Minimum time‐step criteria for the Galerkin finite element methods applied to one‐dimensional parabolic partial differential equations

The finite element method has been well established for numerically solving parabolic partial differential equations (PDEs). Also it is well known that a too large time step should not be chosen in order to obtain a stable and accurate numerical solution. In this article, accuracy analysis shows that a too small time step should not be chosen either for some time‐stepping schemes. Otherwise, the accuracy of the numerical solution cannot be improved or can even be worsened in some cases. Furthermore, the so‐called minimum time step criteria are established for the Crank‐Nicolson scheme, the Galerkin‐time scheme, and the backward‐difference scheme used in the temporal discretization. For the forward‐difference scheme, no minimum time step exists as far as the accuracy is concerned. In the accuracy analysis, no specific initial and boundary conditions are invoked so that such established criteria can be applied to the parabolic PDEs subject to any initial and boundary conditions. These minimum time step criteria are verified in a series of numerical experiments for a one‐dimensional transient field problem with a known analytical solution. The minimum time step criteria developed in this study are useful for choosing appropriate time steps in numerical simulations of practical engineering problems. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

+3价离子掺杂钨酸铅晶体发光性能和微观缺陷的研究

通过透射光谱、x射线激发发射光谱（XSL）的测试，研究了Bridgman法生长的几种不同+3价离子掺杂钨酸铅晶体的发光性能，并利用正电子湮没寿命谱（PAT）和x光电子能谱（XPS）的实验手段，对不同钨酸铅晶体的微观缺陷进行研究.实验表明，不同的+3价离子掺杂，对钨酸铅晶体发光性能的改善不同，并使得晶体中正电子俘获中心和低价氧的浓度发生不同变化.其中掺镧晶体的正电子俘获中心和低价氧浓度均上升，而掺钇和掺铋晶体的正电子俘获中心和低价氧浓度均下降，掺锑晶体则出现了正电子俘获中心浓度上升、低价氧浓度下降的情况.提 关键词： 钨酸铅晶体 +3价离子掺杂 正电子湮没寿命谱 x光电子能谱     

Coherent population trapping states with cold atoms in a magnetic field

Using potassium atoms cooled with a MOT, ground-state hyperfine coherent population trapped (CPT) states were prepared in a magnetic (B) field, and the behavior of CPT states was experimentally studied. We carefully measured the preparation of the CPT state as a function of time and the CPT signal as a function of laser power. The experimental CPT signal linewidth was approximately proportional to the square root of laser intensity in the range of parameters studied, and limits of this relation were explored theoretically.     

DWDM用薄膜窄带滤光片的容差特性模拟分析

讨论了用于DWDM系统的薄膜窄带滤光片在镀制过程中的监控方法及误差产生的机理,利用自行建立的计算机膜厚容差模拟程序,分析了多FabryPerot腔窄带滤光片的容差特性.发现多腔窄带滤光片各腔的误差灵敏度与腔的位置有关,且各腔间隔层组成材料不同,其对误差最敏感的膜层位置也不相同.     

金镍复合膜上碳纳米管的定向生长及生长过程中金的作用

以金镍复合膜作催化剂，在96%的高氢气浓度下实现了碳纳米管的定向生长，并对其生长过 程进行了深入探讨.结果表明，高氢气浓度下碳纳米管生长的实现与本实验所选用的催化剂 ——金镍复合膜有密切关系.催化剂中金的参与，促进了碳在催化剂中的扩散，提高了碳在 催化剂中的活度.与催化剂中没有金的情况相比较，金的参与有利于镍吸收气氛中的碳，从 而使镍更容易达到碳饱和，有利于在高的氢气浓度下实现碳纳米管的定向生长. 关键词： 金镍复合膜 高氢气浓度 原子氢 碳活度     

Assembly of Ag（I） Polymers with Thioether-S Binding and Homochiral Helices

A novel coordination polymer [Ag(pyta)]n (pyta^-=4-pyridylthioacetate) containing bound thioether sulfurs and single-stranded helical chains has been synthesized and structurally characterized.     

The effect of thermal treatment on the magnetic properties of Ge-doped FeNbB alloys

The effects of Ge doping on the magnetic properties of nanocrystalline FeNbB ribbons are investigated. For amorphous Fe₈₀Nb₁₀Ge₃B₇ alloy, three crystallization processes are observed when heated from room temperature to 1173 K. At 973 K, a harder magnetic phase is formed, which brings about a constricted hysteresis loop. A large increase of relaxation frequency and a dramatic drop of permeability of 973 K-annealed Fe₈₀Nb₁₀Ge₃B₇ alloy are observed. The presence of Nb is essential for the nanocrystallization of α-Fe grains. If Nb is replaced by Ge completely, the thermal treatment will lead to the formation of coarse-grained Fe₃Ge phase rather than nanosized α-Fe grains. The coarse-grained Fe₃Ge results in a remarkable drop in magnetic softness. PACS 75.75.+a; 75.50.Bb     

软X射线激光偏折法测量激光等离子体电子密度分布

利用脉宽约为50ps的类镍银139nm软X射线激光作为探针,探测由脉宽80ps的驱动激光打C8H8靶产生的等离子体在1ns后的电子密度分布信息,获得了清晰的莫尔条纹图像.对结果的处理,给出了峰值电子密度为11×1021cm-3,并对在靶面附近莫尔条纹的消失现象作了初步解释 关键词： 软X射线激光探针 莫尔条纹 等离子体电子密度     

涉及微分多项式的正规定则（英文）

本文获得如下结果：设φ（z)为区域G内一不恒为零的亚纯函数，a1(z),a2(z),．…，ak(z)为区域G内的全纯函数，F＝{f}为G内一亚纯函数族，若对每一f∈F，在G内恒有f(z)，f(z)≠0,f^(k)(z) a1(z)f^(f-1)(z) … ak(z)f(z)≠φ（z),且与φ（z)没有公共极点，则F在G内正规。     

稀土元素原子发射光谱及其谱线干扰的高分辨率ICP—AES研究

本工作利用光栅刻线数为３６００条／ｍｍ的高分辨率ＩＣＰ－ＡＥＳ光谱仪，详细研究了镝基体对其他１４个稀土元素共６６条“首选分析线”的光谱干扰情况。