Ultrasonic Caustics and the Inverse Scattering Problem in NDE

This paper explores theoretically the possibility of using caustics, formed in the ultrasonic field diffracted by defects, as an approach to the inverse scattering problem, The case of crack-like defects is considered in detail, using the geometrical theory of diffraction. The involute of the far field caustic reproduces the projection of the crack edge in the incident beam direction, for a plane incident wavefront. This purely geometrical inversion is carried out uniquely for the astroid and its involute, the elliptical edge. For a general edge shape, the complete inversion requires one further length measurement, which may be carried out in some cases by further experiments with caustics, Usefullimitations on the possible shapes of caustics are explained on the basis of catastrophe theory, Calculations show that the inherent intensity-level change (~2-3 dB) and width ( ~ wavelength) over which it occurs for a typical ultrasonic caustic are adequate for observation. Some discussion is given of experimental requirements, as well as of caustics formed in the near field of a crack and of those formed by voids and inclusions. The topology of the far field caustic cannot in general distinguish between volumetric and crack-like defects. Studying caustics may prove to be a useful adjunct to ultrasonic imaging systems for the inspection of fatigue cracks

Midpalatal implants vs headgear for orthodontic anchorage - a randomized clinical trial: Cephalometric results

OBJECTIVE: To compare the clinical effectiveness of the mid-palatal implant as a method of reinforcing anchorage during orthodontic treatment with that of conventional extra-oral anchorage. DESIGN: A prospective, randomized, clinical trial Setting: Chesterfield and North Derbyshire Royal Hospital NHS Trust and the Charles Clifford Dental Hospital, Sheffield. SUBJECTS AND METHODS: 51 orthodontic patients between the ages of 12 and 39, with a class II division 1 malocclusion and ‘absolute anchorage’ requirements were randomly allocated to either receive a mid-palatal implant or headgear to reinforce orthodontic anchorage. The main outcome of the trial was to compare the mesial movement of the molars and incisors of the two treatment groups between T1 (start) and T2 (end of anchorage reinforcement) as measured from cephalometric radiographs. RESULTS: The reproducibility of the measuring technique was acceptable. There were significant differences between the T1 and T2 measurements within the implant group for the position of the maxillary central incisor (p<0.001), position of the maxillary molar (p=0.009) and position of the mandibular molar (p<0.001). There were significant differences within the headgear group for the position of the mandibular central incisor (p<0.045), position of the maxillary molar (p=<0.001) and position of the mandibular molar (p<0.001). All the skeletal and dental points moved mesially more in the headgear group during treatment than in the implant group. These ranged from an average of 0.5mm more mesial for the mandibular permanent molar to 1.5mm more mesial for the maxillary molar and mandibular base. None of the treatment changes between the implant and headgear groups were statistically significant. CONCLUSIONS: Mid-palatal implants are an acceptable technique for reinforcing anchorage in the orthodontic patient

Midpalatal implants vs headgear for orthodontic anchorage - a randomized clinical trial: Cephalometric results

OBJECTIVE: To compare the clinical effectiveness of the mid-palatal implant as a method of reinforcing anchorage during orthodontic treatment with that of conventional extra-oral anchorage. DESIGN: A prospective, randomized, clinical trial Setting: Chesterfield and North Derbyshire Royal Hospital NHS Trust and the Charles Clifford Dental Hospital, Sheffield. SUBJECTS AND METHODS: 51 orthodontic patients between the ages of 12 and 39, with a class II division 1 malocclusion and ‘absolute anchorage’ requirements were randomly allocated to either receive a mid-palatal implant or headgear to reinforce orthodontic anchorage. The main outcome of the trial was to compare the mesial movement of the molars and incisors of the two treatment groups between T1 (start) and T2 (end of anchorage reinforcement) as measured from cephalometric radiographs. RESULTS: The reproducibility of the measuring technique was acceptable. There were significant differences between the T1 and T2 measurements within the implant group for the position of the maxillary central incisor (p<0.001), position of the maxillary molar (p=0.009) and position of the mandibular molar (p<0.001). There were significant differences within the headgear group for the position of the mandibular central incisor (p<0.045), position of the maxillary molar (p=<0.001) and position of the mandibular molar (p<0.001). All the skeletal and dental points moved mesially more in the headgear group during treatment than in the implant group. These ranged from an average of 0.5mm more mesial for the mandibular permanent molar to 1.5mm more mesial for the maxillary molar and mandibular base. None of the treatment changes between the implant and headgear groups were statistically significant. CONCLUSIONS: Mid-palatal implants are an acceptable technique for reinforcing anchorage in the orthodontic patient

