Development of variable‐magnification X‐ray Bragg optics

A novel X‐ray Bragg optics is proposed for variable‐magnification of an X‐ray beam. This X‐ray Bragg optics is composed of two magnifiers in a crossed arrangement, and the magnification factor, M, is controlled through the azimuth angle of each magnifier. The basic properties of the X‐ray optics such as the magnification factor, image transformation matrix and intrinsic acceptance angle are described based on the dynamical theory of X‐ray diffraction. The feasibility of the variable‐magnification X‐ray Bragg optics was verified at the vertical‐wiggler beamline BL‐14B of the Photon Factory. For X‐ray Bragg magnifiers, Si(220) crystals with an asymmetric angle of 14° were used. The magnification factor was calculated to be tunable between 0.1 and 10.0 at a wavelength of 0.112 nm. At various magnification factors (M≥ 1.0), X‐ray images of a nylon mesh were observed with an air‐cooled X‐ray CCD camera. Image deformation caused by the optics could be corrected by using a 2 × 2 transformation matrix and bilinear interpolation method. Not only absorption‐contrast but also edge‐contrast due to Fresnel diffraction was observed in the magnified images.     

Towards a microchannel‐based X‐ray detector with two‐dimensional spatial and time resolution and high dynamic range

X‐ray detectors that combine two‐dimensional spatial resolution with a high time resolution are needed in numerous applications of synchrotron radiation. Most detectors with this combination of capabilities are based on semiconductor technology and are therefore limited in size. Furthermore, the time resolution is often realised through rapid time‐gating of the acquisition, followed by a slower readout. Here, a detector technology is realised based on relatively inexpensive microchannel plates that uses GHz waveform sampling for a millimeter‐scale spatial resolution and better than 100 ps time resolution. The technology is capable of continuous streaming of time‐ and location‐tagged events at rates greater than 10⁷ events per cm². Time‐gating can be used for improved dynamic range.     

Muffin‐tin potentials in EXAFS analysis

Muffin‐tin potentials are the standard tool for calculating the potential surface of a cluster of atoms for use in the analysis of extended X‐ray absorption fine‐structure (EXAFS) data. The set of Cartesian coordinates used to define the positions of atoms in the cluster and to calculate the muffin‐tin potentials is commonly also used to enumerate the scattering paths used in the EXAFS data analysis. In this paper, it is shown that these muffin‐tin potentials are sufficiently robust to be used to examine quantitatively contributions to the EXAFS data from scattering geometries not represented in the original cluster.     

Upgrade of beamline BL08B at Taiwan Light Source from a photon‐BPM to a double‐grating SGM beamline

During the last 20 years, beamline BL08B has been upgraded step by step from a photon beam‐position monitor (BPM) to a testing beamline and a single‐grating beamline that enables experiments to record X‐ray photo‐emission spectra (XPS) and X‐ray absorption spectra (XAS) for research in solar physics, organic semiconductor materials and spinel oxides, with soft X‐ray photon energies in the range 300–1000 eV. Demands for photon energy to extend to the extreme ultraviolet region for applications in nano‐fabrication and topological thin films are increasing. The basic spherical‐grating monochromator beamline was again upgraded by adding a second grating that delivers photons of energy from 80 to 420 eV. Four end‐stations were designed for experiments with XPS, XAS, interstellar photoprocess systems (IPS) and extreme‐ultraviolet lithography (EUVL) in the scheduled beam time. The data from these experiments show a large count rate in core levels probed and excellent statistics on background normalization in the L‐edge adsorption spectrum.     

Flying qubits and entangled photons

Efficient generation of polarized single photons or entangled photon pairs is crucial for the implementation of quantum key distribution (QKD) systems. Self organized semiconductor quantum dots (QDs) are capable of emitting on demand one polarized photon or an entangled photon pair upon current injection. Highly efficient single‐photon sources consist of a pin structure inserted into a microcavity where single electrons and holes are funneled into an InAs QD via a submicron AlOx aperture, leading to emission of single polarized photons with record purity of the spectrum and non‐classicality of the photons. A new QD site‐control technique is based on using the surface strain field of an AlO_x current aperture below the QD. GaN/AlN QD based devices are promising to operate at room temperature and reveal a fine‐structure splitting (FSS) depending inversely on the QD size. Large GaN/AlN QDs show disappearance of the FSS. Theory also suggests QDs grown on (111)‐oriented GaAs substrates as source of entangled photon pairs.     

