Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

Hydrogen-bonding-driven self-assembly of PEGylated organosilica nanoparticles with poly(acrylic acid) in aqueous solutions and in layer-by-layer deposition at solid surfaces

PEGylated organosilica nanoparticles have been synthesized through self-condensation of (3-mercaptopropyl)trimethoxysilane in dimethyl sulfoxide into thiolated nanoparticles with their subsequent reaction with methoxypoly(ethylene glycol) maleimide. The PEGylated nanoparticles showed excellent colloidal stability over a wide range of pH in contrast to the parent thiolated nanoparticles, which have a tendency to aggregate irreversibly under acidic conditions (pH < 3.0). Due to the presence of a poly(ethylene glycol)-based corona, the PEGylated nanoparticles are capable of forming hydrogen-bonded interpolymer complexes with poly(acrylic acid) in aqueous solutions under acidic conditions, resulting in larger aggregates. The use of hydrogen-bonding interactions allows more efficient attachment of the nanoparticles to surfaces. The alternating deposition of PEGylated nanoparticles and poly(acrylic acid) on silicon wafer surfaces in a layer-by-layer fashion leads to multilayered coatings. The self-assembly of PEGylated nanoparticles with poly(acrylic acid) in aqueous solutions and at solid surfaces was compared to the behavior of linear poly(ethylene glycol). The nanoparticle system creates thicker layers than the poly(ethylene glycol), and a thicker layer is obtained on a poly(acrylic acid) surface than on a silica surface, because of the effects of hydrogen bonding. Some implications of these hydrogen-bonding-driven interactions between PEGylated nanoparticles and poly(acrylic acid) for pharmaceutical formulations are discussed.

The study of chiral adsorption systems using synchrotron- based structural and spectroscopic techniques: stereospecific adsorption of serine on Au-modified chiral Cu{531} surfaces

We apply modern synchrotron-based structural techniques to the study of serine adsorbed on the pure andAumodified intrinsically chiral Cu{531} surface. XPS and NEXAFS data in combination with DFT show that on the pure surface both enantiomers adsorb in l4 geometries (with de-protonated b-OH groups) at low coverage and in l3 geometries at saturation coverage. Significantly larger enantiomeric differences are seen for the l4 geometries, which involve substrate bonds of three side groups of the chiral center, i.e. a three-point interaction. The l3 adsorption geometry, where only the carboxylate and amino groups form substrate bonds, leads to smaller but still significant enantiomeric differences, both in geometry and the decomposition behavior. When Cu{531} is modified by the deposition of 1 and 2ML Au the orientations of serine at saturation coverage are significantly different from those on the clean surface. In all cases, however, a l3 bond coordination is found at saturation involving different numbers of Au atoms, which leads to relatively small enantiomeric differences.

A novel bogie design made of glass fibre reinforced plastic

This paper presents a completely new design of a bogie-frame made of glass fibre reinforced composites and its performance under various loading conditions predicted by finite element analysis. The bogie consists of two frames, with one placed on top of the other, and two axle ties connecting the axles. Each frame consists of two side arms and a transom between. The top frame is thinner and more compliant and has a higher curvature compared with the bottom frame. Variable vertical stiffness can be achieved before and after the contact between the two frames at the central section of the bogie to cope with different load levels. Finite element analysis played a very important role in the design of this structure. Stiffness and stress levels of the full scale bogie presented in this paper under various loading conditions have been predicted by using Marc provided by MSC Software. In order to verify the finite element analysis (FEA) models, a fifth scale prototype of the bogie has been made and tested under quasi-static loading conditions. Results of testing on the fifth scale bogie have been used to fine tune details like contact and friction in the fifth scale FEA models. These conditions were then applied to the full scale models. Finite element analysis results show that the stress levels in all directions are low compared with material strengths.

