The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry

The closest tensors of higher symmetry classes are derived in explicit form for a given elasticity tensor of arbitrary symmetry. The mathematical problem is to minimize the elastic length or distance between the given tensor and the closest elasticity tensor of the specified symmetry. Solutions are presented for three distance functions, with particular attention to the Riemannian and log-Euclidean distances. These yield solutions that are invariant under inversion, i.e., the same whether elastic stiffness or compliance are considered. The Frobenius distance function, which corresponds to common notions of Euclidean length, is not invariant although it is simple to apply using projection operators. A complete description of the Euclidean projection method is presented. The three metrics are considered at a level of detail far greater than heretofore, as we develop the general framework to best fit a given set of moduli onto higher elastic symmetries. The procedures for finding the closest elasticity tensor are illustrated by application to a set of 21 moduli with no underlying symmetry.Comment: 48 pages, 1 figur

An Imaging and Spectral Study of Ten X-Ray Filaments around the Galactic Center

We report the detection of 10 new X-ray filaments using the data from the {\sl Chandra} X-ray satellite for the inner $6^{\prime}$ ($\sim 15$ parsec) around the Galactic center (GC). All these X-ray filaments are characterized by non-thermal energy spectra, and most of them have point-like features at their heads that point inward. Fitted with the simple absorbed power-law model, the measured X-ray flux from an individual filament in the 2-10 keV band is $\sim 2.8\times10^{-14}$ to $10^{-13}$ ergs cm$^{-2}$ s$^{-1}$ and the absorption-corrected X-ray luminosity is $\sim 10^{32}-10^{33}$ ergs s$^{-1}$ at a presumed distance of 8 kpc to the GC. We speculate the origin(s) of these filaments by morphologies and by comparing their X-ray images with the corresponding radio and infrared images. On the basis of combined information available, we suspect that these X-ray filaments might be pulsar wind nebulae (PWNe) associated with pulsars of age $10^3 \sim 3\times 10^5$ yr. The fact that most of the filament tails point outward may further suggest a high velocity wind blowing away form the GC.Comment: 29 pages with 7 figures and 3 pages included. Accepted to Ap

Predicting cortical bone adaptation to axial loading in the mouse tibia

The development of predictive mathematical models can contribute to a deeper understanding of the specific stages of bone mechanobiology and the process by which bone adapts to mechanical forces. The objective of this work was to predict, with spatial accuracy, cortical bone adaptation to mechanical load, in order to better understand the mechanical cues that might be driving adaptation. The axial tibial loading model was used to trigger cortical bone adaptation in C57BL/6 mice and provide relevant biological and biomechanical information. A method for mapping cortical thickness in the mouse tibia diaphysis was developed, allowing for a thorough spatial description of where bone adaptation occurs. Poroelastic finite-element (FE) models were used to determine the structural response of the tibia upon axial loading and interstitial fluid velocity as the mechanical stimulus. FE models were coupled with mechanobiological governing equations, which accounted for non-static loads and assumed that bone responds instantly to local mechanical cues in an on–off manner. The presented formulation was able to simulate the areas of adaptation and accurately reproduce the distributions of cortical thickening observed in the experimental data with a statistically significant positive correlation (Kendall's τ rank coefficient τ = 0.51, p < 0.001). This work demonstrates that computational models can spatially predict cortical bone mechanoadaptation to a time variant stimulus. Such models could be used in the design of more efficient loading protocols and drug therapies that target the relevant physiological mechanisms

Performance evaluation of novel square-bordered position-sensitive silicon detectors with four-corner readout

We report on a recently developed novel type of large area (62 mm x 62 mm) position sensitive silicon detector with four-corner readout. It consists of a square-shaped ion-implanted resistive anode framed by additional low-resistivity strips with resistances smaller than the anode surface resistance by a factor of 2. The detector position linearity, position resolution, and energy resolution were measured with alpha-particles and heavy ions. In-beam experimental results reveal a position resolution below 1 mm (FWHM) and a very good non-linearity of less than 1% (rms). The energy resolution determined from 228Th alpha source measurements is around 2% (FWHM).Comment: 13 pages, 10 figures, submitted to Nucl. Instr. and Meth.

Understanding presentations of children with fever to a Sydney emergency department

Background: Fever is a common childhood illness resulting in a potentially high number of presentations to local Emergency Departments (ED). This paper describes the characteristics of these presentations of children, including initial and subsequent diagnosis, disposition from ED and seasonal variations, to inform nursing and other health professionals working within these departments. Methods: The study was conducted at a metropolitan hospital in Sydney, using existing data collected by emergency staff. Data for a 12-month period were extracted from the existing database of all ED presentations. Results: This study demonstrated that the age of the majority of febrile child presentations varied between 13 months and 24 months (53%), and the number of ED visits doubled during the winter months (33%). Most of the child presentations to ED in this study were not urgent (68%). Viral illness, upper respiratory tract infections, and urinary tract infections accounted for 14.9 % of all the ED presentations, with most being discharged to home. Conclusion: This study confirms the continuing pattern of inappropriate presentations to EDs of children with fever. Public education campaigns are needed to reduce these presentations

Conductivity and redox stability of new double perovskite oxide Sr 1.6 K 0.4 Fe 1+ x Mo 1− x O 6− δ (x= 0.2, 0.4, 0.6)

A series of new perovskite oxides Sr1.6K0.4Fe1+xMo1−xO6−δ (x = 0.2, 0.4, 0.6) were synthesised by solid state reaction method. Synthesis of Sr1.6K0.4Fe1+xMo1−xO6−δ (x = 0.2, 0.4, 0.6) was achieved above 700 °C in 5 % H2/Ar, albeit with the formation of impurity phases. Phase stability upon redox cycling was only observed for sample Sr1.6K0.4Fe1.4Mo0.6O6−δ. Redox cycling of Sr1.6K0.4Fe1+xMo1−xO6−δ (x = 0.2, 0.4, 0.6) demonstrates a strong dependence on high temperature reduction to achieve high conductivities. After the initial reduction at 1200 °C in 5 %H2/Ar, then re-oxidation in air at 700 °C and further reduction at 700 °C in 5 %H2/Ar, the attained conductivities were between 0.1 and 58.4 % of the initial conductivity after reduction 1200 °C in 5 %H2/Ar depending on the composition. In the investigated new oxides, sample Sr1.6K0.4Fe1.4Mo0.6O6−δ is most redox stable also retains reasonably high electrical conductivity, ~70 S/cm after reduction at 1200 °C and 2–3 S/cm after redox cycling at 700 °C, indicating it is a potential anode for SOFCs