Marginally Trapped Tubes Generated from Nonlinear Scalar Field Initial Data

We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal, spherically symmetric marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initial data is sufficiently small and decays like O(r^-\frac12){O(r^{-\frac{1}{2}})}, and the potential function V is nonnegative with bounded second derivative. This result can be loosely interpreted as a statement about the stability of ‘nice’ asymptotic behavior of marginally trapped tubes under certain small perturbations of Schwarzschild.     

Mode Finding in Nonlinear Structural Eigenvalue Calculations

Abstract

The eigenvalue problems resulting from stiffness matrix formulations of structural vibration and buckling problems are nonlinear if substructures are analyzed exactly, or if classical frequency (vibration problems) or load factor (buckling problems) dependent member equations are used. This makes rapid calculation of accurate free vibration or buckling modes difficult. This paper presents several techniques which might overcome this difficulty, examines them theoretically and experimentally, and gives some of the ways in which the more successful techniques can be incorporated in mode finding methods. Coincident eigenvalues (i.e., natural frequencies or critical load factors) are included.     

Three-variable solution in the $$$$-dimensional null-surface formulation

The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact \((2+1)\)-dimensional solution that depends nontrivially upon all three of the NSF’s intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of \((2+1)\)-dimensional general relativistic spacetimes discovered by Cavaglià.     

The Preparation, Characterization and X-ray Structural Analysis of Tetrakis[1-Methyl-3-(2-Propyl)-2(3H)-Imidazolethione]Cadmium(II) Hexafluorophosphate

Abstract  A new compound, [Cd(mipit)₄][PF₆]₂ has been synthesized and characterized via standard solid and solution state methods including single crystal X-ray crystallography (mipit = 1-methyl-3-(2-propyl)-2(3H)-imidazolethione). The title compound crystallizes in tetragonal space group I4 ₁ /a with a = 12.478(2) ?, b = 12.478(2) ?, c = 28.806(6) ?, and Z = 4. The complex is a high melting, colorless solid that has a distorted tetrahedral CdS₄ coordination geometry. Thermogravimetric analysis results for the title compound as well as for another potential CdS synthon and two potential CdSe synthons are reported. Graphical Abstract  The synthesis and characterization of the title compound, a new ionic homoleptic cadmium complex, tetrakis[1-methyl-3-(2-propyl)-2(3H)-imidazolethione]cadmium(II) hexafluorophosphate is reported. The results of a single crystal X-ray diffraction analysis reveal a distorted tetrahedral CdS₄ coordination sphere about the cadmium. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Pressure anisotropy effects on nonlinear electrostatic excitations in magnetized electron-positron-ion plasmas

The propagation of linear and nonlinear electrostatic waves is investigated in a magnetized anisotropic electron-positron-ion (e-p-i) plasma with superthermal electrons and positrons. A two-dimensional plasma geometry is assumed. The ions are assumed to be warm and anisotropic due to an external magnetic field. The anisotropic ion pressure is defined using the double adiabatic Chew-Golberger-Low (CGL) theory. In the linear regime, two normal modes are predicted, whose characteristics are investigated parametrically, focusing on the effect of superthermality of electrons and positrons, ion pressure anisotropy, positron concentration and magnetic field strength. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential (disturbance) via a reductive perturbation method. The parametric role of superthermality, positron content, ion pressure anisotropy and magnetic field strength on the characteristics of solitary wave structures is investigated. Following Allen and Rowlands [J. Plasma Phys. 53, 63 (1995)], we have shown that the pulse soliton solution of the ZK equation is unstable to oblique perturbations, and have analytically traced the dependence of the instability growth rate on superthermality and ion pressure anisotropy.     

