合力为零的经典质点拉格朗日函数

运用拉格朗日力学逆问题理论和方法,得到合力为零的经典质点两类等效拉格朗日函数.这些函数可以与时间、质点的位置矢量和速度矢量相关,并非只能是速度大小的函数.     

非对易相空间中阻尼系统的Wigner函数

用量子力学来处理经典的阻尼系统,考虑到空间变量对易关系中包含的坐标-坐标和动量-动量的非对易性,利用Wigner函数在非对易相空间的基本性质,得到了阻尼谐振子在非对易相空间中的Wigner函数与对易空间及非对易空间的形式一致.     

LCAC—SW方法中阻尼函数的研究

研究了在排列通道线性组合散射波方法中阻尼函数的衰减形式，通过计算表明，在三维Ｈ＋Ｈ２交换反应中，阻尼函数应以快于１－ｅｘｐ的形式，如ｆ（Ｒ）＝１－ｅｘｐ，在经典回转点处衰减为０，同时提出闭通道函数应分布在准经典近似不适用的区域。     

逃逸函数算法及其在光学设计中的应用

用阻尼最小二乘法进行光学系统的优化 ,得到的结果往往是评价函数在结构变量空间的一个局部极小值。日本东京工艺大学的一色教授提出了能够跳出此局部极小值继续寻找其它结果的逃逸函数全局优化算法 ,该算法的运行由多个不加或加入逃逸函数的阻尼最小二乘法局部优化组成。描述了逃逸函数的基本原理 ,给出了北京理工大学研制的GOLD软件在加入了这种算法后对光学系统进行全局优化的设计实例。实验证明了逃逸函数算法是提高光学设计效率和质量的一种有效工具。     

从拉格朗日函数的不确定性导出定域规范不变性

从拉格朗日函数的不确定性出发，通过作为积分上发的坐标函娄之作用量Ｓ＝∫ｔｔ１Ｌｄｔ′＝Ｓ（ｘ＾μ）及其不确定性，得到ψ与ψ′＝ｅ＾－ｉｑａ（ｘ＾μ）ψ等效－定域规范不变性或日局域对称性。     

随机扩散模型一种新的密度函数统计方法

引入核函数法对随机扩散方程（SDE）样本的密度分布进行统计,希望用核函数来减少统计涨落。由于SDE样本的密度随时间发展,越来越稀疏,所以核函数也应该越来越大,也就是说核函数应该随时间在变化。通过一个瞬时释放的二维扩散问题（具有解析解）,从定性和定量两个角度比较了变带宽核函数法和传统统计方法在密度分布统计中的性能差别,论述了变带宽核函数法的优缺点,变带宽核函数法在牺牲部分峰值的前提下可以很好地解决SDE样本密度分布统计涨落问题,在工程应用中值得推广。     

27 Al+27Al重离子耗散碰撞中能量自关联函数的分析

测量了2 7Al+ 2 7Al耗散反应产物的激发函数 ,束流2 7Al8+的入射能量从1 1 4MeV到 1 2 7MeV变化 ,能量步长为 2 0 0keV .探测角度覆盖了实验室系1 0°— 57°的连续区域 .用不同的理论模型分析了耗散产物的能量自关联函数 .结果表明 ,反应所形成的中间双核系统的阻尼相干转动造成了激发函数中不可平滑的涨落结构 ,相干转动的阻尼来自量子混沌运动     

小阻尼界面房间声传输函数和声脉冲响应函数的有限元素法

有限元法可用于以声波动方程为基础通过数值计算求解室内声场,适用于分析界面阻抗非均匀分布和复杂形状房间内声场的低频特性。本文首先介绍了小阻尼界面条件下室内声场简正方式、声衰变系数、混响时间的ＦＥＭ计算方法。在此基础上导出了房间内两点之间声传输函数和声脉冲响应函数的ＦＥＭ计算模型,并以矩形房间为例详细讨论了有关细节。本文所讨论的计算模型可以映房间内不同的声源点,接收点位置上的声压频谱特性和脉冲响应的时     

阻尼耦合振动的Lagrange函数和Hamilton函数

本文研究两种阻尼耦合振动的分析力学化.首先,利用坐标变换将方程变换成自伴随形式;其次,根据Engels方法计算得到Lagrange函数;最后,由逆变换导出原始方程的Lagrange函数,以及Hamilton函数.     

