An implicit high-order spectral difference approach for large eddy simulation

The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgrid-scale stress tensor is modelled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm. In order to study the sensitivity of the method, first, the implicit solver is used to compute the two-dimensional (2D) laminar flow around a NACA0012 airfoil at Re = 5 × 10⁵ with zero angle of attack. Afterwards, the accuracy and the reliability of the solver are tested by solving the 2D “turbulent” flow around a square cylinder at Re = 10⁴ and Re =  2.2 × 10⁴. The results show a good agreement with the experimental data and the reference solutions.     

Optical sensing characteristics of the photonic crystal fiber filled with magnetic fluid

A novel photonic crystal fiber sensing theory filled with magnetic fluid is proposed based on the change of the MF refractive index under varied magnetic field. The magnetically induced tuning of the magnetic fluid filled PCF propagation properties were investigated by the full-vector finite element method with a perfectly matched layer. Theoretical calculations show that both the effective refractive index and the effective mode area increase vs. the increased magnetic field, and the PCF filled MF with larger d/Λ is more sensitive to magnetic field. When the wavelength λ = 1550 nm, the duty ratio d/Λ = 0.9, d/Λ = 0.6, the effective refractive indexes increase respectively from 1.598279 to 1.617572, from 1.61948 to 1.632484, and the effective mode areas increase respectively from 3.561115 μm² to 7.052360 μm², from 6.167494 μm² to 37.221998 μm² as the magnetic field changes from 25 Oe to 175 Oe. This scheme provides theoretical foundation to use magnetic field to control light in photonic crystal fiber and also offers a potential method for magnetic field sensing based on the TIR-PCF.     

A parallel algorithm for solving the 3d Schrödinger equation

We describe a parallel algorithm for solving the time-independent 3d Schrödinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between computational nodes. We demonstrate that the compute time, t, scales inversely with the number of computational nodes as t ∝ (N_nodes)^{−0.95 ± 0.04}. This makes it possible to solve the 3d Schrödinger equation on extremely large spatial lattices using a small computing cluster. In addition, we present a new method for precisely determining the energy eigenvalues and wavefunctions of quantum states based on a symmetry constraint on the FDTD initial condition. Finally, we discuss the usage of multi-resolution techniques in order to speed up convergence on extremely large lattices.     

Use of Euler series to fit spectra with application to water

Power series expansions of water eigenstate energies in J and K converge poorly and show alternating signs of the coefficients of the power series. Euler series can be used effectively to change an alternating series into one where all the coefficients have the same sign and where the radius of convergence is increased. This paper extends the Euler series to a two-dimensional series in K² and [J (J + 1) − K²]. Application of this Euler series to the rotational energies of the ground state and the first 4 excited vibrational states of water allows a fit to experimental accuracy to J = 22 and K = 22. This fit has good convergence and also has predictive capability. It is much easier to fit the perturbed states because the Euler series allows the zero-order energy the perturbed states to be predicted with more confidence.     

Two new upwind difference schemes for a coupled system of convection–diffusion equations arising from the steady MHD duct flow problems

In this paper, we develop two new upwind difference schemes for solving a coupled system of convection–diffusion equations arising from the steady incompressible MHD duct flow problem with a transverse magnetic field at high Hartmann numbers. Such an MHD duct flow is convection-dominated and its solution may exhibit localized phenomena such as boundary layers, namely, narrow boundary regions where the solution changes rapidly. Most conventional numerical schemes cannot efficiently solve the layer problems because they are lacking in either stability or accuracy. In contrast, the newly proposed upwind difference schemes can achieve a reasonable accuracy with a high stability, and they are capable of resolving high gradients near the layer regions without refining the grid. The accuracy of the first new upwind scheme is O(h + k) and the second one improves the accuracy to O(ε²(h + k) + ε(h² + k²) + (h³ + k³)), where 0 < ε ? 1/M ? 1 and M is the high Hartmann number. Numerical examples are provided to illustrate the performance of the newly proposed upwind difference schemes.     

Choice of the reduction and of the representation in centrifugal distortion analysis: A case study of dimethylsulfoxide

The millimeter-wave and submillimeter-wave spectra of dimethylsulfoxide have been measured up to 660 GHz, corresponding to maximum values of J = 70 and K_c = 68. A total of 3331 transitions (corresponding to 2133 distinct frequencies) were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although dimethylsulfoxide is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r) but the least-squares system of normal equations is better conditioned with representation I^r. These results are compared to those obtained for a few typical molecules.     

