A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Matrix Method for Acoustic Levitation Simulation

A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.

Square-wave voltametric method for determination of molinate concentration in a biological process using a hanging mercury drop electrode

A square-wave voltammetric (SWV) method using a hanging mercury drop electrode (HMDE) has been developed for determination of the herbicide molinate in a biodegradation process. The method is based on controlled adsorptive accumulation of molinate for 10 s at a potential of -0.8 V versus AgCl/Ag. An anodic peak, due to oxidation of the adsorbed pesticide, was observed in the cyclic voltammogram at ca. -0.320 V versus AgCl/Ag; a very small cathodic peak was also detected. The SWV calibration plot was established to be linear in the range 5.0x10-6 to 9.0x10-6 mol L-1; this corresponded to a detection limit of 3.5x10-8 mol L-1. This electroanalytical method was used to monitor the decrease of molinate concentration in river waters along a biodegradation process using a bacterial mixed culture. The results achieved with this voltammetric method were compared with those obtained by use of a chromatographic method (HPLC–UV) and no significant statistical differences were observed.

Doppler ultrasound in the measurement of pulse wave velocity: agreement with the Complior method

Aortic stiffness is an independent predictor factor for cardiovascular risk. Different methods for determining pulse wave velocity (PWV) are used, among which the most common are mechanical methods such as SphygmoCor or Complior, which require specific devices and are limited by technical difficulty in obtaining measurements. Doppler guided by 2D ultrasound is a good alternative to these methods. We studied 40 patients (29 male, aged 21 to 82 years) comparing the Complior method with Doppler. Agreement of both devices was high (R = 0.91, 0.84-0.95, 95% CI). The reproducibility analysis revealed no intra-nor interobserver differences. Based on these results, we conclude that Doppler ultrasound is a reliable and reproducible alternative to other established methods for themeasurement of aortic PWV

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

A pseudo-spectral method for simulating of poro-elastic seismic wave propagation in complex borehole environments

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.

Accurate calculations of intermolecular interaction energies using explicitly correlated coupled cluster wave functions and a dispersion-weighted MP2 method.

Explicitly correlated coupled-cluster calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerny, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented. Results obtained with the recently proposed CCSD(T)-F12a method and augmented double-zeta basis sets are found to be in very close agreement with basis set extrapolated conventional CCSD(T) results. Furthermore, we propose a dispersion-weighted MP2 (DW-MP2) approximation that combines the good accuracy of MP2 for complexes with predominately electrostatic bonding and SCS-MP2 for dispersion-dominated ones. The MP2-F12 and SCS-MP2-F12 correlation energies are weighted by a switching function that depends on the relative HF and correlation contributions to the interaction energy. For the S22 set, this yields a mean absolute deviation of 0.2 kcal/mol from the CCSD(T)-F12a results. The method, which allows obtaining accurate results at low cost, is also tested for a number of dimers that are not in the training set.

Bargmann-Wigner method and (6S + 1)-component wave equations

A modified Bargmann-Wigner method is used to derive (6s + 1)-component wave equations. The relation between different forms of these equations is shown.

Reconstruction of Fresnel Holograms using partial wave front information

n this work we analyze the behavior of complex information in Fresnel domain taking into account the limited capability to display complex transmittance values of current liquid crystal devices, when used as holographic displays. In order to do this analysis we compute the reconstruction of Fresnel holograms at several distances using the different parts of the complex distribution (real and imaginary parts, amplitude and phase) as well as using the full complex information adjusted with a method that combines two configurations of the devices in an adding architecture. The RMS error between the amplitude of these reconstructions and the original amplitude is used to evaluate the quality of the information displayed. The results of the error analysis show different behavior for the reconstructions using the different parts of the complex distribution and using the combined method of two devices. Better reconstructions are obtained when using two devices whose configurations densely cover the complex plane when they are added. Simulated and experimental results are also presented.

A simple square-wave voltammetric method for the determination of scopolamine in pharmaceuticals using a boron-doped diamond electrode

A simple procedure is described for the determination of scopolamine by square-wave voltammetry using a cathodically pretreated boron-doped diamond electrode. Cyclic voltammetry studies indicate that the oxidation of scopolamine is irreversible at a peak potential of 1.59 V (vs. Ag/AgCl (3.0 mol L-1 KCl)) in a 0.50 mol L-1 sulfuric acid solution. Under optimized conditions, the analytical curve obtained was linear (r = 0.9996) for the scopolamine concentration range of 1.0 to 110 µmol L-1, with a detection limit of 0.84 µmol L-1. The method was successfully applied to the determination of scopolamine in pharmaceutical formulations with minimum sample preparation.

Method and arrangement for collecting wave energy

US-patentti nro: US 7,908,854 B2