用Wagner型本构方程表征低密度聚乙烯熔体的粘弹性及其非线性依时特性的预测

通过实验研究了一种低密度聚乙烯 (LDPE ,PE FSB 2 3D0 2 2 /Q2 0 0 )熔体的粘弹性 ,并用KBKZ类本构方程中的Wagner模型进行了表征 .用Wagner模型预测了LDPE的非线性依时粘弹特性 ,并同已报道的变型Huang方程的结果进行了比较 .在最大剪切速率 5s- 1 下 ,KBKZ方程预测的短剪切时间下的触变环与实验结果吻合较好 ,当剪切时间加长时 ,KBKZ方程的预测结果比实验值偏高 .KBKZ方程能够较好地预测应力增长和应力松弛特性 ,即能够真实地反映出实验中的应力过冲以及应力松弛的过程 ,而变型Huang方程则不能 .变型Huang方程中的参数是孤立地、片面地反映材料在特定条件下的流变特性 ,而KBKZ方程中描述材料流变性质的参数能基本上反映出该LDPE的粘弹性 .因此 ,KBKZ方程描述和预测依时性粘弹特性的综合能力强于变型的Huang方程 .结果还表明KBKZ方程仍不能准确、完整地描述LDPE Q2 0 0的依时性粘弹性 .     

The Perturbed-Soft-Chain Theory: an equation of state based on the Lennard-Jones potential

Perturbed-Soft-Chain theory is a perturbation theory for chain-like molecules which uses a soft-core (Lennard-Jones) intermolecular potential energy function. Three pure-component parameters are required for the PSCT equation of state. These parameters are reported for 13 normal alkanes and 25 other compounds. The PSCT equation of state does very well in predicting the thermodynamic properties of molecules over a wide range of fluid densities and molecular complexities. The PSCT equation of state is tested against the PHCT and Peng-Robinson equation of state by determining the errors in calculated liquid-densities and vapor pressures for normal alkanes. The PSCT equation of state predicts these properties slightly better than the PHCT equation of state and much better than the Peng-Robinson equation of state.     

Step-strain deformations for viscoelastic fluids: Formulation of a strain-coupling constitutive equation

An integral constitutive equation which includes strain-coupling effects is proposed. The constitutive equation is more general than the K-BKZ equation, and it is shown that this equation can explain various important aspects of double-step stress-relaxation data.     

Transcorrelated calculations of homogeneous electron gases

We have constructed the complete transcorrelated equation for homogeneous electron gases and investigated this equation on two- and three-dimensional systems. Correct asymptotic behaviours of the correlation factors can be easily obtained from the transcorrelated equation, both the long-range RPA type decay and the short-range spin dependent cusp conditions. The complete transcorrelated equation is solved numerically and the outcome correlation energies agree very well with variational quantum Monte Carlo results. Possible simplifications of the transcorrelated calculations are discussed, where we find that the RPA equation for the correlation factor can be considerably improved by adding one more term in the equation.     

高分子溶液特性粘度测定的新方法

提出了一个新的一点法测定高分子溶液的特性粘度的经验公式, 并根据文献的一些数据将该公式和常用的程镕时公式进行了比较研究. 结果表明, 该公式具有比程氏公式更高的准确性和广谱性, 还有简单易于操作的优点.     

动力学参数数目与法方程条件数的关系

多相催化反应动力学研究的基本问题是动力学方程中的参数估计，它一直是动力学研究中的活跃领域·在参数估计中最常用的方法是最小二乘法．早在1947年［刘开始用线性最小二乘法处理动力学模型的数据．1958年在线性最小二乘法中应用置信区间问题［21．1959年MarguardM出非线性最小二乘法问．前人提出如何求非线性最小二乘法的初值［4］，及加权最小二乘法的重要性问，并对最小二乘法在动力学中的应用做了综述卜］．在多相催化动力学研究中，关干线性最小二乘法遇到根本性困难的问题前人未涉及．我们曾在动力学研究中发现线性最小二乘法的法…     

On the Kinetics of Nonisothermal Nucleation

The kinetics of supersaturated vapor nucleation is considered with allowance for the possible difference between the temperature of the clusters and that of the gaseous phase. The resultant equation for the steady-state nucleation rate has the same form as the equation of the classical theory but contains the work of the thermodynamically irreversible droplet formation. This equation relates the nucleation rate to the cluster temperatures. It is transformed into the equation of the classical theory if the clusters have the same temperature as the gaseous phase. On the basis of the thermal balance for the clusters, an equation relating their temperature and concentration to the nucleation rate is derived. The form of this equation is similar to the equation of heat propagation in a moving medium in the presence of heat sources and sinks.     

