Teichmüller's extremal ring problem

An algorithmic solution to Teichmüller's extremal ring problem is given.     

Analysis of a bilinear finite element for shallow shells I: Approximation of inextensional deformations

We consider a bilinear reduced-strain finite element formulation for a shallow shell model of Reissner-Naghdi type. The formulation is closely related to the facet models used in engineering practice. We estimate the error of this scheme when approximating an inextensional displacement field. We make the strong assumptions that the domain and the finite element mesh are rectangular and that the boundary conditions are periodic and the mesh uniform in one of the coordinate directions. We prove then that for sufficiently smooth fields, the convergence rate in the energy norm is of optimal order uniformly with respect to the shell thickness. In case of elliptic shell geometry the error bound is furthermore quasioptimal, whereas in parabolic and hyperbolic geometries slightly enhanced smoothness is required, except for the degenerate cases where the characteristic lines are parallel with the mesh lines. The error bound is shown to be sharp.

     

Universal gates with wires in a row

Journal of Algebraic Combinatorics - Koornwinder polynomials are q-orthogonal polynomials equipped with extra five parameters and the $$B C_n$$ -type Weyl group symmetry, which were introduced by...     

Toughness and Fracture Properties in Nacre‐Mimetic Clay/Polymer Nanocomposites

Nacre inspires researchers by combining stiffness with toughness by its unique microstructure of aligned aragonite platelets. This brick‐and‐mortar structure of reinforcing platelets separated with thin organic matrix has been replicated in numerous mimics that can be divided into two categories: microcomposites with aligned metal oxide microplatelets in polymer matrix, and nanocomposites with self‐assembled nanoplatelets—usually clay or graphene oxide—and polymer. While microcomposites have shown exceptional fracture toughness, current fabrication methods have limited nacre‐mimetic nanocomposites to thin films where fracture properties remained unexplored. Yet, fracture resistance is the defining property of nacre, therefore centrally important in any mimic. Furthermore, to make use of these properties in applications, bulk materials are required. Here, up to centimeter‐thick nacre‐mimetic clay/polymer nanocomposites are produced by the lamination of self‐assembled films. The aligned clay nanoplatelets are separated by poly(vinyl alcohol) matrix, with 10⁶–10⁷ nanoplatelets on top of each other in the bulk plates. Fracture testing shows crack deflection and a fracture toughness of 3.4 MPa m^1/2, not far from nacre. Flexural tests show high stiffness (25 GPa) and strength (220 MPa) that, despite the hydrophilic constituents, are not substantially affected by exposure to humidity.     

Vortex pump for dilute bose-einstein condensates

The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed amount of vorticity can be added to the condensate in each cycle. In an adiabatic operation of this vortex pump, the appearance of vortices into the condensate is interpreted as the accumulation of a local Berry phase. Our design can be used as an experimentally realizable vortex source for possible vortex-based applications of dilute Bose-Einstein condensates.     

Analysis of selective androgen receptor modulators by gas chromatography-microchip atmospheric pressure photoionization-mass spectrometry

A gas chromatography-microchip atmospheric pressure photoionization-mass spectrometric (GC-μAPPI-MS) method was developed and used for the analysis of three 2-quinolinone-derived selective androgen receptor modulators (SARMs). SARMs were analyzed from spiked urine samples, which were hydrolyzed and derivatized with N-methyl-N-(trimethylsilyl)trifluoroacetamide before analysis. Trimethylsilyl derivatives of SARMs formed both radical cations (M^+•) and protonated molecules ([M + H]⁺) in photoionization. Better signal-to-noise ratios (S/N) were obtained in MS/MS analysis using the M^+• ions as precursor ions than using the [M + H]⁺ ions, and therefore the M^+• ions were selected for the precursor ions in selected reaction monitoring (SRM) analysis. Limits of detection (LODs) with the method ranged from 0.01 to 1 ng/mL, which correspond to instrumental LODs of 0.2–20 pg. Limits of quantitation ranged from 0.03 to 3 ng/mL. The mass spectrometric response to the analytes was linear (R ≥ 0.995) from the LOQ concentration level up to 100 ng/mL concentration, and intra-day repeatabilities were 5%–9%. In addition to the GC-μAPPI-MS study, the proof-of-principle of gas chromatography-microchip atmospheric pressure chemical ionization-Orbitrap MS (GC-μAPCI-Orbitrap MS) was demonstrated.     

Passivation of black silicon boron emitters with atomic layer deposited aluminum oxide

The nanostructured surface – also called black silicon (b‐Si) – is a promising texture for solar cells because of its extremely low reflectance combined with low surface recombination obtained with atomic layer deposited (ALD) thin films. However, the challenges in keeping the excellent optical properties and passivation in further processing have not been addressed before. Here we study especially the applicability of the ALD passivation on highly boron doped emitters that is present in crystalline silicon solar cells. The results show that the nanostructured boron emitters can be passivated efficiently using ALD Al₂O₃ reaching emitter saturation current densities as low as 51 fA/cm². Furthermore, reflectance values less than 0.5% after processing show that the different process steps are not detrimental for the low reflectance of b‐Si. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spread spectrum magnetic resonance imaging

We propose a novel compressed sensing technique to accelerate the magnetic resonance imaging (MRI) acquisition process. The method, coined spread spectrum MRI or simply s(2)MRI, consists of premodulating the signal of interest by a linear chirp before random k-space under-sampling, and then reconstructing the signal with nonlinear algorithms that promote sparsity. The effectiveness of the procedure is theoretically underpinned by the optimization of the coherence between the sparsity and sensing bases. The proposed technique is thoroughly studied by means of numerical simulations, as well as phantom and in vivo experiments on a 7T scanner. Our results suggest that s(2)MRI performs better than state-of-the-art variable density k-space under-sampling approaches.     

Nonadiabatic Ehrenfest molecular dynamics within the projector augmented-wave method

We derive equations for nonadiabatic Ehrenfest molecular dynamics within the projector augmented-wave (PAW) formalism. The discretization of the electrons is time-dependent as the augmentation functions depend on the positions of the nuclei. We describe the implementation of the Ehrenfest molecular dynamics equations within the real-space PAW method. We demonstrate the applicability of our method by studying the vibration of NaCl, the torsional rotation of H(2)C=NH(2)(+) in both the adiabatic and the nonadiabatic regimes, and the hydrogen bombardment of C(40)H(16).