Modelling resonant arrays of the Helmholtz type in the time domain.

We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic slab replacing the cavity region, associated with transmission, or jump, conditions for the acoustic pressure and for the normal velocity across the region of the necks. The coefficients entering in the effective wave equation are simply related to the fraction of air in the periodic cell of the array. Those entering in the jump conditions are related to near field effects in the vicinity of the necks and they encapsulate the effects of their geometry. The effective problem, which accounts for the coupling of the resonators with the surrounding air, is written in the time domain which allows us to question the equation of energy conservation. This is of practical importance if the numerical implementations of the effective problem in the time domain is sought.

A REVIEW OF NATURAL RADIONUCLIDES IN CANADIAN DRINKING WATER (1975-16).

Historical results of natural radioactivity in drinking water were reviewed for a total of 21 communities across Canada from 1975 to 2016. Analyses for 226Ra, 210Pb and total uranium were carried out on monthly composite samples of drinking water from selected Canadian municipalities. Generally speaking, levels of 226Ra, 210Pb and total uranium were found to be low compared to national and international standards for drinking water quality. Because levels were low, federal monitoring programs were discontinued in most communities in 1986 except for Regina, Elliot Lake and Port Hope. The population-weighted average levels for these three communities, using data from the most recent 5 years, are <1 mBq/L for 226Ra, <5 mBq/L for 210Pb and <0.4 µg/L for total uranium. The average effective dose resulting from drinking water intake at these levels would be <4.3 µSv per year.

Influence of the neck shape for Helmholtz resonators.

The resonance of a Helmholtz resonator is studied with a focus on the influence of the neck shape. This is done using a homogenization approach developed for an array of resonators, and the resonance of an array is discussed when compared to that of a single resonator. The homogenization makes a parameter B appear which determines unambiguously the resonance frequency of any neck. As expected, this parameter depends on the length and on the minimum opening of the neck, and it is shown to depend also on the surface of air inside the neck. Once these three geometrical parameters are known, B has an additional but weak dependence on the neck shape, with explicit bounds.

Improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow.

We present an efficient multimodal method to describe the acoustic propagation in the presence of a uniform flow in a waveguide with locally a wall impedance treatment. The method relies on a variational formulation of the problem, which allows to derive a multimodal formulation within a rigorous mathematical framework, notably to properly account for the boundary conditions on the walls (being locally the Myers condition and the Neumann condition otherwise). Also, the method uses an enriched basis with respect to the usual cosine basis, able to absorb the less converging part of the modal series and thus, to improve the convergence of the method. Using the cosine basis, the modal method has a low convergence, 1/N, with N the order of truncation. Using the enriched basis, the improvement in the convergence is shown to depend on the Mach number, from 1/N5 to roughly 1/N1.5 for M=0 to M close to unity. The case of a continuously varying wall impedance is considered, and we discuss the limiting case of piecewise constant impedance, which defines pressure edge conditions at the impedance discontinuities.

The determination of Fukushima-derived cesium-134 and cesium-137 in Japanese green tea samples and their distribution subsequent to simulated beverage preparation.

Health Canada's Radiation Protection Bureau has identified trace quantities of (134)Cs and (137)Cs in commercially available green tea products of Japanese origin. Referenced to March 11, 2011, the activity ratio ((134)Cs/(137)Cs) has been determined to be 1:1, which supports an origin from the Fukushima Dai-ichi Nuclear Power Plant accident. The upper limits of typical tea beverage preparation conditions were applied to the most contaminated of these green tea samples to determine the proportion of radiocesium contamination that would be available for human consumption. The distribution of radiocesium among the components of the extraction experiments (water, residual tea solid, and filter media) was determined by both conventional and Compton-suppressed gamma spectroscopy. The latter aided tremendously in providing a more complete radiocesium distribution profile, particularly for the shorter-lived (134)Cs. Cesium extraction efficiencies of 64 ± 7% and 64 ± 5% were determined based on (134)Cs and (137)Cs, respectively. Annual, effective dose estimates from ingestion of (137)Cs and (134)Cs (1.8-3.7 µSv), arising from the consumption of tea beverages prepared from the most contaminated of these samples, are insignificant relative to both total (∼ 2.4 mSv) and ingested (∼ 0.28 mSv) annual effective doses received from naturally occurring radioactive sources. As such, there is no health concern arising from the consumption of green tea beverages contaminated with radiocesium at the levels encountered in this study.

