Combination of schlieren and pulsed TV holography in the study of a high-speed flame jet

This paper presents studies of the propagation of a high-speed turbulent flame jet of an air/hydrogen gas mixture. The experimental results are recorded with the schlieren and the pulsed TV holography method. These methods are compared and combined to benefit from the advantages of each of them. Abel inversion has been used to achieve three-dimensional information i.e. refractive index distributions. Evaluation, calibration and Abel inversion algorithms are described together with experimental results. The results obtained from the different techniques show remarkable similarities concerning both qualitative and quantitative aspects.     

Probing structural stability of double-walled carbon nanotubes at high non-hydrostatic pressure by Raman spectroscopy

Theoretical calculations predict that the collapse pressure for double-walled carbon nanotubes (DWCNTs) is proportional to 1/R ³, where R is the effective or average radius of a DWCNT. In order to address the problem of CNT stability at high pressure and stress, we performed a resonance Raman study of DWCNTs dispersed in sodium cholate using 532 and 633 nm laser excitation. Raman spectra of the recovered samples show minor versus irreversible changes with increasing I _D/I _G ratio after exposure to high non-hydrostatic pressure of 23 and 35 GPa, respectively. The system exhibits nearly 70% pressure hysteresis in radial breathing vibrational mode signals recovery on pressure release which is twice that predicted by theory.     

Penrose Type Inequalities for Asymptotically Hyperbolic Graphs

In this paper, we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space ${\mathbb{H}^n}$ . The graphs are considered as unbounded hypersurfaces of ${\mathbb{H}^{n+1}}$ which carry the induced metric and have an interior boundary. For such manifolds, the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence, we estimate the mass by an integral over the inner boundary. In case the inner boundary satisfies a convexity condition, this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam’s article (The graph cases of the Riemannian positive mass and Penrose inequalities in all dimensions. http://arxiv.org/abs/1010.4256, 2010) concerning the asymptotically Euclidean case. Using ideas developed by Huang and Wu (The equality case of the penrose inequality for asymptotically flat graphs. http://arxiv.org/abs/1205.2061, 2012), we can in certain cases prove that equality is only attained for the anti-de Sitter Schwarzschild metric.     

Regression Density Estimation With Variational Methods and Stochastic Approximation

Regression density estimation is the problem of flexibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses finite mixture models and our article considers flexible mixtures of heteroscedastic regression (MHR) models where the response distribution is a normal mixture, with the component means, variances, and mixture weights all varying as a function of covariates. Our article develops fast variational approximation (VA) methods for inference. Our motivation is that alternative computationally intensive Markov chain Monte Carlo (MCMC) methods for fitting mixture models are difficult to apply when it is desired to fit models repeatedly in exploratory analysis and model choice. Our article makes three contributions. First, a VA for MHR models is described where the variational lower bound is in closed form. Second, the basic approximation can be improved by using stochastic approximation (SA) methods to perturb the initial solution to attain higher accuracy. Third, the advantages of our approach for model choice and evaluation compared with MCMC-based approaches are illustrated. These advantages are particularly compelling for time series data where repeated refitting for one-step-ahead prediction in model choice and diagnostics and in rolling-window computations is very common. Supplementary materials for the article are available online.     

Geometric obstruction of black holes

We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The completeness of the latter is then employed to rigorously prove the absence of static spherically symmetric black holes in more than three dimensions. The proof of these new results is preceded by a pedagogic review of the local aspects of sectional curvature bounds for Lorentzian manifolds, which extends and strengthens previous constructions.     

The split network analysis for exploring composition-structure correlations in multi-component glasses: I. Rationalizing bioactivity-composition trends of bioglasses

We present a strategy, referred to as “split network” analysis, for assessing the average network polymerization (r_F) and mean number of bridging oxygen (BO) atoms (N?_BO^F) for each individual network former F in multi-component oxide-based glasses, primarily targeting those involving Al, B, P and Si. This requires a priori knowledge about the parameters {r_F, N?_BO^F} of all network builders, but one, whose values are deduced by the split network procedure. We illustrate split-network concepts for establishing composition/structure/bioactivity correlations in Na-Ca-Si-P-O glasses. The cooperating influences on the bioactivity from the average polymerization degree of the silicate network and the amounts of orthophosphate and sodium ions are discussed.