Random Motions at Finite Speed in Higher Dimensions

We present a general method of studying the transport process , t≥0, in the Euclidean space ℝ ^m , m≥2, based on the analysis of the integral transforms of its distributions. We show that the joint characteristic functions of are connected with each other by a convolution-type recurrent relation. This enables us to prove that the characteristic function (Fourier transform) of in any dimension m≥2 satisfies a convolution-type Volterra integral equation of second kind. We give its solution and obtain the characteristic function of in terms of the multiple convolutions of the kernel of the equation with itself. An explicit form of the Laplace transform of the characteristic function in any dimension is given. The complete solution of the problem of finding the initial conditions for the governing partial differential equations, is given. We also show that, under the standard Kac condition on the speed of the motion and on the intensity of the switching Poisson process, the transition density of the isotropic transport process converges to the transition density of the m-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension m. We give the conditional characteristic functions of the isotropic transport process in terms of the inverse Laplace transform of the powers of the Gauss hypergeometric function. Some important models of the isotropic transport processes in lower dimensions are considered and some known results are derived as the particular cases of our general model by means of the method developed.     

全息光盘存储器的数据存取与像素匹配

全息光盘存储(HDS)技术作为一种非常具有潜力的新型信息存储技术, 是下一代光盘发展的目标。在全息光盘存储系统中, 为了实现数据精确快速地写入和读出, 降低误码率, 需要在整个高分辨率页面上实现空间光调制器(SLM)与光电阵列耦合器(CCD)之间1∶1像素匹配。在体全息存储理论和光学设计理论基础上, 研究实现SLM和CCD像素1∶1匹配的方法, 提出了实现像素匹配的要求和条件, 并且按照此要求完成该全息光盘存储器的光学系统。实验中, 分别使用随机数据掩膜版和SLM实现了对CCD的512×512精确像素匹配, 在光学系统中引入存储介质条件下, 图像质量良好, 掩膜版和SLM原始误码率分别为2.5×10-4和1.5×10-4。     

基于小波变换的堆积啁啾光脉冲时频分析

以复Morlet函数作为小波母函数推导了2M路线性啁啾高斯脉冲堆积形成的整形脉冲的时间分辨能量谱密度解析表达式。通过小波变换获得了堆积啁啾脉冲功率和瞬时波长随时间的分布; 堆积啁啾高斯脉冲功率随时间呈现振荡变化, 瞬时波长在功率接近零的极小值点发生跳变; 啁啾的增大会加剧功率的时域振荡和瞬时波长的跳变; 瞬时波长的跳变仅发生在功率接近零的极小值附近, 脉冲的能量仍然主要集中在由基元脉冲啁啾决定的波长范围内。同时, 研究表明脉冲重叠因子的微小变化会极大地影响整形脉冲峰值功率与等效平均功率之比和包络平坦度, 且两者不能同时达到最佳, 需折衷选取。     

Rotational spectra, nuclear quadrupole hyperfine tensors, and conformational structures of the mustard gas simulent 2-chloroethyl ethyl sulfide

Rotational spectra have been recorded for both the ³⁵Cl and ³⁷Cl isotopic forms of two structural conformations of 2-chloroethyl ethyl sulfide (CEES). The rotational constants of the ³⁵Cl and ³⁷Cl isotopomers were used to identify the conformational isomers. A total of 236 hyperfine transitions have been assigned for 47 rotational transitions of the ³⁵Cl isotope of a GGT conformer, and 146 hyperfine have been assigned for 37 rotational transitions of the ³⁷Cl isotopomer. For the second conformer, a total of 128 (110) hyperfine and 30 (28) rotational transitions have also been assigned to the ³⁵Cl (³⁷Cl) isotopes of a TGT conformation. The extensive hyperfine splitting data, measured to high resolution with a compact Fourier transform microwave spectrometer, were used to determine both the diagonal and off-diagonal elements of the ³⁵Cl and ³⁷Cl nuclear quadrupole coupling tensors in the inertial tensor principal axis system. The experimental rotational constant data, as well as the ³⁵Cl and ³⁷Cl nuclear quadrupole coupling tensors, were compared to the results from 27 optimized ab initio (HF/6-311++G^∗∗ and MP2/6-311++G^∗∗) model structures.     

Spatial anisotropy: a method to study anisotropic flow in heavy ion collisions

We introduce a method to study anisotropic flow parameter v<,n> as a collective probe to Quark Gluon Plasma in relativistic heavy ion collisions. The emphasis is put on the use of the Fourier expansion of initial spatial azimuthal distributions of participant nucleons in the overlapped region. The coefficients ε<,n> of Fourier expansion are called the spatial anisotropy parameter for the n-th harmonic. We propose that collective dynamics can be studied by v<,n>/ε<,n>. In this paper, we will discuss in particular the second (n=2) and the fourth (n=4) harmonics.     

辉光放电聚合物结构及力学性质研究

采用低压等离子体聚合技术,通过调整工作气压和反式二丁烯(T₂B)与H₂流量比制备了辉光放电聚合物(GDP)涂层. 利用傅里叶变换红外吸收光谱和元素分析法讨论了工作气压和T₂B与H₂流量比对GDP涂层内部H原子含量及结构的影响,并且通过纳米压痕技术对GDP涂层的硬度及杨氏模量进行了表征.研究结果表明:降低工作气压和T₂B与H₂流量比,GDP涂层内sp³ C 关键词： 傅里叶变换红外光谱 纳米压痕 杨氏模量 硬度     

Finite difference method for 2-D and 3-D nonlinear free surface wave problems

A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances. This work is supported by the science foundation of Academia Sinica. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.     

On the ν-dimensional one-component classical plasma: The thermodynamic limit problem revisited

We prove theH-stability property and the existence of the thermodynamic limit of the free energy density of the two-dimensional, one-component classical plasma. We give lower and upper bounds on the free energy density in any dimensionv and draw some consequences.     

Quantum statistical hierarchy equation in nonequilibrium systems

An extension is given for the Fourier expansion method with the contraction technique, which was introduced by Balescu for quantum statistical systems. This is attained by introducing a diagrammatic method with a concept of moving contraction. Then the hierarchy equation for the Contracted Fourier coefficient of the Wigner distribution function is obtained. As an application, a generalized master equation involvingn-body collision effects and quantum statistical effects is also derived.