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81.
We consider (in two-dimensional Euclidean space) the scattering of a plane, time-harmonic acoustic wave by an inhomogeneous medium Ω with compact support and a bounded obstacle D lying completely outside of the inhomogeneous medium. We show that one may determine the shape of D and the local speed of sound in Ω from a knowledge of the asymptotic behavior of the scattered wave (i.e. the far field). This is done by considering a constrained optimization problem and employing integral equation and conformal mapping techniques. By assuming a priori that the functions which determine the shape of D and the local speed of sound in Ω lie in given compact sets, we show that the problem is stable, in the sense that the solution of the inverse scattering problem depends continuously on the far field data. 相似文献
82.
T. S. Angell R. E. Kleinman G. C. Hsiao 《Mathematical Methods in the Applied Sciences》1982,4(1):164-193
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. 相似文献
83.
84.
Hsiao C. Kao 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1972,23(4):632-644
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.
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.相似文献
85.
Ya-Lun Tsai Hsiao-Chin Lan Sheng Fu Lin Chia-Chi Chang Hsu-Liang Hsiao Yun-Chih Lee Jenq-Yang Chang Mount-Learn Wu 《Optical Review》2010,17(6):536-540
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. 相似文献
86.
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. 相似文献
87.
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 相似文献
88.
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. 相似文献
89.
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. 相似文献
90.
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. 相似文献