A semi-implicit lagrangian scheme for 3D shallow water flow with a two-layer turbulence model

A semi-implicit Lagrangian finite difference scheme for 3D shallow water flow has been developed to include an eddy viscosity model for turbulent mixing in the vertical direction. The α-co-ordinate system for the vertical direction has been introduced to give accurate definition of bed and surface boundary conditions. The simple two-layer mixing length model for rough surfaces is used with the standard assumption that the shear stress across the wall region at a given horizontal location is constant. The bed condition is thus defined only by its roughness height (avoiding the need for a friction formula relating to depth-averaged flow, e.g. Chezy, used previously). The method is shown to be efficient and stable with an explicit Lagrangian formulation for convective terms and terms for surface elevation and vertical mixing handled implicitly. The method is applied to current flow around a circular island with gently sloping sides which produce periodic recirculation zones (vortex shedding). Comparisons are made with experimental measurements of velocity using laser Doppler anemometry (time histories at specific points) and surface particle-tracking velocimetry.     

Computing Numerically with Functions Instead of Numbers

Symbolic computation with functions of a real variable suffers from combinatorial explosion of memory and computation time. The alternative chebfun system for such computations is described, based on Chebyshev expansions and barycentric interpolation. For Richard Brent on his 60th birthday     

Pseudozeros of polynomials and pseudospectra of companion matrices

Summary. It is well known that the zeros of a polynomial are equal to the eigenvalues of the associated companion matrix . In this paper we take a geometric view of the conditioning of these two problems and of the stability of algorithms for polynomial zerofinding. The is the set of zeros of all polynomials obtained by coefficientwise perturbations of of size ; this is a subset of the complex plane considered earlier by Mosier, and is bounded by a certain generalized lemniscate. The is another subset of defined as the set of eigenvalues of matrices with ; it is bounded by a level curve of the resolvent of $A$. We find that if $A$ is first balanced in the usual EISPACK sense, then and are usually quite close to one another. It follows that the Matlab ROOTS algorithm of balancing the companion matrix, then computing its eigenvalues, is a stable algorithm for polynomial zerofinding. Experimental comparisons with the Jenkins-Traub (IMSL) and Madsen-Reid (Harwell) Fortran codes confirm that these three algorithms have roughly similar stability properties. Received June 15, 1993     

Plane wave source with minimal harmonic distortion for investigating nonlinear acoustic properties

The objective of this investigation is to introduce and validate a practical ultrasound source to be used in the investigation of the nonlinear material properties of liquids and soft tissues studied in vitro. Methods based on the progressive distortion of finite amplitude ultrasonic waves in the low megahertz frequency range are most easily implemented under the assumption of plane wave propagation. However, achieving an approximately planar ultrasonic field over substantial propagation distances can be challenging. Furthermore, undesired harmonic distortion of the ultrasonic field prior to insonification of the specified region of interest represents another serious limitation. This paper introduces an approach based on the use of the ultrasonic field emanating from a stainless-steel delay line. Both simulation and direct experimental measurement demonstrate that such a field exhibits relatively planar wave fronts to a good approximation (such that a 3-mm-diam receiver would be exposed to no more than 3 dB of loss across its face) and is free from the significant harmonic distortion that would occur in a conventional water path.     

Beam-helicity asymmetry in photon and pion electroproduction in the Δ(1232)-resonance region at Q2 = 0.35(GeV/c)2

The beam-helicity asymmetry has been measured simultaneously for the reactions p→epγ and p→epπ ⁰ in the Δ(1232)-resonance region at Q ² = 0.35(GeV/c)². The experiment was performed at MAMI with a longitudinally polarized beam and an out-of-plane detection of the proton. The results are compared with calculations based on dispersion relations for virtual Compton scattering and with the MAID model for pion electroproduction. There is an overall good agreement between experiment and theoretical calculations. The remaining discrepancies may be ascribed to an imperfect parametrization of some γ ^(*) N→πN multipoles, mainly contributing to the non-resonant background. The beam-helicity asymmetry in both channels (γ and π ⁰) shows a good sensitivity to these multipoles and should allow future improvement in their parametrization.     

Chiral Perylene Diimides: Building Blocks for Ionic Self‐Assembly

A chiral perylene diimide building block has been prepared based on an amine derivative of the amino acid L ‐phenylalanine. Detailed studies were carried out into the self‐assembly behaviour of the material in solution and the solid state using UV/Vis, circular dichroism (CD) and fluorescence spectroscopy. For the charged building block BTPPP, the molecular chirality of the side chains is translated into the chiral supramolecular structure in the form of right‐handed helical aggregates in aqueous solution. Temperature‐dependent UV/Vis studies of BTPPP in aqueous solution showed that the self‐assembly behaviour of this dye can be well described by an isodesmic model in which aggregation occurs to generate short stacks in a reversible manner. Wide‐angle X‐ray diffraction studies (WXRD) revealed that this material self‐organises into aggregates with π–π stacking distances typical for π‐conjugated materials. TEM investigations revealed the formation of self‐assembled structures of low order and with no expression of chirality evident. Differential scanning calorimetry (DSC) and polarised optical microscopy (POM) were used to investigate the mesophase properties. Optical textures representative of columnar liquid–crystalline phases were observed for solvent‐annealed samples of BTPPP. The high solubility, tunable self‐assembly and chiral ordering of these materials demonstrate their potential as new molecular building blocks for use in the construction of chiro‐optical structures and devices.     

Structural insight into the inactivation of <Emphasis Type="Italic">Mycobacterium tuberculosis</Emphasis> non-classical transpeptidase Ldt<Subscript>Mt2</Subscript> by biapenem and tebipenem

Background

The carbapenem subclass of β-lactams is among the most potent antibiotics available today. Emerging evidence shows that, unlike other subclasses of β-lactams, carbapenems bind to and inhibit non-classical transpeptidases (L,D-transpeptidases) that generate 3 → 3 linkages in bacterial peptidoglycan. The carbapenems biapenem and tebipenem exhibit therapeutically valuable potencies against Mycobacterium tuberculosis (Mtb).

Results

Here, we report the X-ray crystal structures of Mtb L,D-transpeptidase-2 (Ldt_Mt2) complexed with biapenem or tebipenem. Despite significant variations in carbapenem sulfur side chains, biapenem and tebipenem ultimately form an identical adduct that docks to the outer cavity of Ldt_Mt2. We propose that this common adduct is an enzyme catalyzed decomposition of the carbapenem adduct by a mechanism similar to S-conjugate elimination by β-lyases.

Conclusion

The results presented here demonstrate biapenem and tebipenem bind to the outer cavity of Ldt_Mt2, covalently inactivate the enzyme, and subsequently degrade via an S-conjugate elimination mechanism. We discuss structure based drug design based on the findings and propose that the S-conjugate elimination can be leveraged to design novel agents to deliver and locally release antimicrobial factors to act synergistically with the carbapenem carrier.

     

"Inosaminoacids": novel inositol-amino acid hybrid structures accessed by microbial arene oxidation

Microbial 1,2-dihydroxylation of sodium benzoate permits the rapid construction of novel inositol-amino acid hybrid structures. Both β- and γ-amino acids are accessible by means of an acylnitroso Diels-Alder cycloaddition.