First principles theory of chiral dichroism in electron microscopy applied to 3d ferromagnets

Recently it was demonstrated (Schattschneider et al., Nature 441 (2006), 486), that an analogue of the X-ray magnetic circular dichroism (XMCD) experiment can be performed with the transmission electron microscope (TEM). The new phenomenon has been named energy-loss magnetic chiral dichroism (EMCD). In this work we present a detailed ab initio study of the chiral dichroism in the Fe, Co and Ni transition elements. We discuss the methods used for the simulations together with the validity and accuracy of the treatment, which can, in principle, apply to any given crystalline specimen. The dependence of the dichroic signal on the sample thickness, accuracy of the detector position and the size of convergence and collection angles is calculated.Comment: 9 pages, 6 figures, submitted to Physical Review

Rayleigh scattering in the transmission spectrum of HAT-P-18b

We have performed ground-based transmission spectroscopy of the hot Jupiter HAT-P-18b using the ACAM instrument on the William Herschel Telescope (WHT). Differential spectroscopy over an entire night was carried out at a resolution of $R \approx 400$ using a nearby comparison star. We detect a bluewards slope extending across our optical transmission spectrum which runs from 4750 to 9250\AA. The slope is consistent with Rayleigh scattering at the equilibrium temperature of the planet (852K). We do not detect enhanced sodium absorption, which indicates that a high-altitude haze is masking the feature and giving rise to the Rayleigh slope. This is only the second discovery of a Rayleigh scattering slope in a hot Jupiter atmosphere from the ground, and our study illustrates how ground-based observations can provide transmission spectra with precision comparable to the Hubble Space Telescope.Comment: 11 pages, 9 figures, accepted for publication in MNRA

Calculating effective resistances on underlying networks of association schemes

Recently, in Refs. \cite{jsj} and \cite{res2}, calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on stratification and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effective resistances on more general networks which are underlying networks of association schemes is considered, where by using the algebraic combinatoric structures of association schemes such as stratification and Bose-Mesner algebras, an explicit formula for effective resistances on these networks is given in terms of the parameters of corresponding association schemes. Moreover, we show that for particular underlying networks of association schemes with diameter $d$ such that the adjacency matrix $A$ possesses $d+1$ distinct eigenvalues, all of the other adjacency matrices $A_i$, $i\neq 0,1$ can be written as polynomials of $A$, i.e., $A_i=P_i(A)$, where $P_i$ is not necessarily of degree $i$. Then, we use this property for these particular networks and assume that all of the conductances except for one of them, say $c\equiv c_1=1$, are zero to give a procedure for evaluating effective resistances on these networks. The preference of this procedure is that one can evaluate effective resistances by using the structure of their Bose-Mesner algebra without any need to know the spectrum of the adjacency matrices.Comment: 41 page

A Dynamical Analysis of the Proposed Circumbinary HW Virginis Planetary System

In 2009, the discovery of two planets orbiting the evolved binary star system HW Virginis was announced, based on systematic variations in the timing of eclipses between the two stars. The planets invoked in that work were significantly more massive than Jupiter, and moved on orbits that were mutually crossing - an architecture which suggests that mutual encounters and strong gravitational interactions are almost guaranteed. In this work, we perform a highly detailed analysis of the proposed HW Vir planetary system. First, we consider the dynamical stability of the system as proposed in the discovery work. Through a mapping process involving 91,125 individual simulations, we find that the system is so unstable that the planets proposed simply cannot exist, due to mean lifetimes of less than a thousand years across the whole parameter space. We then present a detailed re-analysis of the observational data on HW Vir, deriving a new orbital solution that provides a very good fit to the observational data. Our new analysis yields a system with planets more widely spaced, and of lower mass, than that proposed in the discovery work, and yields a significantly greater (and more realistic) estimate of the uncertainty in the orbit of the outermost body. Despite this, a detailed dynamical analysis of this new solution similarly reveals that it also requires the planets to move on orbits that are simply not dynamically feasible. Our results imply that some mechanism other than the influence of planetary companions must be the principal cause of the observed eclipse timing variations for HW Vir. If the sys- tem does host exoplanets, they must move on orbits differing greatly from those previously proposed. Our results illustrate the critical importance of performing dynamical analyses as a part of the discovery process for multiple-planet exoplanetary systems.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Societ