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.

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.

Pressure effects revealed by small angle neutron scattering on block copolymer gels

We study the effects of hydrostatic pressure (P) on aqueous solutions and gels of the block copolymer B20E610 (E, oxyethylene; B, oxybutylene; subscripts, number of repeats), by performing simultaneous small angle neutron scattering/pressure experiments. Micellar cubic gels were studied for 9.5 and 4.5 wt% B20E610 at T = 20-80 and 35-55 degrees C, respectively, while micellar isotropic solutions where Studied for 4.5 wt% B20E610 at T > 55 degrees C. We observed that the interplanar distance d(110) (cubic unit cell parameter a = root 2d(110)) decreases while the correlation length of the Cubic order (delta) increases, upon increasing P at a fixed T for 9.5 wt% B20E610. The construction of master Curves for d(110) and delta corresponding to 9.5 wt% B20E610 proved the correlation between changes in T and P. Neither d(110) and delta nor the cubic-isotropic phase transition temperature was affected by the applied pressure for 4.5 wt% B20E610. The dramatic contrast between the pressure-induced behavior observed for 9.5 and 4.5 wt% B20E610 suggests that pressure induced effects might be more effectively transmitted through samples that present wider domains of cubic structure order (9.5 wt% compared to 4.5 wt% B20E610).

Hydrogen adsorption in a copper ZSM5 zeolite: an inelastic neutron scattering study

Currently microporous oxidic materials including zeolites are attracting interest as potential hydrogen storage materials. Understanding how molecular hydrogen interacts with these materials is important in the rational development of hydrogen storage materials and is also challenging theoretically. In this paper, we present an incoherent inelastic neutron scattering (INS) study of the adsorption of molecular hydrogen and hydrogen deuteride (HD) in a copper substituted ZSM5 zeolite varying the hydrogen dosage and temperature. We have demonstrated how inelastic neutron scattering can help us understand the interaction of H-2 molecules with a binding site in a particular microporous material, Cu ZSM5, and by implication of other similar materials. The H-2 molecule is bound as a single species lying parallel with the surface. As H-2 dosing increases, lateral interactions between the adsorbed H-2 molecules become apparent. With rising temperature of measurement up to 70 K (the limit of our experiments), H-2 molecules remain bound to the surface equivalent to a liquid or solid H-2 phase. The implication is that hydrogen is bound rather strongly in Cu ZSM5. Using the simple model for the anisotropic interaction to calculate the energy levels splitting, we found that the measured rotational constant of the hydrogen molecule is reduced as a consequence of adsorption by the Cu ZSM5. From the decrease in total signal intensity with increasing temperature, we were able to observe the conversion of para-hydrogen into ortho-hydrogen at paramagnetic centres and so determine the fraction of paramagnetic sites occupied by hydrogen molecules, ca. 60%. (c) 2006 Elsevier B.V. All rights reserved.

Motivation, rationale and key results from the GERBILS Saharan dust measurement campaign

The Geostationary Earth Radiation Budget Intercomparison of Longwave and Shortwave radiation (GERBILS) was an observational field experiment over North Africa during June 2007. The campaign involved 10 flights by the FAAM BAe-146 research aircraft over southwestern parts of the Sahara Desert and coastal stretches of the Atlantic Ocean. Objectives of the GERBILS campaign included characterisation of mineral dust geographic distribution and physical and optical properties, assessment of the impact upon radiation, validation of satellite remote sensing retrievals, and validation of numerical weather prediction model forecasts of aerosol optical depths (AODs) and size distributions. We provide the motivation behind GERBILS and the experimental design and report the progress made in each of the objectives. We show that mineral dust in the region is relatively non-absorbing (mean single scattering albedo at 550 nm of 0.97) owing to the relatively small fraction of iron oxides present (1–3%), and that detailed spectral radiances are most accurately modelled using irregularly shaped particles. Satellite retrievals over bright desert surfaces are challenging owing to the lack of spectral contrast between the dust and the underlying surface. However, new techniques have been developed which are shown to be in relatively good agreement with AERONET estimates of AOD and with each other. This encouraging result enables relatively robust validation of numerical models which treat the production, transport, and deposition of mineral dust. The dust models themselves are able to represent large-scale synoptically driven dust events to a reasonable degree, but some deficiencies remain both in the Sahara and over the Sahelian region, where cold pool outflow from convective cells associated with the intertropical convergence zone can lead to significant dust production.

