多孔压电线性理论中的唯一性定理、互易定理和特征值问题

假定弹性场和电场为正定,在多孔压电线性理论中建立起唯一性定理和互易定理．在准静态电场近似下,证明多孔压电材料线性理论中的一般性定理．利用弹性场的正定性,唯一性定理得到证明．在与多孔压电体自由振动相联系的特征值问题的研究中,给出了简明的公式．文中还研究了有关算子的某些特性．以简明公式为基础,利用变分法和算子法,研究了由于小扰动产生的频移问题．还给出了特殊情况下的扰动分析．     

基于乘性一致性残缺互补判断矩阵的决策方法

对于满足乘性一致性的残缺互补判断矩阵的决策问题,提出了一种决策方法。首先把互补判断矩阵的乘性一致性定义进行了简化,得到了互补判断矩阵乘性一致性的另外几种表达形式;进一步得到了在已知n-1个特殊元素的条件下,残缺互补判断矩阵中缺失元素的补全方法;然后给出了残缺互补判断矩阵可接受的条件,以及矩阵的一致性检验及调整方法;基于残缺互补判断矩阵,给出了以下决策步骤:残缺互补判断矩阵的一致性检验及调整过程,补全缺失元素的迭代过程和最优方案择优过程。最后给出了一个实例,通过该实例的计算以及本文方法与已有方法的比较,证明了本文方法是简便和有效的。     

基于线性回归算法的春玉米叶面积指数的冠层高光谱反演研究

利用辽宁锦州地区2013年生长季不同土壤水分控制条件下的春玉米冠层高光谱数据,及对应的植株叶面积指数(leaf area index,LAI)数据,分析在不同发育期内不同生长状况下的春玉米冠层高光谱特征及其与植株叶面积指数的关系。采集并计算共313组有效样本,包括350～2 500 nm波段范围光谱的反射率、反射率倒数的对数、反射率一阶导数及LAI,应用多元逐步线性回归法和偏最小二乘回归法,对剔除了受大气水分影响较为严重光谱波段的其他波段数据进行降维,构建叶面积指数的全波段冠层高光谱数据模型,并进行精度检验与比较。结果表明,春玉米LAI与光谱反射率在可见光波段(350～680 nm)、红外波段(1 430～1 800和1 950～2 450 nm)均呈显著的负相关;反射率倒数的对数在对应区间为显著的正相关;反射率一阶导数则在可见光和近红外波段(350～1 350 nm)存在较显著相关波段。三种全波段冠层高光谱数据在春玉米LAI的线性回归中,偏最小二乘法在以冠层反射率为自变量的模型构建中,比多元逐步线性回归拟合度好,其总均方根误差为0.480 7;以冠层光谱反射率的倒数的对数及一阶导数为自变量,应用逐步线性回归法建模,拟合度较好,其总均方根误差分别为0.333 5和0.348 8;三种光谱数据的春玉米LAI两种回归算法中,以冠层反射率倒数的对数为自变量,应用逐步线性回归方法建模的拟合度最佳。     

Bunch evolution study in optimization of MeV ultrafast electron diffraction

Megaelectronvolt ultrafast electron diffraction (UED) is a promising detection tool for ultrafast processes. The quality of diffraction image is determined by the transverse evolution of the probe bunch. In this paper, we study the contributing terms of the emittance and space charge effects to the bunch evolution in the MeV UED scheme, employing a mean-field model with an ellipsoidal distribution as well as particle tracking simulation. The small transverse dimension of the drive laser is found to be critical to improve the reciprocal resolution, exploiting both smaller emittance and larger transverse bunch size before the solenoid. The degradation of the reciprocal spatial resolution caused by the space charge effects should be carefully controlled.     

In situ three‐dimensional reciprocal‐space mapping during mechanical deformation

Mechanical deformation of a SiGe island epitaxically grown on Si(001) was studied by a specially adapted atomic force microscope and nanofocused X‐ray diffraction. The deformation was monitored during in situ mechanical loading by recording three‐dimensional reciprocal‐space maps around a selected Bragg peak. Scanning the energy of the incident beam instead of rocking the sample allowed the safe and reliable measurement of the reciprocal‐space maps without removal of the mechanical load. The crystal truncation rods originating from the island side facets rotate to steeper angles with increasing mechanical load. Simulations of the displacement field and the intensity distribution, based on the finite‐element method, reveal that the change in orientation of the side facets of about 25° corresponds to an applied pressure of 2–3 GPa on the island top plane.     

影响函数与有限元应力计算

用有限元法得到位移场后,总要计算应力场。通常的做法是对位移进行微商计算应变,再根据应力-应变关系计算应力。有限元位移计算的精度比较高,但通过用位移微商来计算应力,精度会大大降低。本文利用Hamilton对偶体系的已有成果,解析求解位移和应力的影响函数,利用有限元法计算得到的位移和节点力,通过功的互等定理,可以求得一点的应力值。因影响函数是分析解,而且计算应力时不必进行微商,应力精度大幅提高。数值结果表明该方法是可行的和有效的。由该方法编制成的计算程序,可作为有限元通用程序应力计算的一个模块,将较大地提高有限元应力计算的精度和稳定性。     

分母为平方因子的二项式系数倒数级数

根据一个已知级数,利用反正弦积分与多对数的结果,用积分-裂项法给出分母为1个平方因子,平方因子与1个,2个,3个奇因子乘积的二项式系数倒数级数.利用反三角函数与反双曲函数关系给出分母为平方因子的交错二项式系数倒数级数.所给出二项式系数倒数级数的和式是函数形式.并给出分母含有平方因子的二项式系数倒数数值级数恒等式.     

Reciprocal space mapping

This review covers the recent advances in reciprocal space mapping. The experimental techniques as well as the theoretical and conceptual developments are discussed. The advantages of reciprocal space mapping over the conventional single scan X-ray scattering methods become clear from the examples presented. Extracting the additional information from mapping in reciprocal space maps has led to a deeper understanding of materials. Imperfect materials benefit enormously from these methods. Near perfect materials also indicate weak diffuse scattering that can now be interpreted in terms of defects, etc., whereas with single scans the influence is difficult to observe and separate from other features. Reciprocal space maps can be collected with both high and low angular resolution diffractometers, depending on the application, although a combination of resolutions may be necessary. It is also growing in importance in the analysis of materials using specular reflectometry. High-resolution reciprocal space mapping is not restricted to good crystalline quality. Examples of reciprocal space mapping are given for semiconductors, metals, ceramics and biological samples. For semiconductor materials, reciprocal space mapping has now become almost routine in the study of lattice relaxation in thin layers and in the assessment of the “quality” of materials. Combinations of mapping with topography and precision lattice parameter determination are also discussed. The latter part of this review discusses the advantages of three-dimensional reciprocal space mapping, which takes the analysis further. With this method the full three-dimensional shapes in reciprocal space can be studied.     

布里渊区与倒格子原胞

用简单数学方法就体心立方晶格和面心立方晶格证明了三维情况下布里渊区体积等于倒格子原胞体积．同时提出证明高阶布里渊区与简约布里渊区体积相等的一种简捷方法．