Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Salt marsh morphodynamics: An investigation of tidal flows and marsh channel equilibrium

Although numerous field studies have evaluated flow and transport processes in salt marsh channels, the overall role of channels in delivering and removing material from salt marsh platforms is still poorly characterised. In this paper, we consider this issue based on a numerical hydrodynamic model for a prototype marsh system and on a field survey of the cross-sectional geometry of a marsh channel network. Results of the numerical simulations indicate that the channel transfers approximately three times the volume of water that would be estimated from mass balance considerations alone. Marsh platform roughness exerts a significant influence on the partitioning of discharge between the channel and the marsh platform edge, alters flow patterns on the marsh platform due to its effects on channel-to-platform transfer and also controls the timing of peak discharge relative to marsh-edge overtopping. Although peak channel discharges and velocities are associated with the flood tide and marsh inundation, a larger volume of water is transferred by the channel during ebb flows, a portion of which transfer takes place after the tidal height is below the marsh platform. Detailed surveys of the marsh channels crossing a series of transects at Upper Stiffkey Marsh, north Norfolk, England, show that the total channel cross-sectional area increases linearly with catchment area in the inner part of the marsh, which is consistent with the increase in shoreward tidal prism removed by the channels. Toward the marsh edge, however, a deficit in the total cross-sectional area develops, suggesting that discharge partitioning between the marsh channels and the marsh platform edge may also be expressed in the morphology of marsh channel systems.

The harmonic force field and rz structure of HNCO

The presently available microwave, millimeter wave, and far-infrared data of five isotopic species of isocyanic acid, namely, HNCO, H15NCO, HN13CO, HNC18O, and DNCO, have been used to obtain improved values of the ground-state rotational constants, the five quartic distortion constants, and some higher-order distortion constants in the Ir S reduced Hamiltonian of Watson. The appropriate planarity relation among the quartic centrifugal distortion constants has been imposed in the fitting procedure. The general harmonic force field of isocyanic acid has been determined using all existing data, and assuming a trans bent equilibrium geometry of the molecule with an NCO angle of 170°. Finally an rz structure has been obtained using the Az, Bz, and Cz rotational constants of five isotopic species. The bending of the NCO chain is found to be 8° in the trans configuration.

Physical properties of Hydropsyche siltalai (Trichoptera) net silk

Most suspension-feeding trichopterans spin a fine-silk capture net that is used to remove suspended matter from the water. The efficiency of these nets has previously been studied by considering the geometry of the web structure but the material from which the nets is constructed has received little attention. We report measurements of the tensile strength and extensibility of net silk from Hydropsyche siltalai. These measurements place caddisfly silk as one of the weakest natural silks so far reported, with a mean tensile strength of 221 +/- 22 megaNewtons (MN)/m(2). We also show that H. siltalai silk can more than double in length before catastrophic breakage, and that the silk is at least 2 orders of magnitude stronger than the maximum force estimated to act upon it in situ. Possible reasons for this disparity include constraints of evolutionary history and safety margins to prevent net failure or performance reduction.

Synthesis, crystal structure and hydrolysis of a dinuclear copper(II) complex constructed by N2O donor Schiff base and 4,4 '-bipyridine: discrete supra-molecular ensembles vs. oligomers

The tridentate Schiff base ligand, 7-amino-4-methyl-5-aza-3-hepten-2-one (HAMAH), prepared by the mono-condensation of 1,2diaminoethane and acetylacetone, reacts with Cu(BF4)(2) center dot 6H(2)O to produce initially a dinuclear Cu(II) complex, [{Cu(AMAH)}(2) (mu-4,4'-bipyJ](BF4)(2) (1) which undergoes hydrolysis in the reaction mixture and finally produces a linear polymeric chain compound, [Cu(acac)(2)(mu-4,4'-bipy)](n) (2). The geometry around the copper atom in compound 1 is distorted square planar while that in compound 2 is essentially an elongated octahedron. On the other hand, the ligand HAMAH reacts with Cu(ClO4)(2) center dot 6H(2)O to yield a polymeric zigzag chain, [{Cu(acac)(CH3OH)(mu-4,4'-bipy)}(ClO4)](n) (3). The geometry of the copper atom in 3 is square pyramidal with the two bipyridine molecules in the cis equatorial positions. All three complexes have been characterized by elemental analysis, IR and UV-Vis spectroscopy and single crystal X-ray diffraction studies. A probable explanation for the different size and shape of the reported polynuclear complexes formed by copper(II) and 4,4'-bipyridine has been put forward by taking into account the denticity and crystal field strength of the blocking ligand as well as the Jahn-Teller effect in copper(II). (c) 2007 Elsevier Ltd. All rights reserved.

