Structure study of simple fluids

The structure function of simple monatomic liquids like neon and argon is studied in an approximation scheme where intermediate functionQ(r) is extended beyond hardcore diameter rather than the direct correlation functionC(r). The calculated values show good agreement with experimental values.     

Effect of Transverse Correlation Function on the Thermodynamic Quantities of Ferromagnetic Systems

The effect of transverse correlation between spins on the thermodynamic properties of ferromagnetic systems is investigated in details. Qualitatively, at finite temperature the transverse correlation reflects the short-range interaction between spins, so that lowers the internal energy and consequently raises the free energy. It also means the introduction of some ordering, and hence lowers the entropy. It is depressed by the field which forces the spins to turn to the field direction, so that it decreases with the field when temperature is fixed. The low-temperature expansion of the energy shows that the inclusion of the transverse correlation at least partly considers the interaction between spin waves.     

关联函数在耗散反应激发函数涨落中的应用

应用关联函数方法,分析耗散反应激发函数中的涨落.通过推导出能量自关联函数、角度互关联函数、反应产物元素之间的互关联函数、反应产物同位素之间的互关联函数,来分析在耗散反应这一由非平衡向平衡演化的系统中,核反应体系演化过程的特点,说明关联函数在研究耗散反应激发函数涨落中的特殊作用.用推导出的函数分析了实验4.5MeV/u ²⁷Al+²⁷Al和102.5MeV ¹⁹F+⁵¹V的数据,并且指出了用这种方法可以提取的耗散反应体系的信息.     

Structure of the square-shoulder fluid

The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical steps, requiring only the numerical solution of a single transcendental equation. The comparison with available simulation data and with numerical solutions of the Percus–Yevick and hypernetted-chain integral equations shows that the present approximation represents an improvement over the Percus–Yevick theory for this system and a reasonable compromise between accuracy and simplicity.     

Determining the radial pair distribution function from X‐ray absorption spectra by use of the Landweber iteration method

The Landweber iteration approach is used to construct the radial pair distribution function (RPDF) from an X‐ray absorption (EXAFS) spectrum. The physical motivation for the presented investigation is the possibility to also reconstruct asymmetric RPDFs from the EXAFS spectra. From the methodical point of view the shell fit analysis in the case of complicated spectra would be much more eased if the RPDF for the first shell(s) are computed precisely and independently. The RPDF, as a solution of the fundamental EXAFS integral equation, is examined for theoretical examples, and a detailed noise analysis is performed. As a real example the EXAFS spectrum of curium(III) hydrate is evaluated in a stable way without supplementary conditions by the proposed iteration, i.e. by a recursive application of the EXAFS kernel.     

Studies on adsorption energy distributions computation from adsorption isotherms by the ansatz method

Since the well-known adsorption integral equation (AIE) is an ill-posed problem, calculation of relevant energetic properties from gas and liquid adsorption isotherms on porous solids still remains a challenging field of research. There are two approaches for solving the AIE: (1) the numerical regularization method and (2) the fitting of the experimental adsorption data by functions possessing an analytical solution. Up to now the latter approach has been treated without consideration of the ill-posedness. The inclusion of ill-posedness in the approach leads to its specification which we call the ansatz method. By showing that a certain class of ansatz functions cannot be used for describing the total isotherms, we were urged to consider more general solutions being connected with the Stieltjes integrals. After applying a general inversion formula we can restrict the theoretically possible total isotherms and outline a feasible general ansatz.     

Continuity Conditions for the Radial Distribution Function of Square-Well Fluids

The continuity properties of the radial distribution function g(r) and its close relative the cavity function y(r) are studied in the context of the Percus–Yevick (PY) integral equation for 3D square-well fluids. The cases corresponding to a well width (–1) equal to a fraction of the diameter of the hard core /m, with m=1, 2, 3, have been considered. In these cases, it is proved that the function y(r) and its first derivative are everywhere continuous, but eventually the derivative of some order becomes discontinuous at the points (n+1)/m, n=0, 1,.... The order of continuity [the highest order derivative of y(r) being continuous at a given point] _n is found to be _nn in the first case (m=1) and _n2n in the other two cases (m=2, 3), for n1. Moreover, derivatives of y(r) up to third order are continuous at r= and r= for =3/2 and =4/3, but only the first derivative is continuous for =2. This can be understood as a nonlinear resonance effect.     

