Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

ϱ → 4π in chirally symmetric models

The decays rho0 → 2π+2π− and rho0 → 2π0π+π− are studied using various effective Lagrangians for π and rho (and in some case a1) mesons, all of which respect the approximate chiral symmetry of the strong interaction. Partial widths of the order of 1 keV or less are found in all cases. These are an order of magnitude smaller than recent predictions based on non-chiral models.

Meson properties in an extended nonlocal NJL model

A nonlocal version of the NJL model is investigated. It is based on a separable quark-quark interaction, as suggested by the instanton liquid picture of the QCD vacuum. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Features of the continuation of amplitudes from Euclidean space to Minkowski energies are discussed. These features lead to restrictions on the model parameters as well as on the range of applicability of the model. Conserved currents are constructed, and their consistency with various Ward identities is demonstrated. In particular, the Gell-Mann-Oakes-Renner relation is derived both in the ladder approximation and at meson loop level. The importance of maintaining chiral symmetry in the calculations is stressed throughout. Calculations with the model are performed to all orders in momentum. Meson masses are determined, along with their strong and electromagnetic decay amplitudes. Also calculated are the electromagnetic form factor of the pion and form factors associated with the processes gamma gamma* --> pi0 and omega --> pi0 gamma*. The results are found to lead to a satisfactory phenomenology and demonstrate a possible dynamical origin for vector-meson dominance. In addition, the results produced at meson loop level validate the use of 1/Nc as an expansion parameter and indicate that a light and broad scalar state is inherent in models of the NJL type.

Direct visualisation of lipid bilayer cubic phases using Atomic Force Microscopy

Inverse bicontinuous cubic (Q(II)) phases are nanostructured materials formed by lipid self-assembly. We have successfully imaged thin films of hydrated Q(II) phases from two different systems using AFM. The images show periodic arrays of water channels with spacing and symmetry consistent with published SAXS data on the bulk materials.

Non-stoichiometric oxide and metal interfaces and reactions

We have employed a combination of experimental surface science techniques and density functional calculations to study the reduction of TiO2(110) surfaces through the doping with submonolayer transition metals. We concentrate on the role of Ti adatoms in self doping of rutile and contrast the behaviour to that of Cr. DFT+U calculations enable identification of probable adsorption structures and their spectroscopic characteristics. Adsorption of both metals leads to a broken symmetry and an asymmetric charge transfer localised around the defect site of a mixed localised/delocalised character. Charge transfer creates defect states with Ti 3d character in the band gap at similar to 1-eV binding energy. Cr adsorption, however, leads to a very large shift in the valence-band edge to higher binding energy and the creation of Cr 3d states at 2.8-eV binding energy. Low-temperature oxidation lifts the Ti-derived band-gap states and modifies the intensity of the Cr features, indicative of a change of oxidation state from Cr3+ to Cr4+. Higher temperature processing leads to a loss of Cr from the surface region, indicative of its substitution into the bulk.

Structure of adsorbed organometallic rhodium: model single atom catalysts

We have determined the structure of a complex rhodium carbonyl chloride [Rh(CO)(2)Cl] molecule adsorbed on the TiO2 (110) surface by the normal incidence x-ray standing wave technique. The data show that the technique is applicable to reducible oxide systems and that the dominant adsorbed species is undissociated with Rh binding atop bridging oxygen and to the Cl found close to the fivefold coordinated Ti ions in the surface. A minority geminal dicarboryl species, where Rh-Cl bond scission has occurred, is found bridging the bridging oxygen ions forming a high-symmetry site.

A geometric approach to generalized Stokes conjectures

We consider the Stokes conjecture concerning the shape of extreme two-dimensional water waves. By new geometric methods including a nonlinear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions.

Guanine specific binding at a DNA junction formed by d[CG(5-BrU)ACG]2 with a topoisomerase poison in the presence of Co2+Ions†,‡

The structure of the duplex d[CG(5-BrU)ACG]2 bound to 9-bromophenazine-4-carboxamide has been solved through MAD phasing at 2.0 Å resolution. It shows an unexpected and previously unreported intercalation cavity stabilized by the drug and novel binding modes of Co2+ ions at certain guanine N7 sites. For the intercalation cavity the terminal cytosine is rotated to pair with the guanine of a symmetry-related duplex to create a pseudo-Holliday junction geometry, with two such cavities linked through the minor groove interactions of the N2/N3 guanine sites at an angle of 40°, creating a quadruplex-like structure. The mode of binding of the drug is shown to be disordered, with the major conformations showing the side chain bound to the N7 position of adjacent guanines. The other end of the duplex exhibits a terminal base fraying in the presence of Co2+ ions linking symmetry-related guanines, causing the helices to intertwine through the minor groove. The stabilization of the structure by the intercalating drug shows that this class of compound may bind to DNA junctions as well as duplex DNA or to strand-nicked DNA (‘hemi-intercalated'), as in the cleavable complex. This suggests a structural basis for the dual poisoning of topoisomerase I and II enzymes by this family of drugs.