Modal method for the 2D wave propagation in heterogeneous anisotropic media.

A multimodal method based on a generalization of the admittance matrix is used to analyze wave propagation in heterogeneous two-dimensional anisotropic media. The heterogeneity of the medium can be due to the presence of anisotropic inclusions with arbitrary shapes, to a succession of anisotropic media with complex interfaces between them, or both. Using a modal expansion of the wave field, the problem is reduced to a system of two sets of first-order differential equations for the modal components of the field, similar to the system obtained in the rigorous coupled wave analysis. The system is solved numerically, using the admittance matrix, which leads to a stable numerical method, the basic properties of which are discussed. The convergence of the method is discussed, considering arrays of anisotropic inclusions with complex shapes, which tend to show that Li's rules are not concerned within our approach. The method is validated by comparison with a subwavelength layered structure presenting an effective anisotropy at the wave scale.

Wave propagation in a waveguide containing restrictions with circular arc shape.

A multimodal method is used to analyze the wave propagation in waveguides containing restrictions (or corrugations) with circular arc shapes. This is done using a geometrical transformation which transforms the waveguide with complex geometry in the real space to a straight waveguide in the transformed space, or virtual space. In this virtual space, the Helmholtz equation has a modified structure which encapsulates the complexity of the geometry. It is solved using an improved modal method, which was proposed in a paper by A. Maurel, J.-F. Mercier, and S. Félix [Proc. R. Soc. A 470, 20130743 (2014)], that increases the accuracy and convergence of usual multimodal formulations. Results show the possibility to solve the wave propagation in a waveguide with a high density of circular arc shaped scatterers.

A report on radioactivity measurements of fish samples from the west coast of Canada.

Even though many studies have shown that radioactive caesium levels in fish caught outside of Japan were below experimental detection limits of a few Bq kg(-1), significant public concern has been expressed about the safety of consuming seafood from the Pacific Ocean following the Fukushima-Daiichi nuclear accident. To address the public concerns, samples of commonly consumed salmon and groundfish harvested from the Canadian west coast in 2013 were analysed for radioactive caesium. None of the fish samples analysed in this study contained any detectable levels of (134)Cs and (137)Cs under given experimental setting with the average detection limit of ∼2 Bq kg(-1). Using a conservative worst-case scenario where all fish samples would contain (137)Cs exactly at the detection limit level and (134)Cs at half of the detection limit level (to account for much shorter half-life of (134)Cs), the resulting radiation dose for people from consumption of this fish would be a very small fraction of the annual dose from exposure to natural background radiation in Canada. Therefore, fish, such as salmon and groundfish, from the Canadian west coast are of no radiological health concern.

Local transformation leading to an efficient Fourier modal method for perfectly conducting gratings.

We present an efficient Fourier modal method for wave scattering by perfectly conducting gratings (in the two polarizations). The method uses a geometrical transformation, similar to the one used in the C-method, that transforms the grating surface into a flat surface, thus avoiding to question the Rayleigh hypothesis; also, the transformation only affects a bounded inner region that naturally matches the outer region; this allows applying a simple criterion to select the ingoing and outgoing waves. The method is shown to satisfy reciprocity and energy conservation, and it has an exponential rate of convergence for regular groove shapes. Besides, it is shown that the size of the inner region, where the solution is computed, can be reduced to the groove depth, that is, to the minimal computation domain.