一个三体问题的解法

应用两次广义坐标变换，将彼此间由弹性力作用的三体问题的拉格朗日函数简化为两个独立的谐振子的拉格朗日函数之和，在理论上提供了解决此三体问题的方法。     

4-N-甲基苯乙烯砒啶盐衍生物振动超极化率的理论研究

在双谐振子近似下，利用耦合微扰Hartree-Fock方法计算了4-N-甲基苯乙烯砒啶盐衍生物分子的静态振动第一超极化率和红外与拉曼光谱，给出了对静态振动第一超极化率起主导贡献的两种简正振动模式. 研究发现，标题分子的静态振动第一超极化率都比较大，且与静态电子第一超极化率呈较好的线性关系. 首次提出了利用红外与拉曼光谱特征峰标识的振动模来估算振动第一超极化率大小的少模方法. 结果表明，少模方法用于估算振动第一超极化率的大小是可行的.     

Determination of the Association Constants of Macrocyclic Ethers by the Aid of 13C Dipole-dipole Relaxation Time Measurements. I.,: Li+, Mg2+ and Ca2+ complexes of 1,4,7,10-tetraoxacyclododecane

Abstract

The association constants of Li⁺, Ca⁺² and Mg⁺² ions complexing with 1, 4, 7, 10-tetraoxcyclododecane in DHO were determined by the aid of ¹³C dipole-dipole relaxation time measurements. To obtain the K_a, association constant, the T^O ₁ values of the stoichiometric complex solutions and the T₁₀ of the free molecules were applied to the equation derived, 1/K_a· A_o + 2 = 1/P + P, for the 1:1 ratio of the complexing and to the equation 1/2K_a·A_o + 3/2 = P + 1/2P for the 1:2 ratio of the complexing where P, is molar ratio of the crown complexed ions.

Accordingly we found that the binding ability of the macrocyclic ether towards to the cations is in the following order of Li⁺ < Mg⁺² ? Ca⁺² in DHO solutions.     

Determination of the Complexing Constants by the Aid of 13C Dipole-Dipole Relaxation Time Measurements. Part. III. Complexing of 15-Crown-5 and 18-Crown-6 with Na+,K+ and Ca2+ in DHOX

The association constants, K_a of KI, Nal and CaCl₂ complexing with 1,4,7,10,13-pentaoxacyclopentadecane and 1,4,7,10,13,16-hexaoxacycloocta-decane in DHO were determined by the aid of ¹³C dipole-dipole relaxation time measurements.

The mole fraction of the complexed ligand, P_C were obtained by the use of the equation of 1/T^obs ₁ - 1/T₁₀ = P_C (1/T^O ₁ - 1/T₁₀) where the T₁₀ and T^o ₁ are the relaxation times of free and complexed macrocyclic ethers respectively.

K_a values obtained from the above given equation depending on the cation concentration, [A⁺ _O] typically reflected the relation between the cationic radius and cyclic ether ring size.     

Isotope effect in hydrogen peroxide formation during H2O and D2O sonication

The kinetics of hydrogen peroxide formation have been studied during H2O and D2O sonication in the presence of argon and oxygen (f = 22 kHz, I = 3.0 W cm-2, Pac = 0.52 W ml-1, V = 20 ml, T = 20 degrees C). It was found that the sonochemical reaction rate W has a zero order with respect to hydrogen peroxide (H2O, D2O or DHO2) concentration. In argon atmosphere the kinetic isotope effect was found to be equal to alpha = WH2O/WD2O = 2.2 +/- 0.3. The alpha value decreases in H2O-D2O mixtures with increasing H2O concentration. In oxygen atmosphere the isotope effect is not observed (alpha = 1.05 +/- 0.10). It is assumed that the revealed isotope effect is related to the mechanism of water sonolysis including the H2O-Ar* and D2O-Ar* energy transition, where Ar* is an argon atom in an excited state, in nonequilibrium plasma generated by the shock-wave.     

