A novel boundary integral equation for surface crack model

A novel boundary integral equation (BIE) is developed for eddy‐current nondestructive evaluation problems with surface crack under a uniform applied magnetic field. Once the field and its normal derivative are obtained for the structure in the absence of cracks, normal derivative of scattered field on the conductor surface can be calculated by solving this equation with the aid of method of moments (MoM). This equation is more efficient than conventional BIEs because of a smaller computational domain needed

Full Wave Modeling of Ultrasonic Scattering Using Nystrom Method for NDE Applications

Approximate methods for ultrasonic scattering like the Kirchhoff approximation and the geometrical theory of diffraction (GTD) can deliver fast solutions with relatively small computational resources compared to accurate numerical methods. However, these models are prone to inaccuracies in predicting scattered fields from defects that are not very large compared to wavelength. Furthermore, they do not take into account physical phenomena like multiple scattering and surface wave generation on defects. Numerical methods like the finite element method (FEM) and the boundary element method (BEM) can overcome these limitations of approximate models. Commercial softwares such as Abaqus FEA and PZFlex use FEM, while CIVA has a 2D FEM solver [1-3]. In this work, we study the performance of the Nyström method (NM) [4,5], an alternative boundary integral equation solver to the BEM, in modeling ultrasonic scattering from defects. To handle larger problems, the Nyström method is accelerated by the multilevel fast multipole algorithm (MLFMA). We apply the NM to benchmark problems and compare its predictions with those of exact and approximate analytical models as well as with experimental results from the World Federation of NDE Centers (WFNDEC). Several examples will be presented to demonstrate the prediction of creeping waves by the NM while also illustrating its improved accuracy over the Kirchhoff approximation. We will conclude with a discussion on the validity and limitations of the NM in modelling practical NDE problems

An Efficient Multilevel Fast Multipole Algorithm to Solve Volume Integral Equation for Arbitrary Inhomogeneous Bi-Anisotropic Objects

A volume integral equation (VIE) based on the mixed-potential representation is presented to analyze the electromagnetic scattering from objects involving inhomogeneous bi-anisotropic materials. By discretizing the objects using tetrahedrons on which the commonly used Schaubert-Wilton-Glisson (SWG) basis functions are defined, the matrix equation is derived using the method of moments (MoM) combined with the Galerkin’s testing. Further, adopting an integral strategy of tetrahedron-to-tetrahedron scheme, the multilevel fast multipole algorithm (MLFMA) is proposed to accelerate the iterative solution, which is further improved by using the spherical harmonics expansion with a faster implementation and low memory requirement. The memory requirement of the radiation patterns of basis functions in the proposed MLFMA is several times less than that in the conventional MLFMA

Efficient Triangular Interpolation Method: Error Analysis and Applications

The interpolation errors of bivariate Lagrange polynomial and triangular interpolations are studied for the plane waves. The maximum and root-mean-square (RMS) errors on the right triangular, equilateral triangular and rectangular (bivariate Lagrange polynomial) interpolations are analyzed. It is found that the maximum and RMS errors are directly proportional to the (p+1)’th power of kh for both one-dimensional (1D) and two-dimensional (2D, bivariate) interpolations, where k is the wavenumber and h is the mesh size. The interpolation regions for the right triangular, equilateral triangular and rectangular interpolations are selected based on the regions with smallest errors. The triangular and rectangular interpolations are applied to evaluate the 2D singly periodic Green’s function (PGF). The numerical results show that the equilateral triangular interpolation is the most accurate interpolation method, while the right triangular interpolation is the most efficient interpolation method

Miniaturized-Element Frequency-Selective Rasorber Design Using Characteristic Modes Analysis