Solving the finite-difference non-linear Poisson–Boltzmann equation

The Poisson–Boltzmann equation can be used to calculate the electrostatic potential field of a molecule surrounded by a solvent containing mobile ions. The Poisson–Boltzmann equation is a non-linear partial differential equation. Finite-difference methods of solving this equation have been restricted to the linearized form of the equation or a finite number of non-linear terms. Here we introduce a method based on a variational formulation of the electrostatic potential and standard multi-dimensional maximization methods that can be used to solve the full non-linear equation. © 1992 by John Wiley & Sons, Inc.     

Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker-Planck equation

The problem of the derivation of the diffusion equation exactly following from the Fokker-Planck (or Klein-Kramers) equation for heavy (or large) particles in a fluid in an external force field is solved in the case in which the particles are ions subject to a uniform (but in general time-varying) electric field. It is found that such a diffusion equation maintains memory of the initial ion velocity distribution, unless sufficiently large values of time are considered. In such temporal asymptotic limit, the diffusion equation exactly becomes (i) the Smoluchowski equation when the electric field is constant in time, and (ii) a new equation generalizing the Smoluchowski equation, when the electric field is arbitrarily time varying. Finally, it is shown that the obtained exact (or asymptotic) results make questionable the procedures and the results of approximate theories developed in the past to get a "corrected" Smoluchowski equation when the external force can also be, in general, position dependent.     

A quartic hard chain equation of state for normal fluids

A new empirical equation of state is proposed which is applicable to mixtures of chain-like molecules. The equation is based on a simple model which uses an approximate chain theory and an approximation of the Carnahan—Starling equation. The results for pure component properties of normal fluids are comparable to the common cubic equations of state. For mixtures of chain-like molecules, the new equation is as good or better than the Peng—Robinson equation.     

Adsorption kinetics at the solid/solution interface: statistical rate theory at initial times of adsorption and close to equilibrium

The kinetics of solute adsorption at the solid/solution interface has been studied by statistical rate theory (SRT) at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. A new kinetic equation has been derived for initial times of adsorption on the basis of SRT. For the first time a theoretical interpretation based on SRT has been provided for the modified pseudo-first-order (MPFO) kinetic equation which was proposed empirically by Yang and Al-Duri. It has been shown that the MPFO kinetic equation can be derived from the SRT equation when the system is close to equilibrium. On the basis of numerically generated points ( t, q) by the SRT equation, it has been shown that we can apply the new equation for initial times of adsorption in a larger time range in comparison to the previous q vs radical t linear equation. Also by numerical analysis of the generated kinetic data points, it is shown that application of the MPFO equation for modeling of whole kinetic data causes a large error for the data at initial times of adsorption. The results of numerical analysis are in perfect agreement with our theoretical derivation of the MPFO kinetic equation from the SRT equation. Finally, the results of the present theoretical study were confirmed by analysis of an experimental system.     

A simplified hard-sphere equation of state meeting the high and low density limits

A simplified hard-sphere equation of state has been developed, which meets the correct limit for close-packed conditions. It is shown that the proposed equation of state for hard spheres can represent accurately the computer simulation compressibility factor data and virial coefficients over a wide density range. The comparison of the results of the calculations using this equation, the Carnahan-Starling equation, and the two equations proposed by Iglesias-Silva and Hall, shows that the equation proposed here represents the compressibility factor data and the virial coefficients with better accuracy.     

Solving the finite-difference,nonlinear, Poisson–Boltzmann equation under a linear approach

Electrostatic interactions are among the key factors in determining the structure and function of biomolecules. Simulating such interactions involves solving the Poisson equation and the Poisson-Boltzmann (P-B) equation in the molecular interior and exterior region, respectively. The P-B equation is a nonlinear partial differential equation. The central processing unit (CPU) time for solving the full nonlinear P-B equation has been severalfold greater than the equivalent linear case. Here a simple method is proposed to solve the full nonlinear P-B equation under a linear approach, which has been tested both on a spherical case and on small molecules. Results show that our method converges rapidly even under highly charged cases. With this method, the CPU time for solving the full nonlinear P-B equation is somewhat less than the equivalent linear case in our calculations. © 1995 by John Wiley & Sons, Inc.     