Copper(II) complexes of mono-anionic glutamate: anionic influence in the variations of molecular and supramolecular structures

Three new polynuclear copper(II) complexes of singly deprotonated L-glutamic acid (L-glu), {[Cu(bipy)(2)][Cu(bipy)(L-glu)H2O](2)(BF4)(4)center dot(H2O)(3)}(n) (1), {[Cu(bipy)(L-glu)H2O][Cu(bipy)(L-glu)(ClO4)]( ClO4)center dot(H2O)(2)}(n) ((2)) and [Cu(phen)(L-glu)H2O](2)(NO3)(2)center dot(H2O)(4) (3) (bipy = 2,2-bipyridine, phen = 1,10-phenanthroline), were synthesized in acidic pH (ca. 2.5) and characterized structurally. In all the complexes, L-glutamic acid acts as a bidentate chelating ligand, leaving the protonated carboxylic acid free. Both in 1 and 2, two different types of species [Cu(bipy)(2)](BF4)(2) and [Cu(bipy)(L-glu)H2O] BF4 for 1 and [Cu(bipy)(L-glu)H2O]ClO4 and [Cu(bipy)(L-glu)(ClO4)] for 2 coexist in the solid state. In complex 1, the [C( bipy)(L-glu)H2O]+ units are joined together by syn-anti carboxylate bridges to form an enantiopure (M) helical chain and the [Cu(bipy)(2)](2+) presents a very rare example of the four-coordinate distorted tetrahedral geometry of Cu(II). In complex 2, the [Cu(bipy)(L gluClO(4))] units are joined together by weakly coordinating perchlorate ions to form a 1D polymeric chain while the [Cu(bipy)(L-glu)H2O]+ units remain as mononuclear species. The different coordinating ability of the two counter anions along with their involvement in the H-bonding network seems likely to be responsible for the difference in the final polymeric structures in the two compounds. Variable-temperature (2-300 K) magnetic susceptibility measurements show negligible coupling for both the complexes. The structure of 3 consists of two independent monomeric [Cu(phen)(L-glu)H2O]+ cations, two nitrate anions and four water molecules. The copper atom occupies a five-coordinate square pyramidal environment with a water molecule in the axial position.

A surface and catalytic study of heterogenised Os-3(CO)(12) species in MCM-41 structures

Immobilised Os species prepared via chemical vapour deposition (CVD) of Os-3(CO)(12) onto MCM-41 are active and selective catalysts for the dihydroxylation of trans-stilbene in acetone and water, using N-methylmorpholine N-oxide as the oxidant. A detailed temperature programmed decomposition study of the solids enables to identify the active sites as Os-x(CO)(y) surface species. The initial loading of the MCM-41 with the trinuclear precursor, as well as the temperature of the post-synthesis oxidising treatment, are found to have a significant impact on the structure/geometry of the resulting surface species, and thus their catalytic properties. We show how it is also affected by the confined environment of the MCM-41 mesopores and especially the curvature of the 30 Angstrom diameter channels. Finally, a careful study of the catalytic properties of the materials together with a study of the reactivity of the reaction products under similar conditions enable to suggest a mechanism involving the reaction of the oxidant with the osmium carbonyl surface species to form the catalytically active Os-oxo sites, and the formation of an osmoate-type species (through adsorption of the alkene onto the Os-oxo site) which subsequently reacts with the solvent to produce the diol. (C) 2003 Elsevier B.V. All rights reserved.

