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Electromagnetic material interrogation using conductive interfaces and acoustic wavefronts

TL;DR: Theoretical methods for dielectrics with supraconductive boundary and physical modeling for general polarization models are described, as well as methods for acoustically backed dielectric models.
Abstract: Preface 1. Introduction 2. Introduction and physical modeling 3. Wellposedness 4. Computational methods for dielectrics with supraconductive boundary 5. Computational methods for general polarization models 6. Computational methods for acoustically backed dielectrics 7. Concluding summary and remarks of potential applications Bibliography Index.
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Journal ArticleDOI
TL;DR: Banks, V A Bokil and N L Gibson as discussed by the authors analyzed stability and dispersion in a Finite Element Method for Debye and Lorentz Media, 25(4), pp 885-917, July 2009.
Abstract: This is the pre-peer reviewed version of the following article: H T Banks, V A Bokil and N L Gibson, Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Media, Numerical Methods for Partial Differential Equations, 25(4), pp 885-917, July 2009, which has been published in final form at http://www3intersciencewileycom/journal/122341241/issue

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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01 Jan 2003
TL;DR: A survey of several recent and emerging ideas and ideas on modeling and system interrogation in the presence of uncertainty that the authors feel have potential for applications related to bioterrorism.
Abstract: In this paper we present a survey of several recent and emerging ideas and e orts on modeling and system interrogation in the presence of uncertainty that we feel have signi cant potential for applications related to bioterrorism. The rst focuses on physiologically based pharmacokinetic (PBPK) type models and the e ects of drugs, toxins and viruses on tissue, organs, individuals and populations wherein both intraand inter-individual variability are present when one attempts to determine kinetic rates, susceptibility, eÆcacy of toxins, antitoxins, etc., in aggregate populations. Methods combining deterministic and stochastic concepts are necessary to formulate and computationally solve the associated estimation problems. Similar issues arise in the HIV infectious models we also present below. A second e ort concerns the use of remote electromagnetic interrogation pulses linked to dielectric properties of materials to carry out macroscopic structural imaging of bulk packages (drugs, explosives, etc.) as well as test for presence and levels of toxic chemical compounds in tissue. These techniques also may be useful in functional imaging (e.g., of brain and CNS activity levels) to determine levels of threat in potential adversaries via changes in dielectric properties and conductivity. The PBPK and cellular level virus infectious models we discuss are special examples of a much wider class of population models that one might utilize to investigate potential agents for use in attacks, such as viruses, bacteria, fungi and other chemical, biochemical or radiological agents. These include general epidemiological models such as SIR infectious

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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Journal ArticleDOI
TL;DR: In this article, the authors consider electromagnetic interrogation problems for complex materials involving distributions of polarization mechanisms and also distributions for the parameters in these mechanisms, and give theoretical and computational results for specific problems with multiple Debye mechanisms.
Abstract: : We consider electromagnetic interrogation problems for complex materials involving distributions of polarization mechanisms and also distributions for the parameters in these mechanisms. a theoretical and computational framework for such problems is given. Computational results for specific problems with multiple Debye mechanisms are given in the case of discrete, uniform, log-normal, and log-Bi-Gaussian distributions.

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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Journal ArticleDOI
TL;DR: The periodic unfolding method for simulating the electromagnetic field in a composite material exhibiting heterogeneous microstructures which are described by spatially periodic parameters is employed.
Abstract: In this paper, we employ the periodic unfolding method for simulating the electromagnetic field in a composite material exhibiting heterogeneous microstructures which are described by spatially periodic parameters. We consider cell problems to calculate the effective parameters for a Debye dielectric medium in the case of a circular microstructure in two dimensions. We assume that the composite materials are quasi-static in nature, i.e., the wavelength of the electromagnetic field is much larger than the relevant dimensions of the microstructure.

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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Journal ArticleDOI
TL;DR: In this article, the authors studied the stability properties of higher-order staggered finite difference schemes for Maxwell's equations coupled with a Debye or Lorentz polarization model and derived a closed-form analytical stability condition as a function of the order of the method.
Abstract: We study the stability properties of, and the phase error present in, several higher-order (in space) staggered finite difference schemes for Maxwell’s equations coupled with a Debye or Lorentz polarization model. We present a novel expansion of the symbol of finite difference approximations, of arbitrary (even) order, of the first-order spatial derivative operator. This alternative representation allows the derivation of a concise formula for the numerical dispersion relation for all (even-) order schemes applied to each model, including the limiting (infinite-order) case. We further derive a closed-form analytical stability condition for these schemes as a function of the order of the method. Using representative numerical values for the physical parameters, we validate the stability criterion while quantifying numerical dissipation. Lastly, we demonstrate the effect that the spatial discretization order, and the corresponding stability constraint, has on the dispersion error.

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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