Asymptotic expansions for field moments of bound states

Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar semi-classical approximation. Application to a couple of widely studied potentials that do not permit closed-form solutions is used to demonstrate surprising accuracy even in cases that are far from any asymptotic limit. We explore the absence of alternate terms in the asymptotic expansions as a way to explain the accuracy of the end results. Those results are expressed in terms of definite integrals with integrands involving the parameter used in the SAFE method to control the extent of the associated elemental field contributions. Importantly, the integrals themselves are shown to be precisely independent of that parameter. Further, although the derivation proceeds by way of an asymptotic expansion for the wavefield that involves the associated classical motion, those entities do not appear in the end results which are expressed in terms of just the potential function and its first four derivatives

Non-existence of Skyrmion-Skyrmion and Skyrmion-anti-Skyrmion static equilibria

We consider classical static Skyrmion-anti-Skyrmion and Skyrmion-Skyrmion configurations, symmetric with respect to a reflection plane, or symmetric up to a $G$-parity transformation respectively. We show that the stress tensor component completely normal to the reflection plane, and hence its integral over the plane, is negative definite or positive definite respectively. Classical Skyrmions always repel classical Skyrmions and classical Skyrmions always attract classical anti-Skyrmions and thus no static equilibrium, whether stable or unstable, is possible in either case. No other symmetry assumption is made and so our results also apply to multi-Skyrmion configurations. Our results are consistent with existing analyses of Skyrmion forces at large separation, and with numerical results on Skymion-anti-Skyrmion configurations in the literature which admit a different reflection symmetry. They also hold for the massive Skyrme model. We also point out that reflection symmetric self-gravitating Skyrmions or black holes with Skyrmion hair cannot rest in symmetric equilibrium with self-gravitating anti-Skyrmions.Comment: v2 Typos corrected, refs added. v3 Journal versio

Structural parameters for globular clusters in M31 and generalizations for the fundamental plane

The structures of globular clusters (GCs) reflect their dynamical states and past histories. High-resolution imaging allows the exploration of morphologies of clusters in other galaxies. Surface brightness profiles from new Hubble Space Telescope observations of 34 globular clusters in M31 are presented, together with fits of several different structural models to each cluster. M31 clusters appear to be adequately fit by standard King models, and do not obviously require alternate descriptions with relatively stronger halos, such as are needed to fit many GCs in other nearby galaxies. The derived structural parameters are combined with corrected versions of those measured in an earlier survey to construct a comprehensive catalog of structural and dynamical parameters for M31 GCs with a sample size similar to that for the Milky Way. Clusters in M31, the Milky Way, Magellanic Clouds, Fornax dwarf spheroidal and NGC 5128 define a very tight fundamental plane with identical slopes. The combined evidence for these widely different galaxies strongly reinforces the view that old globular clusters have near-universal structural properties regardless of host environment.Comment: AJ in press; 59 pages including 16 figure

Atherosclerotic carotid plaque composition: a 3T and 7T MRI-histology correlation study

Background and Purpose Carotid artery atherosclerotic plaque composition may influence plaque stability and risk of thromboembolic events, and non-invasive plaque imaging may therefore permit risk stratification for clinical management. Plaque composition was compared using non-invasive in-vivo (3T) and ex-vivo (7T) MRI and histopathological examination. Methods Thirty three endarterectomy cross sections, from 13 patients, were studied. The datasets consisted of in-vivo 3T MRI, ex-vivo 7T MRI and histopathology. Semi-automated segmentation methods were used to measure areas of different plaque components. Bland- Altman plots and mean difference with 95% confidence interval were carried out. Results There was general quantitative agreement between areas derived from semi-automated segmentation of MRI data and histology measurements. The mean differences and 95% confidence bounds in the relative to total plaque area between 3T versus Histology were: fibrous tissue 4.99 % (-4.56 to 14.56), lipid-rich/necrotic core (LR/NC) with haemorrhage - 1.81% (-14.11 to 10.48), LR/NC without haemorrhage -2.43% (-13.04 to 8.17), and calcification -3.18% (-11.55 to 5.18). The mean differences and 95% confidence bounds in the relative to total plaque area between 7T and histology were: fibrous tissue 3.17 % (-3.17 to 9.52), LR/NC with haemorrhage -0.55% (-9.06 to 7.95), LR/NC without haemorrhage - 12.62% (-19.8 to -5.45), and calcification -2.43% (-9.97 to 4.73). Conclusions This study provides evidence that semi-automated segmentation of 3T/7T MRI techniques can help to determine atherosclerotic plaque composition. In particular, the high resolution of ex-vivo 7T data was able to highlight greater detail in the atherosclerotic plaque composition. High field MRI may therefore have advantages for in vivo carotid plaque MR imaging

Distinguishing Solar Flare Types by Differences in Reconnection Regions

Observations show that magnetic reconnection and its slow shocks occur in solar flares. The basic magnetic structures are similar for long duration event (LDE) flares and faster compact impulsive (CI) flares, but the former require less non-thermal electrons than the latter. Slow shocks can produce the required non-thermal electron spectrum for CI flares by Fermi acceleration if electrons are injected with large enough energies to resonate with scattering waves. The dissipation region may provide the injection electrons, so the overall number of non-thermal electrons reaching the footpoints would depend on the size of the dissipation region and its distance from the chromosphere. In this picture, the LDE flares have converging inflows toward a dissipation region that spans a smaller overall length fraction than for CI flares. Bright loop-top X-ray spots in some CI flares can be attributed to particle trapping at fast shocks in the downstream flow, the presence of which is determined by the angle of the inflow field and velocity to the slow shocks.Comment: 15 pages TeX and 2 .eps figures, accepted to Ap.J.Let