On Johnson-Mehl-Avrami equation

The contention of Sarkar and Ray that Johnson-Mehl-Avrami equation is not a true kinetic equation is disproved. It is shown that this equation can be expressed in the form of a standard kinetic equation. The results of the authors are only an approximation of Johnson-Mehl-Avrami kinetics when the fraction transformed is small.     

Retention model of protein for mixedmode interaction mechanism in ion exchange and hydrophobic interaction chromatography

A unified retention equation of proteins was proved to be valid for a mixed-mode interaction mechanism in ion exchange chromatography (IEC) and hydrophobia interaction chro-matography (HIC). The reason to form a "U" shape retention curve of proteins hi both HIC and IEC was explained and the concentration range of the strongest elution ability for the mobile phase was determined with this equation. The parameters in this equation could be used to characterize the difference for either HIC or IEC adsorbents and the changes in the molecular conformation of proteins. With the parameters in this equation, the contributions of salt and water in the mobile phase to the protein retention in HIC and IEC were discussed, respectively. In addition, the comparison between the unified equation and Melander' s three-parameter equation for mixed-mode interaction chromatography was also investigated and better results were obtained in former equation.     

论化学平衡中的独立等量关系

物料平衡等式(MBE)、电荷平衡等式(CBE)和质子平衡等式(PBE)是化学平衡定量解析中的常用等量关系。本文从理论上证明了CBE可以由MBE导出,因此在计算中不是一个必不可少的独立条件。由于H~+来源的多样性,在涉及酸碱的化学平衡中,CBE比MBE的计算效率更高。这些结论与计算实践相一致,即在配位平衡、氧化还原平衡和沉淀平衡的计算中,MBE为主,CBE起辅助作用;在酸碱平衡计算中,CBE为主,MBE为辅。PBE也不是一个独立等量关系,而且仅适用于酸碱平衡,可以完全被效率更高的CBE代替。本研究明确了化学平衡中的独立等量关系,不仅有助于提高化学平衡定量解析的效率,而且使其理论结构更加简洁明晰。     

影响磷酸脲生成质量因素的实验研究

目前,关于磷酸脲制备工艺的报道比较含糊、数据不一,原料中杂质对磷酸脲质量的影响探讨不够深入。本文对磷酸与尿素为原料制备磷酸脲工艺中的结晶环节进行了实验研究,采用正交实验方法分析了影响磷酸脲质量的四个因素：中和温度、磷酸浓度、磷酸中硫、氟含量,并用回归分析法从宏观上建立数学模型,以预期和指导生产实际。     

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order Ω(-3∕2) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order Ω(-1∕2) and variance estimates accurate to order Ω(-3∕2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.     

Haar wavelet method for solving some nonlinear Parabolic equations

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, we develop an accurate and efficient Haar transform or Haar wavelet method for some of the well-known nonlinear parabolic partial differential equations. The equations include the Nowell-whitehead equation, Cahn-Allen equation, FitzHugh-Nagumo equation, Fisher’s equation, Burger’s equation and the Burgers-Fisher equation. The proposed scheme can be used to a wide class of nonlinear equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.     

Release from or through a wax matrix system. VI. Analysis and prediction of the entire release process of the wax matrix tablet

Analysis of the entire release process of the wax matrix tablet was examined. Wax matrix tablet was prepared from a physical mixture of drug and wax powder to obtain basic or clear release properties. The release process began to deviate from Higuchi equation when the released amount reached at around the half of the initial drug amount. Simulated release amount increase infinitely when the Higuchi equation was applied. Then, the Higuchi equation was modified to estimate the release process of the wax matrix tablet. The modified Higuchi equation was named as the H-my equation. Release process was well treated by the H-my equation. Release process simulated by the H-my equation fitted well with the measured entire release process. Also, release properties from and through wax matrix well coincident each other. Furthermore, it is possible to predict an optional release process when the amount of matrix and composition of matrix system were defined.