从相关测量的数据恢复超短激光脉冲的波形

本文证明了,只要测量了脉冲光强的二阶相关函数G~(2)(τ)和单延迟的三阶相关函数G~(3)(τ),便可以恢复超短激光脉冲的强度波形。并提出一种恢复脉冲波形的计算方法,编制了计算机程序,对实验数据作了处理,证实这种计算方法是可行的。在此基础上建议一种通过相关测量确定超短激光脉冲波形的新型仪器。     

Calculation of the Gluon Distribution Function Using Alternative Method for the Proton Structure Function

A calculation of the proton structure function F2(x,Q2) is reported with an approximation method that relates the reduced cross section derivative and the F2(x, Q2) scaling violation at low x by using quadratic form for the structure function. This quadratic form approximation method can be used to determine the structure function F2 (x, Q2)from the HERA reduced cross section data taken at low x. This new approach can determine the structure functions F2(x,Q2) with reasonable precision even for low x values which have not been investigated. We observe that the Q2 dependence is quadratic over the full kinematic covered range. To test the validity of our new determined structure functions, wefind the gluon distribution function in the leading order approximation with our new calculation for the structure functions and compare them with the QCD parton distribution functions.     

Extraction of Structure Function and Gluon Distribution Function at Low-x from Cross Section Derivative by Regge Behavior

An approximation method based on Regge behavior is presented. This new method relates the reduced cross section derivative and the structure function Regge behavior at low x. With the use of this approximation method, the C and λ parameters are calculated from the HERA reduced cross section data taken at low-x. Also, we calculate the structure functions F₂(x,Q²) even for low-x values, which have not been investigated. To test the validity of calculated structure functions, we find the gluon distribution function in the Leading order approximation based on Regge behaviour of structure function and compare to the NLO QCD fit to H1 data and NLO parton distribution function.     

Solution of Ornstein-Zernike equation for one-dimensional fluids

The application of Wiener-Hopf factorisation procedure as adopted by Baxter has been used to solve the one-dimensional Ornstein and Zernike (oz) equation for a fluid of interacting hard rods. Exact solution is obtained for the Kac potential in the van der Waals limit. We also obtain perturbative results which agree exactly with the lowest order calculations of Kac, Uhlenbeck and Hemmer.     

Calculation of the Gluon Distribution Function Using Alternative Method for the Proton Structure Function

A calculation of the proton structure function F2(x,Q^2) is reported with an approximation method that relates the reduced cross section derivative and the F2(x, Q^2) scaling violation at low x by using quadratic form for the structure function. This quadratic form approximation method can be used to determine the structure function F2 (x, Q^2) from the HERA reduced cross section data taken at low x. This new approach can determine the structure functions F2(x,Q^2) with reasonable precision even for low x values which have not been investigated. We observe that the Q^2 dependence is quadratic over the full kinematic covered range. To test the validity of our new determined structure functions, we find the gluon distribution function in the leading order approximation with our new calculation for the structure functions and compare them with the QCD parton distribution functions.     

On the second-moment condition of Stillinger and Lovett

The Stillinger-Lovett second-moment condition of electrolyte solutions is derived rigorously and simply from only some reasonable (but apparently never proven rigorously) assumptions concerning the asymptotic form of the direct correlation function and the Ornstein-Zernike equation. The derivation suggests that this condition is not the first member of a hierarchy of moment conditions and that there exists no simple result for a fourth-moment condition.Alfred P. Sloan Fellow.This work was partially supported by a grant from the National Institutes of Health, RO1 GM 20800-03 (to D.A.M.), by the Research Foundation of the State University of New York (USAEC Contract No. AT (30-1) 3668B) and the USAFOSR under Grant No. 68-1416B (to J.G.), and by the Petroleum Research Fund (A.S.).     

