Analytical approximations to numerical solutions of theoretical emission measure distributions

Emission line fluxes from cool stars are widely used to establish an apparent emission measure distribution, EmdApp(Te), between temperatures characteristic of the low transition region and the low corona. The true emission measure distribution, EmdTrue(Te), is determined by the energy balance and geometry adopted and, with a numerical model, can be used to predict EmdApp(Te), to guide further modelling. The scaling laws that exist between coronal parameters arise from the dimensions of the terms in the energy balance equation. Here, analytical approximations to numerical solutions for EmdTrue(Te) are presented, which show how the constants in the coronal scaling laws are determined. The apparent emission measure distributions show a minimum value at some T0 and a maximum at the mean coronal temperature Tc (although in some stars, emission from active regions can contribute). It is shown that, for the energy balance and geometry adopted, the analytical values of the emission measure and electron pressure at T0 and Tc depend on only three parameters: the stellar surface gravity and the values of T0 and Tc. The results are tested against full numerical solutions for e Eri (K2 V) and are applied to Procyon (a CMi, F5 IV/V). The analytical approximations can be used to restrict the required range of full numerical solutions, to check the assumed geometry and to show where the adopted energy balance may not be appropriate. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.

An in situ spatially resolved analytical technique to simultaneously probe gas phase reactions and temperature within the packed bed of a plug flow reactor

This paper reports the detailed description and validation of a fully automated, computer controlled analytical method to spatially probe the gas composition and thermal characteristics in packed bed systems. As an exemplar, we have examined a heterogeneously catalysed gas phase reaction within the bed of a powdered oxide supported metal catalyst. The design of the gas sampling and the temperature recording systems are disclosed. A stationary capillary with holes drilled in its wall and a moveable reactor coupled with a mass spectrometer are used to enable sampling and analysis. This method has been designed to limit the invasiveness of the probe on the reactor by using the smallest combination of thermocouple and capillary which can be employed practically. An 80 mu m (O.D.) thermocouple has been inserted in a 250 mu m (O.D.) capillary. The thermocouple is aligned with the sampling holes to enable both the gas composition and temperature profiles to be simultaneously measured at equivalent spatially resolved positions. This analysis technique has been validated by studying CO oxidation over a 1% Pt/Al2O3 catalyst and the spatial resolution profiles of chemical species concentrations and temperature as a function of the axial position within the catalyst bed are reported.

Using geostatistical Bayesian Updating to integrate airborne radiometrics and soil geochemistry to improve mapping for mineral exploration

Mineral exploration programmes around the world use data from remote sensing, geophysics and direct sampling. On a regional scale, the combination of airborne geophysics and ground-based geochemical sampling can aid geological mapping and economic minerals exploration. The fact that airborne geophysical and traditional soil-sampling data are generated at different spatial resolutions means that they are not immediately comparable due to their different sampling density. Several geostatistical techniques, including indicator cokriging and collocated cokriging, can be used to integrate different types of data into a geostatistical model. With increasing numbers of variables the inference of the cross-covariance model required for cokriging can be demanding in terms of effort and computational time. In this paper a Gaussian-based Bayesian updating approach is applied to integrate airborne radiometric data and ground-sampled geochemical soil data to maximise information generated from the soil survey, to enable more accurate geological interpretation for the exploration and development of natural resources. The Bayesian updating technique decomposes the collocated estimate into a production of two models: prior and likelihood models. The prior model is built from primary information and the likelihood model is built from secondary information. The prior model is then updated with the likelihood model to build the final model. The approach allows multiple secondary variables to be simultaneously integrated into the mapping of the primary variable. The Bayesian updating approach is demonstrated using a case study from Northern Ireland where the history of mineral prospecting for precious and base metals dates from the 18th century. Vein-hosted, strata-bound and volcanogenic occurrences of mineralisation are found. The geostatistical technique was used to improve the resolution of soil geochemistry, collected one sample per 2 km2, by integrating more closely measured airborne geophysical data from the GSNI Tellus Survey, measured over a footprint of 65 x 200 m. The directly measured geochemistry data were considered as primary data in the Bayesian approach and the airborne radiometric data were used as secondary data. The approach produced more detailed updated maps and in particular maximized information on mapped estimates of zinc, copper and lead. Greater delineation of an elongated northwest/southeast trending zone in the updated maps strengthened the potential to investigate stratabound base metal deposits.

When are total concentrations not total? Factors affecting geochemical analytical techniques for measuring element concentrations in soil

Inductively coupled plasma (ICP) following aqua regia digestion and X-ray fluorescence (XRF) are both geochemical techniques used to determine ‘total’ concentrations of elements in soil. The aim of this study is to compare these techniques, identify elements for which inconsistencies occur and investigate why they arise. A study area (∼14,000 km2) with a variety of total concentration controls and a large geochemical dataset (n = 7950) was selected. Principal component analysis determined underlying variance in a dataset composed of both geogenic and anthropogenic elements. Where inconsistencies between the techniques were identified, further numerical and spatial analysis was completed. The techniques are more consistent for elements of geogenic sources and lead, whereas other elements of anthropogenic sources show less consistency within rural samples. XRF is affected by sample matrix, while the form of element affects ICP concentrations. Depending on their use in environmental studies, different outcomes would be expected from the techniques employed, suggesting the choice of analytical technique for geochemical analyses may be more critical than realised.

