若干高精度恒稳的半显式差分格式

本文构造了解色散方程u₁=au_xxx的若干三层恒稳的半显式差分格式。第Ⅰ、Ⅱ类格式的局部截断误差的阶为O(τ²+h²+(τ²)/(h³));而第Ⅲ、Ⅳ类格式的局部截断误差的阶为O(τ²+h⁴+((τ)/(h))²+τh)。用判别稳定性的Von Neumann准则可证明:第Ⅰ、Ⅱ类格式及当参数α≤1时的第Ⅲ、Ⅳ类格式都是无条件稳定的,并且当必须的边界条件给定时它们可以显式地进行计算。     

时间分数阶亚扩散方程的高阶差分方法

提出两差分格式求解时间分数阶亚扩散方程.两个格式都是绝对稳定的,收敛阶均为O(τ^q+h²),其中q(q=2-β或2)与方程解的光滑性有关,β(0 < β < 1)是分数阶导数的阶、τ和h分别是时间和空间方向步长.数值实验验证了理论结果的正确性,并与其他方法进行比较,显示了本文方法的有效性和精确性.     

用二维含时Fokker-Planck方程分析Tokamak中α粒子的输运

按分布函数的定义不同,描述高能带电粒子在等离子体中输运的-Planck方程有不同的形式。从数值计算的观点出发对两种不同形式的Fokker-Planck方程作了比较和评价,并指出Fokker-Planck碰撞项可解释为速度空间的对流扩散项。在此基础上用有限差分方法求解二维(速度一维,几何一维)含时Fokker-Planck方程,编制了计算程序CAPT,并将其应用于α粒子的输运研究。最后计算了典型的Tokamak D-T聚变堆参数下α粒子的损失,并给出了堆内α粒子的分布及损失α粒子的速度分布。     

栅状表面液晶盒的光学属性

基于栅状表面等效锚定能公式和弹性理论,对Bryan-Brown等人提出的混和排列向列相液晶盒进行研究.通过变分理论得到指向矢倾角和扭曲角满足的方程和边界条件.根据这些方程和边界条件,利用差分迭代方法计算出指向矢倾角和扭曲角对应某一个δ/λ值在不同电压下的分布.应用琼斯矩阵方法,研究这种液晶盒的电光效应.这些结果都与栅状表面的几何参数有关,即与周期λ和振幅δ有关.     

α-Ti2Zr高压物性的第一性原理计算研究

基于密度泛函理论的第一性原理计算获得了α-Ti₂Zr的晶体结构、弹性常数、德拜温度和电子分布情况, 研究了它们与压力的关系. 计算得到的晶体结构参数与实验值一致. 运用有限应变方法计算得到了α-Ti₂Zr的体积模量B、剪切模量G、杨氏模量E和泊松比σ. B和E的零压值分别为101.2和35.6 GPa. G/B的值较小, 并且随着压力的增加而减小, 表明α-Ti₂Zr具有优异的延展性. 基于弹性常数得到平均声速, 从而获得了德拜温度Θ=321.7 K. 通过解Christoffel方程获得的压缩波和剪切波数据揭示α-Ti₂Zr具有较强的各向异性. 此外, 压力诱导电子从s轨道到d轨道的转移说明在一定压力下α-Ti₂Zr将转变为β相. 关键词： 第一性原理 α-Ti₂Zr')" href="#">α-Ti₂Zr 物性 高压     

λ格式及其改进

本文利用λ格式做了两个典型的一维流体力学问题的数值模拟。由于λ格式色散效应过强,出现非线性不稳定性,笔者针对这一现象给出了λ格式的改进格式,所得结果比较令人满意。     

聚变堆燃烧等离子体温度剖面数值分析

采用聚变等离子体中α粒子慢化、扩散的多能群计算方法,结合本底等离子体的能量平衡方程,对α粒子自加热及扩散情形下对聚变堆而言甚为重要的等离子体温度剖面进行了自洽性的数值分析。对动态及稳态等离子体运行方式的模拟结果表明燃烧等离子体温度剖面比起目前实验得出的剖面更峰状化。这一特性不依α粒子在其慢化过程有无显著的扩散损失而改变,在今后对聚变堆α粒子行为及效应的严格分析中应加以考虑。     

α稳定噪声驱动的非对称双稳随机共振现象

以微弱周期信号激励的非对称双稳系统为模型, 以信噪比增益为指标, 首先针对加性和乘性α 稳定噪声共同作用的随机共振现象展开了研究, 然后针对单独加性α 稳定噪声激励的随机共振现象进行了研究, 探究了α 稳定噪声特征指数α 和对称参数β 分别取不同值时, 系统结构参数a, b, 刻画双稳系统非对称性的偏度r以及α 稳定噪声强度放大系数Q或D对非对称双稳系统共振输出的作用规律. 研究结果表明, 无论在加性和乘性α 稳定噪声共同作用下还是在单独加性α 稳定噪声作用下, 通过调节a和b或者r均可诱导随机共振, 实现微弱信号的检测, 且有多个参数区间与之对应, 这些区间不随α 或β 的变化而变化; 在研究噪声诱导的随机共振现象时发现, 调节噪声强度放大系数也可使系统产生随机共振现象, 且达到共振状态时D的区间也不随α 或β 的变化而变化. 这些结论为α 稳定噪声环境下参数诱导随机共振中系统参数以及噪声诱导随机共振中噪声强度的合理选取提供了依据.     

