Microscopic Hydrodynamic Modes in a Binary Hard Sphere Mixture

We derive analytic microscopic expressions for the shear viscosity, the speed of sound, and the decay rates of the hydrodynamic modes in a hard sphere binary gas mixture directly from the spectral properties of coupled Boltzmann equations. We show that the analytic expressions give good agreement with experimental viscosity data and to the results of light scattering experiments on noble gas binary mixtures.     

同轴型强流电子束二极管的一种解析近似

 从描述电子束运动的基本方程出发,引入一定条件下的近似,获得了一种实用的同轴二极管电流、电压与几何参数关系的近似解析解。给出了同轴二极管阻抗、间隙电压分布与二极管外加电压以及结构参数之间的关系式,并与1维模型精确数值解进行比较分析。采用了PIC数值模拟方法对该理论分析结果在常用参数范围内的准确性进行了验证,获得了一致的结果。与相对论条件下的实验结果数据相比,在二极管电压为300～700 kV时实验结果与该理论估算值非常接近。     

Molecular simulation of binary phase diagrams from the osmotic equilibrium method: vapour pressure and activity in water–ethanol mixtures

ABSTRACT

Herein, an approach for simulating phase diagrams of binary mixtures is presented, where a bulk liquid and its corresponding vapour phase are simulated by means of molecular dynamics using explicit polarisation. Time-averaged density profiles for the pure compounds and mixtures at different mole fractions provide information about the spatial distribution in the bulk liquid and the amount of evaporated species in the adjacent vapour phase. The activities in the liquid phase are calculated from the mean vapour phase densities at a given composition, providing a good qualitative agreement compared to experimental data and the precision of the method follows a previously developed Poisson model of evaporation. With the Redlich–Kister approach for the activities in a binary mixture, the directly obtained activities are fitted providing corrected activity coefficients of the two species. This method is applied to ethanol water mixtures at different mole fractions. The obtained structural data are in good agreement with experimental data and time-averaged density profiles provide a detailed insight into the composition of the liquid–vapour interface. An azeotropic point is obtained for an excess concentration of ethanol at 87% as percentage by mass compared to the experimental value of 95%.     

频闪剪切散斑干涉术的研究

提出了一种用于振动研究的方法——频闪剪切散斑干涉照相法。该方法由于采用了剪切镜,能得到较为精确的散斑剪切图,提高了测量的精度,是一种用于振动研究较为理想的散斑照相的新方法。讨论了频闪剪切散斑干涉术的基本原理,给出了频闪剪切散斑图的全场分析的平均光强分析的解析式,并给出了实验结果。理论和实验都表明频闪剪切散斑干涉照相法要优于时间平均剪切散斑干涉照相法。该方法在全场滤波分析时,能给出任一瞬时物体振动信息,得到清晰的、高衬比的全场干涉条纹图,是一种实用可行的方法。     

脉冲激光探测方位角磁电检测技术

针对常规弹药脉冲激光周向探测系统无法精确获取目标方位信息的问题,设计了基于磁电检测的单光束激光引信全向方位角探测方案.对磁电检测系统进行建模,建立圆柱形永磁体转动磁场模型,推导出磁阻传感器所测位置磁场的解析式,验证所测磁场为一正弦磁场信号.依据此正弦信号,设计了上升沿阈值周期检测算法,并运用FPGA与TDC-GP21对激光回波出现时间与电机转速信号周期进行高准确度时间间隔测量实现方位角的解算.依据方案设计原理样机并编写上位机程序,进行方位角探测实验.实验结果表明:磁电检测系统采用多重屏蔽方法,能有效抑制电磁干扰;并能实时监测电机转速,实现方位角解算,方位角解算误差在±2°以内.满足激光引信方位角测量的高准确度、抗干扰能力强等要求.     

Rigorous Computation of Diffusion Coefficients for Expanding Maps

For real analytic expanding interval maps, a novel method is given for rigorously approximating the diffusion coefficient of real analytic observables. As a theoretical algorithm, our approximation scheme is shown to give quadratic exponential convergence to the diffusion coefficient. The method for converting this rapid convergence into explicit high precision rigorous bounds is illustrated in the setting of Lanford’s map \(x\mapsto 2x +\frac{1}{2}x(1-x) \pmod 1 \).     

A Novel Method to Calculate the Initial Phase Difference between the Two Fibre Arms of Laser Homodyne Iuterferometer

We suggest a novel method to calculate the initial phase difference between two fibre arms of a laser homodyne interferometer. Put the two fibre arms in a temperature controller, whose short term stability is 0.02° C （measured in an hour）, then measure the interference photocurrent and the photocurrents from the two fibre arms at a fixed temperature. With these three photocurrents we can calculate the value of the initial phase difference. We set up a simple laser homodyne interferometer to test the theory. The experimental results are repeatable and the measurement precision is about 0.04°. It is theoretically and experimentally proven that this method is potentially easy and practical.     

