Real-time measurement of stress and damage evolution during initial lithiation of crystalline silicon

Crystalline to amorphous phase transformation during initial lithiation in (100) Si wafers is studied in an electrochemical cell with Li metal as the counter and reference electrode. During initial lithiation, a moving phase boundary advances into the wafer starting from the surface facing the lithium electrode, transforming crystalline Si into amorphous Li(x)Si. The resulting biaxial compressive stress in the amorphous layer is measured in situ, and it was observed to be ca. 0.5 GPa. High-resolution TEM images reveal a very sharp crystalline-amorphous phase boundary, with a thickness of ～1 nm. Upon delithiation, the stress rapidly reverses and becomes tensile, and the amorphous layer begins to deform plastically at around 0.5 GPa. With continued delithiation, the yield stress increases in magnitude, culminating in a sudden fracture of the amorphous layer into microfragments, and the cracks extend into the underlying crystalline Si.     

Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link

We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.     

Tunable coupling in circuit quantum electrodynamics using a superconducting charge qubit with a V-shaped energy level diagram

We introduce a new type of superconducting charge qubit that has a V-shaped energy spectrum and uses quantum interference to provide independently tunable qubit energy and coherent coupling to a superconducting cavity. Dynamic access to the strong coupling regime is demonstrated by tuning the coupling strength from less than 200 kHz to greater than 40 MHz. This tunable coupling can be used to protect the qubit from cavity-induced relaxation and avoid unwanted qubit-qubit interactions in a multiqubit system.     

Local realism of macroscopic correlations

We identify conditions under which correlations resulting from quantum measurements performed on macroscopic systems (systems composed of a number of particles of the order of the Avogadro number) can be described by local realism. We argue that the emergence of local realism at the macroscopic level is caused by an interplay between the monogamous nature of quantum correlations and the fact that macroscopic measurements do not reveal properties of individual particles.     

Ferrite-ferroelectric phase shifters controlled by electric and magnetic fields

Planar phase shifters fabricated based on ferrite-ferroelectric layered structures are studied experimentally. The structures served as waveguides for spin-electromagnetic waves, whose phase shift was controlled by both electric and magnetic fields. The measurements were performed in the magnetic field range from 900 to 2100 Oe, which corresponds to operating frequencies from 4.0 to 8.5 GHz, with 5- to 20-μm-thick yttrium-iron garnet ferrite films and 200- to 500-μm-thick barium-strontium titanate ferroelectric plates. It is shown that the phase shift may exceed 180° and is a function of the magnetic and electric fields and also of the thickness of the ferrite and ferroelectric layers.     

Influence of post-deposition annealing on the structural,optical and electrical properties of Li and Mg co-doped ZnO thin films deposited by sol–gel technique

Lithium (Li) and magnesium (Mg) co-doped zinc oxide (ZnO) thin films were deposited by sol–gel method using spin coating technique. The films were deposited on glass substrates and annealed at different temperatures. The effects of annealing temperature on the structural, optical and electrical properties of the deposited films were investigated using X-ray diffraction (XRD), Ultraviolet–Visible absorption spectra (UV–VIS), photoluminescence spectra (PL), X-ray photo electron spectroscopy (XPS) and Hall measurements. XRD patterns indicated that the deposited films had a polycrystalline hexagonal wurtzite structure with preferred (0 0 0 2) orientation. All films were found to exhibit a good transparency in the visible range. Analysis of the absorption edge revealed that the optical band gap energies of the films annealed at different temperatures varies between 3.49 eV and 3.69 eV. Room temperature PL spectra of the deposited films annealed at various temperatures consist of a near band edge emission and visible emission due to the electronic defects, which are related to deep level emissions, such as oxide antisite (O_Zn), interstitial zinc (Zn_i), interstitial oxygen (O_i) and zinc vacancy (V_Zn) which are generated during annealing process. The influence of annealing temperature on the chemical state of the dopants in the film was analysed by XPS spectra. Ion beam analysis (Rutherford back scattering) experiments were performed to evaluate the content of Li and Mg in the films. Hall measurements confirmed the p-type nature of the deposited films.     

Simultaneous velocity and temperature measurements in gaseous flow fields using the VENOM technique

We present an initial demonstration of simultaneous velocity and temperature mapping in gaseous flow fields using a new nitric oxide planar laser-induced fluorescence-based method. The vibrationally excited NO monitoring (VENOM) technique is an extension of two-component velocimetry using vibrationally excited NO generated from the photodissociation of seeded NO(2) [Appl. Opt. 48, 4414 (2009)], where the two sequential fluorescence images are obtained probing two different rotational states to provide both velocity and temperature maps. Comparisons to computational fluid dynamics simulations show that the initial VENOM measurements provide good velocity and temperature maps in the relatively high-density regions of the flow, where the rms uncertainties are approximately 5% for velocity and 9% for temperature.     

Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood

We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility of the result. We have also shown that our argument can be extended to the m-tuple conjecture of Hardy and Littlewood.     

Uniform convergence analysis of hybrid numerical scheme for singularly perturbed problems of mixed type

In this article, we consider a class of singularly perturbed mixed parabolic‐elliptic problems whose solutions possess both boundary and interior layers. To solve these problems, a hybrid numerical scheme is proposed and it is constituted on a special rectangular mesh which consists of a layer resolving piecewise‐uniform Shishkin mesh in the spatial direction and a uniform mesh in the temporal direction. The domain under consideration is partitioned into two subdomains. For the spatial discretization, the proposed scheme is comprised of the classical central difference scheme in the first subdomain and a hybrid finite difference scheme in the second subdomain, whereas the time derivative in the given problem is discretized by the backward‐Euler method. We prove that the method converges uniformly with respect to the perturbation parameter with almost second‐order spatial accuracy in the discrete supremum norm. Numerical results are finally presented to validate the theoretical results.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1931–1960, 2014     

A unified approach to the integrals of Mellin–Barnes–Hecke type

In this paper, we provide a unified approach to a family of integrals of Mellin–Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of distributions via smooth submersive maps defined by Hörmander. We derive by this method the integrals of Hecke and Sonine related to various types of Bessel functions which have found applications in analytic and algebraic number theory.