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

Consumer insights and the importance of competitiveness Factors for mature and developing destinations

This article aims to understand the importance of various destination attributes to the competitiveness of tourism destinations from a consumer perspective, while at the same time contrasting these in a mature versus developing destination. A sample of Australian-based domestic tourists were surveyed to assess the relative importance of tourism destination competitiveness (TDC) attributes in the context of developing and mature destinations. This research firstly appears to verify that the importance of many TDC elements, highlighted by consumers, is not dissimilar from other stakeholder-based TDC studies. Furthermore, this research effort established that in terms of attribute performance, relative destination immaturity may well constrain a developing destination’s ability to satisfy the needs of consumers

Influence of oat components on lipid digestion using an in vitro model: impact of viscosity and depletion flocculation mechanism

Depletion flocculation is a well-known instability mechanism that can occur in oil-in-water emulsions when the concentration of non-adsorbed polysaccharide exceeds a certain level. This critical flocculation concentration depends on the molecular characteristics of the polysaccharide molecules, such as their molecular weight and hydrodynamic radius. In this study, a range of analytical methods (dynamic shear rheology, optical microscopy, and static light-scattering) were used to investigate the interaction between lipid droplets and polysaccharides (guar gum and β-glucans) of varying weight-average molecular weight and hydrodynamic radius, and concentration. The aim of this work was to see if the health benefits of soluble fibers like β-glucans could be explained by their influence on the structure and digestibility of lipid emulsions. The apparent viscosity of the emulsions increased with increasing polysaccharide concentration, molecular weight, and hydrodynamic radius. Droplet flocculation was observed in the emulsions only at certain polysaccharide concentrations, which was attributed to a depletion effect. In addition, the water-soluble components in oat flakes, flour, and bran were extracted using aqueous solutions, to examine their impact on emulsion stability and properties. Then, the rate and extent of lipolysis of a sunflower oil-in-water emulsion in the presence of these oat extracts were monitored using the pH-stat method. However, the inhibition of lipolysis was not linearly related to the viscosity of the oat solutions. The water-soluble extracts of β-glucan collected from oat flakes had a significant inhibitory effect on lipolysis. The results of this study increase our understanding of the possible mechanisms influencing the impact of oat constituents on lipid digestion. This work also highlights the importance of considering the molecular properties of polysaccharides, and not just their impact on solution viscosity

The origin of high δ18O zircons: marbles, megacrysts, and metamorphism

The oxygen isotope ratios (δ18O) of most igneous zircons range from 5 to 8‰, with 99% of published values from 1345 rocks below 10‰. Metamorphic zircons from quartzite, metapelite, metabasite, and eclogite record δ18O values from 5 to 17‰, with 99% below 15‰. However, zircons with anomalously high δ18O, up to 23‰, have been reported in detrital suites; source rocks for these unusual zircons have not been identified. We report data for zircons from Sri Lanka and Myanmar that constrain a metamorphic petrogenesis for anomalously high δ18O in zircon. A suite of 28 large detrital zircon megacrysts from Mogok (Myanmar) analyzed by laser fluorination yields δ18O from 9.4 to 25.5‰. The U–Pb standard, CZ3, a large detrital zircon megacryst from Sri Lanka, yields δ18O = 15.4 ± 0.1‰ (2 SE) by ion microprobe. A euhedral unzoned zircon in a thin section of Sri Lanka granulite facies calcite marble yields δ18O = 19.4‰ by ion microprobe and confirms a metamorphic petrogenesis of zircon in marble. Small oxygen isotope fractionations between zircon and most minerals require a high δ18O source for the high δ18O zircons. Predicted equilibrium values of Δ18O(calcite-zircon) = 2–3‰ from 800 to 600°C show that metamorphic zircon crystallizing in a high δ18O marble will have high δ18O. The high δ18O zircons (>15‰) from both Sri Lanka and Mogok overlap the values of primary marine carbonates, and marbles are known detrital gemstone sources in both localities.The high δ18O zircons are thus metamorphic; the 15–25‰ zircon values are consistent with a marble origin in a rock-dominated system (i.e., low fluid(external)/rock); the lower δ18O zircon values (9–15‰) are consistent with an origin in an external fluid-dominated system, such as skarn derived from marble, although many non-metasomatized marbles also fall in this range of δ18O. High δ18O (>15‰) and the absence of zoning can thus be used as a tracer to identify a marble source for high δ18O detrital zircons; this recognition can aid provenance studies in complex metamorphic terranes where age determinations alone may not allow discrimination of coeval source rocks. Metamorphic zircon megacrysts have not been reported previously and appear to be associated with high-grade marble. Identification of high δ18O zircons can also aid geochronology studies that seek to date high-grade metamorphic events due to the ability to distinguish metamorphic from detrital zircons in marble