poisson方程的预示校正差分格式

本文提出求解二维、三维Poisson方程的Dirichlet和Neumann两类边值问题的预示校正差分格式。它完整地包括求解区域的内结点格式、边界面结点格式、边界线结点格式和边界角结点格式。这种新的差分格式达到四阶精度,并可通过对选择因子的优越使计算误差达到最小。     

色散方程的一类具任意稳定性的显格式

本文对色散方程u_r=au_xxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。     

SOME OBSERVATIONS ON THE CHARACTERIZATION OF STRUCTURAL DAMPING

This paper deals with the characterization of damping in dynamical structural systems. In particular, the problem of how the modal damping ratios change with different boundary conditions is addressed. It is shown that only Rayleigh-type damping is actually independent of boundary conditions and modal damping ratios can be easily converted from one boundary condition to another. This condition applies independently to continuous, discrete and discretized systems.     

Level comparison theorems

Two theorems are established which state that in certain circumstances the nth eigenvalue of one Schrödinger operator is higher or lower than the (n − 1)th eigenvalue of a second Schrödinger operator. One condition is the positivity of the difference of the two potentials and a certain behavior of this difference at the boundary. The other condition is in each theorem a differential inequality of the second order on one of the potentials. The proof involves a comparsion of the second logarithmic derivative of wave functions. By specifying the difference of the two potentials, specific forms of the theorems give new theorems on level spacings as well as old and new theorems on level ordering. A third theorem deals with perturbations of factorizable systems. Here explicit formulas connect the level splittings again with second order differential expressions of the perturbing potential.     

A basic study on the sound field analysis of periodic structures by boundary integral equation method

This study deals with the development of the approximate method to analyze the sound field around equally spaced finite obstacles, using the periodic boundary condition. First, on the assumption that the equally spaced finite obstacles are the periodically arranged obstacles, the sound field is analyzed by boundary integral equation method with a Green’s function which satisfies the periodic boundary condition. Furthermore, by comparing these results and the exact solution by using the fundamental solution as Green’s function, the validity of the approximate method is also investigated. Next, in order to evaluate the applicability of the approximate method, the simple formula using some parameters, i.e., the frequency, the period, and the number of obstacles, etc., is proposed. The results of the sound field analysis applied the formula are presented.     

Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation

This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aure?gan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications.     

The melting and solidification of nanowires

A mathematical model is developed to describe the melting of nanowires. The first section of the paper deals with a standard theoretical situation, where the wire melts due to a fixed boundary temperature. This analysis allows us to compare with existing results for the phase change of nanospheres. The equivalent solidification problem is also examined. This shows that solidification is a faster process than melting; this is because the energy transfer occurs primarily through the solid rather than the liquid which is a poorer conductor of heat. This effect competes with the energy required to create new solid surface which acts to slow down the process, but overall conduction dominates. In the second section, we consider a more physically realistic boundary condition, where the phase change occurs due to a heat flux from surrounding material. This removes the singularity in initial melt velocity predicted in previous models of nanoparticle melting. It is shown that even with the highest possible flux the melting time is significantly slower than with a fixed boundary temperature condition.     

A note on the dynamic boundary conditions in Munk-like circulation models

The present note deals with Munk's ocean model and proposes an alternative approach to find its solution, with special regard to the western boundary layer. We introduce a suitable “distance” between the related Sverdrup streamfunction and all the admissible streamfunctions which are valid in the western boundary layer. We prove that such distance has a minimum that singles out a unique solution. Unlike the traditional method, this procedure works without assuming a priori any dynamic boundary condition. Received 16 July 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: fulcri@itt.ts.cnr.it     

双凹盘形解开口膜泡形状的解析法研究

随着开口膜泡在实验上的发现,对开口泡形状的数值及解析研究逐渐成为该领域的一个热点.讨论了如何由欧阳双凹盘形闭合解构造开口泡的解析解的问题.首先将开口泡要满足的三个不独立的边界条件简化为两个独立的边界条件,给出高斯测地曲率kg=-2,边界条件2可满足,然后由边界条件1得到确定膜泡边界的几何方程.进而讨论了由欧阳双凹盘解可构造的开口泡的各种可能形状,得到了三类管型拓扑解,它们是外凸管形解、类环管形解、类悬链面管形解.     

双相各向同性介质BISQ模型弹性波方程数值模拟方法

本文从Taylor级数展开式出发,推导出了交错网格一阶空间导数的任意偶数阶精度展开式和相应差分系数计算式;从本构方程和运动方程推导出了BISQ模型双相介质一阶双曲型应力-速度弹性波方程交错网格任意偶数阶精度差分格式以及推导出二维双相各向同性介质完全吸收层边界条件公式和相应的高阶交错网格差分格式。通过数值模拟研究表明,该方法边界吸收效果好,稳定性好,能够高精度模拟双相介质中地震弹性波场,且计算效率也高。