Numerical solution of the two-dimensional Poincaré equation

This paper deals with numerical approximation of the two-dimensional Poincaré equation that arises as a model for internal wave motion in enclosed containers. Inspired by the hyperbolicity of the equation we propose a discretisation particularly suited for this problem, which results in matrices whose size varies linearly with the number of grid points along the coordinate axes. Exact solutions are obtained, defined on a perturbed boundary. Furthermore, the problem is seen to be ill-posed and there is need for a regularisation scheme, which we base on a minimal-energy approach.     

High-power CW diode-side-pumped 1341 nm Nd:YAP laser

A high-power CW diode-side-pumped Nd:YAP laser with linearly polarization at 1341 nm has been described. The laser characteristics including thermal lens and stability of flat–flat resonator were studied. By comparing the output powers at different resonator lengths and different output couplers, the c-axis polarized laser working at 1341 nm has been obtained with a maximum output power of 121 W at the pumping power of 555 W. The optical–optical efficiency is 21.8% and the optical slope efficiency is 40%. The a-axis polarized laser at 1339 nm has also been successfully obtained when the c-axis polarized laser had become instable with the increase of pumping power.     

Error bounds for rational quadrature formulae of analytic functions

We study the error of rational quadrature rules when functions which are analytic on a neighborhood of the set of integration are considered. A computable upper bound of the error is presented which is valid for a broad range of rational quadrature formulae and a comparison is made with the exact error for a number of numerical examples.This work was supported by the Dirección General de Investigación (DGI), Ministerio de Ciencia y Tecnología, under grants BFM2003-06335-C03-02 and BFM2002-04315- C02-01.     

Convex bodies of constant width and constant brightness

In 1926 Nakajima (= Matsumura) showed that any convex body in R³ with constant width, constant brightness, and boundary of class C² is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness.     

Optimal $\mathcal{L}^2$ error bounds for MITC3 type element

Summary. In this paper, we derive the optimal error bounds for the stabilized MITC3 element [3], the MIN3 type element [7] and the T3BL element [8]. In this way we have solved the problem proposed recently in [5] in a positive manner. Moreover, we estimate the difference between stabilized MITC3 and MIN3 and show it is of order uniform in the plate thickness. Received May 31, 2000 / Revised version received April 2, 2001 / Published online September 19, 2001     

A “multigrid” extension of theFFT for the numerical inversion of Fourier and Laplace Transforms

An algorithm for accurate numerical inversion of slowly convergent Fourier and Laplace Transforms is studied. It makes use of several equidistant grids with the same number of points, covering different symmetric intervals of the time and frequency axes. Typically, the number of operations per computed function value is about twice as large as for an ordinary FFT. The distribution of points is, however, for many applications much more adequate because, globally, the union of the grids is an approximately equidistant point set on a logarithmic scale.Dedicated to Gene H. Golub on the occasion of his 60'th birthday     

Degenerate two-phase incompressible flow II: regularity, stability and stabilization

In this paper, we analyze a coupled system of highly degenerate elliptic-parabolic partial differential equations for two-phase incompressible flow in porous media. This system involves a saturation and a global pressure (or a total flow velocity). First, we show that the saturation is Hölder continuous both in space and time and the total velocity is Hölder continuous in space (uniformly in time). Applying this regularity result, we then establish the stability of the saturation and pressure with respect to initial and boundary data, from which uniqueness of the solution to the system follows. Finally, we establish a stabilization result on the asymptotic behavior of the saturation and pressure; we prove that the solution to the present system converges (in appropriate norms) to the solution of a stationary system as time goes to infinity. An example is given to show typical regularity of the saturation.     

Blended implicit methods for solving ODE and DAE problems,and their extension for second-order problems

The use of implicit numerical methods is mandatory when solving general stiff ODE/DAE problems. Their use, in turn, requires the solution of a corresponding discrete problem, which is one of the main concerns in the actual implementation of the methods. In this respect, blended implicit methods provide a general framework for the efficient solution of the discrete problems generated by block implicit methods. In this paper, we review the main facts concerning blended implicit methods for the numerical solution of ODE and DAE problems.     

LD泵浦Cr∶YAG被动调Q 556nm黄光激光器

通过对谐振腔镜镀制合理的激光薄膜，成功实现了LD泵浦Nd∶YAG 1.111 μm激光谱线的运转.利用LBO腔内倍频Nd∶YAG/Cr∶YAG结构获得了高重复频率被动调Q556 nm全固态黄光激光器，在注入泵浦功率为1.6 W时，得到平均功率51 mW，脉冲宽度48 ns,重复频率8.9 kHz,峰值功率高达119 W的脉冲黄光输出.