应用二维偏振红外与拉曼相关光谱研究反铁电液晶的分子结构

应用偏振红外、拉曼光谱研究了一种反铁电液晶化合物在78℃时,SCA 相中的烷基链、刚性核部分的构象、分子排布。用二维相关技术对所得到的偏振红外、拉曼光谱进行分析,把与手性碳相连的甲基的反对称及对称伸缩振动谱带同烷基链中的甲基伸缩振动谱带区分开,并发现在反铁电相中同时存在s-cis和s-trans两种构象。     

热镀铜层冷凝过程的分子动力学模拟

采用常温、常压分子动力学模拟方法和FS(Finnis Sinclair)势 ,研究了在周期性边界条件下由 5 0 0个原子构成的液态Cu模型系统的凝固过程 ,考察了不同降温速率下Cu的凝固行为 ,得到了不同温度、不同冷却速率下Cu的双体分布函数 ;采用HA键型指数法统计了各种小原子团在不同温度下所占比例 ,采用键取向序分析了体系降温全过程的局域取向对称性 ,得到原子体系微观结构组态变化的重要信息 ;最后 ,利用能量分析的方法对体系微观结构的变化进行了说明 ,给出了液态Cu冷凝过程中微观结构转变的重要信息 .     

Density functional theory of freezing of a system of highly elongated ellipsoidal oligomer solutions

We have used the density functional theory of freezing to study the liquid crystalline phase behavior of a system of highly elongated ellipsoidal conjugated oligomers dispersed in three different solvents namely chloroform, toluene and their equimolar mixture. The molecules are assumed to interact via solvent-implicit coarse-grained Gay–Berne potential. Pair correlation functions needed as input in the density functional theory have been calculated using the Percus–Yevick (PY) integral equation theory. Considering the isotropic and nematic phases, we have calculated the isotropic–nematic phase transition parameters and presented the temperature–density and pressure–temperature phase diagrams. Different solvent conditions are found not only to affect the transition parameters but also determine the capability of oligomers to form nematic phase in various thermodynamic conditions. In principle, our results are verifiable through computer simulations.     

Analysis of the Initial Slope of the Small‐Angle Scattering Correlation Function of a Particle

The small‐angle scattering correlation function of a particle γ(r) results from scattering experiments. This function possesses a well‐defined slope γ′(0) at the origin. This slope is defined by the particle volume V and the whole surface area S of the particle via γ′(0) = –S/(4V). In this paper it is demonstrated that this slope defines the mean chord length of the particle, . This theorem involves non‐convex particles, especially the case of particles with hollow parts. Consequently, for a large class of particle shapes the mean chord length is defined in terms of V and S. This extension of the Cauchy theorem is developed by closer analysis of the set covariance C(r), of the small‐angle scattering correlation function γ(r), and of the so‐called linear erosion P(r) near the origin r→0. The cases of a single hollow sphere, of two touching spheres, and of the single hollow cylinder are discussed.     

35MeV/u 36Ar+112,124Sn反应中中等质量碎片关联函数的入射道依赖

³⁶Ar+^112,124Sn反应中小角关联出射的中等质量碎片(IMF)约化速度关联函数. 结果表明³⁶Ar+¹²⁴Sn反应系统中的约化速度关联函数在小约化速度处的反关联程度比³⁶Ar+¹¹²Sn反应系统中的强, 表现出明显的入射道依赖性. 考察出射粒子对的单核子总动量时, 发现这种差异主要来自于高动量粒子对的贡献. 用三体弹道理论模型MENEKA分别计算了两个系统的IMF发射时标, 在³⁶Ar+¹¹²Sn反应系统中约为150fm/c, 而在³⁶Ar+¹²⁴Sn反应系统中, 约为120fm/c. 同位旋相关的量子分子动力学计算表明, ³⁶Ar+¹²⁴Sn系统中IMF的发射时间谱比³⁶Ar+¹¹²Sn系统略有前移, 相应地, 其中心密度从最高点随时间的下降亦比³⁶Ar+¹¹²Sn系统略快.     

A Lower Bound on Longitudinal Structure Function at Small x from a Self-Similarity Based Model of Proton

Self-similarity based model of proton structure function at small x was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region 6.2 × 10-7 ≤ x ≤ 10-2 and 0.045 ≤ Q2 ≤ 120 GeV2. We use momentum sum rule to pin down the corresponding self-similarity-based gluon distribution function valid in the same kinematical region. The model is then used to compute bound on the longitudinal structure function FL（X, Q2） for A1tarelli-Martinelli equation in QCD and is compared with the recent HERA data.