Monte Carlo方法计算晶体析出相的X射线发射强度

本文提出了用Monte Carlo模拟计算晶体中析出相X射线发射强度的理论和方法。作为实例,对不同加速电压下Au,Cu基体中Cr—Fe—Ni合金析出相的X射线发射强度作了计算,并得出一些规律。     

纳米摩擦学的分子动力学模拟研究

用分子动力学模拟研究了纳米级润滑薄膜的固液相变和界面滑移现象以及固体接触和黏着的微观机制.结果表明：纳米薄膜中液体的固化相变压力随膜厚减薄而下降,说明润滑剂可能处于类固态状态.薄膜中的界面滑移现象可能在较低的剪切速率下发生,并与液体的固化程度有较好的对应关系.光滑晶体表面在相互接近或分离过程中可能因部分原子突然跃迁而发生微观黏着,这对于理解界面摩擦的起源具有重要意义.     

纳米单晶与多晶铜薄膜力学行为的数值模拟研究

通过对不同温度下单晶薄膜的拉伸性能的分子动力学模拟，从微观角度揭示了温度效应对材料性能的影响. 结果表明温度效应对材料的变形机理影响很大.0K温度下由于缺乏热激活软化的影响, 粒子运动所受到的阻碍较大, 薄膜的强度较高, 塑性变形主要来自于粒子的短程滑移.温度升高，粒子的热运动加剧，屈服强度降低, 塑性变形将主要来自于大范围的位错长程扩展.多晶薄膜的模拟结果表明, 虽然其晶粒形状较为特殊, 但是它仍然遵循反Hall-Petch关系.在模拟过程中，侧向应力最大值比拉伸方向应力的最大值滞后出现.位错只会从晶界产生并向晶粒内部传播，晶粒间界滑移是多晶薄膜塑性变形的主要来源.     

低密度和高密度水化硅酸钙的纳米压痕数值模拟

水化硅酸钙(C-S-H)是决定以硅酸盐水泥为主要组分的水泥基材料性能的关键组分,水化硅酸钙(C-S-H)是存在于水化产物中连续的固体物质,占水化水泥浆体体积的50%～60%,是水泥浆体中决定硬化水泥浆体物理结构和性能的主要成分,同时水化硅酸钙(C-S-H)也是混凝土结构宏观尺度的凝聚性和耐久性的重要影响因素．模型的建立对于预测水泥的体积性能如收缩、蠕变、渗透率和裂缝等方面越来越重要．通过将水化硅酸钙(C-S-H)分为低密度和高密度两种数值模型,并且将水化硅酸钙(C-S-H)视为在纳米尺度上具有实际微观粒子性能的离散颗粒的集合,运用分子动力学方法,通过控制水化硅酸钙(C-S-H)的紧密堆积体积分数和保持颗粒级别的其他材料属性不变来进行纳米压痕实验模拟,进而验证了压痕模量和硬度符合纳米压痕实验数据的规律．     

多晶石墨烯力学性质的分子动力学研究

实验中纳米压痕被广泛用于测量单晶或多晶石墨烯的力学性质,而分子动力学模拟中研究者们更多地使用单轴拉伸来测量石墨烯的力学性质.两种测量方法对于多晶石墨烯弹性模量和破坏强度的预测是否存在差异?多晶石墨烯的力学性质是否依赖于其晶粒大小?对于固定晶粒大小的多晶石墨烯,拓扑结构的不同是否影响其力学性质?围绕以上问题,通过对比纳米压痕和单轴拉伸两种方法的分子动力学模拟,研究了多晶石墨烯弹性模量和破坏强度对晶粒尺寸、拓扑结构和测量方法的依赖性.     