Extraordinary transmission through subwavelength dielectric gratings in the microwave range.

We address the problem of the transmission through subwavelength dielectric gratings. Following Maurel et al. [Phys. Rev. B 88, 115416 (2013)], the problem is reduced to the transmission by an homogeneous slab, either anisotropic (for transverse magnetic waves, TM) or isotropic (for transverse electric waves, TE), and an explicit expression of the transmission coefficient is derived. The optimum angle realizing perfect impedance matching (Brewster angle) is shown to depend on the contrasts of the dielectric layers with respect to the air. Besides, we show that the Fabry-Perot resonances may be dependent on the incident angle, in addition to the dependence on the frequency. These facts depart from the case of metallic gratings usually considered; they are confirmed experimentally both for TE and TM waves in the microwave regime.

Propagation in waveguides with varying cross section and curvature: a new light on the role of supplementary modes in multi-modal methods.

We present an efficient multi-modal method to describe the acoustic propagation in waveguides with varying curvature and cross section. A key feature is the use of a flexible geometrical transformation to a virtual space in which the waveguide is straight and has unitary cross section. In this new space, the pressure field has to satisfy a modified wave equation and associated modified boundary conditions. These boundary conditions are in general not satisfied by the Neumann modes, used for the series representation of the field. Following previous work, an improved modal method (MM) is presented, by means of the use of two supplementary modes. Resulting increased convergences are exemplified by comparison with the classical MM. Next, the following question is addressed: when the boundary conditions are verified by the Neumann modes, does the use of supplementary modes improve or degrade the convergence of the computed solution? Surprisingly, although the supplementary modes degrade the behaviour of the solution at the walls, they improve the convergence of the wavefield and of the scattering coefficients. This sheds a new light on the role of the supplementary modes and opens the way for their use in a wide range of scattering problems.

Improved multimodal admittance method in varying cross section waveguides.

An improved version of the multimodal admittance method in acoustic waveguides with varying cross sections is presented. This method aims at a better convergence with respect to the number of transverse modes that are taken into account. It is based on an enriched modal expansion of the pressure: the N first modes are the local transverse modes and a supplementary (N+1)th mode, called boundary mode, is a well-chosen transverse function orthogonal to the N first modes. This expansion leads to the classical form of the coupled mode equations where the component of the boundary mode is of evanescent character. Under this form, the multimodal admittance method based on the Riccati equation on the admittance matrix (the Dirichlet-to-Neumann operator) is straightforwardly implemented. With this supplementary mode, in addition to the improvement of the convergence of the pressure field, results show a superconvergence of the scattered field outside of the varying cross sections region.

Wave propagation through penetrable scatterers in a waveguide and through a penetrable grating.

A multimodal method based on the admittance matrix is used to analyze wave propagation through scatterers of arbitrary shape. Two cases are considered: a waveguide containing scatterers, and the scattering of a plane wave at oblique incidence to an infinite periodic row of scatterers. In both cases, the problem reduces to a system of two sets of first-order differential equations for the modal components of the wavefield, similar to the system obtained in the rigorous coupled wave analysis. The system can be solved numerically using the admittance matrix, which leads to a stable numerical method, the basic properties of which are discussed (convergence, reciprocity, energy conservation). Alternatively, the admittance matrix can be used to get analytical results in the weak scattering approximation. This is done using the plane wave approximation, leading to a generalized version of the Webster equation and using a perturbative method to analyze the Wood anomalies and Fano resonances.

Discovery of novel small-molecule HIV-1 replication inhibitors that stabilize capsid complexes.

