A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

4,4 '-Dipyridyl-N,N '-dioxide complexes of metal-thiocyanate/selenocyanate: pi-stacked molecular rods as three-dimensional support for two-dimensional polymeric sheets and intra/interchain S center dot center dot center dot S interaction dependent architecture of the R-2(2)(8) synthon driven assembly of one-dimensional polymeric chains

Three supramolecular complexes of Co(II) using SCN-/SeCN- in combination with 4,4'-dipyridyl-N,N'-dioxide (dpyo), i.e., {[Co(SCN)(2)(dpyo)(2)].(dpyo)}(n) ( 1), {[Co(SCN)(2)(dpyo)(H2O)(2)].(H2O)}(n) ( 2), {[Co(SeCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 3), have been synthesized and characterized by single-crystal X-ray analysis. Complex 1 is a rare example of a dpyo bridged two-dimensional (2D) coordination polymer, and pi-stacked dpyo supramolecular rods are generated by the lattice dpyo, passing through the rhombic grid of stacked layers, resulting in a three-dimensional (3D) superstructure. Complexes 2 and 3 are isomorphous one-dimensional (1D) coordination polymers [-Co-dpyo-Co-] that undergo self-assembly leading to a bilayer architecture derived through an R-2(2)(8) H-bonding synthon between coordinated water and dpyo oxygen. A reinvestigation of coordination polymers [Mn(SCN)(2)(dpyo)( H2O)(MeOH)](n) ( 4) and {[Fe(SCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 5) reported recently by our group [ Manna et al. Indian J. Chem. 2006, 45A, 1813] reveals brick wall topology rather than bilayer architecture is due to the decisive role of S center dot center dot center dot S/Se center dot center dot center dot Se interactions in determining the helical nature in 4 and 5 as compared to zigzag polymeric chains in 2 and 3, although the same R-2(2)(8) synthon is responsible for supramolecular assembly in these complexes.

Macrocyclic amines as structure-directing agents for the synthesis of three-dimensional antimony-sulfide frameworks

A new family of antimony sulfides, incorporating the macrocyclic tetramine 1,4,8,11-tetraazacyclotetradecane ( cyclam), has been prepared by a hydrothermal method. [C10N4H26][Sb4S7] (1), [Ni(C10N4H24)][Sb4S7] (2), and [Co(C10N4H24)](x)[C10N4H26](1-x)[Sb4S7] (0.08 <= x <= 0.74) (3) have been characterized by single-crystal X-ray diffraction, elemental analysis, thermogravimetry, and analytical electron microscopy. All three materials possess the same novel three-dimensional Sb4S72- framework, constructed from layers of parallel arrays of Sb4S84- chains stacked at 90 to one another. In 1, doubly protonated macrocyclic cations reside in the channel structure of the antimonysulfide framework. In 2 and 3, the cyclam acts as a ligand, chelating the divalent transition- metal cation. Analytical and X-ray diffraction data indicate that the level of metal incorporation in 2 is effectively complete, whereas in 3, both metalated and nonmetalated forms of the macrocycle coexist within the structure.

An efficient finite difference scheme for three-dimensional, non-equilibrium flows using operator splitting

An efficient finite difference scheme is presented for the inviscid terms of the three-dimensional, compressible flow equations for chemical non-equilibrium gases. This scheme represents an extension and an improvement of one proposed by the author, and includes operator splitting.

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.

A comparison of stratosphere-troposphere transport in convection-permitting and convection-parameterizing simulations of three mesoscale convective systems

The transport of stratospheric air into the troposphere within deep convection was investigated using the Met Office Unified Model version 6.1. Three cases were simulated in which convective systems formed over the UK in the summer of 2005. For each of these three cases, simulations were performed on a grid having 4 km horizontal grid spacing in which the convection was parameterized and on a grid having 1 km horizontal grid spacing, which permitted explicit representation of the largest energy-containing scales of deep convection. Cross-tropopause transport was diagnosed using passive tracers that were initialized above the dynamically defined tropopause (2 potential vorticity unit surface) with a mixing ratio of 1. Although the synoptic-scale environment and triggering mechanisms varied between the cases, the total simulated transport was similar in all three cases. The total stratosphere-to-troposphere transport over the lifetime of the convective systems ranged from 25 to 100 kg/m2 across the simulated convective systems and resolutions, which corresponds to ∼5–20% of the total mass located within a stratospheric column extending 2 km above the tropopause. In all simulations, the transport into the lower troposphere (defined as below 3.5 km elevation) accounted for ∼1% of the total transport across the tropopause. In the 4 km runs most of the transport was due to parameterized convection, whereas in the 1 km runs the transport was due to explicitly resolved convection. The largest difference between the simulations with different resolutions occurred in the one case of midlevel convection considered, in which the total transport in the 1 km grid spacing simulation with explicit convection was 4 times that in the 4 km grid spacing simulation with parameterized convection. Although the total cross-tropopause transport was similar, stratospheric tracer was deposited more deeply to near-surface elevations in the convection-parameterizing simulations than in convection-permitting simulations.

Object-based three-dimensional X-ray imaging

A form of three-dimensional X-ray imaging, called Object 3-D, is introduced, where the relevant subject material is represented as discrete ‘objects’. The surface of each such object is derived accurately from the projections of its outline, and of its other discontinuities, in about ten conventional X-ray views, distributed in solid angle. This technique is suitable for many applications, and permits dramatic savings in radiation exposure and in data acquisition and manipulation. It is well matched to user-friendly interactive displays.

Speciation and variation in the occurrence of haloacetic acids in three water supply systems in England

An investigation into the speciation and occurrence of nine haloacetic acids (HAAs) was conducted during the period of April 2007 to March 2008 and involved three drinking water supply systems in England, which were chosen to represent a range of source water conditions; these were an upland surface water, a lowland surface water and a groundwater. Samples were collected seasonally from the water treatment plants and at different locations in the distribution systems. The highest HAA concentrations occurred in the upland surface water system, with an average total HAA concentration of 21.3 μg/L. The lowest HAA levels were observed in the groundwater source, with a mean concentration of 0.6 μg/L. Seasonal variations were significant in the HAA concentrations; the highest total HAA concentrations were found during the autumn, when the concentrations were approximately two times higher than in winter and spring. HAA speciation varied among the water sources, with dichloroacetic acid and trichloroacetic acid dominant in the lowland surface water system and brominated species dominant in the upland surface water system. There was a strong correlation between trihalomethanes and HAAs when considering all samples from the three systems in the same data set (r2=0.88); however, the correlation was poor/moderate when considering each system independently.