The Dipole-dipole Relaxation Time and Internal Motions of the Cyclic Oligoethers. Part. III The Activation Energies of Pseudorotation of 1,4,7,10-tetraoxacyclododecane and its Li,+ Ca2+ Mg2+ Complexes

The ¹³C Dipole-dipole relaxation time and the activation energies of internal motion of cyclic ether backbone were obtained for the 1,4,7,10-tetraoxacyclododecane(12. crown. 4) and its cationic complexes. ¹³C dipolar relaxation time,T^DD ₁ of free tetraoxacyclododecane molecule and its Li,⁺ Ca²⁺ and Mg²⁺ complexes were determined at various temperatures in DHO and CH₃OD solutions at 15.0 MHz. The pseudorotation barriers of oxyethylene bridges were investigated throughout the temperature dependence of dipole-dipole relaxation times which verified that the T^DD ₁ values closely depend on the energy requirements of the particular dynamic processes of molecular systems as well as ion-dipole interactions of cation-cyclic ether. Namely, we concluded a simple analogy between the correlation times of the ¹³C spins and the observed T^DD ₁ values in the vicinity of free and complexing systems. On the other hand our experimental results were correlated with the strain energy minimization calculations previously published, which have strongly proved our presented results.     

闪光X射线照相系统调制传递函数测量

本文叙述调制传递函数(MTF)的基本概念.介绍了闪光X射线辐射照相屏-片记录系统的调制传递函数的常用测量方法.我们分别用矩形波光栅、台阶楔、针孔作输入激励,测出了高能闪光X射线照相系统的调制传递函数,并对测量结果进行分析对比.这些实测的MTF对成象系统成象性能的定量认识、照相条件的最佳选择、照相图象的事前预估、模糊图象的事后处理都有很重要的实用价值.     

On a Mathematical Framework for the Constitutive Equations of Anisotropic Dielectric Relaxation

Three classes of time-domain non-relativistic anisotropic dielectric constitutive equations of increasing generality are discussed. In each class dissipativity is ensured by the choice of a class of convolution kernels in the D-to-E constitutive equation expressing the electric field E in terms of the electric displacement field D. Defining properties of the inverse (E-to-D) kernels and their Fourier-Laplace transforms (complex dielectric functions) are determined by inversion of the D-to-E constitutive equation. By this procedure it is shown that dielectric functions of the dipolar dielectrics are tensor-valued Bernstein functions while the dielectric functions of the Drude-Lorentz type are tensor-valued negative definite functions. The properties of the complex dielectric permittivities are also determined for either class. The theory is applied to an exhaustive review of empirical response functions of real dielectric materials encountered in the literature. Each class of convolution kernels is consistent with existence of a conserved energy, but in one case a strictly dissipative energy can be constructed.     

乔治·格林及格林函数法

乔治.格林是一位重要的数学物理学家.简要介绍了乔治.格林的生平和科学研究经历,揭示了帮助他取得重要科学研究成果的主要因素,介绍了格林函数法的建立过程及其重要性.     

光衍射数值模拟中不同抽样方法的适用性分析

基于标量衍射理论和快速傅里叶变换,分析了光衍射的数值模拟时可以采用的不同抽样方法及其适用性。理论分析表明,按照抽样对象的不同,存在三种适用范围不同的算法:传递函数抽样法、点扩展函数抽样法和加权函数抽样法。其适用范围分别为衍射距离小于、大于和等于特征距离的情况。在Matlab软件环境下给出了三种算法的模拟计算实例,并与相应的实验结果进行了比较,证明了理论分析的正确性。最后还给出了一种无需改变抽样点数和抽样间隔就可计算任意距离衍射过程的自适应抽样算法及其在数字全息再现中的应用实例。     

Collective modes,damping, and the scattering function in classical liquids

An exact representation for the density-density response function is presented. This representation is a generalization of the result obtained in the mean field approximation and amounts to replacing the static, effective potential by one which is both wavenumber- and frequency-dependent. This potential possesses both a real and an imaginary part; the latter describes the collisional damping of collective modes. Analyticity and sum rule arguments are used to describe the basic properties of this complex potential. The formalism allows us to write an exact formula for the scattering functionS(k, ) in which the basic unknown is the collisional damping function. Using a small portion of the recent experimental data on coherent neutron scattering in liquid argon, we are able to calculateS(k, ) and other quantities of interest and to make comparisons with the rest of the data.