Experimental investigation of a strongly shocked gas bubble

A free-falling, spherical, soap-film bubble filled with argon is subjected to a planar M=2.88 shock in atmospheric nitrogen; vorticity is deposited on the surface of the bubble during shock interaction, and the Richtmyer-Meshkov instability ensues. The geometrical development of the shocked bubble is diagnosed with laser sheet imaging and a planar slice showing two cross sections of both the major vortex ring and a secondary vortex ring is revealed experimentally for the first time. Quantitative measurements of the experimental data include the vortex velocity defect, and subsequent circulation calculations, along with a new set of relevant length scales. The shock wave strength, leading to a post-shock compressible regime, allows the study of the instability development in a regime between low Mach number shock tube experiments and high Mach number laser driven experiments that has not been investigated previously.     

First total synthesis of the 4a-methyltetrahydrofluorene diterpenoids (+/-)-dichroanal B and (+/-)-dichroanone

[reaction: see text] A simple synthesis of the 4a-methyltetrahydrofluorene diterpenoids (+/-)-dichroanal B and (+/-)-dichroanone has been achieved through a common hexahydrofluorenone intermediate obtained via Pd(0)-catalyzed reductive cyclization of a substituted 2-(2-bromobenzyl) methylene cyclohexane.     

Busemann Functions in a Harmonic Manifold

For a noncompact complete and simply connected harmonic manifold M, we prove the analyticity of Busemann functionson M. This is the main result of this paper. An application of it shows that the harmonic spaces having minimal horospheres have the bi-asymptotic property. Finally, we prove that the total Busemann functionis continuous in C topology. As a consequence, we show that the uniform divergence of geodesics holds in these spaces.     

Connectivity constant of the kagomé lattice

From the computation of self-avoiding walks on the kagomé lattice, its connectivity constant is found to be 2·569 ± 0·008.     

Investigation of the optical gain and noise figure for multi-channel amplification in EDFA under optimized pump condition

We present the results of an investigation of optical gain and noise figure for simultaneous multi-channel amplification of an erbium doped fibre amplifier (EDFA) under optimized pump condition. Different pump configurations with varying input signal levels show interesting features on gain flatness. In the experiment, population inversion along the fibre length which determines the gain-spectra and noise characteristics of the amplifier is adjusted through optimized fibre length and injected pump power in order to minimize the gain-tilt at C-band. It is observed that bi-directional pumping manifests the best combination of low noise and high gain of EDFA which are useful as in-line repeaters in WDM network. We obtain 30 ± 1.5 dB intrinsically flat small signal gain from 1538 nm to 1558 nm band of wavelength with noise figure <4 dB for 16-channel simultaneous amplification in a single stage EDFA without gain flattening filter.     

Analysis of stone column-supported geosynthetic-reinforced embankments

In the present paper, the behavior of stone column-supported geosynthetic-reinforced embankments has been studied. The soil arching effect is incorporated in the study to determine the stresses acting on stone columns as well as soft soil. The effect of stiffness of the stone column is also incorporated in the present study. Based on the stress action in the improved ground, stress concentration ratio, axial strain of geosynthetic reinforcement, tension developed in it and settlement of the improved soft ground are determined by using the developed methodology. Present analytical method is also verified with several current design methods. It is observed from parametric studies that modular ratio or stiffness of the stone columns, spacing to diameter ratio, height of the embankment, depth of the soft soil, stiffness of the geosynthetic reinforcement significantly affect the behavior of geosynthetic-reinforced stone column-supported embankments resting on soft soil.     

The Graphical Horseshoe Estimator for Inverse Covariance Matrices

We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive properties compared to other popular estimators, such as the graphical lasso and the graphical smoothly clipped absolute deviation. The most prominent benefit is that when the true inverse covariance matrix is sparse, the graphical horseshoe provides estimates with small information divergence from the sampling model. The posterior mean under the graphical horseshoe prior can also be almost unbiased under certain conditions. In addition to these theoretical results, we also provide a full Gibbs sampler for implementing our estimator. MATLAB code is available for download from github at http://github.com/liyf1988/GHS. The graphical horseshoe estimator compares favorably to existing techniques in simulations and in a human gene network data analysis. Supplementary materials for this article are available online.