solutions can be expressed through fundamental solutions (in general variation-of-parameters representations)— (see [3] for details)....

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40 citations

### Cites background or methods from "Electromagnetic material interrogat..."

...To generate these plots we have assumed the following values of the physical parameters: ∞ = 1, s = 78.2, τ = 8.1 × 10−12 s. (6.11) These are appropriate constants for modelling water and are representative of a large class of Debye type materials (see, e.g., Banks et al., 2000)....

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...These simulations have very important applications in diverse areas including noninvasive detection of cancerous tumours and the investigation of the effect of precursors on the human body (see Banks et al., 2000; Fear et al., 2003 and references therein)....

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...2.2 Electronic polarization: the Lorentz model A (single-pole) Lorentz model can be represented in (macroscopic) differential form (see, e.g., Banks et al., 2000) as ∂2P ∂t2 + ν ∂P ∂t + ω20P = 0ω 2 pE, (2.4) along with equation (2.2a)....

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