Magnetic resonance imaging of acoustic streaming: absorption coefficient and acoustic field shape estimation

In this study, magnetic resonance imaging (MRI) is used to visualize acoustic streaming in liquids. A single-shot spin echo sequence (HASTE) with a saturation band perpendicular to the acoustic beam permits the acquisition of an instantaneous image of the flow due to the application of ultrasound. An average acoustic streaming velocity can be estimated from the MR images, from which the ultrasonic absorption coefficient and the bulk viscosity of different glycerol-water mixtures can be deduced. In the same way, this MRI method could be used to assess the acoustic field and time-average power of ultrasonic transducers in water (or other liquids with known physical properties), after calibration of a geometrical parameter that is dependent on the experimental setup.     

广义Morse流体解析状态方程及对氮的应用

 根据Ross变分微扰理论以及硬球流体Percus-Yevick（PY） 径向分布函数表达式,建立了广义Morse势流体的解析状态方程。与模拟结果的比较一方面证实了广义Morse 势模型的合理性;另一方面表明了解析Ross变分微扰理论的精度相当或略好于非解析的Weeks-Chandler-Anderson （mWCA）理论,而优于复杂的优化超网络链积分方程理论（RHNC）。该解析状态方程被应用于拟合处于环境温度和压强小于1 GPa情形流体氮的实验数据,所得到的势能参数被用于预测高温高密度情形氮流体的压强,预测结果证实,该解析状态方程可以很好地适用于较宽的压强和温度范围。     

Mixing rules and effective potentials in gaseous mixtures

We generate exact mixing rules for dilute gaseous mixtures with nonconformal interactions by introducing an adequate effective potential. The general mixing rule leads to several approximations of the van der Waals type. The work uses nonconformal model pair potentials that accurately describe the pure fluid properties. The validity of the approximate mixing rules is assessed by comparison with exact results for binary mixtures over wide ranges of temperature and composition. Large differences in energy, size and potential profile are considered. The simplest mixing rules are straightforward generalizations of the van der Waals rules and one version, based on a square-well (SW) approximation, performs with high precision for all systems except for those with extreme differences in molecular size. The SW mixing rule is used to predict excess virial coefficients of mixtures involving Ar, Kr, H₂ and CF₄.     

Ground State Properties for Bose-Condensed Gas in Anisotropic Traps

Based on the energy functional and variational method, we present a new method to investigate the ground state properties for a weakly interacting Bose-condensed gas in an anisotropic harmonic trap at zero temperature. With this method we are able to find the analytic expression of the ground-state wavefunction and to explore the relevant quantities, such as energy, chemical potential, and the aspect ratio of the velocity distribution. These results agree well with previous ground state numerical solutions of the Gross-Pitaevskii equation given by Dalfovo et al. [Phys. Rev. A 53 （1996） 2477] This new method is simple compared to other methods used to solve numerically the Gross-Pitaevskii equation, and one can obtain analytic and reliable results.     

Numerical computation of the asymptotic size of the rotation domain for the Arnold family

We consider the Arnold Tongue of the Arnold family of circle maps associated to a fixed Diophantine rotation number θ. The corresponding maps of the family are analytically conjugate to a rigid rotation. This conjugation is defined on a (maximal) complex strip of the circle and, after a suitable scaling, the size of this strip is given by an analytic function of the perturbative parameter.The main purpose of this paper is to perform a numerical accurate computation of this function and of its Taylor expansion. This allows us to verify previous theoretical results. The rotation numbers we select are quadratic irrationals, mainly the Golden Mean.By introducing a nonstandard extrapolation process, especially suited for the problem, we compute all the quantities required (rotation numbers, Arnold Tongues, Fourier and Taylor coefficients) with high precision.     

Catching the PEG-induced attractive interaction between proteins

We present the experimental and theoretical background of a method to characterize the protein-protein attractive potential induced by one of the mostly used crystallizing agents in the protein-field, the poly(ethylene glycol) (PEG). This attractive interaction is commonly called, in colloid physics, the depletion interaction. Small-Angle X-ray Scattering experiments and numerical treatments based on liquid-state theories were performed on urate oxidase-PEG mixtures with two different PEGs (3350 Da and 8000 Da). A “two-component” approach was used in which the polymer-polymer, the protein-polymer and the protein-protein pair potentials were determined. The resulting effective protein-protein potential was characterized. This potential is the sum of the free-polymer protein-protein potential and of the PEG-induced depletion potential. The depletion potential was found to be hardly dependent upon the protein concentration but strongly function of the polymer size and concentration. Our results were also compared with two models, which give an analytic expression for the depletion potential. Received 29 April 2002 RID="a" ID="a"Present address: CRMC2-CNRS, Campus de Luminy, case 913, F-13288 Marseille Cedex 09, France; e-mail: vivares@crmc2.univ-mrs.fr RID="b" ID="b"e-mail: bonnete@crmc2.univ-mrs.fr RID="c" ID="c"Laboratory associated to Universities Aix-Marseille II and III.     