The adsorption and stability of sulfur containing amino acids on Cu{531}

The adsorption of L-CySteine and L-methionine amino acids on a chiral Cu{5 3 1} surface was investigated with high resolution X-ray photoelectron spectroscopy (XPS) and carbon K-edge near edge X-ray absorption fine structure (NEXAFS) Spectroscopy using synchrotron radiation. XPS shows that at 300 K L-cysteine adsorbs through two oxygen, a nitrogen and a sulfur atom, in a four point 'quadrangular footprint', whereas L-methionine adsorbs through only two oxygen and a nitrogen atom in a 'triangular footprint'. NEWS was used to clarify the adsorption geometry of both molecules, which suggests a binding orientation to the top layer and second layer atoms in two different orientations associated with adsorption sites on {1 1 0} and {3 1 1} microfacets; of the Cu{5 3 1} surface. (C) 2009 Elsevier B.V. All rights reserved.

Consequences of N,C,N '- and C,N,N '-coordination modes on electronic and photophysical properties of cyclometalated aryl ruthenium(II) complexes

The effects of isoelectronic replacement of a neutral nitrogen donor atom by an anionic carbon atom in terpyridine ruthenium(II) complexes on the electronic and photophysical properties of the resulting N,C,N'- and C,N,N'-cyclometalated aryl ruthenium(II) complexes were investigated. To this end, a series of complexes was prepared either with ligands containing exclusively nitrogen donor atoms, that is, [Ru(R-1-tpy)(R-2-tpy)](2+) (R-1, R-2 = H, CO2Et), or bearing either one N,C,N'- or C,N,N'-cyclometalated ligand and one tpy ligand, that is, [Ru(R-1-(NCN)-C-Lambda-N-Lambda)(R-2-tpy)](+) and [Ru(R-1-(CNN)-N-Lambda-N-Lambda)(R-2-tpy)](+), respectively. Single-crystal X-ray structure determinations showed that cyclometalation does not significantly alter the overall geometry of the complexes but does change the bond lengths around the ruthenium(II) center, especially the nitrogen-to-ruthenium bond length trans to the carbanion. Substitution of either of the ligands with electron-withdrawing ester functionalities fine-tuned the electronic properties and resulted in the presence of an IR probe. Using trends obtained from redox potentials, emission energies, IR spectroelectrochemical responses, and the character of the lowest unoccupied molecular orbitals from DFT studies, it is shown that the first reduction process and luminescence are associated with the ester-substituted C,N,N'-cyclometalated ligand in [Ru(EtO2C-(CNN)-N-Lambda-N-Lambda)(tpy)](+). Cyclometalation in an N,C,N'-bonding motif changed the energetic order of the ruthenium d(zx), d(yz), and d(xy) orbitals. The red-shifted absorption in the N,C,N'-cyclometalated complexes is assigned to MLCT transitions to the tpy ligand. The red shift observed upon introduction of the ester moiety is associated with an increase in intensity of low-energy transitions, rather than a red shift of the main transition. Cyclometalation in the C,N,N'-binding motif also red-shifts the absorption, but the corresponding transition is associated with both ligand types. Luminescence of the cyclometalated complexes is relatively independent of the mode of cyclometalation, obeying the energy gap law within each individual series.

Cutting, by 'pressing and slicing,' of thin floppy slices of materials illustrated by experiments on cheddar cheese and salami

Why it is easier to cut with even the sharpest knife when 'pressing down and sliding' than when merely 'pressing down alone' is explained. A variety of cases of cutting where the blade and workpiece have different relative motions is analysed and it is shown that the greater the 'slice/push ratio' xi given by ( blade speed parallel to the cutting edge/blade speed perpendicular to the cutting edge), the lower the cutting forces. However, friction limits the reductions attainable at the highest.. The analysis is applied to the geometry of a wheel cutting device (delicatessan slicer) and experiments with a cheddar cheese and a salami using such an instrumented device confirm the general predictions. (C) 2004 Kluwer Academic Publishers.