A dual-polarization frequency-selective rasorber with two absorptive bands at both sides of a passband is presented. Based on the characteristic mode analysis, a circuit analog absorber is designed using a lossy FSS that consists of miniaturized meander lines and lumped resistors. The positions and values of resistors are determined according to the analysis of modal significances and modal current. After that, the presented rasorber is designed by cascading of the lossy FSS and a lossless bandpass FSS. Equivalent circuits of the frequency-selective rasorber are modelled, and surface current distributions of both FSSs are illustrated to explain the operation mechanism. Measurement results show that, under the normal incidence, a minimum insertion loss of 0.27 dB is achieved at a passband around 6 GHz, and the absorption bands with an absorption rate higher than 80% are 2.5 to 4.6 GHz in the lower band and 7.7 to 12 GHz in the higher band, respectively. Our results exhibit good agreements between measurements and simulations

Efficient and accurate approximation of infinite series summation using asymptotic approximation and fast convergent series

We present an approach for very quick and accurate approximation of infinite series summation arising in electromagnetic problems. This approach is based on using asymptotic expansions of the arguments and the use of fast convergent series to accelerate the convergence of each term. It has been validated by obtaining very accurate solution for propagation constant for shielded microstrip lines using spectral domain approach (SDA). In the spectral domain analysis of shielded microstrip lines, the elements of the Galerkin matrix are summations of infinite series of product of Bessel functions and Green\u27s function. The infinite summation is accelerated by leading term extraction using asymptotic expansions for the Bessel function and the Green\u27s function, and the summation of the leading terms is carried out using the fast convergent series

Effects of Severe Water Stress on Maize Growth Processes in the Field

In this study, we investigated the effects of water stress on the growth and yield of summer maize (Zea mays L.) over four phenological stages: Seedling, jointing, heading, and grain-filling. Water stress treatments were applied during each of these four stages in a water-controlled field in the Guanzhong Plain, China between 2013 and 2016. We found that severe water stress during the seedling stage had a greater effect on the growth and development of maize than stress applied during the other three stages. Water stress led to lower leaf area index (LAI) and biomass owing to reduced intercepted photosynthetically active radiation (IPAR) and radiation-use efficiency (RUE). These effects extended to the reproductive stage and eventually reduced the unit kernel weight and yield. In addition, the chlorophyll content in the leaf remained lower, even though irrigation was applied partially or fully after the seedling stage. Severe and prolonged water stress in maize plants during the seedling stage may damage the structure of the photosynthetic membrane, resulting in lower chlorophyll content, and therefore RUE, than those in the plants that did not experience water stress at the seedling stage. Maize plants with such damage did not show a meaningful recovery even when irrigation levels during the rest of the growth period were the same as those applied to the plants not subjected to water stress. The results of our field experiments suggest that an unrecoverable yield loss could occur if summer maize were exposed to severe and extended water stress events during the seedling stage

Effects of Langmuir Kinetics of Two-Lane Totally Asymmetric Exclusion Processes in Protein Traffic

In this paper, we study a two-lane totally asymmetric simple exclusion process (TASEP) coupled with random attachment and detachment of particles (Langmuir kinetics) in both lanes under open boundary conditions. Our model can describe the directed motion of molecular motors, attachment and detachment of motors, and free inter-lane transition of motors between filaments. In this paper, we focus on some finite-size effects of the system because normally the sizes of most real systems are finite and small (e.g., size $\leq 10,000$). A special finite-size effect of the two-lane system has been observed, which is that the density wall moves left first and then move towards the right with the increase of the lane-changing rate. We called it the jumping effect. We find that increasing attachment and detachment rates will weaken the jumping effect. We also confirmed that when the size of the two-lane system is large enough, the jumping effect disappears, and the two-lane system has a similar density profile to a single-lane TASEP coupled with Langmuir kinetics. Increasing lane-changing rates has little effect on density and current after the density reaches maximum. Also, lane-changing rate has no effect on density profiles of a two-lane TASEP coupled with Langmuir kinetics at a large attachment/detachment rate and/or a large system size. Mean-field approximation is presented and it agrees with our Monte Carlo simulations.Comment: 15 pages, 8 figures. To be published in IJMP