Approximate Approximations from scattered data

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by suitable polynomials such that their sum is an approximate partition of unity. For Gaussian functions we propose a method to construct the approximate partition of unity and describe the application of the new quasi-interpolation approach to the cubature of multi-dimensional integral operators.Comment: 29 pages, 17 figure

Construction of Nonlinear Symplectic Six-Dimensional Thin-Lens Maps by Exponentiation

The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as described by W. Groebner and for canonical systems by A.J. Dragt. We firstly use an approximate Hamiltonian obtained by a series expansion of the square root. Furthermore, nonlinear crossing terms due to the curvature in bending magnets are neglected. An improved Hamiltonian, excluding solenoids, is introduced in Appendix A by using the unexpanded square root mentioned above, but neglecting again nonlinear crossing terms...Comment: 57 pages, late

Computation of volume potentials over bounded domains via approximate approximations

We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced to the quadrature of one dimensional integrals over the halfline. We conclude the paper providing numerical tests which show that these formulas give very accurate approximations and confirm the predicted order of convergence.Comment: 18 page

Sun direction detection system

One of the detectors is an illumination detector consisting of two spaced apart elongated strips with a strip of cadmium sulphide (Cds) deposited therebetween. Whenever the line image impinges the CdS strip, the resistance between the two other strips is relatively low, while being high when the line image is outside the field of view of the illumination detector. Also included is a sun angle detector which consists of a vapor deposited resistor strip connected at one end to plus 10v and at the other end to minus 10v. Spaced apart from the resistor strip is an elongated strip of low resistance material acting as an output strip, with a CdS strip between the two strips. When the line image is within the field of view of the sun angle detector, the output voltage at the output strip depends on the position of the line image across the sun angle detector

Aerodynamic performances of three fan stator designs operating with rotor having tip speed of 337 meters per second and pressure ratio of 1.54. Relation of analytical code calculations to experimental performance

A hub-to-shroud and a blade-to-blade internal-flow analysis code, both inviscid and basically subsonic, were used to calculate the flow parameters within four stator-blade rows. The produced ratios of maximum suction-surface velocity to trailing-edge velocity correlated well in the midspan region, with the measured total-parameters over the minimum-loss to near stall operating range for all stators and speeds studied. The potential benefits of a blade designed with the aid of these flow analysis codes are illustrated by a proposed redesign of one of the four stators studied. An overall efficiency improvement of 1.6 points above the peak measured for that stator is predicted for the redesign

Sidewall depletion in nano-patterned LAO/STO heterostructures

We report the fabrication of nanostructures from the quasi-two-dimensional electron gas (q2DEG) formed at the LaAlO$_{3}$/ SrTiO$_{3}$ (LAO/STO) interface. The process uses electron beam lithography in combination with reactive ion etching. This technique allows to pattern high-quality structures down to lateral dimensions as small as $100$nm while maintaining the conducting properties without inducing conductivity in the STO substrate. Temperature dependent transport properties of patterned Hall bars of various widths show only a small size dependence of conductivity at low temperature as well as at room temperature. The deviation can be explained by a narrow lateral depletion region. All steps of the patterning process are fully industry compatible.Comment: 5 pages, 4 figure

A General-applications Direct Global Matrix Algorithm for Rapid Seismo-acoustic Wavefield Computations

A new matrix method for rapid wave propagation modeling in generalized stratified media, which has recently been applied to numerical simulations in diverse areas of underwater acoustics, solid earth seismology, and nondestructive ultrasonic scattering is explained and illustrated. A portion of recent efforts jointly undertaken at NATOSACLANT and NORDA Numerical Modeling groups in developing, implementing, and testing a new fast general-applications wave propagation algorithm, SAFARI, formulated at SACLANT is summarized. The present general-applications SAFARI program uses a Direct Global Matrix Approach to multilayer Green's function calculation. A rapid and unconditionally stable solution is readily obtained via simple Gaussian ellimination on the resulting sparsely banded block system, precisely analogous to that arising in the Finite Element Method. The resulting gains in accuracy and computational speed allow consideration of much larger multilayered air/ocean/Earth/engineering material media models, for many more source-receiver configurations than previously possible. The validity and versatility of the SAFARI-DGM method is demonstrated by reviewing three practical examples of engineering interest, drawn from ocean acoustics, engineering seismology and ultrasonic scattering