Computer-aided spillway design using the boundary element method and non-linear programming

The general context of this paper is to support the design of spillways by a direct mathematical approach instead of trial-and-error methods. First, a two-dimensional model is formulated to determine the free surface and the discharge for a stationary, incompressible, homogeneous, non-viscous and irrotational flow over a fixed spillway. The flow satisfies the Laplace equation and the Bernoulli equation (potential flow). An important feature of the model is that it can be extended to design the spillway structure when the spillway is not fixed but the pressure on the spillway is described by a cavitation criterion. Next, the continuous model is discretized by the boundary element method (BEM). We use a non-linear programming algorithm to calculate the pressures and the shape of the spillway. A computer-aided design package is developed on a PC using the equations describing the free surface, the BEM and standard optimization techniques. The input and output of the model are realized using graphical routines. Finally, we discuss the convergence and the computation time of the algorithms.     

解三维Stokes方程的Q./Q。有限元分析

本文给出了解三维Stokes方程的Q:/Q。有限元的梯度算子核的特征，证明了广义的LBD条件     

Multiscale methods for elliptic homogenization problems

In this article we study two families of multiscale methods for numerically solving elliptic homogenization problems. The recently developed multiscale finite element method [Hou and Wu, J Comp Phys 134 (1997), 169–189] captures the effect of microscales on macroscales through modification of finite element basis functions. Here we reformulate this method that captures the same effect through modification of bilinear forms in the finite element formulation. This new formulation is a general approach that can handle a large variety of differential problems and numerical methods. It can be easily extended to nonlinear problems and mixed finite element methods, for example. The latter extension is carried out in this article. The recently introduced heterogeneous multiscale method [Engquist and Engquist, Comm Math Sci 1 (2003), 87–132] is designed for efficient numerical solution of problems with multiscales and multiphysics. In the second part of this article, we study this method in mixed form (we call it the mixed heterogeneous multiscale method). We present a detailed analysis for stability and convergence of this new method. Estimates are obtained for the error between the homogenized and numerical multiscale solutions. Strategies for retrieving the microstructural information from the numerical solution are provided and analyzed. Relationship between the multiscale finite element and heterogeneous multiscale methods is discussed. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

On the existence of f-local subgroups in a group

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of locally finite subgroups in the groups with almost finite almost solvable elements of prime orders and in the groups with generally finite elements.     

Efficient computation of mean drag for the subcritical flow past a circular cylinder using general Galerkin G2

General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient c_D for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate c_D to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 10⁵ mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is c_D. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

THE OPTIMAL CONVERGENCE ORDER OF THE DISCONTINUOUS FINITE ELEMENT METHODS FOR FIRST ORDER HYPERBOLIC SYSTEMS

In this paper, a discontinuous finite element method for the positive and symmetric, first-order hyperbolic systems （steady and nonsteady state） is constructed and analyzed by using linear triangle elements, and the O（h^2）-order optimal error estimates are derived under the assumption of strongly regular triangulation and the Ha-regularity for the exact solutions. The convergence analysis is based on some superclose estimates of the interpolation approximation. Finally, we discuss the Maxwell equations in a two-dimensional domain, and numerical experiments are given to validate the theoretical results.     

MAXIMUM NORM ERROR ESTIMATES OF CROUZEIX-RAVIART NONCONFORMING FINITE ELEMENT APPROXIMATION OF NAVIER-STOKES PROBLEM

1. IntroductionThere are many research works on finite element approximation of Navier-Stokesproblem in the case of lower Reynold number, by using the so-called velocity--pressuremixed by Teman [26], the optimal results were also obtained. The other nonconforming finiteelement schemes for Navie--Stokes problem may be found in [4,8,9,14,15,23,26]. But sofar, maximum norm error estimates for any nonconforming finite element schemes werenot considered.Recently, the quasi--optimal maximum norm …     

Alpha Decay, Shell Structure, and New Elements

We systematically analyze the experimental data of alpha decay in even-even heavy nuclei far from stabilityand find that the Geiger-Nuttall law breaks for an isotopic chain when its neutron number is across a magic numberor there is a deformed subshell. This break can be used to identify new magic numbers of superheavy nuclei. It is alsodiscovered that there is a new linear relation between the logarithm of half-life and the reciprocal of the square root ofdecay energy for N = 126 and N = 152 isotones. It could be a new law of alpha decay for nuclei with magic neutronnumbers but the physics behind it is to be explored. The significance of these researches for the search of new elementsis discussed.     

深蚀刻二元光学元件

提出一种新颖的，蚀刻位相深度超过２π的深蚀刻二元光学技术，并从理论上分析深蚀刻二元光这元件与衍射效率的关系，然后用计算机进行模拟与分析，得到深蚀刻二元光学元件特性后一些初步研究结果。     

聚氨酯抛光片在透镜高效生产中的应用

本文对聚氨酯抛光片的性能、特点作了概要介绍，在透镜生产中应用聚氨酯抛光片单块加工及成盘加工的方法分别作了讨论，以及众多的工艺因素作了较为详细的分析，介绍了常出现的光圈异常现象的排除方法，从而达到稳定、高效的目的。