Onnes方程位力系数的确定与讨论

本文在系综理论巨配分函数的基础上，提出求解Ｏｎｎｅｓ方程位力系数的新方法，既简单又严谨的得出与Ｍａｙｅｒ理论相同的结论，并进一步推出考虑分子三重相互作用时位力系数的形式，同时将结论由单原子分子气体推广到双原子分子气体．     

论范德瓦尔斯a和b参数与温度的关系

范德瓦尔斯方程中a、b参数是否与温度相关,不但不同文献中的说法互不相同,而且有同一文献前后的结论相互矛盾.本文分析了这个令人迷惑的问题.在热力学中a和b参量被处理为与温度无关,它仅仅在临界点附近有效并可以把范德瓦尔斯方程表述为对应态定律;在更加广泛的温度区间a、b参量和温度有关,但是范德瓦尔斯方程却丧失了其独特性.统计...     

任意维经典非理想气体位力系数的研究

求出了任意维经典非理想气体的硬心势、方阱势和Lennard-Jones势的第二位力系数,并给出了计算更高位力系数的方法与途径.结果表明:对于Lennard-Jones势,只有当维数n<6时,第二位力系数才收敛.     

高压熔化的自由体积理论

根据液体的自由体积理论导出了高压熔化的积分表达式。利用熔点处粒子的自由体积与其平均体积之比很小这一特性,给出了简化的自由体积高压熔化公式,简化公式具有与通常使用的高压Lindemann熔化公式完全相同的形式。初步探讨了Lindemann定律的物理内涵。     

非退化的Ashtekar理论中的正能证明

由于Ashtekar理论中所有动力学约束均为第一类,其哈密顿量可明确写出,当加上渐近平坦流形的边界修正后,便得到引力能量的积分表述.特殊的时空分解及3-标架选取将给出Ashtekar理论的正能证明.关键词：     

浅谈两个误差公式的证明

在误差理论中,Bessel公式σ_x~2=1/n-1 sum from i=1 to n(x_i-x)~2 (1)是估算测量列x_1,…,x_n方差的基本公式(式中x=1/n sum from i=1 to n x_i为平均值).对于它的证明,一般有两种方法:一种按误差是随机变量的观点,通过求上式的数学期望来证明。这对不熟悉概率论的初学者(例如大学低年级学生)来说,恐怕不易接受。另一种是按方差的下述定义:     

基于自由体积理论及跨接方程的黏度推算模型

结合自由体积理论黏度模型与跨接方程,本文建立了一个适用于从气相到液相且包含临界区在内的黏度推算模型。以水为研究对象,对其对比密度ρ_r(0.01～2.57)、对比温度T_r(0.46～1.12)范围内的黏度进行了计算,计算值与文献实验值的相对偏差绝对平均值为1.81%,近临界区域相对偏差绝对平均值为4.6%。与现有的自由体积理论黏度模型相比,本文建立的黏度推算模型显著提升了近临界区域黏度的计算精度。     

颗粒堆的体积分数与制备流量关系的实验研究

通过实验研究发现,颗粒堆的体积分数随制备颗粒堆的颗粒流流量指数衰减,减小或增加流量到一定程度时,体积分数都达到饱和;出料口直径与颗粒粒径的比值小到一临界值时,随着流量的减小体积分数增加急剧变缓;颗粒粒径小到一临界值时,随着流量的增加,体积分数的减小急剧变缓.结合颗粒物质的强耗散性、空气作用、瓶颈效应和碰撞理论解释了实验现象,从连续性原理出发推出的颗粒堆体积分数随制备流量变化的函数与实验数据的拟合公式相同.     

卡诺定理及其推广的简捷证明

本文提供了关于卡诺定理及其推广的一种证明方法，它与传统的证明方法相比较，显得直观而且简捷．     

体积算符对任意价顶角的本征作用与本征值谱

利用体积算符所含抓三元组对自旋网任意价顶角中圈线作用的反称化和双元恒等式,证明了这种作用均为本征作用,本征值为-2.用代数方法给出了对任意价顶角求体积算符本征值的系统程式,得到了普遍情况下的3,4,5和6顶角体积本征值的具体代数表式.关键词：体积算符任意价顶角本征作用证明本征值谱     

Inversion of the classical second virial coefficient

It is shown that, on the basis of some weak assumptions regarding the nature of the intermolecular pair potential, the classical second virial coefficient determines the potential uniquely.Research supported by NSF Grant GP-19881.     

On the inversion of the classical second virial coefficient

For a large class of intermolecular potentials, the values of the second virial coefficient at a discrete set of temperature points in an arbitrarily small neighborhood of the origin determine the potential uniquely.     

Second virial coefficient and mechanical moduli of metallic glasses

The relationship between the bulk, shear moduli and second virial coefficient of amorphous materials is derived according to their dependences with the radial distribution function. Lennard-Jones–Gaussian potential is used to investigate the relationship between second virial coefficient and temperature, where Lennard-Jones potential represents interactions with the nearest neighbor atoms, and Gaussian potential is responsible for the multi-atom interactions including the next nearest neighbor atoms and heterogeneous structures for a metallic glass. The results show that deep potential well formed by Gaussian potential causes a large second virial coefficient at low temperatures, which is very obvious for the larger fragility glasses. The quadratic form relationship of shear modulus and compositions is proposed, and confirmed by the experimental results of Pd_xNi_100−x−20P₂₀ alloy.     

