Numerical solution of scattering problems using pseudo-differential impedance operators

Direct numerical solutions of scattering problems based on boundary-integral equations are computationally costly at high frequencies. A numerical method is presented that efficiently computes accurate approximations to unknown surface quantities given known surface data (an approximate Dirichlet-to-Neumann map). The method is based on a pseudo-differential impedance operator (PIO) numerically implemented using rational approximations. An example of a PIO is the so-called on-surface radiation condition (OSRC) method. For a convex obstacle, the method can be viewed as applying a parabolic equation directly on the surface of a scatterer. In contrast to past OSRCs, the use of rational approximations provides accuracy for wide scattering angles which is needed for grazing angles of incidence. Generalization to impedance operators for two-dimensional acoustic scatterers with concave parts is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spin-lattice coefficients of Mn2+ in II–VI compounds

The spin-lattice coefficients of Mn²⁺ in CdTe and ZnTe have been measured. Our data allow us to evaluate the random stress distribution within the samples. Our results are compared with values obtained for Mn²⁺ in MgO and CaO.     

Permanent and interaction-induced far-infrared spectra of CO in dense Ar: a molecular dynamics approach

Permanent and electric multipole induced contributions to the far-infrared absorption spectrum of CO in Ar for dense gas and liquid densities have been calculated by means of classical molecular dynamics simulations. The comparison of the simulated spectra with experiments let us to give an estimation of some multipole moments of CO: quadrupole, octupole and hexadecapole. Although the experimental profiles lack of a fine rotational structure, the results of the simulations and their comparison with previous theoretical works, indicate that at low temperatures, the consideration of a quantum time correlation function for the dipole moment is necessary to get a good agreement with experiments. Finally, it is shown that the permanent-induced and induced-induced cross terms in the absorption coefficient, that usually are difficult to calculate from a theoretical viewpoint, are not very relevant for this system.     

A finite volume–multigrid method for flow simulation on stratified porous media on curvilinear co‐ordinate systems

This paper presents a numerical study of infiltration processes on stratified porous media. The study is carried out to examine the performance of a finite volume method on problems with discontinuous solutions due to the transmission conditions in the interfaces. To discretize the problem, a curvilinear co‐ordinate system is used. This permits matching the interface with the boundary of the control volumes that interchange fluxes between layers. The use of the multigrid algorithm for the resulting systems of equations allows problems involving a large number of nodes with low computational cost to be solved. Finally, some numerical experiments, which show the capillary barrier behaviour depending on the material used for the different layers and the geometric design of the interface, are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

On the axiomatization of the τ-value

Summary The τ-value is a solution concept for a subclass of games with transferable utility introduced and axiomatized by Tijs (1981, 1987). In this note an alternative characterization of the τ-value by means of five axioms is offered. Two of them are well-known: efficiency and translation equivalence; the other three relate the solution of a game with the minimal and maximal aspiration vectors involved in the definition of the τ-value. This work was partially supported by Universidad del País Vasco (projects UPV 036.321-H061/91 and UPV 036.321-HA186/92).     

Fresnel diffraction by deterministic fractal gratings: An experimental study

Experimental results are presented for light diffraction under the Fresnel regime by two types of fractal gratings: triadic Cantor bars and Vicsek fractals. It is shown that the evolution of the diffraction patterns in the Fresnel regions reveals the hierarchical structure of deterministic fractal gratings.     

Approximate preservation of quadratic first integrals by explicit Runge–Kutta methods

The approximate preservation of quadratic first integrals (QFIs) of differential systems in the numerical integration with Runge–Kutta (RK) methods is studied. Conditions on the coefficients of the RK method to preserve all QFIs up to a given order are obtained, showing that the pseudo-symplectic methods studied by Aubry and Chartier (BIT 98(3):439–461, 1998) of algebraic order p preserve QFIs with order q = 2p. An expression of the error of conservation of QFIs by a RK method is given, and a new explicit six-stage formula with classical order four and seventh order of QFI-conservation is obtained by choosing their coefficients so that they minimize both local truncation and conservation errors. Several formulas with algebraic orders 3 and 4 and different orders of conservation have been tested with some problems with quadratic and general first integrals. It is shown that the new fourth-order explicit method preserves much better the qualitative properties of the flow than the standard fourth-order RK method at the price of two extra function evaluations per step and it is a practical and efficient alternative to the fully implicit methods required for a complete preservation of QFIs.     

Surface-enhanced Raman spectrometry of amiloride on colloidal silver

Surface-enhanced Raman spectrometry (SERS) of the diuretic drug amiloride is discussed. The SERS-active substrate used is colloidal silver, which is prepared at room temperature by simple tetrahydroborate reduction of an aqueous solution of silver nitrate. SERS detection of amiloride in human urine is illustrated. The reproducibility of quantitative SERS data is supported by the simultaneous measurement of the scattering signal and transmitted light. Relative standard deviations at the 5% level are compatible with many practical analytical situations.