On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Structure and biogenesis of the capsular F1 antigen from Yersinia pestis: Preserved folding energy drives fiber formation

Most gram-negative pathogens express fibrous adhesive virulence organelles that mediate targeting to the sites of infection. The F1 capsular antigen from the plague pathogen Yersinia pestis consists of linear fibers of a single subunit (Caf1) and serves as a prototype for nonpilus organelles assembled via the chaperone/usher pathway. Genetic data together with high-resolution X-ray structures corresponding to snapshots of the assembly process reveal the structural basis of fiber formation. Comparison of chaperone bound Caf1 subunit with the subunit in the fiber reveals a novel type of conformational change involving the entire hydrophobic core of the protein. The observed conformational change suggests that the chaperone traps a high-energy folding intermediate of Caf1. A model is proposed in which release of the subunit allows folding to be completed, driving fiber formation.

Streptococcus castoreus sp nov., isolated from a beaver (Castor fiber)

A previously undescribed, Gram-positive, catalase-negative, Streptococcus-like organism originating from a European beaver (Castor fiber) was subjected to a taxonomic study. The organism displayed beta-haemolytic activity and gave a positive reaction with Lancefield group A antisera. Based on the results of biochemical testing, the organism was tentatively identified as a member of the genus Streptococcus, but it did not correspond phenotypically to any recognized species of this genus. Comparative 16S rRNA gene sequencing studies confirmed this assignment, with the bacterium forming a hitherto unknown subline within the genus. Sequence divergence values of greater than 3% from other reference streptococcal species, however, demonstrated that the unidentified coccus-shaped organism represents a hitherto unknown species. Based on phenotypic and molecular phylogenetic evidence, it is therefore proposed that the unknown organism from a beaver be classified as a novel species, Streptococcus castoreus sp. nov. The type strain is M605815/03/2(T) (=CCUG 48115(T) = CIP 108205(T)).

Neuromuscular junction morphology, fiber-type proportions, and satellite-cell proliferation rates are altered in MyoD(-/-) mice

Gene compensation by members of the myogenic regulatory factor (MRF) family has been proposed to explain the apparent normal adult phenotype of MyoD(-/-) mice. Nerve and field stimulation were used to investigate contraction properties of muscle from MyoD(-/-) mice, and molecular approaches were used to investigate satellite-cell behavior. We demonstrate that MyoD deletion results in major alterations in the organization of the neuromuscular junction, which have a dramatic influence on the physiological contractile properties of skeletal muscle. Second, we show that the lineage progression of satellite cells (especially initial proliferation) in the absence of MyoD is abnormal and linked to perturbations in the nuclear localization of beta-catenin, a key readout of canonical Wnt signaling. These results show that MyoD has unique functions in both developing and adult skeletal muscle that are not carried out by other members of the MRF family.

Radiometric analysis of the light coupled by optimally cut plastic optical fiber amplitude modulating reflectance displacement sensors

A radiometric analysis of the light coupled by optical fiber amplitude modulating extrinsic-type reflectance displacement sensors is presented. Uncut fiber sensors show the largest range but a smaller responsivity. Single cut fiber sensors exhibit an improvement in responsivity at the expense of range. A further increase in responsivity as well as a reduction in the operational range is obtained when the double cut sensor configuration is implemented. The double cut configuration is particularly suitable in applications where feedback action is applied to the moving reflector surface. © 2000 American Institute of Physics.

Local gratings due to angular hole burning in a photorefractive polymer

We investigate the processes involved in writing real-time holographic gratings in a photorefractive polymer (PRP) that incorporates an azo-dye. In such systems there may be gratings due to mechanisms associated with trans–cis isomerization (angular hole burning (AHB) and/or angular redistribution), which appear in addition to those arising from the photorefractive (PR) effect. The work presented here helps to understand the interactions which may occur between these different gratings. The formation of local gratings due to mechanisms associated with photoisomerization is studied, in a new PRP based on the photoconductor poly(N-vinylcarbazole):2, 4, 7-trinitro-9-fluorenone, plasticized with N-ethylcarbazole. The polymer includes the azo-dye 4-nitro-4'-pentyloxy-azobenzene and we observe both PR and photoisomerization gratings. The gratings are shown to be both polarization-sensitive and reversible. The presence of the photoisomerization gratings (which diffract almost as strongly as the PR gratings) significantly affects the field-dependent diffractive behaviour of the composite. A measurement of the lifetime of the cis state is made (τcis = 38 s) using photoinduced dichroism. This is close to the decay time constant of the local gratings (τdecay = 42 s), and it is suggested that the local grating mechanism is AHB of the azo-dye. This is the first time (to the knowledge of the authors) that a local grating due to AHB has been demonstrated in a PRP.

Prebiotics and the health benefits of fiber: current regulatory status, future research, and goals.

First defined in the mid-1990s, prebiotics, which alter the composition and activity of gastrointestinal (GI) microbiota to improve health and well-being, have generated scientific and consumer interest and regulatory debate. The Life Sciences Research Organization, Inc. (LSRO) held a workshop, Prebiotics and the Health Benefits of Fiber: Future Research and Goals, in February 2011 to assess the current state of the science and the international regulatory environment for prebiotics, identify research gaps, and create a strategy for future research. A developing body of evidence supports a role for prebiotics in reducing the risk and severity of GI infection and inflammation, including diarrhea, inflammatory bowel disease, and ulcerative colitis as well as bowel function disorders, including irritable bowel syndrome. Prebiotics also increase the bioavailability and uptake of minerals and data suggest that they reduce the risk of obesity by promoting satiety and weight loss. Additional research is needed to define the relationship between the consumption of different prebiotics and improvement of human health. New information derived from the characterization of the composition and function of different prebiotics as well as the interactions among and between gut microbiota and the human host would improve our understanding of the effects of prebiotics on health and disease and could assist in surmounting regulatory issues related to prebiotic use.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

Impact of dietary polydextrose fiber on the human gut metabolome

The aim of the present study was to elucidate the impact of polydextrose PDX an soluble fiber, on the human fecal metabolome by high-resolution nuclear magnetic resonance (NMR) spectroscopy-based metabolomics in a dietary intervention study (n = 12). Principal component analysis (PCA) revealed a strong effect of PDX consumption on the fecal metabolome, which could be mainly ascribed to the presence of undigested fiber and oligosaccharides formed from partial degradation of PDX. Our results demonstrate that NMR-based metabolomics is a useful technique for metabolite profiling of feces and for testing compliance to dietary fiber intake in such trials. In addition, novel associations between PDX and the levels of the fecal metabolites acetate and propionate could be identified. The establishment of a correlation between the fecal metabolome and levels of Bifidobacterium (R2 = 0.66) and Bacteroides (R2 = 0.46) demonstrates the potential of NMR-based metabolomics to elucidate metabolic activity of bacteria in the gut.