Second virial coefficient in one dimension as a function of asymptotic quantities

A result from Dodd and Gibbs (J. Math. Phys., 15, 41 (1974)) for the second virial coefficient of particles in one dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms. The result is important in work to follow, for the third virial coefficient, for which a similar formalism is being developed. We examine a number of fine points in the quantum mechanical formalisms.     

Modified 2CLJDQP model and the second virial coefficients for linear molecules

A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperaturedependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules（such as O2, Cl2, CH3CH3, and CF3CF3） and heteronuclear molecules（such as CO, NO, CH3 F, CH3 Cl, CH3CF3,CH3CHF2, and CF3CH2F） are calculated. Then the Lorentz–Berthelot mixing rule is modified with a temperaturedependent expression, and the second virial coefficients of the heteronuclear molecules（such as CH3 F, CH3 Cl, and CH3CF3） are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model.It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.     

Accurate second Kerr virial coefficient of rare gases from the state-of-the-art ab initio potentials and (hyper)polarizabilities

The second Kerr virial coefficient of rare gases is studied in this work using the best ab initio potentials and (hyper)polarizabilities in the literature. The second Kerr virial coefficient of helium-4, helium-3, neon, argon, and krypton and its polarizability component of xenon are computed by the semi-classical method together with the Padé approximant over a wide temperature range. In addition, the uncertainty of second Kerr virial coefficient is estimated from the uncertainties of the ab initio interaction-induced properties. The experimental and theoretical data in the literature is compared with our calculated values to examine the quality of this work. It is shown that our computed values in the supplementary materials are as accurate as the literature data at medium and high temperatures and are more reliable at low temperatures.     

Interaction second virial co-efficient of polar-quadrupolar gas mixtures

The interaction second virial coefficient of a binary polar-quadrupolar gas mixtures of non-spherical molecules of arbitrary symmetry has been calculated for a set of unlike force parameters which is obtained from the force parameters for like interactions by using empirical combination rules. In the calculation the influence of anisotropic interactions has been considered. The relative contribution of each branch of interactions has been evaluated as a function of temperature. The theoretical results have been compared with the experimental data of CH₃F + N₂, CH₃F + CO₂ and CH₃Cl + CS₂. The agreement between theory and experiment is satisfactory.     

On the relationship between the apparent diffusion coefficient and extravascular extracellular volume fraction in human breast cancer

MRI techniques have been developed that can noninvasively probe the apparent diffusion coefficient (ADC) of water via diffusion-weighted MRI (DW-MRI). These methods have found much application in cancer where it is often found that the ADC within tumors is inversely correlated with tumor cell density, so that an increase in ADC in response to therapy can be interpreted as an imaging biomarker of positive treatment response. Dynamic contrast enhanced MRI (DCE-MRI) methods have also been developed and can noninvasively report on the extravascular extracellular volume fraction of tissues (denoted by v_e). By conventional reasoning, the ADC should therefore also be directly proportional to v_e. Here we report measurements of both ADC and v_e obtained from breast cancer patients at both 1.5 and 3.0 T. The 1.5-T data were acquired as part of normal standard of care, while the 3.0-T data were obtained from a dedicated research protocol. We found no statistically significant correlation between ADC and v_e for the 1.5- or 3.0-T patient sets on either a voxel-by-voxel or a region-of-interest (ROI) basis. These data, combined with similar results from other disease sites in the literature, may indicate that the conventional interpretation of either ADC, v_e or their relationship is not sufficient to explain experimental findings.     

Integral-equation theories and Mayer-sampling Monte Carlo: a tandem approach for computing virial coefficients of simple fluids

Mayer-sampling Monte Carlo (MSMC) has enabled computation of higher-order virial coefficients than previously possible for a variety of potential models, but it is not required for computation of the entire virial coefficient for models that are spherically symmetric: approximations that result from the hypernetted-chain (HNC) or Percus–Yevick (PY) integral-equation theories in conjunction with the compressibility equation (c) or virial equation (v) can be computed quickly by fast Fourier transforms. For the fourth and fifth virial coefficients of the Lennard–Jones potential (with parameters σ and ε), we demonstrate that the corrections to each of the four approximations (HNC(c), HNC(v), PY(c), and PY(v)) are faster to compute to a desired precision by MSMC than the full coefficient itself, with the exception of the PY(v) correction at fifth order, and that the optimal decomposition with regard to precision can be identified using a fraction of the steps required to obtain precise virial coefficients. At reduced temperatures kT/ε greater than 4, the PY(c) correction is fastest to compute by MSMC at both fourth and fifth orders. For lower temperatures, the HNC(v) decomposition is most efficient at fourth order, while the HNC(c) decomposition is most efficient at fifth order. These results are specific to the Lennard–Jones potential, but the method for determining the optimal decomposition is applicable to any spherically symmetric potential.     

The complete proof of the virial theorem in the refined TFD theory for all electrons of an atom in a solid

The complete proof of the virial theorem in refined Thomas－Fermi－Dirac theory for all electrons of an atom in a solid is given.