Boundary integral equations for the Helmholtz equation: The third boundary value problem

In this paper we study the application of boundary integral equation methods for the solution of the third, or Robin, boundary value problem for the exterior Helmholtz equation. In contrast to earlier work, the boundary value problem is interpreted here in a weak sense which allows data to be specified in L_∞ (?D), ?D being the boundary of the exterior domain which we assume to be Lyapunov of index 1. For this exterior boundary value problem, we employ Green's theorem to derive a pair of boundary integral equations which have a unique simultaneous solution. We then show that this solution yields a solution of the original exterior boundary value problem.     

An optically thin radiating gas jet

A radiating gas jet near the optically thin limit is examined. The gas is assumed to be inviscid, optically grey, and in the state of chemical equilibrium or to obey the ideal gas law. The jet is assumed to be plane-symmetric or axi-symmetric and is fully expanded. Under these conditions and by the method of quasi-one-dimensional flow, the problem is analyzed. In addition to this, numerical examples are also included to illustrate the radiative effects.

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Zusammenfassung Es wird ein strahlender Gasstrahl untersucht, nahe zum optisch dünnen Grenzfall. Das Gas wird reibungsfrei, optisch grau und im chemischen Gleichgewicht (oder als ideales Gas) vorausgesetzt. Der Strahl wird eben oder axisymmetrisch angenommen und ist voll expandiert. Unter diesen Voraussetzungen und mit der Methode der fast-eindimensionalen Strömung wird das Problem analysiert. Zudem sind numerische Beispiele angegeben, um den Strahlungseffekt zu veranschaulichen.

     

Design of low-loss tapered waveguide by applying photonic-crystal-based microlenses in telescopic structure

In this paper, the design of low-loss tapered waveguides by applying photonic-crystal-based microlenses is presented. The microlenses are realized by using two-dimensional photonic crystal (PhC) structures with a hexagonal periodic lattice of air-holes. In order to make the PhC structures behave as homogeneous and isotropic microlenses, the PhC structures are designed to operate in the low-frequency domain with light wavelength sufficiently larger than the PhC lattice constant. The effective indices of the PhC are calculated and the structures are properly arranged in microlenslike shapes. By monolithically integrating the effective microlenses in the tapered area between the two optical waveguides with different core dimensions, the wavefront of the eigenmode can be coupled from the larger core to the smaller core effectively and also the radiation loss in the tapered area between the two connected optical waveguides can be effectively suppressed. The results show that the PhC-based microlens in the telescopic structure can serve as an optical element in the tapered waveguide with the advantages of low loss, high efficiency and compactness.     

One-pot synthesis of hollow Au3Cu1 spherical-like and biomineral botallackite Cu2(OH)3Cl flowerlike architectures exhibiting antimicrobial activity

A new form of Au3Cu1 hollow nanostructure was prepared by the reaction of Cu nanoparticles with HAuCl4. Following a course of aging, the biomineral botallackite Cu2(OH)3Cl nanoflowers were developed with the aid of Au3Cu1 hollow nanostructures at room temperature. It was proposed that the hollow nanospheres could serve as active centers for heterogeneous nucleation and mediated a mineralization process. Scanning electron microscopy and high-resolution transmission electron microscopy indicated that the nanoflowers are three-dimensional in appearance with a range of 500 nm-- to 1 microm in size and made of several nanopetals with about 25 nm in thickness. In addition, we found that the shape separation could be achieved by using cationic cetyltrimethylammonium bromide to filter the different morphology spherical- and flowerlike structures due to the negative charge of hollow nanospheres. Both hollow nanospheres and nanoflowers presented antimicrobial activity toward Streptococcus aureus with MIC50 at 39.6 and 127.2 microg/mL, respectively.     

The coupling of bem and fem for the two-dimensional viscous flow problem

In this paper we propose a numerical scheme for treating the problem of sJow viscous flow past an obstacle in the plane. This scheme is a combination of boundary element and finite element methods. By introducing an auxiliary boundary curve, we divide the region under consideration into two subregions, an inner and an outer region. In the inner region, we employ a finite element method (FEM) for solving a system of simplified field equations with proper natural boundary conditions. In the outer region, the solution is expressed in the form of a simple-layer potential with density function satisfying a system of modified integral equations of the first kind. The latter are solved by a boundary element method (BEM). Both solutions are matched on the common auxiliary boundary curve. Error estimates in suitable function spaces are derived in terms of the mesh widths as well as the small parameters, the Reynolds numbers     

The Two-Dimensional,Linear Orthotropic Plate

We First define a continuous extension of the Laquerre polynomials and give some properties of this continuous extension. Then we define a continuous Laguerre transform for square integrable functions, give some properties of this transform and give a sampling theorem that is similar to the well known Shannon-Whittaker Sampling Theorem for Fourier transform. The inverse of this transform is also given.     

Innovative solution of a 2D elastic transmission problem¶

This article is concerned with a boundary-field equation approach to a class of boundary value problems exterior to a thin domain. A prototype of this kind of problems is the interaction problem with a thin elastic structure. We are interested in the asymptotic behavior of the solution when the thickness of the elastic structure approaches to zero. In particular, formal asymptotic expansions will be developed, and their rigorous justification will be considered. As will be seen, the construction of these formal expansions hinges on the solutions of a sequence of exterior Dirichlet problems, which can be treated by employing boundary element methods. On the other hand, the justification of the corresponding formal procedure requires an independence on the thickness of the thin domain for the constant in the Korn inequality. It is shown that in spite of the reduction of the dimensionality of the domain under consideration, this class of problems are, in general, not singular perturbation problems, because of appropriate interface conditions.     

The development of a portable line-shaping optical system for silicon surface treatment

This study proposes a beam shaper for converting a circle beam profile generated with a Gaussian intensity distribution by an 808 nm diode laser into a line beam profile for silicon surface treatment applications. To produce a hand-held and low-cost device with a large spot-size laser, this study uses a portable optical system consisting of a diode laser source, a collimator, a cylindrical lens, and a plano-convex lens to generate an approximately 40 × 3:5mm² line beam profile at a working distance of 200 mm. The silicon surface treated by the line-shaped laser beam has significantly reduced reflectance spectra. The proposed system is also suitable for the surface cleaning of materials.     

A scribing laser marking system using DSP controller

Laser marking is an important branch of laser processing technology, and has been widely used in many fields of industry. Digital signal processor (DSP) is an incredibly fast and powerful microprocessor that can deal with signals in real time. Not only it is portable but has the ability to integrate the processing signals of subsystems. In this research, it is emphasized that we designed a scribing laser marking system based on a DSP in galvanometric marking method. To control the rotating angle of the galvanometric scanning mirrors more accurately, we combine the D/A converter of the DSP with the human–machine interface successfully. The whole marking system is not only inexpensive, but also miniaturized.