Time-resolved in situ X-ray scattering studies of aqueous hydroxypropylcellulose solutions

The evolution of the global orientation parameter for a series of aqueous hydroxypropylcellulose solutions both during and following the cessation of a steady-state shear flow is reported. Time-resolved orientation measurements were made in situ through a novel X-ray rheometer coupled with a two-dimensional electronic X-ray camera, and using an intense X-ray source at the LURE synchrotron. After the cessation of flow, the global orientation decreases from the steady-state orientation level to zero following shear flow at low shear rate or to a small but finite value after flow at a high shear rate. The decrease of orientation with time shows different behaviour, dependent upon the previously applied shear rate.

Measurement of molecular orientation in thermotropic liquid crystalline polymers

Procedures for obtaining molecular orientational parameters from wide angle X-ray scattering patterns of samples of thermotropic liquid crystalline polymers are presented. The methods described are applied to an extrusion-aligned sample of a random copolyester of poly(ethylene terephthalate) (PET) and p-acetoxybenzoic acid. Values of the orientational parameters are obtained from both the interchain and intrachain maxima in the scattering pattern. The differences in the values so derived suggest some level of local rotational correlation

Effects of Thomson-scattering geometry on white-light imaging of an interplanetary shock: synthetic observations from forward magnetohydrodynamic modelling

Stereoscopic white-light imaging of a large portion of the inner heliosphere has been used to track interplanetary coronal mass ejections. At large elongations from the Sun, the white-light brightness depends on both the local electron density and the efficiency of the Thomson-scattering process. To quantify the effects of the Thomson-scattering geometry, we study an interplanetary shock using forward magnetohydrodynamic simulation and synthetic white-light imaging. Identifiable as an inclined streak of enhanced brightness in a time–elongation map, the travelling shock can be readily imaged by an observer located within a wide range of longitudes in the ecliptic. Different parts of the shock front contribute to the imaged brightness pattern viewed by observers at different longitudes. Moreover, even for an observer located at a fixed longitude, a different part of the shock front will contribute to the imaged brightness at any given time. The observed brightness within each imaging pixel results from a weighted integral along its corresponding ray-path. It is possible to infer the longitudinal location of the shock from the brightness pattern in an optical sky map, based on the east–west asymmetry in its brightness and degree of polarisation. Therefore, measurement of the interplanetary polarised brightness could significantly reduce the ambiguity in performing three-dimensional reconstruction of local electron density from white-light imaging.

A review of measurement-based assessments of the aerosol direct radiative effect and forcing

Aerosols affect the Earth's energy budget directly by scattering and absorbing radiation and indirectly by acting as cloud condensation nuclei and, thereby, affecting cloud properties. However, large uncertainties exist in current estimates of aerosol forcing because of incomplete knowledge concerning the distribution and the physical and chemical properties of aerosols as well as aerosol-cloud interactions. In recent years, a great deal of effort has gone into improving measurements and datasets. It is thus feasible to shift the estimates of aerosol forcing from largely model-based to increasingly measurement-based. Our goal is to assess current observational capabilities and identify uncertainties in the aerosol direct forcing through comparisons of different methods with independent sources of uncertainties. Here we assess the aerosol optical depth (τ), direct radiative effect (DRE) by natural and anthropogenic aerosols, and direct climate forcing (DCF) by anthropogenic aerosols, focusing on satellite and ground-based measurements supplemented by global chemical transport model (CTM) simulations. The multi-spectral MODIS measures global distributions of aerosol optical depth (τ) on a daily scale, with a high accuracy of ±0.03±0.05τ over ocean. The annual average τ is about 0.14 over global ocean, of which about 21%±7% is contributed by human activities, as estimated by MODIS fine-mode fraction. The multi-angle MISR derives an annual average AOD of 0.23 over global land with an uncertainty of ~20% or ±0.05. These high-accuracy aerosol products and broadband flux measurements from CERES make it feasible to obtain observational constraints for the aerosol direct effect, especially over global the ocean. A number of measurement-based approaches estimate the clear-sky DRE (on solar radiation) at the top-of-atmosphere (TOA) to be about -5.5±0.2 Wm-2 (median ± standard error from various methods) over the global ocean. Accounting for thin cirrus contamination of the satellite derived aerosol field will reduce the TOA DRE to -5.0 Wm-2. Because of a lack of measurements of aerosol absorption and difficulty in characterizing land surface reflection, estimates of DRE over land and at the ocean surface are currently realized through a combination of satellite retrievals, surface measurements, and model simulations, and are less constrained. Over the oceans the surface DRE is estimated to be -8.8±0.7 Wm-2. Over land, an integration of satellite retrievals and model simulations derives a DRE of -4.9±0.7 Wm-2 and -11.8±1.9 Wm-2 at the TOA and surface, respectively. CTM simulations derive a wide range of DRE estimates that on average are smaller than the measurement-based DRE by about 30-40%, even after accounting for thin cirrus and cloud contamination. A number of issues remain. Current estimates of the aerosol direct effect over land are poorly constrained. Uncertainties of DRE estimates are also larger on regional scales than on a global scale and large discrepancies exist between different approaches. The characterization of aerosol absorption and vertical distribution remains challenging. The aerosol direct effect in the thermal infrared range and in cloudy conditions remains relatively unexplored and quite uncertain, because of a lack of global systematic aerosol vertical profile measurements. A coordinated research strategy needs to be developed for integration and assimilation of satellite measurements into models to constrain model simulations. Enhanced measurement capabilities in the next few years and high-level scientific cooperation will further advance our knowledge.