Second order gauge theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama’s program. A novel field strength G = ∂F + fAF arises besides the one of the first order treatment, F = ∂A − ∂A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L_P ∝ G². In this application the photon mass is estimated. The SU (N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov’s Lagrangian.     

High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics

We present a class of hybridizable discontinuous Galerkin (HDG) methods for the numerical simulation of wave phenomena in acoustics and elastodynamics. The methods are fully implicit and high-order accurate in both space and time, yet computationally attractive owing to their following distinctive features. First, they reduce the globally coupled unknowns to the approximate trace of the velocity, which is defined on the element faces and single-valued, thereby leading to a significant saving in the computational cost. In addition, all the approximate variables (including the approximate velocity and gradient) converge with the optimal order of k + 1 in the L²-norm, when polynomials of degree k ? 0 are used to represent the numerical solution and when the time-stepping method is accurate with order k + 1. When the time-stepping method is of order k + 2, superconvergence properties allows us, by means of local postprocessing, to obtain better, yet inexpensive approximations of the displacement and velocity at any time levels for which an enhanced accuracy is required. In particular, the new approximations converge with order k + 2 in the L²-norm when k ? 1 for both acoustics and elastodynamics. Extensive numerical results are provided to illustrate these distinctive features.     

Centrifugal distortion analysis of the rotational spectrum of aziridine: Comparison of different Hamiltonians

Previous measurements of rotational spectrum of aziridine up to 1.85 THz have been supplemented by new data in 225-660 GHz frequency range. A total of 1465 transitions (915 of them are newly assigned ones) with maximum values of J = 59 and K_c = 50 were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although aziridine is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r). It is explained that the failure of the combination (A, III^r) is due to the large value of the parameter σ=(2C-A-B)/(A-B) which makes some sextic centrifugal distortion constants much too large impeding the convergence of the Hamiltonian. It is also shown that the calculation of the centrifugal distortion constants from a force field is sometimes an ill-conditioned operation. Finally, the use of a non-reduced Hamiltonian (with six quartic centrifugal distortion constants) was successful in the particular case thanks to the method of predicate observations.     

Spectroscopy of AlO: Combined analysis of the AΠi → XΣ and BΣ → XΣ transitions

A combined analysis of the A²Π_i → X²Σ⁺ and B²Σ⁺ → X²Σ⁺ band systems of AlO, involving 21,500 line assignments, has been performed. The analysis indicates that the previously reported γ values of the B²Σ⁺ state are questionable. The present analysis shows that γ(B²Σ⁺) ≈ 0.014 cm⁻¹, essentially independent of the vibrational level. The positive sign is consistent with second order interaction with the higher-lying C²Π_r and lower-lying A²Π_i states. It also appears that many of the previously reported γ and γ_D values of X²Σ⁺ (v > 0) are doubtful. In fact, γ(X²Σ⁺) is observed to become increasingly negative for v″ > 1, due to second order interaction with the low-lying A²Π_i state. The present results are based on models where the hyperfine structure of the ²Σ⁺ states has been taken into account explicitly. Intensity patterns of the branches of the B²Σ⁺ → X²Σ⁺ system have been shown to be influenced by the case bβ_S coupling in the ground state v = 0,1 levels. This gives rise to intensity differences of around 10 percent in the R₁/R₂ and P₁/P₂ doublet components. The synthesized intensity patterns are fully in accord with the F₁/F₂ assignments of the present work.     

ICLAS of weak transitions of water between 11 300 and 12 850 cm: Comparison with FTS databases

Very weak water vapor absorption lines have been investigated by intracavity laser absorption spectroscopy (ICLAS) in the 11 335-11 947 and 12 336-12 843 cm⁻¹ spectral regions dominated by the ν₁ + 3ν₂ + ν₃ and ν₂ + 3ν₃ bands, respectively. A detectivity on the order of α_min ∼ 10⁻⁹ cm⁻¹ was achieved with an ICLAS spectrometer based on a Ti: Sapphire laser. It allowed detecting transitions with an intensity down to 5 × 10⁻²⁸ cm/molecule which is about 10 times lower than the weakest line intensities previously detected in the considered region. A line list corresponding to 1281 transitions with intensity lower than 5 × 10⁻²⁶ cm/molecule has been generated. A detailed comparison with the line lists provided by the HITRAN database and by recent investigations by Fourier transform spectroscopy associated with very long multi pass cell is presented. The rovibrational assignment performed on the basis of the ab initio calculations of Schwenke and Partridge, has allowed for determining 176 new energy levels belonging to a total of 16 vibrational states.     

