A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

The occipital lateral plate mesoderm is a novel source for vertebrate neck musculature

In vertebrates, body musculature originates from somites, whereas head muscles originate from the cranial mesoderm. Neck muscles are located in the transition between these regions. We show that the chick occipital lateral plate mesoderm has myogenic capacity and gives rise to large muscles located in the neck and thorax. We present molecular and genetic evidence to show that these muscles not only have a unique origin, but additionally display a distinct temporal development, forming later than any other muscle group described to date. We further report that these muscles, found in the body of the animal, develop like head musculature rather than deploying the programme used by the trunk muscles. Using mouse genetics we reveal that these muscles are formed in trunk muscle mutants but are absent in head muscle mutants. In concordance with this conclusion, their connective tissue is neural crest in origin. Finally, we provide evidence that the mechanism by which these neck muscles develop is conserved in vertebrates.

The influence of the carbon surface chemical composition on Dubinin-Astakhov equation parameters calculated from SF(6) adsorption data-grand canonical Monte Carlo simulation

Using grand canonical Monte Carlo simulation we show, for the first time, the influence of the carbon porosity and surface oxidation on the parameters of the Dubinin-Astakhov (DA) adsorption isotherm equation. We conclude that upon carbon surface oxidation, the adsorption decreases for all carbons studied. Moreover, the parameters of the DA model depend on the number of surface oxygen groups. That is why in the case of carbons containing surface polar groups, SF(6) adsorption isotherm data cannot be used for characterization of the porosity.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

A 96-well plate fluorescence assay for assessment of cellular permeability and active efflux in Salmonella enterica serovar Typhimurium and Escherichia coli

Multiply antibiotic-resistant (MAR) mutants of Escherichia coli and Salmonella enterica are characterized by reduced susceptibility to several unrelated antibiotics, biocides and other xenobiotics. Porin loss and/or active efflux have been identified as a key mechanisms of MAR. A single rapid test was developed for MAR. The intracellular accumulation of the fluorescent probe Hoechst (H) 33342 (bisbenzimide) by MAR mutants and those with defined disruptions in efflux pump and porin genes was determined in 96-well plate format. The accumulation of H33342 was significantly (P < 0.0001) reduced in MAR mutants of S. enterica serovar Typhimurium (n = 4) and E. coli (n = 3) by 41 +/- 8% and 17.3 +/- 7.2%, respectively, compared with their parental strains, which was reversed by the transmembrane proton gradient-collapsing agent carbonyl cyanide-m-chlorophenyl hydrazone (CCCP) and the efflux pump inhibitor phenylalanine-arginine-beta-naphthylamide (PA beta N). The accumulation of H33342 was significantly reduced in mutants of Salmonella Typhimurium with defined disruptions in genes encoding the porins OmpC, OmpF, OmpX and OmpW, but increased in those with disruptions in efflux pump components TolC, AcrB and AcrF. Reduced accumulation of H33342 in three other MAR mutants of Salmonella Typhimurium correlated with the expression of porin and efflux pump proteins. The intracellular accumulation of H33342 provided a sensitive and specific test for MAR that is cheap and relatively rapid. Differential sensitivity to CCCP and PA beta N provided a further means to phenotypically identify MAR mutants and the role of active efflux in each strain.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

A modified rapid enzymatic microtiter plate assay for the quantification of intracellular γ-aminobutyric acid and succinate semialdehyde in bacterial cells

The GABase assay is widely used to rapidly and accurately quantify levels of extracellular γ-aminobutyric acid (GABA). Here we demonstrate a modification of this assay that enables quantification of intracellular GABA in bacterial cells. Cells are lysed by boiling and ethanolamine-O-sulphate, a GABA transaminase inhibitor is used to distinguish between GABA and succinate semialdehyde.

Investigation of flux in flat-plate modules for membrane distillation

A theoretical model for predicting the behaviour of membrane distillation by incorporating mass and heat transfer equations has been used to find permeate fluxes, and has been validated experimentally. The model accurately predicts mass and heat transfer. The main work studied the effect of module design using a flat-plate module in laminar flow conditions. Areas of investigation included the use of channels across the membrane surface, decreasing the available membrane surface area, and widening the inlet and outlet channels. The work showed that widening the channels increased the flux. Increased flux was also obtained by the use of channels on the permeate side, though not on the feed side.

Balitskiǐ-Fadin-Kuraev-Lipatov equation versus data from DESY HERA

The BFKL equation and the kT-factorization theorem are used to obtain predictions for F2 in the small Bjo/rken-x region over a wide range of Q2. The dependence on the parameters, especially on those concerning the infrared region, is discussed. After a background fit to recent experimental data obtained at DESY HERA and at Fermilab (E665 experiment) we find that the predicted, almost Q2 independent BFKL slope λ≳0.5 appears to be too steep at lower Q2 values. Thus there seems to be a chance that future HERA data can distinguish between pure BFKL and conventional field theoretic renormalization group approaches. © 1995 The American Physical Society.