Applications of the artificial compressibility method for turbulent open channel flows

A three‐dimensional (3‐D) numerical method for solving the Navier–Stokes equations with a standard k–ε turbulence model is presented. In order to couple pressure with velocity directly, the pressure is divided into hydrostatic and hydrodynamic parts and the artificial compressibility method (ACM) is employed for the hydrodynamic pressure. By introducing a pseudo‐time derivative of the hydrodynamic pressure into the continuity equation, the incompressible Navier–Stokes equations are changed from elliptic‐parabolic to hyperbolic‐parabolic equations. In this paper, a third‐order monotone upstream‐centred scheme for conservation laws (MUSCL) method is used for the hyperbolic equations. A system of discrete equations is solved implicitly using the lower–upper symmetric Gauss–Seidel (LU‐SGS) method. This newly developed numerical method is validated against experimental data with good agreement. Copyright © 2005 John Wiley & Sons, Ltd.     

Low energy (e,2e) studies from CH4: results from symmetric coplanar experiments and molecular three-body distorted wave theory

Low energy experimental and theoretical triply differential cross sections are presented for electron impact ionization of methane (CH(4)) for both the highest occupied molecular orbital (HOMO) and next highest occupied molecular orbital (NHOMO). The HOMO is a predominantly p-type orbital which is labeled 1t(2) and the NHOMO is predominantly s-type labeled 2a(1). Coplanar symmetric (symmetric both in final state electron energies and observation angles) are presented for final state electron energies ranging from 2.5 to 20 eV. The theoretical M3DW (molecular three-body distorted wave) results are in surprisingly good agreement with experiment for the HOMO state and less satisfactory agreement for the NHOMO state. The molecular NHOMO results are also compared with the ionization of the 2s shell of neon which is the isoelectronic atom.     

Enhanced coherence of weakly coupled lasers

We present the phase-locking and coherence properties between two weakly coupled lasers. We show how the degree of coherence between the two lasers can be enhanced by nearly 1 order of magnitude after taking into account the effects of coupling on both their phases as well as their amplitudes. Specifically, correlations between synchronized spikes in the amplitude dynamics and the phase dynamics of the lasers allow for an interference pattern with a fringe visibility of 90%, even when the coupling strength is far below the critical value and they are not phase locked.     

Exponential Asymptotics for Line Solitons in Two‐Dimensional Periodic Potentials

As a first step toward a fully two‐dimensional asymptotic theory for the bifurcation of solitons from infinitesimal continuous waves, an analytical theory is presented for line solitons, whose envelope varies only along one direction, in general two‐dimensional periodic potentials. For this two‐dimensional problem, it is no longer viable to rely on a certain recurrence relation for going beyond all orders of the usual multiscale perturbation expansion, a key step of the exponential asymptotics procedure previously used for solitons in one‐dimensional problems. Instead, we propose a more direct treatment which not only overcomes the recurrence‐relation limitation, but also simplifies the exponential asymptotics process. Using this modified technique, we show that line solitons with any rational line slopes bifurcate out from every Bloch‐band edge; and for each rational slope, two line‐soliton families exist. Furthermore, line solitons can bifurcate from interior points of Bloch bands as well, but such line solitons exist only for a couple of special line angles due to resonance with the Bloch bands. In addition, we show that a countable set of multiline‐soliton bound states can be constructed analytically. The analytical predictions are compared with numerical results for both symmetric and asymmetric potentials, and good agreement is obtained.     

Compensation of gradient-induced magnetic field perturbations

Pulsed magnetic field gradients are essential for MR imaging and localized spectroscopy applications. However, besides the desired linear field gradients, pulsed currents in a strong external magnetic field also generate unwanted effects like eddy currents, gradient coil vibrations and acoustic noise. While the temporal magnetic field perturbations associated with eddy currents lead to spectral line shape distortions and signal loss, the vibration-related modulations lead to anti-symmetrical sidebands of any large signal (i.e. water), thereby obliterating the signals from low-concentration metabolites. Here the measurement, characterization and compensation of vibration-related magnetic field perturbations is presented. Following a quantitative evaluation of the various temporal components of the main magnetic field, a digital B0 magnetic field waveform is generated which reduces all temporal variations of the main magnetic field to within the spectral noise level.     

Electronic structure and bonding studies on triple-decker sandwich complexes with a P6 middle ring

DFT and hybrid HF-DFT studies of structure and bonding of CpMP6MCp triple-decker sandwich complexes, ranging from 18-28 valence electrons (VE) with M=Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, and W, show that the middle P6 ring complexes adopt symmetric planar (28 valence electron count [VEC]), asymmetric planar (26 VEC), and puckered (24 VEC) geometries. According to the mno Rule, 50 skeletal electrons are needed for these triple-decker cluster frameworks. For 28 VEC, this corresponds to 10 electrons more than the 50 electrons of the mno Rule if all VE of the metal are included. These additional electrons control the distortion of a P6 middle ring and other finer structural details. Completely filled 2a* and 2b* orbitals in 28 VE complexes lead to a planar symmetrical P6 middle ring, while the occupancy in either 2a* or 2b* alone explains the in-plane distortions (asymmetric) in 26 VE complexes. In comparison with 28 VE complexes, the puckering of P6 middle ring in 24 VE complexes is due to the greater stabilization of 5a and the extra stabilization of the +4 oxidation state of Ti. The quintet state of 22 VE complexes is planar as 2a* and 2b* are half filled. Similar geometrical and bonding patterns of CpScP6ScCp and C2P3H2ScC3P3H3ScC2P3H2 support the carbon-phosphorus analogy further. The 18 VE systems, CpScC3B3H6ScCp+ and CpScP3B3H3ScCp+, have the 50 skeletal electrons as stipulated by the mno Rule. Corresponding anions have 52 skeletal electrons (20 VE); the middle rings here are distorted in the plane.