Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders---including Wood anomalies

This paper presents a full-spectrum Green function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application to wire gratings, particle arrays and reflectarrays and, indeed, general arrays of conducting or dielectric bounded obstacles under both TE and TM polarized illumination. The proposed method, which, for definiteness is demonstrated here for arrays of perfectly conducting particles under TE polarization, is based on use of the shifted Green-function method introduced in the recent contribution (Bruno and Delourme, Jour. Computat. Phys. pp. 262--290 (2014)). A certain infinite term arises at Wood anomalies for the cylinder-array problems considered here that is not present in the previous rough-surface case. As shown in this paper, these infinite terms can be treated via an application of ideas related to the Woodbury-Sherman-Morrison formulae. The resulting approach, which is applicable to general arrays of obstacles even at and around Wood-anomaly frequencies, exhibits fast convergence and high accuracies. For example, a few hundreds of milliseconds suffice for the proposed approach to evaluate solutions throughout the resonance region (wavelengths comparable to the period and cylinder sizes) with full single-precision accuracy

On the evaluation of quasi-periodic Green functions and wave-scattering at and around Rayleigh-Wood anomalies

This article presents full-spectrum, well-conditioned, Green-function methodologies for evaluation of scattering by general periodic structures, which remains applicable on a set of challenging singular configurations, usually called Rayleigh-Wood (RW) anomalies (at which the quasi-periodic Green function ceases to exist), where most existing quasi-periodic solvers break down. After reviewing a variety of existing fast-converging numerical procedures commonly used to compute the classical quasi-periodic Green-function, the present work explores the difficulties they present around RW-anomalies and introduces the concept of hybrid “spatial/spectral” representations. Such expressions allow both the modification of existing methods to obtain convergence at RW-anomalies as well as the application of a slight generalization of the Woodbury-Sherman-Morrison formulae together with a limiting procedure to bypass the singularities. (Although, for definiteness, the overall approach is applied to the scalar (acoustic) wave-scattering problem in the frequency domain, the approach can be extended in a straightforward manner to the harmonic Maxwell's and elasticity equations.) Ultimately, this thorough study of RW-anomalies yields fast and highly-accurate solvers, which are demonstrated with a variety of simulations of wave-scattering phenomena by arrays of particles, crossed impenetrable and penetrable diffraction gratings and other related structures. In particular, the methods developed in this article can be used to “upgrade” classical approaches, resulting in algorithms that are applicable throughout the spectrum, and it provides new methods for cases where previous approaches are either costly or fail altogether. In particular, it is suggested that the proposed shifted Green function approach may provide the only viable alternative for treatment of three-dimensional high-frequency configurations with either one or two directions of periodicity. A variety of computational examples are presented which demonstrate the flexibility of the overall approach

High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: O(1)\mathcal{O}(1) Sampling Cost via Incident-Field Windowing and Recentering

This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains. Relying on Fourier Transformation in time, the method utilizes a fixed (time-independent) number of frequency-domain integral-equation solutions to evaluate, with superalgebraically-small errors, time domain solutions for arbitrarily long times. The approach relies on two main elements, namely, 1) A smooth time-windowing methodology that enables accurate band-limited representations for arbitrarily-long time signals, and 2) A novel Fourier transform approach which, in a time-parallel manner and without causing spurious periodicity effects, delivers numerically dispersionless spectrally-accurate solutions. A similar hybrid technique can be obtained on the basis of Laplace transforms instead of Fourier transforms, but we do not consider the Laplace-based method in the present contribution. The algorithm can handle dispersive media, it can tackle complex physical structures, it enables parallelization in time in a straightforward manner, and it allows for time leaping---that is, solution sampling at any given time $T$ at $\mathcal{O}(1)$-bounded sampling cost, for arbitrarily large values of $T$, and without requirement of evaluation of the solution at intermediate times. The proposed frequency-time hybridization strategy, which generalizes to any linear partial differential equation in the time domain for which frequency-domain solutions can be obtained (including e.g. the time-domain Maxwell equations), and which is applicable in a wide range of scientific and engineering contexts, provides significant advantages over other available alternatives such as volumetric discretization, time-domain integral equations, and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now including direct comparisons to existing CQ and TDIE solver implementations) (Part I of II

High-resolution onshore seismic imaging of complex volcanic structures: An example from Vulcano Island, Italy

Detailed seismic images of subsurface structures of volcanic calderas are fundamental to improve the structural and volcanological knowledge of these high-risk volcanoes. However, high-quality seismic data are difficult to obtain in volcanic areas, especially on shore. We report the results of a high-resolution seismic profiling of the western sector of La Fossa Caldera (Vulcano Island, Italy). Using a high-resolution vibrating source and both alternative acquisition and processing techniques, we were able to overcome most of the inconvenience caused by volcanic lithotypes. This study provides the subsurface distribution of volcanic deposits as well as the recognition of some significant intracaldera structures. We located a parasitic vent or hyaloclastite mound buried under La Fossa Caldera, which is dissipating CO 2 in an area where earthquakes have been recorded at about 1 km depth. Furthermore, the deformation pattern found at the southernmost part of the profile is consistent with a caldera collapse after a dome intrusion. The results suggest that the use of high-resolution vibrating sources combined with alternative seismic acquisition techniques and nonconventional processing could help to recover detailed information on the shallow structures of volcanic areas. Copyright 2009 by the American Geophysical Union

Helicobacter pylori infection and gastric dysbiosis: Can probiotics administration be useful to treat this condition?

Helicobacter pylori (Hp) is responsible for one of the most common infections in the world. 'e prevalence exceeds 50% of the population in developing countries, and approximately one-third of the adults are colonized in North Europe and North America. It is considered a major pathogenic agent of chronic gastritis, peptic ulcer, atrophic gastritis, gastric cancer, and mucosa-associated lymphoid tissue lymphoma (MALT). Hp colonization modifies the composition of gastric microbiota that could drive the development of gastric disorders. Currently, an emerging problem in Hp treatment is represented by the increasing rate of antimicrobial therapy resistance. In this context, the search for adjuvant agents can be very useful to overcome this issue and probiotics administration can represent a valid option. The aim of this review is to describe the gastric microbiota changes during Hp colonization, the mechanisms of action, and a possible role of probiotics in the treatment of this infection