Multiband processing of multimode light: combining 3D photonic lanterns with waveguide Bragg gratings

The first demonstration of narrowband spectral filtering of multimode light on a 3D integrated photonic chip using photonic lanterns and waveguide Bragg gratings is reported. The photonic lanterns with multi‐notch waveguide Bragg gratings were fabricated using the femtosecond direct‐write technique in boro‐aluminosilicate glass (Corning, Eagle 2000). Transmission dips of up to 5 dB were measured in both photonic lanterns and reference single‐mode waveguides with 10.4‐mm‐long gratings. The result demonstrates efficient and symmetrical performance of each of the gratings in the photonic lantern. Such devices will be beneficial to space‐division multiplexed communication systems as well as for units for astronomical instrumentation for suppression of the atmospheric telluric emission from OH lines.     

Bacterial Cellulose Nanopaper as Reinforcement for Polylactide Composites: Renewable Thermoplastic NanoPaPreg

Bacterial cellulose (BC) is often regarded as a prime candidate nano‐reinforcement for the production of renewable nanocomposites. However, the mechanical performance of most BC nanocomposites is often inferior compared with commercially available polylactide (PLLA). Here, the manufacturing concept of paper‐based laminates is used, i.e., “PaPreg,” to produce BC nanopaper reinforced PLLA, which has been called “nanoPaPreg” by the authors. It is demon­strated that high‐performance nanoPaPreg (v_f = 65 vol%) with a tensile modulus and strength of 6.9 ± 0.5 GPa and 125 ± 10 MPa, respectively, can be fabricated. It is also shown that the tensile properties of nanoPaPreg are predominantly governed by the mechanical performance of BC nanopaper instead of the individual BC nanofibers, due to difficulties impregnating the dense nanofibrous BC network.

     

Comparison of detectability limits for elemental mapping by EF-TEM and STEM-XEDS

The analytical sensitivity in terms of the signal-to-noise ratio (SNR) was investigated for elemental mapping by a transmission electron microscope equipped with an energy filter (EF-TEM) and a scanning transmission electron microscope with an X-ray energy dispersive spectrometer (STEM-XEDS). To compare the detectability limits of the elemental maps by the two techniques, homogeneous Cu-0.98+/-0.34 wt% Mn and Cu-4.93+/-0.49 wt% Mn thin specimens were used. Elemental maps can be considered as either an image or a spectrum. Therefore, the detectability limits of the elemental maps were characterized by the spectral SNR. To evaluate the detectability limits of the elemental maps with statistical confidence limits such as 1 sigma, 2 sigma and 3 sigma, the SNR values were reviewed from the statistical point of view. In STEM-XEDS mapping, the spectral SNR values improve as the specimen thickness increases since the signal intensity increases. Conversely, the spectral SNR in EF-TEM mapping is maximized at a certain thickness and then reduces as the thickness increases. To compare the two mapping techniques with regard to the analytical sensitivity, a method to estimate the minimum mass fraction (MMF) from measured signal and background intensities was developed. In this experimental approach, the MMF value can be evaluated by selecting the appropriate SNR value corresponding to the statistical confidence limits. In comparing the estimated MMF values from the two mapping approaches, EF-TEM mapping can be more sensitive than STEM-XEDS mapping up to specimen thicknesses <20-30 nm in the 1 sigma confidence limit and < approximately 50 nm in the 3 sigma limits. However, as the specimen thickness increases, the XEDS maps provide better detectability limits in the Cu-Mn dilute alloy specimens.     

Improving spatiotemporal resolution of USPIO-enhanced dynamic imaging of rat kidneys

This paper addresses the problem of enhancing spatiotemporal resolution of ultra-small superparamagnetic iron oxide (USPIO)-enhanced dynamic MRI of rat kidneys. To alleviate the limited resolution problem of conventional full-scan Fourier imaging methods, we use a generalized series-based imaging scheme to reduce coverage of kappa-space. Experimental results demonstrate that the generalized series imaging method with basis functions constructed using two references (pre- and post-contrast) can reduce the number of phase encodings measured during the dynamic contrast wash-in process by a factor of 4 with a negligible or minimal loss of image quality. The method is expected to make 3D studies possible using USPIO-enhanced dynamic imaging of rat kidneys, and prove valuable for early detection of renal rejection after kidney transplantation.