Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers

In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of its permittivity. This is accomplished by introducing an auxiliary eigenvalue problem, based on a volume integral operator. With this modal basis the expansion coefficients of the scattered field are simple rational functions of the permittivity of the scatterer. We show, by studying the electromagnetic scattering from a sphere and a cylinder of dimensions comparable to the incident wavelength, that only a moderate number of modes is needed to accurately describe the scattered far field. This method can be used to investigate resonant scattering phenomena, including plasmonic and photonic resonances, and to design the permittivity of the object to pursue a prescribed tailoring of the scattered field. Moreover, the presented modal expansion is computationally advantageous compared to direct solution of the volume integral equation when the scattered field has to be computed for many different values of the dielectric permittivity, given the size and shape of the dielectric body

Differential Geometry Based Model for Eddy Current Inspection of U-Bend Sections in Steam Generator Tubes

A numerical finite element model, capable of simulating eddy current testing (ECT) of steam generator (SG) tubing in power plants is an ongoing project at MSU. The simulation model software SGTSIM models the free span and tube support regions of the tube with a variety of commercial probes, such as bobbin, pancake, +Point and array probes. The simulation model predicts defect signals which have been validated by experimental ECT data. The modeling of U-Bend segment in steam generator tubes for predicting eddy current probe signals from cracks, wear and pitting in this region poses challenges and is non-trivial. Meshing the geometry in the Cartesian coordinate system will require a large number of elements to model the U-bend region. Also, since the lift-off distance between the probe and tube wall is usually very small, a very fine mesh is required near the lift-off region to accurately describe the eddy current field. This paper presents a U-bend model using differential geometry principles that exploit the result that Maxwell’s equations are covariant with respect to changes of coordinates and independent of metrics [1-2]. The equations remain unaltered in their form, regardless of the choice of the co-ordinate system, provided the electric and magnetic field quantities are represented in the proper tensor densities (contravariant or covariant components) [3-4]. The complex shapes are mapped into simple straight sections, while small lift-off is mapped to larger values thus reducing the intrinsic dimension of the mesh and stiffness matrix

Magnetoquasistatic resonances of small dielectric objects

A small dielectric object with positive permittivity may resonate when the free-space wavelength is large in comparison with the object dimensions if the permittivity is sufficiently high. We show that these resonances are described by the magnetoquasistatic approximation of the Maxwell's equations in which the normal component of the displacement current density field vanishes on the surface of the particle. They are associated to values of permittivities and frequencies for which source-free quasistatic magnetic fields exist, which are connected to the eigenvalues of a magnetostatic integral operator. We present the general physical properties of magnetoquasistatic resonances in dielectrics with arbitrary shape. They arise from the interplay between the polarization energy stored in the dielectric and the energy stored in the magnetic field. Our findings improve the understanding of resonances in high-permittivity dielectric objects and provide a powerful tool that greatly simplifies the analysis and design of high-index resonators

A Model Assisted Probability of Detection Study for Eddy Current Testing of Multi-layer Structures

Eddy current (EC) excitation with GMR (Giant MagnetoResistive) sensors [1] for measuring induced fields has been used successfully in many industrial applications for detecting flaws in materials and components. This article focuses on the detection of cracks at fastener sites in multi- layered structures, which are commonly seen on aircraft skin, and develops a model assisted method of assessing the probability of detection (POD). In an EC-GMR system the conductive specimen under investigation is excited with a time-varying magnetic field. The perturbations in induced magnetic field introduced by flaws are picked up by GMR sensors which provide high sensitivity even under very low frequency fields. Despite limitations of skin depth and sensititivity to lift-off, a well-designed EC-GMR system can potentially detect buried defects in a multi-layered structure [2]. Further, it is shown that using rotating current excitation, EC-GMR system is sensitive to defects with arbitrary orientations [1]. In practice, the GMR signal of a defect is not only a function of the defect size but also of geometrical features in the vicinity such as edges, adjacent rivets and properties of the layered structure. As it is expensive and time consuming to manufacture a variety of samples including these factors, numerical models can be used to provide fast and accurate estimates of defect signals. In order to take advantage of this, we adopt the concept of model assisted probability of detection (MAPOD) and consider it in a multi parameter framework [3-5]. We use a meta-model to reduce the computational effort and Monte Carlo simulations to propagate the uncertainties essential for calculating POD. The multi parameter approach estimates POD not only w.r.t. the flaw size but also w.r.t. critical parameter combinations during inspection

