Averaging approximation to singularly perturbed nonlinear stochastic wave equations

An averaging method is applied to derive effective approximation to the following singularly perturbed nonlinear stochastic damped wave equation \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain $D\subset\R^n$\,, $1\leq n\leq 3$\,. Here $\nu>0$ is a small parameter characterising the singular perturbation, and $\nu^\alpha$\,, $0\leq \alpha\leq 1/2$\,, parametrises the strength of the noise. Some scaling transformations and the martingale representation theorem yield the following effective approximation for small $\nu$, u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of \ord{\nu^\alpha}\,.Comment: 16 pages. Submitte

Relative contributions of lean and fat mass to bone mineral density: Insight from Prader-Willi syndrome

© 2018 Viardot, Purtell, Nguyen and Campbell. Context: Low bone mineral density (BMD) is the most important risk factor for fragility fracture. Body weight is a simple screening predictor of difference in BMD between individuals. However, it is not clear which component of body weight, lean (LM), or fat mass (FM), is associated with BMD. People with the genetic disorder of Prader-Willi syndrome (PWS) uniquely have a reduced LM despite increased FM. Objective: We sought to define the individual impact of LM and FM on BMD by investigating subjects with and without PWS. Design, Setting and Participants: This cross-sectional study was conducted at the Clinical Research Facility of the Garvan Institute of Medical Research, with PWS and control participants recruited from a specialized PWS clinic and from the general public by advertisement, respectively. The study involved 11 adults with PWS, who were age- and sex-matched with 12 obese individuals (Obese group) and 10 lean individuals (Lean group). Main Outcome Measures: Whole body BMD was measured by dual-energy X-ray absorptiometry. Total body FM and LM were derived from the whole body scan. Differences in BMD between groups were assessed by the analysis of covariance model, taking into account the effects of LM and FM. Results: The PWS group had significantly shorter height than the lean and obese groups. As expected, there was no significant difference in FM between the Obese and PWS group, and no significant difference in LM between the Lean and PWS group. However, obese individuals had greater LM than lean individuals. BMD in lean individuals was significantly lower than in PWS individuals (1.13 g/cm2 vs. 1.21 g/cm2, p < 0.05) and obese individuals (1.13 g/cm2 vs. 1.25 g/cm2, p < 0.05). After adjusting for both LM and FM, there was no significant difference in BMD between groups, and the only significant predictor of BMD was LM. Conclusions: These data from the human genetic model Prader-Willi syndrome suggest that LM is a stronger determinant of BMD than fat mass

Prevalence of bacterial contamination of powdered infant feeds in a hospital environment

Background The study arose as part of a nutrition model regarding the introduction of ready-to-use (RTU) infant feeds in place of powdered infant feeds (PIFs) as a standard formula for infants under the age of 1 year who are unable to be breastfed. Internationally and locally there is grave concern regarding the safety and efficacy of PIFs, especially in a hospital setting, and the resultant bacterial contamination causing enteric infections, in premature, immunocompromised and sick infants.Objective. To evaluate the of bacterial contamination of PIPs given to infants at Red Cross War Memorial Children's Hospital, Cape Town.Methods. Quantitative levels of bacterial contamination were determined and were expressed as colony-forming units (CFUs) per millilitre of sample. Aliquots of milk were inoculated onto agar, and the milk samples were then incubated at 25°C overnight (N = 10), 30°C overnight (N = 48) and 30°C for 6 hours (N 34). Post-incubation milk samples were cultured again Contamination was defined as any positive culture administration (i.e. pre incubation) or&gt; 102 CFU/ ml after administration (i.e. post incubation).Results. Fifty samples of PIFs (N 82) were contaminated pre incubation, with (30.4%) being heavily contaminated(&gt; 104 CFU /ml). Post incubation, 43/92 samples (46.7%) were contaminated with&gt; 102 CFU /mi. The acidified PIFs appeared to have some bactericidal effect against some of the organisms, but not all.Conclusions. RTU infant feeds are sterile and are recommended for use in all hospitalised infants. The results of this study indicate that even when milk is prepared in a controlled environment there is bacterial contarnination of PIFs post production. As feeds are now readily available in South Africa every attempt should be made to use a sterile RTU system for hospitalised infants

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques

Electron doping evolution of the neutron spin resonance in NaFe1−x_{1-x}Cox_{x}As

Neutron spin resonance, a collective magnetic excitation coupled to superconductivity, is one of the most prominent features shared by a broad family of unconventional superconductors including copper oxides, iron pnictides, and heavy fermions. In this work, we study the doping evolution of the resonances in NaFe$_{1-x}$Co$_x$As covering the entire superconducting dome. For the underdoped compositions, two resonance modes coexist. As doping increases, the low-energy resonance gradually loses its spectral weight to the high-energy one but remains at the same energy. By contrast, in the overdoped regime we only find one single resonance, which acquires a broader width in both energy and momentum, but retains approximately the same peak position even when $T_c$ drops by nearly a half compared to optimal doping. These results suggest that the energy of the resonance in electron overdoped NaFe$_{1-x}$Co$_x$As is neither simply proportional to $T_c$ nor the superconducting gap, but is controlled by the multi-orbital character of the system and doped impurity scattering effect.Comment: accepted by PR