The identification of novel antiretroviral agents is required to provide alternative treatment options for HIV-1-infected patients. The screening of a phenotypic cell-based viral replication assay led to the identification of a novel class of 4,5-dihydro-1H-pyrrolo[3,4-c]pyrazol-6-one (pyrrolopyrazolone) HIV-1 inhibitors, exemplified by two compounds: BI-1 and BI-2. These compounds inhibited early postentry stages of viral replication at a step(s) following reverse transcription but prior to 2 long terminal repeat (2-LTR) circle formation, suggesting that they may block nuclear targeting of the preintegration complex. Selection of viruses resistant to BI-2 revealed that substitutions at residues A105 and T107 within the capsid (CA) amino-terminal domain (CANTD) conferred high-level resistance to both compounds, implicating CA as the antiviral target. Direct binding of BI-1 and/or BI-2 to CANTD was demonstrated using isothermal titration calorimetry and nuclear magnetic resonance (NMR) chemical shift titration analyses. A high-resolution crystal structure of the BI-1:CANTD complex revealed that the inhibitor bound within a recently identified inhibitor binding pocket (CANTD site 2) between CA helices 4, 5, and 7, on the surface of the CANTD, that also corresponds to the binding site for the host factor CPSF-6. The functional consequences of BI-1 and BI-2 binding differ from previously characterized inhibitors that bind the same site since the BI compounds did not inhibit reverse transcription but stabilized preassembled CA complexes. Hence, this new class of antiviral compounds binds CA and may inhibit viral replication by stabilizing the viral capsid.

Novel inhibitor binding site discovery on HIV-1 capsid N-terminal domain by NMR and X-ray crystallography.

The HIV-1 capsid (CA) protein, a domain of Gag, which participates in formation of both the mature and immature capsid, represents a potential target for anti-viral drug development. Characterization of hits obtained via high-throughput screening of an in vitro capsid assembly assay led to multiple compounds having this potential. We previously presented the characterization of two inhibitor series that bind the N-terminal domain of the capsid (CA(NTD)), at a site located at the bottom of its helical bundle, often referred to as the CAP-1 binding site. In this work we characterize a novel series of benzimidazole hits. Initial optimization of this series led to compounds with improved in vitro assembly and anti-viral activity. Using NMR spectroscopy we found that this series binds to a unique site on CA(NTD), located at the apex of the helical bundle, well removed from previously characterized binding sites for CA inhibitors. 2D (1)H-(15)N HSQC and (19)F NMR showed that binding of the benzimidazoles to this distinct site does not affect the binding of either cyclophilin A (CypA) to the CypA-binding loop or a benzodiazepine-based CA assembly inhibitor to the CAP-1 site. Unfortunately, while compounds of this series achieved promising in vitro assembly and anti-viral effects, they also were found to be quite sensitive to a number of naturally occurring CA(NTD) polymorphisms observed among clinical isolates. Despite the negative impact of this finding for drug development, the discovery of multiple inhibitor binding sites on CA(NTD) shows that capsid assembly is much more complex than previously realized.

Monitoring binding of HIV-1 capsid assembly inhibitors using (19)F ligand-and (15)N protein-based NMR and X-ray crystallography: early hit validation of a benzodiazepine series.

The emergence of resistance to existing classes of antiretroviral drugs underlines the need to find novel human immunodeficiency virus (HIV)-1 targets for drug discovery. The viral capsid protein (CA) represents one such potential target. Recently, a series of benzodiazepine inhibitors was identified via high-throughput screening using an in vitro capsid assembly assay (CAA). Here, we demonstrate how a combination of NMR and X-ray co-crystallography allowed for the rapid characterization of the early hits from this inhibitor series. Ligand-based (19)F NMR was used to confirm inhibitor binding specificity and reversibility as well as to identify the N-terminal domain of the capsid (CA(NTD)) as its molecular target. Protein-based NMR ((1)H and (15)N chemical shift perturbation analysis) identified key residues within the CA(NTD) involved in inhibitor binding, while X-ray co-crystallography confirmed the inhibitor binding site and its binding mode. Based on these results, two conformationally restricted cyclic inhibitors were designed to further validate the possible binding modes. These studies were crucial to early hit confirmation and subsequent lead optimization.