Control and analysis of oriented thin films of lipid inverse bicontinuous cubic phases using grazing incidence small-angle X‑ray scattering

Lipid cubic phases are complex nanostructures that form naturally in a variety of biological systems, with applications including drug delivery and nanotemplating. Most X-ray scattering studies on lipid cubic phases have used unoriented polydomain samples as either bulk gels or suspensions of micrometer-sized cubosomes. We present a method of investigating cubic phases in a new form, as supported thin films that can be analyzed using grazing incidence small-angle X-ray scattering (GISAXS). We present GISAXS data on three lipid systems: phytantriol and two grades of monoolein (research and industrial). The use of thin films brings a number of advantages. First, the samples exhibit a high degree of uniaxial orientation about the substrate normal. Second, the new morphology allows precise control of the substrate mesophase geometry and lattice parameter using a controlled temperature and humidity environment, and we demonstrate the controllable formation of oriented diamond and gyroid inverse bicontinuous cubic along with lamellar phases. Finally, the thin film morphology allows the induction of reversible phase transitions between these mesophase structures by changes in humidity on subminute time scales, and we present timeresolved GISAXS data monitoring these transformations.

Computer simulations of the structure of colloidal ferrofluids

The structure of a ferrofluid under the influence of an external magnetic field is expected to become anisotropic due to the alignment of the dipoles into the direction of the external field, and subsequently to the formation of particle chains due to the attractive head to tail orientations of the ferrofluid particles. Knowledge about the structure of a colloidal ferrofluid can be inferred from scattering data via the measurement of structure factors. We have used molecular-dynamics simulations to investigate the structure of both monodispersed and polydispersed ferrofluids. The results for the isotropic structure factor for monodispersed samples are similar to previous data by Camp and Patey that were obtained using an alternative Monte Carlo simulation technique, but in a different parameter region. Here we look in addition at bidispersed samples and compute the anisotropic structure factor by projecting the q vector onto the XY and XZ planes separately, when the magnetic field was applied along the z axis. We observe that the XY- plane structure factor as well as the pair distribution functions are quite different from those obtained for the XZ plane. Further, the two- dimensional structure factor patterns are investigated for both monodispersed and bidispersed samples under different conditions. In addition, we look at the scaling exponents of structure factors. Our results should be of value to interpret scattering data on ferrofluids obtained under the influence of an external field.

Aerosol scattering and absorption during the EUCAARI-LONGREX flights of the Facility for Airborne Atmospheric Measurements (FAAM) BAe-146: can measurements and models agree?

Scattering and absorption by aerosol in anthropogenically perturbed air masses over Europe has been measured using instrumentation flown on the UK’s BAe-146-301 large Atmospheric Research Aircraft (ARA) operated by the Facility for Airborne Atmospheric Measurements (FAAM) on 14 flights during the EUCAARI-LONGREX campaign in May 2008. The geographical and temporal variations of the derived shortwave optical properties of aerosol are presented. Values of single scattering albedo of dry aerosol at 550 nm varied considerably from 0.86 to near unity, with a campaign average of 0.93 ± 0.03. Dry aerosol optical depths ranged from 0.030 ± 0.009 to 0.24 ± 0.07. An optical properties closure study comparing calculations from composition data and Mie scattering code with the measured properties is presented. Agreement to within measurement uncertainties of 30% can be achieved for both scattering and absorption,but the latter is shown to be sensitive to the refractive indices chosen for organic aerosols, and to a lesser extent black carbon, as well as being highly dependent on the accuracy of the absorption measurements. Agreement with the measured absorption can be achieved either if organic carbon is assumed to be weakly absorbing, or if the organic aerosol is purely scattering and the absorption measurement is an overestimate due to the presence of large amounts of organic carbon. Refractive indices could not be inferred conclusively due to this uncertainty, despite the enhancement in methodology compared to previous studies that derived from the use of the black carbon measurements. Hygroscopic growth curves derived from the wet nephelometer indicate moderate water uptake by the aerosol with a campaign mean f (RH) value (ratio in scattering) of 1.5 (range from 1.23 to 1.63) at 80% relative humidity. This value is qualitatively consistent with the major chemical components of the aerosol measured by the aerosol mass spectrometer, which are primarily mixed organics and nitrate and some sulphate.

