单点子域积分与多点子域积分

基于单点子域精细积分的思想,针对抛物线型热传导方程初边值问题,提出了多点子域积分的概念,推出了一种多点子域积分的FTCS格式。该格式为显格式,并证明其为无条件稳定。数值算例表明,多点子域积分的FTCS格式具有比单点子域积分的FTCS格式收敛速度快的特点。     

Geometric Integration Methods that Preserve Lyapunov Functions

We consider ordinary differential equations (ODEs) with a known Lyapunov function V. To ensure that a numerical integrator reflects the correct dynamical behaviour of the system, the numerical integrator should have V as a discrete Lyapunov function. Only second-order geometric integrators of this type are known for arbitrary Lyapunov functions. In this paper we describe projection-based methods of arbitrary order that preserve any given Lyapunov function. AMS subject classification (2000) 65L05, 65L06, 65L20, 65P40     

组合刻蚀法制备窄带滤光片列阵

介绍了组合刻蚀法制备窄带滤光片列阵的基本原理和制备工艺,这是一种效率非常高的制备方法,只需N次刻蚀就可以完成2N通道窄带滤光片列阵的制备,而且可以用于制备不同波段窄带滤光片列阵。展示了可见-近红外波段32通道窄带滤光片列阵和中红外波段16通道窄带滤光片列阵的实验结果,其中32通道窄带滤光片列阵的带通峰位基本呈线性分布在774.7~814.2 nm之间,所有滤光片的半峰全宽都非常窄(δλ<1.5 nm),相应于δλ/λ<0.2%,半峰全宽最窄的滤光片达到0.8 nm,相应于δλ/λ<0.1%,其带通峰位λ=794.3 nm;各通道的带通透过率在21.2%~32.4%之间,大部分在30%左右。     

普物实验教学应科学引导学生进行知能整合

以“电池电动势和内阻的测定”为例,简述了在普物实验教学中,科学引导学生进行知能整合的过程,使科学知识与相关知识的应用实现了最佳的整合,提高了学生设计实验、实验测量、科学评定实验过程及测量结果的能力。     

Optimal Runge–Kutta smoothers for the p-multigrid discontinuous Galerkin solution of the 1D Euler equations

This work presents a family of original Runge–Kutta methods specifically designed to be effective relaxation schemes in the numerical solution of the steady state solution of purely advective problems with a high-order accurate discontinuous Galerkin space discretization and a p-multigrid solution algorithm. The design criterion for the construction of the Runge–Kutta methods here developed is different form the one traditionally used to derive optimal Runge–Kutta smoothers for the h-multigrid algorithm, which are designed in order to provide a uniform damping of the error modes in the high-frequency range only. The method here proposed is instead designed in order to provide a variable amount of damping of the error modes over the entire frequency spectrum. The performance of the proposed schemes is assessed in the solution of the steady state quasi one-dimensional Euler equations for two test cases of increasing difficulty. Some preliminary results showing the performance for multidimensional applications are also presented.     

PBL as a pedagogical approach for integrated STEM: Evidence from prospective teachers

Problem-based learning (PBL) and science, technology, engineering, and mathematics (STEM) are two acronyms widely visible in education literature today. However, few studies have explored these in connection with one another, specifically with regard to teacher preparation. This study investigated how 47 prospective elementary teachers developed PBL units and how they integrated STEM and other disciplines into those units. It also addressed the affordances and constraints of integrated STEM as perceived by the prospective elementary teachers. Data sources in this multimethod study included PBL units and interviews. Findings revealed that all of the units integrated at least two of the STEM disciplines, as well as literacy, in a variety of ways. The prospective teachers articulated perceived benefits of integrated STEM, such as: making connections across content areas, preparing students for the real world, teaching students that failure is not a bad thing, and providing future opportunities. They also addressed perceived barriers of integrated STEM, such as: having limited experience with the content, diminishing the effect of individual content areas, and needing better curriculum alignment. Overall, this study provides evidence that PBL can be a pedagogical approach to integrate STEM. Implications for teachers, teacher educators, and curriculum specialists are discussed.     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

转动相对论Birkhoff系统动力学的场方法

给出转动相对论Birkhoff系统动力学方程的一种积分方法,并举例说明方法的应用. 关键词： 转动相对论 Birkhoff动力学 积分方法     

Some algorithms for numerical quadrature using the derivatives of the integrand in the integration interval

Some quadrature formulae using the derivatives of the integrand are discussed. As special cases are obtained generalizations of both the ordinary and the modified Romberg algorithms. In all cases the error terms are expressed in terms of Bernoulli polynomials and functions.     

Time-stepping in Petrov-Galerkin methods based on cubic B-splines for compactons

Four numerical methods with first- to fourth-order of accuracy have been developed for the time integration of the Rosenau-Hyman K(2, 2) equation. The error in the solution and the invariants for the propagation of one-compacton, and the stability in collisions among compactons have been studied using these methods. Numerically-induced radiation has also been characterized by means of wavefront velocity and wavefront amplitude, showing that the self-similarity of the radiation wavepackets observed in the numerical results is a consequence of the time-stepping method. Among the four methods studied in this paper, the best results in terms of accuracy, computational cost, and stability have been obtained by means of using the second-order time integration method.