Distinct effects of two HIV-1 capsid assembly inhibitor families that bind the same site within the N-terminal domain of the viral CA protein.

The emergence of resistance to existing classes of antiretroviral drugs necessitates finding new HIV-1 targets for drug discovery. The viral capsid (CA) protein represents one such potential new target. CA is sufficient to form mature HIV-1 capsids in vitro, and extensive structure-function and mutational analyses of CA have shown that the proper assembly, morphology, and stability of the mature capsid core are essential for the infectivity of HIV-1 virions. Here we describe the development of an in vitro capsid assembly assay based on the association of CA-NC subunits on immobilized oligonucleotides. This assay was used to screen a compound library, yielding several different families of compounds that inhibited capsid assembly. Optimization of two chemical series, termed the benzodiazepines (BD) and the benzimidazoles (BM), resulted in compounds with potent antiviral activity against wild-type and drug-resistant HIV-1. Nuclear magnetic resonance (NMR) spectroscopic and X-ray crystallographic analyses showed that both series of inhibitors bound to the N-terminal domain of CA. These inhibitors induce the formation of a pocket that overlaps with the binding site for the previously reported CAP inhibitors but is expanded significantly by these new, more potent CA inhibitors. Virus release and electron microscopic (EM) studies showed that the BD compounds prevented virion release, whereas the BM compounds inhibited the formation of the mature capsid. Passage of virus in the presence of the inhibitors selected for resistance mutations that mapped to highly conserved residues surrounding the inhibitor binding pocket, but also to the C-terminal domain of CA. The resistance mutations selected by the two series differed, consistent with differences in their interactions within the pocket, and most also impaired virus replicative capacity. Resistance mutations had two modes of action, either directly impacting inhibitor binding affinity or apparently increasing the overall stability of the viral capsid without affecting inhibitor binding. These studies demonstrate that CA is a viable antiviral target and demonstrate that inhibitors that bind within the same site on CA can have distinct binding modes and mechanisms of action.

Propagation of guided waves through weak penetrable scatterers.

The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed.

Quantitative predictions for DNA two-dimensional display according to size and nucleotide sequence composition.

2-D DNA display is a simple separation method that provides a fast and economical way of visualizing polymorphism and comparing genomes. The DNA fragments are separated first according to their size by standard gel electrophoresis and then according to their sequence composition using denaturing gradient gel electrophoresis. First developed by Fischer and Lerman (Cell 1979, 16, 191-200), this method has recently been used to distinguish strains within a bacterial species. The genomic restriction fragments are displayed as spots on a 2-D surface. Although most of the relevant physical mechanisms are understood, this technique is mostly empirical and remains essentially qualitative. In view of optimizing this procedure, we combine our understanding of the different physical mechanisms at play to develop a complete numerical model to predict the relative coordinates of the spots as a function of the corresponding DNA sequence and of the experimental conditions. We experimentally validate our model by predicting the outcome of a 2-D display of the lambda phage genome. It thus becomes possible to optimize in silico the experimental parameters, to predict whether specific mutations as well as yet undescribed genetic polymorphisms can be resolved, and to assist in interpreting the experimental data.

Effective molecular diffusion coefficient in a two-phase gel medium.

We derive a mean-field expression for the effective diffusion coefficient of a probe molecule in a two-phase medium consisting of a hydrogel with large gel-free solvent inclusions, in terms of the homogeneous diffusion coefficients in the gel and in the solvent. Upon comparing with exact numerical lattice calculations, we find that our expression provides a remarkably accurate prediction for the effective diffusion coefficient, over a wide range of gel concentration and relative volume fraction of the two phases. Moreover, we extend our model to handle spatial variations of viscosity, thereby allowing us to treat cases where the solvent viscosity itself is inhomogeneous. This work provides robust grounds for the modeling and design of multiphase systems for specific applications, e.g., hydrogels as novel food agents or efficient drug-delivery platforms.