The anions [(ZrOH(CO3)3)2]6− and [(ZrOH(C2O4)3)2]6−: single crystal X-ray diffraction studies of the complexes guanidinium zirconium carbonate [(C(NH2)3)3ZrOH(CO3)3·H2O]2 and sodium zirconium oxalate Na6(ZrOH(C2O4)3)2·7H2O

The complex [(C(NH2)3)3ZrOH(CO3)3·H2O]2 (A) has been shown by means of a single crystal X-ray diffraction study to contain [C(NH2)3]+ cations and dimeric anions of formulation [(ZrOH(CO3)3)2]6−. The anion is centrosymmetric with each metal being bonded to two bridging OH groups and three chelating CO2−3 ions. The Zr atoms are thus eight coordinate with a dodecahedral environments. The ZrO distances formed by the bridgng OH groups are shorter than those formed through zirconiu carbonate interactions. The non-bonded Zr…Zr distance is 3.47(2) Å. An infrared spectroscopic investigation of A provides data which support the findings of the crystallographic study. Likewise the complex Na6(ZrOH(CO2O4)3)2·7H2O (B) contains the anion [(ZrOH(C2O4)3)2]6−. This anion is structurally related to the anion in A as each Zr atom has an eight-coordinate dodecahedral environment being bonded to two bridging OH groups and three chelating oxalate ligands, but has no imposed crysallographic symmetry. The Zr…Zr non-bonded distance is 3.50(1) Å. The OZrO bridge angles are 69.7(4)° and A and 67.4(3)° in B.

Simultaneous bridge-localized and mixed-valence character in diruthenium radical cations featuring diethynylaromatic bridging ligands

A series of bimetallic ruthenium complexes [{Ru(dppe)Cp*}2(μ-C≡CArC≡C)] featuring diethynylaromatic bridging ligands (Ar = 1,4-phenylene, 1,4-naphthylene, 9,10-anthrylene) have been prepared and some representative molecular structures determined. A combination of UV–vis–NIR and IR spectroelectrochemical methods and density functional theory (DFT) have been used to demonstrate that one-electron oxidation of compounds [{Ru(dppe)Cp*}2(μ-C≡CArC≡C)](HC≡CArC≡CH = 1,4-diethynylbenzene; 1,4-diethynyl-2,5-dimethoxybenzene; 1,4-diethynylnaphthalene; 9,10-diethynylanthracene) yields solutions containing radical cations that exhibit characteristics of both oxidation of the diethynylaromatic portion of the bridge, and a mixed-valence state. The simultaneous population of bridge-oxidized and mixed-valence states is likely related to a number of factors, including orientation of the plane of the aromatic portion of the bridging ligand with respect to the metal d-orbitals of appropriate π-symmetry.

Coverage-dependent molecular tilt of carbon monoxide chemisorbed on Pt{110}: A combined LEED and DFT structural analysis

The adsorption of carbon monoxide on the Pt{110} surface at coverages of 0.5 ML and 1.0 ML was investigated using quantitative low-energy electron diffraction (LEED IV) and density-functional theory (DFT). At 0.5 ML CO lifts the reconstruction of the clean surface but does not form an ordered overlayer. At the saturation coverage, 1.0 ML, a well-ordered p(2×1) superstructure with glide line symmetry is formed. It was confirmed that the CO molecules adsorb on top of the Pt atoms in the top-most substrate layer with the molecular axes tilted by ±22° with respect to the surface normal in alternating directions away from the close packed rows of Pt atoms. This is accompanied by significant lateral shifts of 0.55 Å away from the atop sites in the same direction as the tilt. The top-most substrate layer relaxes inwards by −4% with respect to the bulk-terminated atom positions, while the consecutive layers only show minor relaxations. Despite the lack of long-range order in the 0.5 ML CO layer it was possible to determine key structural parameters by LEED IV using only the intensities of the integer-order spots. At this coverage CO also adsorbs on atop sites with the molecular axis closer to the surface normal (b10°). The average substrate relaxations in each layer are similar for both coverages and consistent with DFT calculations performed for a variety of ordered structures with coverages of 1.0 ML and 0.5 ML.

Eliminating the small-angle component of the scattering calculated for models

A straightforward procedure (assuming spherical symmetry) is described, which enables the unwanted small-angle component of the scattering for a finite model to be calculated. The method may be applied to models of any shape or size. It is illustrated by means of a single polymer chain.

Complete Experimental Structure Determination of the p(3x2)pg Phase of Glycine on Cu{110}

We present a quantitative low energy electron diffraction (LEED) surface-crystallograpic study of the complete adsorption geometry of glycine adsorbed on Cu{110} in the ordered p(3×2) phase. The glycine molecules form bonds to the surface through the N atoms of the amino group and the two O atoms of the de-protonated carboxylate group, each with separate Cu atoms such that every Cu atom in the first layer is involved in a bond. Laterally, N atoms are nearest to the atop site (displacement 0.41 Å). The O atoms are asymmetrically displaced from the atop site by 0.54 Å and 1.18 Å with two very different O-Cu bond lengths of 1.93 Å and 2.18 Å. The atom positions of the upper-most Cu layers show small relaxations within 0.07 Å of the bulk-truncated surface geometry. The unit cell of the adsorbate layer consists of two glycine molecules, which are related by a glide-line symmetry operation. This study clearly shows that a significant coverage of adsorbate structures without this glide-line symmetry must be rejected, both on the grounds of the energy dependence of the spot intensities (LEED-IV curves) and of systematic absences in the LEED pattern.

A simple analysis of thermodynamic properties for classical plasmas: I. theory

By eliminating the short range negative divergence of the Debye–Hückel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.