Nonlinear stability of large k-value shallow spherical shells with a symmetrically distributed line load

In this paper, we treat the nonlinear stability problem of shallow spherical shells with large values ofk(k=12(1–v) · 2f/h,f = shell rise,h = shell thickness) under the action of uniformly distributed line load along a circle concentric with the shell boundary. Load-deflection curves are computed at successive increments of uniformly distributed line loads by using both cubic B-spline approximations and iterative techniques. Our algorithm yields fairly good convergent results for values ofk as large as 400. The limiting case in which shells are loaded along a circle of small radius has been specially investigated and the computed critical loads are compared with those obtained with central point loads by other authors.     

离子热合成微球方钠石

在1-甲基-3-乙基咪唑溴盐离子液体([emim]Br)中合成了球形的方钠石分子筛,分别通过X射线衍射仪(XRD)和扫描电子显微镜(SEM)等表征手段对产物进行了表征。结果表明,在反应物料配比相同的条件下,离子热合成有利于球形方钠石结构的形成。在反应物料中nNa2SiO3·9H2O/nNaAlO2为1.1(即nSiO2/nAl2O3=2.2)和5.0时(即nSiO2/nAl2O3=10)时,离子热合成得到了粒径为0.2和1.4μm的球形方钠石分子筛,而水热合成分别得到了X型分子筛和一种未知结构的产物。     

Landau-Lifshitz方程派生的球面锥对称族及其演化

直至2008年,尚未见到讨论同时具有外磁场和各向异性场的多维Landau-Lifshitz方程的显式动态解的文献.当缺少外加磁场或各向异性场时,许多作者曾经尝试过Hirota的著名方法,Lie代数结构与Backlund变换,双线性变换等,但精确解仍然没有构造出来.本文首先给出了一种求解具有外磁场和各向异性场的Landa...     

线度和势垒宽度对球状纳米系统电子散射截面的影响

在有效质量近似和球形方形势模型下,计算了开放型球状纳米系统电子散射截面及电子按能量的概率分布,探讨了线度、势垒宽度对电子散射截面和共振能量以及共振宽度的影响.结果表明:电子的散射截面随能量的分布曲线有一极大值和极小值,而且电子能量的概率分布曲线的极大值位置总是介于散射截面分布曲线的极大值与极小值的能量位置之间;散射截面随内核半径r₀的增大而增大,而且散射截面分布曲线随r₀的增大由较平滑变得较尖锐;散射截面随势垒宽度Δ的增大而增大,但在Δ＝1.4a_CdS–1.7a_CdS的范围内,变化出现异常,在Δ=1.6a_CdS时散射截面出现极小;电子共振能量E_l 随Δ的变化与电子所处状态有关,而电子共振宽度Γ_l随Δ的增大而减小;不论Δ取何值, E_l和Γ_l都满足能量和时间的测不准关系. 关键词： 球状纳米系统 势垒宽度 电子散射截面 电子概率分布     

界面动力学对过冷熔体中球晶生长界面形态的影响

考虑了在非平衡凝固条件下球晶生长过程中界面动力学系数随界面温度的变化,利用渐近分析方法求出了在过冷熔体中球晶生长温度场和界面的近似解析解,研究了非线性界面动力学过冷对于过冷熔体中球晶界面形态和生长速度的影响.研究表明,界面动力学系数越大,球晶的生长速度越快; 反之,表明界面动力学系数越小,球晶的生长速度越慢.与忽略界面动力学的情形比较,在球晶生长过程中依赖于界面温度变化的界面动力学显著地减缓了晶体生长的速度. 关键词： 球晶 界面形态 渐近分析     

球面空间中的Pedoe不等式与张-杨不等式及应用

本文应用距离几何的理论与方法,研究了n维球面空间中n维单形与有限点集的几何不等式问题,建立了球面空间中n维单形一种形式的Pedoe不等式与有限点集一种形式的张-杨不等式,并应用它获得n维球面空间中Veljan-Korchmaros型不等式与Finsler-Hadwinger型不等式.     

REMARKS ON THE LIFESPAN FOR THE SOLUTION TO NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

The authors consider the Cauchy problem for the following nonlinear wave equationswhere x ∈ R3, t ≥ 0, ε > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ε, then the lifespan T(ε) satisfies the folowing inequalities     

Nonlinear Spherical Caps and Associated Plate and Membrane Problems

This paper deals with the existence and multiplicity problem of the equilibrium solutions of an elastic spherical cap within nonlinear strain theory. We pose the problem in the form of a three parameter bifurcation problem, one parameter being related to the load, the others to the geometry. When the geometrical parameters are different from zero, the so-called generic case, we revisit the nonuniqueness results, and explore the solutions in the parameter space. Then we analyze the formal limits as the geometrical parameters tend to zero. When the curvature tends to zero, we obtain from the nonlinear shell a von Kármán plate, a new, although natural, result. When the thickness parameter tends to zero, we get a nonlinear membrane problem. A study of the latter gives infinitely many solutions, and we discuss the construction, shapes, and stability in detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Diffusion from within a Spherical Body with Partially Blocked Surface: Diffusion through a Constant Surface Area

Diffusion from spherical bodies has been a subject of interest since the earliest times of modern sciences and a few equivalent analytical formulations of the problem are taught in engineering textbooks dealing with cooling rates of hot spheres. However, all these former studies assume that the diffusing material is transferable to/from the surrounding space through the whole surface of the spherical body. Conversely, the development of nanoscience and the improved knowledge of microscopic biological events have evidenced that diffusion from spherical bodies is a ubiquitous problem. It often occurs in situations where the nanosphere surfaces are not isotropic and partly impermeable to diffusing materials. This work elaborates on this issue and theoretically establishes that—with some specific allowance—the basic analytical equation of diffusion from/to fully accessible spherical bodies may be used.     

两种D III型有界对称域的逆ABEL变换

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