Multi-step laser excitation of the highly excited states of zinc

We report experimental data on the highly excited states of zinc in the energy range 74,625-75,740 cm⁻¹ using two-step laser excitation scheme in conjunction with a thermionic diode ion detector. The 4s4p ³P₁ inter-combination level at 32501.399 cm⁻¹ was populated using a frequency doubled dye laser. The 4s5s ³S₁ level at 53672.28 cm⁻¹ gets populated from the ASE (amplified spontaneous emission) of the second step dye laser. The Rydberg series 4snp ³P₂ (12 ? n ? 60), 4snp ¹P₁ (16 ? n ? 30) and parity forbidden transitions 4sns ³S₁ (19 ? n ? 44) have been observed. A two parameter fit to excitation energies of the observed series yields the binding energy of the 4s5s ³S₁ level as 22097.03 ± 0.03 cm⁻¹ and consequently, the first ionization potential of zinc is determined as 75769.31 ± 0.05 cm⁻¹, that is in excellent agreement with the earlier work.     

Designing of endlessly single mode polarization maintaining highly birefringent nonlinear micro-structure fiber at telecommunication window by FV-FEM

An endlessly single mode highly polarization maintaining nonlinear microstructure fiber at telecommunication window is reported via full-vector finite element method. By taking three ring hexagonal PCF with suitable fiber parameter such as air hole diameter in cladding region d = 0.8 μm, pitch 2.3 μm and introducing four symmetrical large air holes near core region d′ = 2 μm, single mode (V_eff ≤ π), small effective mode area 2.7 μm², nonlinear co-efficient 44.39 W⁻¹ km⁻¹, high phase birefringence of the order of 10⁻³ and group birefringence of the order of 10⁻⁴ with beat length 0.3 μm at wavelength 1.55 μm are achieved.     

Global fittings of NNO and NNO vibrational-rotational line positions using the effective Hamiltonian approach

An effective Hamiltonian built up to sixth order in the Amat-Nielsen ordering scheme describing all rovibrational energy levels in the ground electronic state and containing in explicit form all resonance interaction terms due to the approximate relations between harmonic frequencies ω₁≈2ω₂ and ω₃≈4ω₂ was applied to model the observed rovibrational line positions (collected from the literature) of ¹⁴N¹⁵N¹⁶O and ¹⁵N¹⁴N¹⁶O isotopologues of nitrous oxide. For ¹⁴N¹⁵N¹⁶O, 124 effective Hamiltonian parameters were fitted to near 28 000 observed line positions covering the 0.8-8860 cm⁻¹ spectral range. The RMS of the weighted fit is 0.00126 cm⁻¹ and dimensionless standard deviation is 1.48. For ¹⁵N¹⁴N¹⁶O, 121 effective Hamiltonian parameters were fitted to more than 31 000 observed line positions covering the same spectral interval. The RMS of the weighted fit is 0.00185 cm⁻¹ and dimensionless standard deviation is 1.85. In both cases the models describe all available line positions with precision compatible to the measurement uncertainties. A number of local resonance perturbations was found and discussed. Among these perturbations there are interpolyad resonance Coriolis interactions. A comparison of HITRAN-2008 data with the calculations based on the fitted models is presented.     

Frequency stabilization of a Q-switched Nd:YAG laser oscillator with stability better 300 kHz following an rf-sideband scheme

A frequency stabilization scheme following the Pound-Drever-Hall technique modified with a sample and hold circuit has been applied to a Q-switched diode-pumped Nd:YAG ring oscillator. The high-power ring is injection seeded by a monolithic non-planar ring laser oscillator (NPRO). The slave oscillator emits pulses of 23 ns duration and 20 mJ pulse energy with almost diffraction limited beam quality (M² = 1.2) at a repetition rate of 400 Hz. The short-term fluctuation of the center frequency from pulse to pulse is 290 kHz. The oscillator is designed for applications within lidar measurements.     