A Feynman-Kac Formula for Anticommuting Brownian Motion

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.Comment: 21 page

Two Neoarchean tectonothermal events on the western edge of the North Atlantic Craton, as revealed by SIMS dating of the Saglek Block, Nain Province, Labrador

The Saglek Block forms the northern part of the Nain Province and underwent widespread metamorphism at c. 2.7 Ga, producing the dominant gneissosity and intercalation of supracrustal sequences. Zircon dating of gneiss samples collected along 80 km of the Labrador coast from Ramah Bay in the north to Hebron Fjord in the south confirms the widespread extent of high-grade metamorphism between 2750 and 2700 Ma. In addition, a distinct event between 2550 and 2510 Ma produced felsic melt with peritectic garnet in metavolcanic gneiss and granoblastic recrystallization in mafic granulite. Ductile deformation of granite emplaced at c. 2550 Ma indicates that this later event involved a degree of tectonism during high-T metamorphism. Such tectonism may be related to a hypothesized post-2.7 Ga juxtaposition of the predominantly Eoarchean Saglek Block against the Mesoarchean Hopedale Block, along a north–south boundary that extends from the coast near Nain to offshore of Saglek Bay. Evidence of reworking of c. 2.7 Ga gneisses by c. 2.5 Ga tectonothermal activity has been found elsewhere on the margins of the North Atlantic Craton, of which the Nain Province represents thewestern margin. In particular, a recent suggestion that c. 2.5 Ga metamorphic ages along the northern margin of the North Atlantic Craton inSWGreenland may record the final assembly of the craton could also apply to the western margin as represented by the rocks of the Nain Province

New insight into tuning magnetic phases of RMn6Sn6 kagome metals

Kagome metals with magnetic order offer the possibility of tuning topological electronic states via external control parameters such as temperature or magnetic field. ErMn$_6$Sn$_6$ (Er$166$) is a member of a group of $R166$, $R=$~rare earth, compounds hosting ferromagnetic Mn kagome nets whose magnetic moment direction and layer-to-layer magnetic correlations are strongly influenced by coupling to $R$ magnetic moments in neighboring triangular layers. Here, we use neutron diffraction and magnetization data to examine the temperature-driven transition in Er$166$ from a planar-ferrimagnetic to distorted-triple-spiral magnetic order. These data inform mean-field calculations which highlight the fragile, tunable nature of the magnetism caused by competing Mn-Mn and Mn-Er interlayer magnetic exchange couplings and Mn and Er magnetic anisotropies. This competition results in the near degeneracy of a variety of collinear, non-collinear, and non-coplanar magnetic phases which we show are readily selected and adjusted via changing temperature or magnetic field. Thermal fluctuations of the Er moment direction provide the key to this tunability.Comment: 10 pages, 7 figures, Supplementary Informatio

Intrinsic wheat lipid composition effects the interfacial and foaming properties of dough liquor

Doughs were prepared from a single variety breadmaking flour (cv. Hereward), from three successive harvests (years; 2011, 2012 and 2013). A preparation of the aqueous phase from dough, known as dough liquor (DL), was prepared by ultracentrifugation and its physico-chemical properties were investigated. Surface tension and interfacial rheology, showed that the interface of DL was lipid-dominated and that 2013 DL had a different type of interface to 2011 and 2012 DL. This data was consistent with the improved foam stability observed for 2013 DL and with the types of lipids identified. All foams collapsed quickly, but the most stable foam was from 2013 DL with 89.2% loss in foam, followed by 2011 DL with 91.7% loss and 2012 had the least stable foam with a loss of 92.5% of the foam structure. Glycolipids (DGDG and MGDG) were enriched in 2013 DL, and were also present in DL foam, contributing towards improved stability. Neutral lipids, such as FFAs, were enriched in DL foams contributing towards instability and rapid foam collapse. Baking trials using 2012 and 2013 flour, showed increased loaf volumes and gas bubble diameter in 2013 bread compared to 2012 bread, highlighting the potential impact that surface active polar lipids, enriched in the aqueous phase of dough, could have on improving breadmaking quality