高压流体相平衡的分子热力学模型

本文应用物质分子聚集与解集理论阐述了高压流体相平衡机理并提出了分子聚集型状态方程.应用此方程能精确地描述流体高压下的PVT关系,且用于预测相平衡数据也获得了满意结果.     

流体的格鲁尼森数及其对状态方程的检验

格鲁尼森数是一个无量纲的热力学参数,通常被用来描述固体的热力学性质.由于其对流体的临界点不敏感,它对于检验非理想流体的热力学性质也有指导意义.本文通过计算多种流体在不同温度和压力下的格鲁尼森数,发现其数值在宽广区域里变化稳定,进而论述了格鲁尼森数与其他热力学参数的关系.以PR方程和BWR方程为例,阐述了格鲁尼森数对于检验状态方程完善性的标尺性作用.     

方阱链流体在固液界面分布的密度泛函理论研究

应用Yethiraj的加权密度近似泛函理论研究平板狭缝中方阱链流体的密度分布，系统的Helm holtz自由能泛函分为理想气体的贡献利剩余贡献两部分，其中剩余贡献部分分别采用刘洪 来等人建立的基于空穴相关函数的方阱链流体状态方程和Gil-Villegas等人提出的统计缔合 流体理论状态方程(SAFT-VR)结合简单加权密度近似计算.考察了不同链长、温度、系统密度 和壁面吸引强度下平板狭缝中方阱链流体的密度分布，并与Monte Carlo(MC)模拟结果进行 了比较.结果表明采用不同的状态方程对密度分布的计算有明显的影响，对于受限于硬壁狭 缝中的方阱链流体，温度和密度比较高时，两种状态方程计算的结果均与MC模拟符合得比较 好，在低温和低密度下效果变差，SAFT-VR方程的计算结果更接近于MC模拟结果.对于受限于 方阱壁狭缝中的方阱链流体，由于系统密度分布的非均匀性加强，采用两种状态方程计算的 结果均与MC模拟结果有一定偏差，寻找更合适的权重函数是进一步改进的关键. 关键词： 密度泛函理论 非均匀流体 密度分布 固液界面 方阱链     

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。     

低温流体状态方程研究

本研究了可用于低温流体热力学性质计算的状态方程，提出一个改进型的Ｐａｔｅｌ－Ｔｅｊａ状态方程，给出了２４种常用低温流体的方程常数、其中包括氢、氦等量子气体。用新方程对２４种常用低温流体的饱和蒸汽压，饱和蒸汽比容，饱和液体比容等进行了计算并与传统方程进行了比较。     

基于Bernstein多项式的自适应混沌时间序列预测算法

提出了利用Bernstein多项式对混沌时间序列的动力学方程进行建模的方法,并将该方法与递推最小二乘(RLS)算法相结合,从而可以自适应地逼近混沌时间序列的动力学特性,以达到预测的目的.理论分析和仿真实验表明该方法对一些常见的混沌时间序列具有较高的预测精度和较理想的准确预测率.由于RLS算法的收敛速度较快,因此该方法比较适合于对短混沌时间序列进行实时预测. 关键词： 混沌 预测 Bernstein多项式 RLS算法     

临界点附近流体比热计算方法

一、引 言 临界点是气液相变的终点.在该点附近流体显示出奇异特性.奇异特性使得临界点附近流体热力学性质的实验测量与理论计算变得非常困难. 为了更好地表示临界点附近的热力学性质,状态方程应能表达流体在临界点的奇异性.Schofield首先提出能满足上述要求的参数标度状态方程——线性模型与立方模型两种.该方程用两个参变数R,θ表示.可以证明:在限定立方模型中,等温压缩率KT仅与R有关,与θ无关,所以R是KT大小的直接度量.KT具有强烈发散性,且又与密度涨落相关.从而,KT更能表征流体的临界特性.可见,从理论上讲,限定立方模型能更好地表…     

混沌时间序列全局预测新方法——连分式法

拓展了多项式逼近理论，利用连分式法建立了混沌时间序列非线性全局预测模型，此模型替代混沌序列的动力学方程，实现对其动力学特性分析，达到预测目的. 理论分析和仿真实验表明，连分式法能够有效预测一些混沌序列，该方法预测精度高，并且能得到显式的预测表达式. 关键词： 混沌时间序列 全局预测 连分式     

R13B1与R152a专用状态方程的研究

一、引言 表示流体P、V、T关系的专用状态方程是流体热物性研究最基础的工作,它是计算流体PVT性质及对实验数据进行内插外推及计算其导出热力性质(如焓、熵等)的工具,也是用来制作热物性图表的基础方程.一般对专用状态方程的要求应包括:1)能适用于宽广的参数范围及整个流体区域;2)不仅在计算PVT性质时精度高,而且能正确地描述其     

多组份流动质量分数保极值原理算法

对基于质量分数的Mie-Gruneisen状态方程多流体组份模型提出了新的数值方法.该模型保持混合流体的质量、动量、和能量守恒,保持各组份分质量守恒,在多流体组份界面处保持压力和速度一致.该模型是拟守恒型方程系统.对该模型系统的离散采用波传播算法.与直接对模型中所有守恒方程采用相同算法不同的是,在处理分介质质量守恒方程时,对波传播算法进行了修正,使之满足质量分数保极值原理.而不作修改的算法则不能保证质量分数在[0,1]范围.数值实验验证了该方法有效.     