On a discrimination problem for a class of stochastic processes with ordered first‐passage times

Consider the Bayes problem in which one has to discriminate if the random unknown initial state of a stochastic process is distributed according to either of two preassigned distributions, on the base of the observation of the first‐passage time of the process through 0. For processes whose first‐passage times to state 0 are increasing in the initial state according to the likelihood ratio order, such problem is solved by determining the Bayes decision function and the corresponding Bayes error. The special case of fixed initial values including a family of first‐passage times with proportional reversed hazard functions is then studied. Finally, various applications to birth‐and‐death and to diffusion processes are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Stability and convergence of optimum spectral non‐linear Galerkin methods

Our objective in this article is to present some numerical schemes for the approximation of the 2‐D Navier–Stokes equations with periodic boundary conditions, and to study the stability and convergence of the schemes. Spatial discretization can be performed by either the spectral Galerkin method or the optimum spectral non‐linear Galerkin method; time discretization is done by the Euler scheme and a two‐step scheme. Our results show that under the same convergence rate the optimum spectral non‐linear Galerkin method is superior to the usual Galerkin methods. Finally, numerical example is provided and supports our results. Copyright © 2001 John Wiley & Sons, Ltd.     

A particular solution of Heun equation for Hulthen and Woods‐Saxon potentials

In this article a particular solution of Heun equation is derived by making use of the Nikiforov‐Uvarov (NU) method which provides exact solutions for general hypergeometric equation and eigenvalues together with eigenfunctions of the Heun equation for this particular solution are obtained. One to one correspondence (isomorphism) of the aforesaid equation with the radial Schrödinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions (Hulthen and Woods‐Saxon potentials).

     

Computational study of singlet and triplet sulfonylnitrenes insertion into 1,3‐butadienes: 1,2‐ or 1,4‐cycloaddition?

The formation of N‐trifluoromethylsulfonyl‐2‐vinylaziridine and N‐trifluoromethylsulfonyl‐3‐pyrroline by the reaction of the singlet and triplet trifluoromethanesulfonylnitrenes with s‐cis‐ and s‐trans‐1,3‐butadienes was studied theoretically at the B3LYP/6‐311++G(d,p) and M06‐2X/6‐311++G(d,p) levels of theory. The singlet trifluoromethanesulfonylnitrene adds to s‐cis‐ and s‐trans‐1,3‐butadiene exothermally in one step to give the product of 1,2‐cycloaddition, N‐trifluoromethylsulfonyl‐2‐vinylaziridine, the energy decreasing by 88.5 and 86.2 kcal/mol at the B3LYP level and by 105.2 and 103.0 kcal/mol at the M06‐2X level, respectively. The formed 2‐vinylaziridine can undergo rotation about the C(2)–C_sp2 bond with the barrier not exceeding 3.5 kcal/mol and to rearrange into N‐trifluoromethylsulfonyl‐3‐pyrroline. The triplet trifluoromethanesulfonylnitrene reacts with s‐cis‐ and s‐trans‐1,3‐butadiene in two steps. The first exothermic step is the formation of the triplet diradical adducts. The second step is the spin inversion with the energy raising by 5.8 and 17.8 kcal/mol at the B3LYP level and by 11.0 and 20.8 kcal/mol at the M06‐2X level for the adducts to s‐cis‐ and s‐trans‐1,3‐butadiene, respectively. Recombination of the radical centers occurs selectively to give N‐trifluoromethylsulfonyl‐2‐vinylaziridine that is exothermally rearranged into N‐trifluoromethylsulfonyl‐3‐pyrroline with the energy barrier of 40 kcal/mol at the B3LYP level and of 50 kcal/mol at the M06‐2X level. Copyright © 2014 John Wiley & Sons, Ltd.     

Density functional theory study on a fluorescent chemosensor device of aza‐crown ether

Three derivatives of alkyl anthracene covalently bonded to aza‐18‐crown‐6 at the nitrogen position, anthracene(CH₂)_n, (n = 1–3) which act as an on–off fluorogenic photoswitch have been theoretically studied using a computational strategy based on density functional theory at B3LYP/6‐31 + G(d,p) method. The fully optimized geometries have been performed with real frequencies which indicate the minima states. The binding energies, enthalpies and Gibbs free energies have been calculated for aza‐18‐crown‐6 ( L ) and their metal complexes. The natural bond orbital analysis is used to explore the interaction of host–guest molecules. The absorption spectra differences between L and their metal ligands, the excitation energies and absorption wavelength for their excited states have been studied by time‐dependent density functional theory with the basis set 6‐31 + G(d,p). These fluorescent sensors and switchers based on photoinduced electron transfer mechanism have been investigated. The PET process from aza‐crown ether to fluorophore can be suppressed or completely blocked by the entry of alkali metal cations into the aza‐crown ether‐based receptor. Such a suppression of the PET process means that fluorescence intensity is enhanced. The binding selectivity studies of the aza‐crown ether part of L indicate that the presence of the alkali metal cations Li⁺, Na⁺ and K⁺ play an important role in determining the internal charge transfer and the fluorescence properties of the complexes. In addition, the solvent effect has been investigated. Copyright © 2014 John Wiley & Sons, Ltd.