Effect of Mechanical Strain on the Optical Properties of Nodal-Line Semimetal ZrSiS

Optical properties of nodal-line semimetal ZrSiS are studied using first-principles calculations. Frequency-independent optical conductivity is a fingerprint of the infrared optical response in ZrSiS. It is found that this characteristic feature is robust with respect to uniaxial compressive strain of up to 10 GPa, yet with the flat region being narrowed with increasing strain. Upon uniaxial tensile stress of 2 GPa, the Fermi surface undergoes a Lifshitz transition accompanied by a weakening of the interband screening, which reduces the spectral weight of infrared excitations. It is also shown that the high-energy region is characterized by low-loss plasma excitations at ≈20 eV with essentially anisotropic dispersion. Strongly anisotropic dielectric properties suggest the existence of a hyperbolic regime for plasmons in the deep ultraviolet range. Although the frequencies of high-energy plasmons are virtually unaffected by external uniaxial deformation, their dispersion can be effectively tuned by strain. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimNational Natural Science Foundation of China, NSFC: 117742692018FYA0305800S.Y. acknowledges financial support from the National Key R & D Program of China (Grant No. 2018FYA0305800) and National Science Foundation of China (Grant No. 11774269). A.N.R. acknowledges travel support from FLAG-ERA JTC2017 Project GRANSPORT. Numerical calculations presented in this paper were performed on a supercomputing system in the Supercomputing Center of Wuhan University

Searching for biosignatures by their rotational spectrum: global fit and methyl group internal rotation features of dimethylsulphoxide up to 116 GHz

The identification and quantification of molecules in interstellar space and atmospheres of planets in the solar systems and in exoplanets rely on spectroscopicmethods and laboratory work is essential to provide the community with the spectral features needed to analyse cosmological observations. Rotational spectroscopy in particular, with its intrinsic high resolution, allows the unambiguous identification of biomolecular building blocks and biosignature gases which can be correlated with the origin of life or the identification of habitable planets.We report the extension of the measured rotational transition frequencies of dimethylsulphoxide and its 34S and 13C isotopologues in the millimetrewave range (59.6–78.4 GHz) by use of an absorption spectrometer based on the supersonic expansion technique. Hyperfine patterns related to the methyl group internal rotation were analysed in the microwave range region (6–18 GHz) with a Pulsed Jet Fourier Transform spectrometer at extremely high resolution (2 kHz) and reliable predictions up to 116 GHz are provided. The focus on sulphur-bearing molecules is motivated by the fact that sulphur is largely involved in the intra- and inter-molecular hydrogen bonds in proteins and although it is the 10th most abundant element in the known Universe, understanding its chemistry is still amatter of debate.Moreover, sulphur-bearingmolecules, in particular dimethylsulphoxide, have been indicated as possible biosignature gases to be monitored in the search of habitable exoplanets

Electron Accumulation and Emergent Magnetism in LaMnO3/SrTiO3 Heterostructures

Emergent phenomena at polar-nonpolar oxide interfaces have been studied intensely in pursuit of next-generation oxide electronics and spintronics. Here we report the disentanglement of critical thicknesses for electron reconstruction and the emergence of ferromagnetism in polar-mismatched LaMnO3/SrTiO3 (001) heterostructures. Using a combination of element-specific X-ray absorption spectroscopy and dichroism, and first-principles calculations, interfacial electron accumulation and ferromagnetism have been observed within the polar, antiferromagnetic insulator LaMnO3. Our results show that the critical thickness for the onset of electron accumulation is as thin as 2 unit cells (UC), significantly thinner than the observed critical thickness for ferromagnetism of 5 UC. The absence of ferromagnetism below 5 UC is likely induced by electron over-accumulation. In turn, by controlling the doping of the LaMnO3, we are able to neutralize the excessive electrons from the polar mismatch in ultrathin LaMnO3 films and thus enable ferromagnetism in films as thin as 3 UC, extending the limits of our ability to synthesize and tailor emergent phenomena at interfaces and demonstrating manipulation of the electronic and magnetic structures of materials at the shortest length scales.Comment: Accepted by Phys. Rev. Let

Quickly routing searches without having to move content

Abstract. A great deal of work has been done to improve peer-to-peer routing by strategically moving or replicating content. However, there are many applications for which a peer-to-peer architecture might be appropriate, but in which content movement is not feasible. We argue that even in such applications, progress can be made in developing techniques that ensure efficient searches. We present several such techniques. First, we show that organizing the network into a square-root topology, where peer degrees are proportional to the square root of the popularity of their content, provides much better performance than power-law networks. Second, we present routing optimizations based on the amount of content stored at peers, and tracking the “best ” peers, that can further improve performance. These and other techniques can make searches efficient, even when content movement or replication is not feasible.