Hydrogen bond-induced pair formation of glycine on the chiral Cu{531} surface

Enantio-specific interactions on intrinsically chiral or chirally modified surfaces can be identified experimentally via comparison of the adsorption geometries of similar nonchiral and chiral molecules. Information about the effects of substrate-related and in interactions on the adsorption geometry of glycine, the only natural nonchiral amino acid, is therefore important for identifying enantio-specific interactions of larger chiral amino acids. We have studied the long- and short-range adsorption geometry and bonding properties of glycine on the intrinsically chiral Cu{531} surface with low-energy electron diffraction, near-edge X-ray absorption One structure spectroscopy, X-ray photoelectron spectroscopy, and temperature-programmed desorption. For coverages between 0.15 and 0.33 ML (saturated chemisorbed layer) and temperatures between 300 and 430 K, glycine molecules adsorb in two different azimuthal orientations, which are associated with adsorption sites on the {110} and {311} microfacets of Cu{531}. Both types of adsorption sites allow a triangular footprint with surface bonds through the two oxygen atoms and the nitrogen atom. The occupation of the two adsorption sites is equal for all coverages, which can be explained by pair formation due to similar site-specific adsorption energies and the possibility of forming hydrogen bonds between molecules on adjacent {110} and {311} sites. This is not the ease for alanine and points toward higher site specificity in the case of alanine, which is eventually responsible for the enantiomeric differences observed for the alanine system.

Processing system accepting exceptional numbers

A processing system comprises: input means arranged to receive at least one input group of bits representing at least one respective input number; output means arranged to output at least one output group of bits representing at least one respective output number; and processing means arranged to perform an operation on the at least one input group of bits to produce the at least one output group of bits such that the at least one output number is related to the at least one input number by a mathematical operation; and wherein each of the numbers can be any of a set of numbers which includes a series of numbers, positive infinity, negative infinity and nullity.

Global and local expression of chirality in serine on the Cu{110} surface

Establishing a molecular-level understanding of enantioselectivity and chiral resolution at the organic−inorganic interfaces is a key challenge in the field of heterogeneous catalysis. As a model system, we investigate the adsorption geometry of serine on Cu{110} using a combination of low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. The chirality of enantiopure chemisorbed layers, where serine is in its deprotonated (anionic) state, is expressed at three levels: (i) the molecules form dimers whose orientation with respect to the substrate depends on the molecular chirality, (ii) dimers of l- and d-enantiomers aggregate into superstructures with chiral (−1 2; 4 0) lattices, respectively, which are mirror images of each other, and (iii) small islands have elongated shapes with the dominant direction depending on the chirality of the molecules. Dimer and superlattice formation can be explained in terms of intra- and interdimer bonds involving carboxylate, amino, and β−OH groups. The stability of the layers increases with the size of ordered islands. In racemic mixtures, we observe chiral resolution into small ordered enantiopure islands, which appears to be driven by the formation of homochiral dimer subunits and the directionality of interdimer hydrogen bonds. These islands show the same enantiospecific elongated shapes those as in low-coverage enantiopure layers.

A refined LEED analysis of water on Ru{0001}: an experimental test of the partial dissociation model

Despite a number of earlier studies which seemed to confirm molecular adsorption of water on close-packed surfaces of late transition metals, new controversy has arisen over a recent theoretical work by Feibelman, according to which partial dissociation occurs on the Ru{0001} surface leading to a mixed (H2O + OH + H) superstructure. Here, we present a refined LEED-IV analysis of the (root3 x root3)R30degrees-D2O-Ru{0001} structure, testing explicitly this new model by Feibelman. Our results favour the model proposed earlier by Held and Menzel assuming intact water molecules with almost coplanar oxygen atoms and out-of-plane hydrogen atoms atop the slightly higher oxygen atoms. The partially dissociated model with an almost identical arrangement of oxygen atoms can, however, not unambiguously be excluded, especially when the single hydrogen atoms are not present in the surface unit cell. In contrast to the earlier LEED-IV analysis, we can, however, clearly exclude a buckled geometry of oxygen atoms.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.