散斑杨氏条纹图的全自动处理与识别

本文应用数字图象处理技术在AppleⅡ和IBM-PC图象处理系统上实现了散斑杨氏条纹图的全自动分析。文中采用二维灰度值检测的方法获取条纹的准峰值或谷值二值图,然后通过细化得到条纹中心。识别条纹间距时充分利用了整幅图杨氏条纹间距信息使识别结果具有高的精度。提出了用记忆跟踪算法结合线性回归的方法识别杨氏条纹倾角。最后给出了实验结果。     

Precision Calculations of Atomic Polarizabilities: A Relevant Physical Quantity in Modern Atomic Frequency Standard

Electric dipole polarizabilities of atoms are very important in many different physical applications, such as the precision atomic frequency standard. Calculations of these properties are very important and challenging. We propose a calculation strategy to calculate the frequency dependent dipole polarizabilities with high precision variationally by using a set of high quality orbital bases where the electron correlations can be taken into account adequately. The static polarizabilitiez of the ground state of Na are calculated accurately by such a method and can be compared with precision experiment measurement directly. The calculation result is in excellent agreement with the available experimental measurements within about 0.1~, which demonstrates the validity of our strategy. Our calculation strategy has a wide usage, not only in polarizibilies, but also in other fields such as theoretical treatment of electron-atom scattering processes. Using the same orbital bases, we carry out precision calculation of Na- affinities. Our calculated affinity is in excellent agreement with precision laser spectroscopy measurements within 0. 1%.     

Accurate analytic presentation of solution of the Schrödinger equation with arbitrary physical potential

High precision approximate analytic expressions of the ground state energies and wave functions for the arbitrary physical potentials are found by first casting the Schrödinger equation into the nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. The choice of zero iteration is based on general features of exact solutions near the boundaries. The approach is illustrated on the examples of the Yukawa, Woods-Saxon and funnel potentials. For the latter potential, solutions describing charmonium, bottonium and topponium are analyzed. Comparison of our approximate analytic expressions for binding energies and wave functions with the exact numerical solutions demonstrates their high accuracy in the wide range of physical parameters. The accuracy ranging between 10⁻⁴ and 10⁻⁸ for the energies and, correspondingly, 10⁻² and 10⁻⁴ for the wave functions is reached. The derived formulas enable one to make accurate analytical estimates of how variation of different interactions parameters affects correspondent physical systems.     

Accurate analytic presentation of solution for the spiked harmonic oscillator problem

High precision approximate analytic expressions of the ground state energies and wave functions for the spiked harmonic oscillator are found by first casting the correspondent Schrödinger equation into the nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is treated by approximating the nonlinear terms with a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. The choice of zero iteration is based on general features of exact solutions near the boundaries. Comparison of our approximate analytic expressions for binding energies and wave functions with the exact numerical solutions demonstrates their high accuracy in the wide range of parameters. The accuracy ranging between 10⁻³ and 10⁻⁷ for the energies and, correspondingly, 10⁻² and 10⁻⁷ for the wave functions in the regions, where they are not extremely small is reached. The derived formulas enable one to make accurate analytical estimates of how variation of different interactions parameters affects the correspondent physical systems.     

Windowed Fourier transform applied in the wavelength domain to process the spectral interference signals

We report on processing the spectral interference signals by a new method based on a windowed Fourier transform applied in the wavelength domain. First, the numerical simulations are performed to demonstrate high precision of the phase retrieval from the spectral signal. Second, the feasibility of the method is confirmed in processing experimental data from a dispersive Michelson interferometer comprising a cube beamsplitter made of BK7 glass. From the retrieved spectral phase difference, the effective thickness of the beamsplitter is determined precisely.     

2D and 3D SIMS investigations on sintered steels

Powder metallurgy (PM) is a well-established method for manufacturing ferrous precision parts. Sintering is one of the important production steps and can be strongly enhanced (activated) by formation of a liquid phase during the sintering process. The liquid phase can be reached by the addition of alloying elements (e.g., copper) or sintering activators (e.g., phosphorus) and is formed by melting of eutectic phase mixtures or by incipient melting. The main investigations presented in this work are done by secondary ion mass spectrometry (SIMS): 2D and 3D elemental distribution. Additionally, impact energy and hardness measurements were performed in order to study the influence of phosphorus on mechanical properties. The concentration of P in different samples was varied between 0 and 1 weight percent (wt.%), the carbon content was consistently 0.5 wt.%. Nominal specimens were sintered at 1120 and 1250 °C in protective atmosphere of flowing nitrogen to determine the influence of sintering temperature.     

Planar imaging of rayleigh and fluorescence light from H2-air combustion inside a bomb using tunable 193 nm light

Rayleigh scattering and planar laser induced predissociative fluorescence are used to obtain 2-D images of total and specific densities inside a combustion bomb. The experimental arrangement is the same for both methods except for the selection of laser wavelength and the filtering of the radiated light. The former method yields a distribution of total densities while the latter provides densities of hot O₂, i.e., those with v=2, J=17 and 33. Hydrogen-air mixtures of various compositions are used. Because the thermodynamics are well known, a bomb may serve as a reference device for diagnostics for high temperature species, and the results are in accord with calculations. Additional Rayleigh experiments are described which yield a) scattering cross sections at 193 nm, b) a 2-D temperature distribution in a hot air stream, and c) a 2-D temperature distribution, of limited precision, inside the bomb.