带球形空腔的广义热弹性无限大材料的弹性模量和传热系数与材料参考温度的相关性

利用具某一松弛时间的广义热弹性方程求解了带球形空腔的无限大材料问题．该材料的弹性模量和传热系数是可变的．空腔的内表面没有力作用,但有热冲击作用．利用Laplace变换求得直接逼近解．数值求解了Laplace逆变换．给出了温度、位移和应力的分布图．     

GaAs/Si外延层X射线双晶衍射摇摆曲线的动力学模拟和位错密度的测量

利用X射线衍射动力学理论和位错的小角晶界模型,分析了GaAs/Si外延层中位错对X射线双晶衍射摇摆曲线的影响,认为GaAs/Si外延层并不是严格取向一致的完整单晶膜,而是存在着许多小角晶界的镶嵌晶体,并推导出了其中镶嵌块的晶向分布函数和晶格应变分布函数,模拟出了GaAs/Si外延层X射线双晶衍射摇摆曲线,由此曲线计算出了GaAs/Si外延层中的位错密度.同时还得到了Si衬底上GaAs外延层中镶嵌块的大小.为分析高失配外延材料的双晶衍射摇摆曲线提供了新的方法.     

Ag/Si纳米颗粒多层膜的合成

使用多靶离子束溅射沉积方法制备出Ag/Si多层膜 .利用原位低角X射线衍射技术和截面高分辨透射电子显微镜观察 5 0～ 30 0℃退火过程中Ag/Si多层膜各亚层间发生的扩散现象 ,并由此分析研究Ag/Si多层膜微观结构变化 ,即Ag/Si纳米颗粒多层膜的形成过程 .计算出Si在Ag亚层中的扩散激活能和频率因子分别为 0 .2 4eV和 2 .0 2× 1 0 ^-20 m² /s,纳米Ag颗粒的尺寸约为5nm .     

软X射线图象反演对TOKAMAK装置运行区结构的研究

用高灵敏、高时空分辨的软X图象反演系统研究了HT-6B TOKAMAK装置中3个运行区的磁面结构,形成锯齿放电的必要条件之一是在中心区出现有效的加热作用,锯齿区存在5个发展阶段,出现同心、偏心、双心、“MHD型”和“超MHD型”5种磁面结构,MHD振荡区有稳定的“MHD型”磁岛结构,它由弯月形“热芯”和圆形“冷泡”组成,并沿电子逆磁方向旋转,共振区中共振螺旋场改善了加热状况,抑制了MHD扰动,使单一“MHD型”磁面转变为锯齿型磁面.     

自激活激光晶体硼酸铝钕的研究

本文报道了我们对自激活激光晶体硼酸铝钕的生长、激光性能以及化学成分与荧光浓度猝灭效应之间关系的研究。引进原子参数L,定性地说明不同化学成分的基质中激活离子的不同荧光浓度猝灭效应,并从理论上说明了引进这一参数的合理性。我们获得了每个脉冲1205mJ的1.063μm激光输出和49mJ的1.34μm的激光输出。对1.06μm激光倍频,即0.53μm的激光输出为25.5mJ。     

振动砖砌体应力与应变的弹性模量

杨玉林、朱成．振动砖砌体应力与应变的弹性模量本文根据对７２个振动砖砌体试件的中心抗压强度及弹性模量试验,利用非线性回归的方法确定了振动砖砌体的应力σ对应变ε之间的对数相关关系,从而说明了以往认为振动砖砌体的应力与应变为线性相关且弹性模量为常数的不合理性     

On the Existence of Positive Eigenvalues for the Isotropic Linear Elasticity System with Negative Shear Modulus

Abstract

In this note well-known PDE and functional analyis results are used to prove that the set of real eigenvalues for the linear isotropic elasticity with negative shear modulus is unbounded from above as well as from below.     

The Direct Method of Lines for Forward and Inverse Linear Elasticity Problems of Composite Materials in Star-Shaped Domains

In this paper, we generalize the direct method of lines for linear elasticity problems of composite materials in star-shaped domains and consider its application to inverse elasticity problems. We assume that the boundary of the star-shaped domain can be described by an explicit $C^1$ parametric curve in the polar coordinate. We introduce the curvilinear coordinate, in which the irregular star-shaped domain is converted to a regular semi-infinite strip. The equations of linear elasticity are discretized with respect to the angular variable and we solve the resulting semi-discrete approximation analytically using a direct method. The eigenvalues of the semi-discrete approximation converge quickly to the true eigenvalues of the elliptic operator, which helps capture the singularities naturally. Moreover, an optimal error estimate of our method is given. For the inverse elasticity problems, we determine the Lamé coefficients from measurement data by minimizing a regularized energy functional. We apply the direct method of lines as the forward solver in order to cope with the irregularity of the domain and possible singularities in the forward solutions. Several numerical examples are presented to show the effectiveness and accuracy of our method for both forward and inverse elasticity problems of composite materials.     

