Near-field imaging of locally perturbed periodic surfaces

This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer quasi-periodic. Thus the classical method for quasi-periodic scattering problems no longer works. In this paper, we apply a Floquet-Bloch transform based numerical method to reconstruct both the unknown periodic part and the unknown local perturbation from the near-field data. By transforming the original scattering problem into one defined in an infinite rectangle, the information of the surface is included in the coefficients. The numerical scheme contains two steps. The first step is to obtain an initial guess, i.e., the locations of both the periodic surfaces and the local perturbations, from a sampling method. The second step is to reconstruct the surface. As is proved in this paper, for some incident fields, the corresponding scattered fields carry little information of the perturbation. In this case, we use this scattered field to reconstruct the periodic surface. Then we could apply the data that carries more information of the perturbation to reconstruct the local perturbation. The Newton-CG method is applied to solve the associated optimization problems. Numerical examples are given at the end of this paper to show the efficiency of the numerical method

A genetic study of resistance to kernel infection by Aspergillus flavus in maize (Zea mays L.)

Maize (Zea mays L.) kernel infection by Aspergillus flavus is a chronic problem in the southern USA. Genetic resistance to A. flavus is needed to solve this problem. To ascertain and understand the inheritance of resistance to field kernel infection by A. flavus, a five-parent diallel analysis and a half-sib family analysis of 35 maize crosses were conducted during 2003 and 2004 for percent kernel infection (PKI) rates. All parents contained the leafy gene (Lfy). From the combining ability analysis of the five maize parents and their 20 F1s, highly significant general combining ability (GCA), specific combining ability (SCA), and reciprocal effects were found. The analysis of genetic effects showed that the parents 914 and A619 had desirable GCA effects to enhance the average performance of A. flavus resistance in hybrid progeny. The crosses 914 �� A632, 914 �� WF9, and HY �� WF9 had consistently negative SCA effects across the two years. These results suggested that resistance to kernel infection by A. flavus existed among the parents and some of their crosses. Their potential performance with desired GCAs and SCAs could be exploited to develop resistant lines in breeding programs and to produce resistant hybrids. The reciprocal effects in the crosses across years reflected the presence of maternal effects in the maize kernel. These effects were partly responsible for resistance to A. flavus and should be considered in making crosses. The cross A632 �� HY had the highest negative significant reciprocal effect, indicating that it should promote resistance to A. flavus. Analyses of the 35 half-sib crosses derived from seven maize breeding lines indicated that both the genotype and genotype-by-year effects were highly significant. Broad-sense heritability for PKI estimated from variance components was 73.8%. A North Carolina Design-II analysis of 12 crosses was used to estimate additive and dominance genetic variances. Narrow-sense heritability and the average degree of dominance for PKI were 37.6% and 1.67, respectively. A comparison of a laboratory-based infection resistance screening (LIRS) with field-based PKI demonstrated that LIRS was effective and could be used to improve maize germplasm screening and to expedite A. flavus resistance breeding

Higher order convergence of perfectly matched layers in 3D bi-periodic surface scattering problems

The perfectly matched layer (PML) is a very popular tool in the truncation of wave scattering in unbounded domains. In Chandler-Wilde & Monk et al. 2009, the author proposed a conjecture that for scattering problems with rough surfaces, the PML converges exponentially with respect to the PML parameter in any compact subset. In the author's previous paper (Zhang et al. 2022), this result has been proved for periodic surfaces in two dimensional spaces, when the wave number is not a half integer. In this paper, we prove that the method has a high order convergence rate in the 3D bi-periodic surface scattering problems. We extend the 2D results and prove that the exponential convergence still holds when the wavenumber is smaller than $0.5$. For lareger wavenumbers, although exponential convergence is no longer proved, we are able to prove that a higher order convergence for the PML method

Fast convergence for of perfectly matched layers for scattering with periodic surfaces: the exceptional case

In the author's previous paper (Zhang et al. 2022), exponential convergence was proved for the perfectly matched layers (PML) approximation of scattering problems with periodic surfaces in 2D. However, due to the overlapping of singularities, an exceptional case, i.e., when the wave number is a half integer, has to be excluded in the proof. However, numerical results for these cases still have fast convergence rate and this motivates us to go deeper into these cases. In this paper, we focus on these cases and prove that the fast convergence result for the discretized form. Numerical examples are also presented to support our theoretical results