Internal nanoparticle structure of temperature-responsive self-assembled PNIPAM-b-PEG-b-PNIPAM triblock copolymers in aqueous solutions: NMR, SANS and light scattering studies

In this study we report detailed information on the internal structure of PNIPAM-b-PEG-b-PNIPAM nanoparticles formed from self-assembly in aqueous solutions upon increase in temperature. NMR spectroscopy, light scattering and small-angle neutron scattering (SANS) were used to monitor different stages of nanoparticle formation as a function of temperature, providing insight into the fundamental processes involved. The presence of PEG in a copolymer structure significantly affects the formation of nanoparticles, making their transition to occur over a broader temperature range. The crucial parameter that controls the transition is the ratio of PEG/PNIPAM. For pure PNIPAM, the transition is sharp; the higher the PEG/PNIPAM ratio results in a broader transition. This behavior is explained by different mechanisms of PNIPAM block incorporation during nanoparticle formation at different PEG/PNIPAM ratios. Contrast variation experiments using SANS show that the structure of nanoparticles above cloud point temperatures for PNIPAM-b-PEG-b-PNIPAM copolymers is drastically different from the structure of PNIPAM mesoglobules. In contrast with pure PNIPAM mesoglobules, where solid-like particles and chain network with a mesh size of 1-3 nm are present; nanoparticles formed from PNIPAM-b-PEG-b-PNIPAM copolymers have non-uniform structure with “frozen” areas interconnected by single chains in Gaussian conformation. SANS data with deuterated “invisible” PEG blocks imply that PEG is uniformly distributed inside of a nanoparticle. It is kinetically flexible PEG blocks which affect the nanoparticle formation by prevention of PNIPAM microphase separation.

Measurement of thermal neutron cross section and resonance integral for the (165)Ho(n, gamma)(166g)Ho reaction

The ground state thermal neutron cross section and the resonance integral for the (165)Ho(n, gamma)(166)Ho reaction in thermal and 1/E regions, respectively, of a thermal reactor neutron spectrum have been measured experimentally by activation technique. The reaction product, (166)Ho in the ground state, is gaining considerable importance as a therapeutic radionuclide and precisely measured data of the reaction are of significance from the fundamental point of view as well as for application. In this work, the spectrographically pure holmium oxide (Ho(2)O(3)) powder samples were irradiated with and without cadmium covers at the IEA-RI reactor (IPEN, Sao Paulo), Brazil. The deviation of the neutron spectrum shape from 1/E law was measured by co-irradiating Co, Zn, Zr and Au activation detectors with thermal and epithermal neutrons followed by regression and iterative procedures. The magnitudes of the discrepancies that can occur in measurements made with the ideal 1/E law considerations in the epithermal range were studied. The measured thermal neutron cross section at the Maxwellian averaged thermal energy of 0.0253 eV is 59.0 +/- 2.1 b and for the resonance integral 657 +/- 36b. The results are measured with good precision and indicated a consistency trend to resolve the discrepant status of the literature data. The results are compared with the values in main libraries such as ENDF/B-VII, JEF-2.2 and JENDL-3.2, and with other measurements in the literature.

Challenging measurement of the (16)O+(27)Al elastic and inelastic angular distributions up to large angles

The (16)O+(27)Al elastic and inelastic angular distributions have been measured in a broad angular range (13 degrees < theta(lab) < 52 degrees) at about 100 MeV incident energy. The use of the MAGNEX large acceptance magnetic spectrometer and of the ray-reconstruction analysis technique has been crucial in order to provide, in the same experiment, high-resolution energy spectra and cross-section measurements distributed over more than seven orders of magnitude down to hundreds of nb/sr. (C) 2011 Elsevier B.V. All rights reserved.