Modelling the structure of a polymer glass poly(methylmethacrylate) through neutron scattering experiments

Determination of the local structure of a polymer glass by scattering methods is complex due to the number of spatial and orientational correlations, both from within the polymer chain (intrachain) and between neighbouring chains (interchain), from which the scattering arises. Recently considerable advances have been made in the structural analysis of relatively simple polymers such as poly(ethylene) through the use of broad Q neutron scattering data tightly coupled to atomistic modelling procedures. This paper presents the results of an investigation into the use of these procedures for the analysis of the local structure of a-PMMA which is chemically more complex with a much greater number of intrachain structural parameters. We have utilised high quality neutron scattering data obtained using SANDALS at ISIS coupled with computer models representing both the single chain and bulk polymer system. Several different modelling approaches have been explored which encompass such techniques as Reverse Monte Carlo refinement and energy minimisation and their relative merits and successes are discussed. These different approaches highlight structural parameters which any realistic model of glassy atactic PMMA must replicate.

A flow system for the on-line quantitative measurement of the retention of dosage forms on biological surfaces using spectroscopy and image analysis

Measuring the retention, or residence time, of dosage forms to biological tissue is commonly a qualitative measurement, where no real values to describe the retention can be recorded. The result of this is an assessment that is dependent upon a user's interpretation of visual observation. This research paper outlines the development of a methodology to quantitatively measure, both by image analysis and by spectrophotometric techniques, the retention of material to biological tissues, using the retention of polymer solutions to ocular tissue as an example. Both methods have been shown to be repeatable, with the spectrophotometric measurement generating data reliably and quickly for further analysis.

Optimizing layer-by-layer deposition of interpolymer complexes on solid substrates using Biacore

The layer-by-layer deposition of polymers onto surfaces allows the fabrication of multilayered materials for a wide range of applications, from drug delivery to biosensors. This work describes the analysis of complex formation between poly(acrylic acid) and methylcellulose in aqueous solutions using Biacore, a surface plasmon resonance analytical technique, traditionally used to examine biological interactions. This technique characterized the layer-by-layer deposition of these polymers on the surface of a Biacore sensor chip. The results were subsequently used to optimize the experimental conditions for sequential layer deposition on glass slides. The role of the solution pH and poly(acrylic acid) molecular weight on the formation of interpolymer multilayered coatings was researched, and showed that the optimal deposition of the polymer complexes was achieved at pHs ≤2.5 with a poly(acrylic acid) molecular weight of 450 kDa.

The role of SEF14 and SEF17 fimbriae in the adherence of Salmonella enterica serotype Enteritidis to inanimate surfaces

To gain an understanding of the role of fimbriae and flagella in the adherence of Salmonella enterica serotype Enteritidis to inanimate surfaces, the extent of adherence of viable wild-type strains to a polystyrene microtitration plate was determined by a crystal violet staining assay, Elaboration of surface antigens by adherent bacteria was assayed by fimbriae- and flagella-specific ELISAs, Wild-type Enteritidis strains adhered well at 37 degrees C and 25 degrees C when grown in microtitration wells in Colonisation Factor Antigen broth, but not in other media tested, At 37 degrees C, adherent bacteria elaborated copious quantities of SEF14 fimbrial antigen, whereas at 25 degrees C adherent bacteria elaborated copious quantities of SEF17 fimbrial antigen. Non-fimbriate and non-flagellate knock-out mutant strains were also assessed in the adherence assay. Mutant strains unable to elaborate SEF14 and SEF17 fimbriae adhered poorly at 37 degrees C and 25 degrees C, respectively, but adherence was not abolished. Non-motile mutant strains showed reduced adherence whilst type-1, PEF and LPF fimbriae appeared not to contribute to adherence in this assay. These data indicate that SEF17 and SEF14 fimbriae mediate bacterial cell aggregation on inanimate surfaces under appropriate growth conditions.

Sub-surface terahertz imaging through uneven surfaces: visualizing Neolithic wall paintings in Çatalhöyük

Pulsed terahertz imaging is being developed as a technique to image obscured mural paintings. Due to significant advances in terahertz technology, portable systems are now capable of operating in unregulated environments and this has prompted their use on archaeological excavations. August 2011 saw the first use of pulsed terahertz imaging at the archaeological site of Çatalhöyük, Turkey, where mural paintings dating from the Neolithic period are continuously being uncovered by archaeologists. In these particular paintings the paint is applied onto an uneven surface, and then covered by an equally uneven surface. Traditional terahertz data analysis has proven unsuccessful at sub-surface imaging of these paintings due to the effect of these uneven surfaces. For the first time, an image processing technique is presented, based around Gaussian beam-mode coupling, which enables the visualization of the obscured painting.

A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.