Synthesis of resonant modes in electromagnetics

Resonant modes determine the response of electromagnetic devices, including dielectric and plasmonic resonators. Relying on the degrees of freedom that metamaterials provide, this contribution shows how to design, at will, the resonant modes of a dielectric object placed in an unbounded space. Specifically, the proposed method returns in analytical form the spatial distribution of the dielectric susceptibility tensor for which the object exhibits resonances at prescribed frequencies and spatial distribution of the polarization. Together with the synthesis of the material, two key concepts are introduced: the controlled tunability of the resonant modes and the number of essential modes, i.e. the number of modes that uniquely characterize the spatial distribution of the dielectric susceptibility. Moreover, this approach can be applied to design the resonant modes of any system where the constitutive relationship is linear and local

Monotonicity Principle in Tomography of Nonlinear Conducting Materials

We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents operations. In this framework, a key role is played by the Monotonicity Principle, which establishes a monotonic relation connecting the unknown material property to the (measured) Dirichlet-to-Neumann operator (DtN). Monotonicity Principles are the foundation for a class of non-iterative and real-time imaging methods and algorithms. In this article, we prove that the Monotonicity Principle for the Dirichlet Energy in nonlinear problems holds under mild assumptions. Then, we show that apart from linear and $p$-Laplacian cases, it is impossible to transfer this Monotonicity result from the Dirichlet Energy to the DtN operator. To overcome this issue, we introduce a new boundary operator, identified as an Average DtN operator.Comment: 28 pages, 6 figure

An Eddy-Current Testing Method for Measuring the Thickness of Metallic Plates

Thickness measurements of metallic plates are mandatory in many industrial scenarios. Methods based on eddy-current testing (ECT) are ideal for fast and accurate online contactless thickness measurements, making them very attractive in the Industry 4.0 scenario. This contribution is focused on a specific and robust ECT technique proposed in the past by the scientific community. The main limitation is its applicability to thin materials only, where the thickness of the material is much smaller than the overall size of the ECT probe. Extending the range of applicability to thicker materials introduces a progressive and severe degradation of the measurement accuracy. In this article, we analyze the theoretical foundation of this method with an entirely original approach based on the celebrated Buckingham π theorem. In doing this, we draw the complete theoretical picture of the method, providing a simple, clear, and rigorous view of its performance and intrinsic limitations. Moreover, we propose two solutions, one analytical and the other iterative, to accurately estimate the thickness of the materials from thin to thick values. Finally, a numerical analysis combined with an experimental campaign confirms the effectiveness of the proposed solutions, making the method suitable for industrial and other applications

Differential vulnerability of retinal layers to early age-related macular degeneration: evidence by SD-OCT segmentation analysis.

PURPOSE We evaluated layer-by-layer retinal thickness in spectral-domain optical coherence tomography (SD-OCT), determined by automated segmentation analysis (ASA) software in healthy and early age-related maculopathy (ARM) eyes. METHODS There were 57 eyes (specifically, 19 healthy eyes under 60 years old, 19 healthy eyes over 60, and 19 ARM eyes) recruited into this cross-sectional study. The mean ages were 36.78 (SD, ±13.82), 69.89 (SD, ±6.14), and 66.10 (SD, ±8.67) years, respectively, in the three study groups. The SD-OCT scans were transferred into a dedicated software program that performed automated segmentation of different retinal layers. RESULTS Automated layer segmentation showed clear boundaries between the following layers: retinal nerve fiber layer (RNFL), ganglion cell layer plus inner plexiform layer (GCL+IPL), inner nuclear layer plus outer plexiform layer (INL+OPL), outer nuclear layer (ONL), and RPE complex. The thickness of the RNFL, ONL, and RPE layers did not show a statistically significant change across the three groups by ANOVA (P = 0.10, P = 0.09, P = 0.15, respectively). The thickness of GCL+IPL and INL+OPL was significantly different across the groups (P < 0.01), being reduced in the ARM eyes compared to healthy eyes, under and over 60 years old. CONCLUSIONS The early morphologic involvement of the GCL+IPL and INL+OPL layers in ARM eyes, as revealed by the ASA, could be related to early anatomic changes described in the inner retina of ARM eyes. This finding may represent a morphologic correlation to the deficits in postreceptoral retinal function in ARM eyes

A Fast Matrix Compression Method for Large Scale Numerical Modelling of Rotationally Symmetric 3D Passive Structures in Fusion Devices

This paper illustrates the development of a recursive QR technique for the analysis of transient events, such as disruptions or scenario evolution, in fusion devices with three-dimensional conducting structures using an integral eddy current formulation. An integral formulation involves the solution, at each time step, of a large full linear system. For this reason, a direct solution is impractical in terms of time and memory consumption. Moreover, typical fusion devices show a symmetric/periodic structure. This can be properly exploited when the plasma and other sources possess the same symmetry/periodicity of the structure. Indeed, in this case, the computation can be reduced to only a single sector of the overall structure. In this work the periodicity and the symmetries are merged in the recursive QR technique, exhibiting a huge decrease in the computational cost. Finally, the proposed technique is applied to a realistic large-scale problem related to the International Thermonuclear Experimental Reactor (ITER)