On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

A new approach to potential flow around axisymmetric bodies

A new method is introduced to solve potential flow problems around axisymmetric bodies. The approach relies on expressing the infinite series expansion of the Laplace equation solution in terms of a finite sum which preserves the Laplace solution for the potential function under a Neumann-type boundary condition. Then the coefficients of the finite sum are calculated in a least squares approximation sense using the Gram-Schmidt orthonormalization method. Sample benchmark problems are presented and discussed in some detail. The solutions are accurate and converged faster when a rather small number of terms were used. The method is simple and can be easily programmed.     

Chiral discrimination of a helically organized crown ether array parallel to the helix axis of polyisocyanate

The asymmetric polymerization of 4′‐isocyanatobenzo‐18‐crown‐6 with the lithium amide of (S)‐(2‐methoxymethyl)pyrrolidine successfully proceeded to afford end‐functionalized poly(4′‐isocyanatobenzo‐18‐crown‐6) with (S)‐(2‐methoxymethyl)pyrrolidine (polymer 2 ). In the circular dichroism (CD) spectrum of 2 , a clear positive Cotton effect was observed in the range of 240–350 nm corresponding to the absorption of the polymer backbone, indicating that 2 partially formed a one‐handed helical structure, which was preserved by the chirality of (S)‐(2‐methoxymethyl)pyrrolidine bonding to the terminal end in 2 . In the titration experiments for the CD intensity of 2 in the presence of D ‐ and L ‐Phe·HClO₄ (where Phe is phenylalanine), a small but remarkable difference was observed in the amount of the chiral guest needed for saturation of the CD intensity and in the saturated CD intensity, indicating that the extremely stable, one‐handed helical part should exist in the main chain of 2 , which was not inverted even when the unfavorable chiral guest for the predominant helical sense, L ‐Phe·HClO₄, was added. In addition, helical polymer 2 exhibited a chiral discrimination ability toward racemic guests; that is, the guests were extracted from the aqueous phase into the organic phase with enantiomeric excess. The driving force of the chiral discrimination ability of 2 should certainly be attributed to the one‐handed helical structure in 2 . © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 325–334, 2006     

Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern

The problem considered is that of determining the shape of aplane acoustically sound-soft obstacle from the knowledge ofthe far-field pattern for one time-harmonic incident field.An iterative procedure is proposed based on two boundary integralsrepresenting the incident field and the far-field pattern, respectively.Numerical examples are included which show that the proceduregives accurate numerical approximations in relatively few iterations.     

Synthesis of mono meso-pyridyl 21,23-dithiaporphyrins and unsymmetrical non-covalent porphyrin dimers

A new method has been developed to synthesize 21,23-dithiaporphyrins having one pyridyl group at the meso position. The method required easily available unknown precursors and the condensation resulted in mono meso-pyridyl 21,23-dithiaporphyrins as single products in 8-11% yield. Two of the three mono meso-pyridyl N₂S₂ porphyrins were used to synthesize non-covalent unsymmetrical porphyrin dimers containing one N₂S₂ and one N₄ porphyrin cores.     

On a class of least-element complementarity problems

The present paper studies the linear complementarity problem of finding vectorsx andy inR ₊ ⁿ such thatc + Dx + y 0,b – x 0 andx ^T (c + Dx + y) = y ^T (b – x) = 0 whereD is aZ-matrix andb > 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of least-element solution is presented. Finally, applications and computational experience with its implementation are discussed.Research partially supported by the National Science Foundation Grant MCS 71-03341 A04 and the Air Force Office of Scientific Research Contract F 44620 14 C 0079.     

The use of diode array detectors in conjunction with continuous wave gas lasers for anti-Stokes Raman spectroscopy

The Raman spectrum of any molecule consists of two mirror-image signals, th e Stokes and anti-Stokes Raman spectra. In most cases, unless highly specific sampling conditions are used, the anti-Stokes signal is much weaker than that of the Stokes. The recent application of intensified diode array detectors to Raman spectroscopy has produced a marked increase in the sensitivity of the technique which makes a study of the anti-Stokes spectrum potentially more rewarding than it has been to date. The present study has shown that, although of limited use for general purposes, there are some specific instances where the anti-Stokes spectrum can be of considerable practical use. Such applications are to extend the operating range of the Raman spectrometer, to study photodegradable samples and for the analysis of samples which exhibit strong fluorescence.     

First-order system least squares and the energetic variational approach for two-phase flow

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen–Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.     

Ultrasonic sensor for predicting sugar concentration using multivariate calibration

This paper presents a multivariate regression method for the prediction of maltose concentration in aqueous solutions. For this purpose, time and frequency domain of ultrasonic signals are analyzed. It is shown, that the prediction of concentration at different temperatures is possible by using several multivariate regression models for individual temperature points. Combining these models by a linear approximation of each coefficient over temperature results in a unified solution, which takes temperature effects into account. The benefit of the proposed method is the low processing time required for analyzing online signals as well as the non-invasive sensor setup which can be used in pipelines. Also the ultrasonic signal sections used in the presented investigation were extracted out of buffer reflections which remain primarily unaffected by bubble and particle interferences.