关于需求价格弹性的探讨

需求价格弹性是管理经济学中的一个重要概念,是指导市场行为的重要指标,如何理解需求价格弹性概念,掌握弹性的计算方法就显得格外重要.本文探讨需求价格弹性的概念及计算方法.     

需求价格弹性与边际收益研究

研究特定需求价格弹性条件下需求函数的确定问题和特定边际收益条件下需求函数的确定问题,并给出了有关的计算公式.研究结果表明,为了实现既定的需求价格弹性或边际收益,对应的需求函数有无穷多个.     

Maximum Modulus of Polynomials

Let P(z) =n∑j=0 a_jz~j be a polynomial of degree n and let M(P, r) = max|z|=r|P(z)|. If P(z) ≠ 0 in |z| 1, then M( P, r) ≥ ((1 + r)/ (1 + ρ))~ n M( P, ρ).The result is best possible. In this paper we shall present a refinement of this result and some other related results.     

Development of the Tangent Modulus from the Euler-Problem to Nonsmooth Materials

History and development of the tangent modulus from the origins to the recent nonsmooth damaging versions are presented. Load history and stability analyses of structures of nonlinear reversible or irreversible materials are based on the concept of tangent modulus. Generally, instantaneously changing tangent modulus is needed and the solution yields iteration process. In the case of inelastic problems, the switch from loading to unloading of the material behaviour results in nonsmooth material functions. Nonsmooth, generally saw-tooth like behaviour happens in composite, laminated or rock type materials, or in the interaction of concrete and the reinforcement, too. Recently, damage and localization are in the focus of structural analyses, extending the tangent modulus to the negative cases, as well. Consequently, an overview of the history and development of the tangent modulus containing the recent modifications seems to be necessary. On the other hand, the more than a century long history of the tangent modulus is a marvellous study of the parallel development of mechanics and mathematics, by following the mutual inspiring effect of them through the activity of such pioneers like P.D. Panagiotopoulos in creating Nonsmooth Mechanics.     

Development of the Tangent Modulus from the Euler-Problem to Nonsmooth Materials

History and development of the tangent modulus from the origins to the recent nonsmooth damaging versions are presented. Load history and stability analyses of structures of nonlinear reversible or irreversible materials are based on the concept of tangent modulus. Generally, instantaneously changing tangent modulus is needed and the solution yields iteration process. In the case of inelastic problems, the switch from loading to unloading of the material behaviour results in nonsmooth material functions. Nonsmooth, generally saw-tooth like behaviour happens in composite, laminated or rock type materials, or in the interaction of concrete and the reinforcement, too. Recently, damage and localization are in the focus of structural analyses, extending the tangent modulus to the negative cases, as well. Consequently, an overview of the history and development of the tangent modulus containing the recent modifications seems to be necessary. On the other hand, the more than a century long history of the tangent modulus is a marvellous study of the parallel development of mechanics and mathematics, by following the mutual inspiring effect of them through the activity of such pioneers like P.D. Panagiotopoulos in creating Nonsmooth Mechanics.     

关于Wiener过程泛函连续模的精确收敛速度

设{W（t）,t≥0}是一标准Wiener过程,记S是Strassen重对数律的紧集类·本文中我们讨论了两个变量sup_0≤t≤1-h inf_f∈S sup_0≤x≤1 |(W(t+hx)-W(t))(2h log h^-1)^-1/2 - f(x)|及inf_0≤t≤1-h sup_0≤x≤1 |(W(t + hx) - W(t))(2hlogh^-1)^-1/2- f(x)|（对任何f∈S）趋于零的精确的收敛速度.作为一个推广,我们建立了Wiener过程的不可微模与泛函的连续模之间的一种关系.