A solution to Bloch NMR flow equations for the analysis of hemodynamic functions of blood flow system using m-Boubaker polynomials

This paper proposes a solution to Bloch NMR flow equations in biomedical fluid dynamics using a new set of real polynomials. In fact, the authors conjugated their efforts in order to take benefit from similarities between independent Bloch NMR flow equations yielded by a recent study and the newly proposed characteristic differential equation of the m-Boubaker polynomials. The main goal of this study is to establish a methodology of using mathematical techniques so that the accurate measurement of blood flow in human physiological and pathological conditions can be carried out non-invasively and becomes simple to implement in medical clinics. Specifically, the polynomial solutions of the derived Bloch NMR equation are obtained for use in biomedical fluid dynamics. The polynomials represent the T₂-weighted NMR transverse magnetization and signals obtained in terms of Boubaker polynomials, which can be an attractive mathematical tool for simple and accurate analysis of hemodynamic functions of blood flow system. The solutions provide an analytic way to interpret observables made when the rF magnetic fields are designed based on the Chebichev polynomials. The representative function of each component is plotted to describe the complete evolution of the NMR transverse magnetization component for medical and biomedical applications. This mathematical technique may allow us to manipulate microscopic blood (cells) at nano-scale. We may be able to theoretically simulate nano-devices that may travel through tiny capillaries and deliver oxygen to anemic tissues, remove obstructions from blood vessels and plaque from brain cells, and even hunt down and destroy viruses, bacteria, and other infectious agents.     

Semidefinite Optimization Estimating Bounds on Linear Functionals Defined on Solutions of Linear ODEs

In this paper, semidefinite optimization method is proposed to estimate bounds on linear functionals defined on solutions of linear ordinary differential equations (ODEs) with smooth coefficients. The method can get upper and lower bounds by solving two semidefinite programs, not solving ODEs directly. Its convergence theorem is proved. The theorem shows that the upper and lower bounds series of linear functionals discussed can approach their exact values infinitely. Numerical results show that the method is effective for the estimation problems discussed. In addition, in order to reduce calculation amount, Cheybeshev polynomials are applied to replace Taylor polynomials of smooth coefficients in computing process.     

Force multipole moments for a spherically symmetric particle in solution

We present a general theorem for the force multipole moments of arbitrary order induced in a spherically symmetric particle immersed in a fluid whose motion satisfies the linear Navier-Stokes equation for steady incompressible viscous flow. The multipole moments are expressed in terms of the unperturbed fluid velocity field. It is shown that for a particle with a finite extension only a few terms give rise to fluid perturbations which are not confined to the interior of the particle. We give explicit results for a polymer satisfying the Debye-Bueche-Brinkman equations and for a hard sphere with mixed slip-stick boundary conditions.     

Wave equation for dark coherence in three-level media

We report the derivation of a wave equation for coherence in "dark state" two-photon-resonance spectroscopy. One of its consequences is a dark state area theorem. The dark area theorem is a single ordinary differential equation which is globally equivalent, in a way we describe, to the full set of five coupled nonlinear partial differential equations that govern space-time evolution of two-pulse coherence in a lambda medium. The predictions of the dark area theorem are open to test via laser spectroscopy in dilute vapors and inhomogeneously broadened solids.     

Application of jacobi polynomial methods to the one-speed transport equation

The transport equations associated with radiation damage studies are often solved using expansions in Legendre polynomials. The radiation damage distribution functions which satisfy these equations may be sharply peaked in the forward direction, while the Legendre polynomials, as a set, are isotropic. This situation requires the use of many terms in the Legendre expansion in order to adequately represent the distribution functions. The Jacobi polynomials, on the other hand, can have strong peaking built into their associated weight function. To test the usefulness of the Jacobi polynomials we use them to solve the simple, one-speed, neutron transport equation. The results are then compared to the exact theory and to the results of applying Legendre methods to the same problem. This sample calculation demonstrates the advantage of the Jacobi polynomials in strongly non-isotropic situations.     

The elastic dielectric

Macroscopic field equations, boundary conditions and equations of state are derived for the non-linear, macroscopic elastic and dielectric response of an insulator. A centrosymmetric polynomial representation of order four is introduced for the energy density; the equations of state for the electric field and stress tensor are then deduced as polynomials of degree three in the displacement gradients and electric displacement field. The results are applied to the special case of m3m material symmetry.

A finite, point-charge model of a centrosymmetric ionic crystal is introduced and used to determine 0°K microscopic expressions for the electric field and stress tensor equation of state coefficients introduced in the macroscopic analysis. The results are used to calculate the full set of second and third-order non-linear coefficients for NaI, based on a Born-Mayer potential and the 4·2°K elastic stiffness data of Claytor and Marshall.     

涉及Hermite多项式的二项式定理和Laguerre多项式的负二项式定理

提出量子力学算符Hermite多项式方法,即将若干常用的特殊函数的宗量由普通数变为算符,并用它来发现涉及Hermite多项式（单变数和双变数）的二项式定理和涉及Laguerre多项式的负二项式定理,它们在计算若干量子光场的物理性质时有实质性的应用. 该方法不但具有简捷的优点,而且能导出很多新的算符恒等式,成为发展数学物理理论的一个重要分支. 关键词： 量子力学 Hermite多项式 二项式定理 Laguerre多项式     

Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials

In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.     

A new model for the reformulation of compressible fluid equations

Stimulating the biquaternionic generalization of electric and magnetic fields in electromagnetism, a new model has been proposed to present the Maxwell type equations of compressible fluids. The fluid wave equation has been expressed in a compact and elegant manner. Similarly, the generalized Poynting theorem for fluids has been derived analogous to electromagnetism and linear gravity. Moreover, a brief survey on biquaternionic matrices and the corresponding matrix representations of fluid equations have been given.