An anatomical and analytical study of the Modiolus: Enlightening its relevance to plastic surgery

Background: This study was designed to evaluate the structures, muscles, and fasciae of which the modiolus is composed. It can aid in the understanding and, therefore, the utilization of plastic surgery for the aesthetic or reconstructive treatment of that region, especially the angle of the mouth. Methods: Dissections of the midface were done on five different cadavers. They were of different races (3 males, 2 females). The anatomy of the modiolus was studied in detail. New anatomical observations were classified as type I through type VI. Results: The perifacial artery fascia contributed to the modiolus in four (80%) specimens and was not part of it in 1 (20%) specimen. The facial artery was anterior to it in one (20%) specimen, lateral in four (80%) specimens, and never medial to it. No significant relationship was observed between the perifacial artery fascia contribution to the modiolus and gender or race. Also, the location of the facial artery lateral or anterior to the modiolus was not significantly related to gender or race. In addition, the deep and superficial fasciae of the face converged not anterior to the masseter muscle but actually at the modiolus, which was different from observations made by others. Conclusion: The modiolus is of critical importance in aesthetic and reconstructive plastic surgery of the face. © 2008 Springer Science+Business Media, LLC and International Society of Aesthetic Plastic Surgery.

The lip:A histologic and analytical approach of relevance to esthetic plastic surgery

This is a study done for the first time to understand the histologic features of the lip deeply, quantitatively, and analytically and identify the differences between the outer, intermediate, and inner parts of the lips. Previous researchers did not tackle the histologic features of the lip from this point of view. Half lip was obtained from different well-preserved cadavers where the upper lip, lower lip, and lip angle were evaluated by coronal histologic sections. A total of 43 slides were studied and photographed using light and digital microscopes (Nikon COOLSCOPE, Nikon Corporation, Tokyo, Japan), respectively. The cadavers (26 men and 17 women) were in the age group of 45 to 65 years old, and older than 65 years. Data were entered on a study pro forma and statistically analyzed. Normal histologic features of the upper lip, intermediate, and the inner lip sections were observed. Fibrous septations that sometimes had muscular components inserting into them could be identified. In between these septations, there were loose areas (chambers). The mean numbers of chambers identified in the upper and lower lips were higher in the red areas, and more septations and chambers were identified in the lower lip. New histologic observations were classified into types 1 to 7. Significant relations were identified between the total number of septations and chambers in relation to age group and sex. Higher means of septations and chambers were detected in the age group older than 65 years, and in women as a whole. In conclusion, the findings detected in this work could explain the congenital lip pits that are familial or syndromic and many post-lip augmentation complications. © 2009 Lippincott Williams & Wilkins, Inc.

Anatomic dissection of the arterial supply of the lips:an anatomical and analytical approach

Previous investigators have not described some of the new anatomic variations or provided quantitative and analytical data of the arterial anatomy of the lips in as much depth as in this study. Dissections of 14 different facial sides of cadavers were done. Through investigating the arterial supply of the upper and lower lips, measurements were performed and statistically analyzed. The main arterial supply of the upper lip was from the superior labial artery (SLA, mean external diameter, 1.8 mm [SD, 0.74 mm]); in addition, the subalar and septal branches contributed to its vascularization. The origin of the SLA was above the labial commissure in 78.6%. The subalar branch was not found but replaced by the alar artery that arose from the infraorbital artery in 1 specimen. The main arterial supply of the lower lip was derived from 3 branches of the facial artery, the inferior labial artery (mean external diameters, 1.4 mm [SD, 0.31 mm]) and the horizontal and vertical labiomental arteries. The inferior labial artery originated mostly below the labial commissure in 42.9% and formed a common trunk with the SLA in 28.6%. The horizontal labiomental artery was present in all, but vertical labiomental artery was absent in 21.4% of specimens. Overall, observed anatomic variations were classified into types I to VIII. Significant relations between the demographic variables and measured parameters were reported including the correlation coefficient among evaluated parameters. In conclusion, this study provides various information that aids in creating new flaps and supports the vascular base for clinical procedures in reconstructive surgery of the lip.

Analytical model of interwoven spiral arrays

Interweaving planar spiral conductors in doubly periodic arrays enable substantially sub-wavelength resonant response along with broadening fractional bandwidth. A self-contained analytical model is proposed to accurately predict the characteristics of the intertwined quadrifilar spiral array near the fundamental resonance. The model, based upon a multiconductor transmission line (MTL) approach, provides physical insight into the unique properties of the distributed interactions between the interleaved counter-wound spiral arms extended beyond a single unit cell and elucidates the mechanisms underlying the array performance at normal and oblique incidence of TE and TM polarised waves. The developed MTL model is instrumental in the design of the artificial surfaces with the specified response.