Illumination dependence of I-V and C-V characterization of Au/InSb/InP(1 0 0) Schottky structure

The effects of surface preparation and illumination on electric parameters of Au/InSb/InP(100) Schottky diode were investigated, in the later diode InSb forms a fine restructuration layer allowing to block In atoms migration to surface. In order to study the electric characteristics under illumination, we make use of an He-Ne laser of 1 mW power and 632.8 nm wavelength. The current-voltage I(V_G), the capacitance-voltage C(V_G) measurements were plotted and analysed. The saturation current I_s, the serial resistance R_s and the mean ideality factor n are, respectively, equal to 2.03 × 10⁻⁵ A, 85 Ω, 1.7 under dark and to 3.97 × 10⁻⁵ A, 67 Ω, 1.59 under illumination. The analysis of I(V_G) and C(V_G) characteristics allows us to determine the mean interfacial state density N_ss and the transmission coefficient θ_n equal, respectively, to 4.33 × 10¹² eV⁻¹ cm⁻², 4.08 × 10⁻³ under dark and 3.79 × 10¹² eV⁻¹ cm⁻² and 5.65 × 10⁻³ under illumination. The deep discrete donor levels presence in the semiconductor bulk under dark and under illumination are responsible for the non-linearity of the C⁻²(V_G) characteristic.     

Electron spectrum of δ-doped quantum wells by the Thomas-Fermi method at finite temperatures

The electron spectrum of δ-doped quantum wells in n-GaAs is investigated by means of the Thomas-Fermi (TF) method at finite temperatures. This method shows rapid convergence and good accuracy. Under two-dimensional (2D) doping concentrations 10¹³…2×10¹³ cm⁻², the simplest TF method (T=0 K) can be used to calculate the profiles of the potential well up to T≈200 K. The simplest TF method yields correct results for the electron concentrations and the differences of the electron energy sublevels in the quantum well up to room temperature (T∼300 K).     

On the cΠ (v = 0) state of carbon monoxide

A full analysis of the near infrared c³Π-b³Σ⁺ (0-0) band is given and term values for both states determined. The c³Π (v = 0) state was jointly analysed with the perturbing k³Π (v = 2) state and data from the c³Π-X¹Σ⁺ (0-0) transition and 3A band system were included. It is shown that the available data are consistent with the c³Π (v = 0) state having near Hund’s case b coupling with a spin-orbit constant of A = 0.45 ± 0.02 cm⁻¹, a homogeneous perturbation with the k³Π (v = 2) state, and Λ-type doubling arising predominantly from its interaction with the j³Σ⁺ state. A discrepancy with a more recent report of the 3A band system is identified and discussed. The perturbed b³Σ⁺ state term values are consistent with a previously reported five state interaction model.     

Femtosecond laser-induced damage of gold films

Single- and multi-shot ablation thresholds of gold films in the thickness range of 31-1400 nm were determined employing a Ti:sapphire laser delivering pulses of 28 fs duration, 793 nm center wavelength at 1 kHz repetition rate. The gold layers were deposited on BK7 glass by an electron beam evaporation process and characterized by atomic force microscopy and ellipsometry. A linear dependence of the ablation threshold fluence F_th on the layer thickness d was found for d ≤ 180 nm. If a film thickness of about 180 nm was reached, the damage threshold remained constant at its bulk value. For different numbers of pulses per spot (N-on-1), bulk damage thresholds of ∼0.7 J cm⁻² (1-on-1), 0.5 J cm⁻² (10-on-1), 0.4 J cm⁻² (100-on-1), 0.25 J cm⁻² (1000-on-1), and 0.2 J cm⁻² (10000-on-1) were obtained experimentally indicating an incubation behavior. A characteristic layer thickness of L_c ≈ 180 nm can be defined which is a measure for the heat penetration depth within the electron gas before electron-phonon relaxation occurs. L_c is by more than an order of magnitude larger than the optical absorption length of α⁻¹ ≈ 12 nm at 793 nm wavelength.     

Highly efficient Nd:GdVO4/BiBO laser at 456 nm under direct 880 nm diode laser pumping

The continuous-wave high-efficiency laser emission of Nd:GdVO₄ at the second-harmonic of 456 nm obtained by intracavity frequency doubling with an BiB₃O₆(BiBO) nonlinear crystal is investigated under pumping by diode laser at 880 nm into emitting level ⁴F_3/2. About 3.8 W at 456 nm with M² = 1.4 was obtained from a 5 mm-thick 0.4 at.% Nd:GdVO₄ laser medium and a 12 mm-long BiBO nonlinear crystal in a Z-type cavity for 13.9 W absorbed pump power. An optical-to-optical efficiency with respect to the absorbed pump power was 0.274. Comparative results obtained for the pump with diode laser at 808 nm, into the highly-absorbing ⁴F_5/2 level, are given in order to prove the advantages of the 880 nm wavelength pumping.