Geometric quantization of localized surface plasmons

We consider the quasi-static problem governing the localized surface plasmon modes and permittivity eigenvalues $\epsilon $ of smooth, arbitrarily shaped, axisymmetric inclusions. We develop an asymptotic theory for the dense part of the spectrum, i.e. close to the accumulation value $\epsilon =-1$ at which a flat interface supports surface plasmons; in this regime, the field oscillates rapidly along the surface and decays exponentially away from it on a comparable scale. With $\tau =-(\epsilon +1)$ as the small parameter, we develop a surface-ray description of the eigenfunctions in a narrow boundary layer about the interface; the fast phase variation, as well as the slowly varying amplitude and geometric phase, along the rays are determined as functions of the local geometry. We focus on modes varying at most moderately in the azimuthal direction, in which case the surface rays are meridian arcs that focus at the two poles. Asymptotically matching the diverging ray solutions with expansions valid in inner regions in the vicinities of the poles yields the quantization rule \begin{equation*}\frac{1}{\tau} \sim \frac{\pi n }{\varTheta}+\frac{1}{2}\left(\frac{\pi}{\varTheta}-1\right)+o(1),\end{equation*}where $n\gg 1$ is an integer and $\varTheta $ a geometric parameter given by the product of the inclusion length and the reciprocal average of its cross-sectional radius along its symmetry axis. For a sphere, $\varTheta =\pi $, whereby the formula returns the exact eigenvalues $\epsilon =-1-1/n$. We also demonstrate good agreement with exact solutions in the case of prolate spheroids.

Community-deliverable exercise and anxiety in adults with arthritis and other rheumatic diseases: a systematic review with meta-analysis of randomised controlled trials

Background/purposeGiven conflicting findings, the purpose of this study was to use the meta-analytic approach to examine the effects of exercise (aerobic, strength training or both) on anxiety in adults with arthritis and other rheumatic diseases (AORD).MethodsRandomised controlled exercise intervention trials ≥4weeks in adults ≥18 years of age with osteoarthritis, rheumatoid arthritis or fibromyalgia were included. Studies were located by searching eight electronic databases, cross-referencing and expert review. Dual selection and data abstraction of studies were performed. Hedge’s standardised effect size (ES) was calculated for each result and pooled using the recently developed inverse heterogeneity model. Two-tailedz-alpha values ≤0.05 and non-overlapping 95% CI were considered statistically significant. Heterogeneity was estimated using Q andI2with alpha values ≤0.10 for Q considered statistically significant. Small-study effects were examined using funnel plots and Egger’s regression test. In addition, the number needed to treat (NNT), percentile improvement and meta-regression were conducted.ResultsOf the 639 citations screened, 14 studies representing 926 initially enrolled participants (539 exercise, 387 control) met the criteria for inclusion. Length of training (mean±SD) averaged 15.8±6.7 weeks, frequency 3.3±1.3 times per week and duration 28.8±14.3 min per session. Overall, statistically significant reductions in anxiety were found (exercise minus control changes ES=−0.40, 95% CI −0.65 to −0.15, tau2=0.14; Q=40.3, P=0.0004;I2=62.8%). The NNT was 6 with a percentile improvement of 15.5% and an estimated 5.3 million inactive US adults with AORD improving their anxiety if they started exercising regularly. Statistically significant small-study effects were observed (P<0.0001).ConclusionsExercise is associated with reductions in anxiety among adults with selected types of AORD. However, a need exists for additional, well-designed, randomised controlled trials on this topic.PROSPERO registration numberCRD42016048728.

A Comprehensive Model for Assessing the Impact of Steel Cleanliness on Bearing Performance

Steel cleanliness as measured by nonmetallic inclusion content in steel plays a major role in affecting bearing durability. A high-fidelity virtual bearing life test model was developed to predict the impact of inclusions on bearing fatigue life. This model analyzes distributions of inclusion size, shape, orientation, and location, and computes stress alterations to bearing material due to inclusions and the resulting life reduction. Comparisons between model predictions and experimental test results were made, confirming the validity of the model. Parametric studies were conducted to explore the effects of inclusion counts, inclusion size distributions, and the effect of overall bearing size on bearing life. A regression equation was proposed based on simulation results, linking the bearing life reduction factor (LRF) to the accumulative inclusion length within the stressed volume under contact load.

Impedance measurements of the complex dielectric permittivity of sea ice at 50 MHz: pore microstructure and potential for salinity monitoring

We report impedance measurements of the complex dielectric permittivity ε = ε′ − jε″ of sea ice and laboratory-grown NaCl single crystals using 50 MHz Stevens Water Monitoring Systems Hydra Probes. Temperature cycling of the single-crystal samples shows hydrohalite precipitation, and hysteresis in ε′ and ε″ qualitatively consistent with the expected evolution of brine-inclusion microstructure. Measurements parallel and perpendicular to intra-crystalline brine layers show weak (<10%) anisotropy in ε′ and a 20–40% difference in ε″ due to enhanced d.c. conductivity along the layers. Measurements in landfast, first-year ice near Barrow, Alaska, USA, indicate brine motion in warming ice as the brine volume fraction vb increases above 5%. Plots of vb derived from salinity profiles against ε′ and ε″ for these and previous measurements display too much variability between datasets for unguided inversion of vb. Contributing to this variability are intrinsic microstructural dependence, uncertainties in vb, and sub-representative sample volumes. A standard model of sea-ice permittivity is inverted to derive the apparent brine-inclusion aspect ratio and bulk d.c. conductivity at a spatial scale complementary to previous measurements. We assess Hydra Probe performance in high-salinity environments and conclude that they are not generally suited for autonomous sea-ice salinity measurements, partly due to the range of relevant brine pocket inclusion length scales.