Generic van der Waals equation of state for polymers, modified free volume theory, and the self-diffusion coefficient of polymeric liquids

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site-site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions necessary for the generic van der Waals equation of state, which in turn makes it possible to calculate the self-diffusion coefficient on the basis of the modified free volume theory of diffusion. A random distribution is assumed for minimum free volumes for monomers along the chain in the melt. More specifically, a stretched exponential is taken for the distribution function. If the exponents of the distribution function for minimum free volumes for monomers are chosen suitably for linear polymer melts of N monomers, the N dependence of the self-diffusion coefficient is N⁻¹ for the small values of N, an exponent predicted by the Rouse theory, whereas in the range of 2.3?lnN?4.5 the N dependence smoothly crosses over to N⁻², which is reminiscent of the exponent by the reptation theory. However, for lnN?4.5 the N dependence of the self-diffusion coefficient differs from N⁻², but gives an N dependence, N^−2−δ(0<δ<1), consistent with experiment on polymer melts in the range. For polyethylene δ≈0.48 for the parameters chosen for the stretched exponential. Because the stretched exponential function contains undetermined parameters, the N dependence of diffusion becomes semiempirical, but once the parameters are chosen such that the N dependence of D can be successfully given for a polymer melt, the temperature dependence of the self-diffusion coefficient can be well predicted in comparison with experiment. The theory is satisfactorily tested against experimental and simulation data on the temperature dependence of D for polyethylene and polystyrene melts.     

Molecular theory of thermal conductivity of the Lennard-Jones fluid

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for computing the mean free volume and the coefficient in the potential-energy and virial contributions to the thermal conductivity. The theoretical results are compared with our own molecular dynamics simulation results and with those reported in the literature. They agree in good accuracy over wide ranges of density and temperature examined in molecular dynamics simulations. Thus the combined theory represents a molecular theory of thermal conductivity of the Lennard-Jones fluid and by extension simple fluids, which enables us to compute the nonequilibrium quantity by means of the Monte Carlo simulations for the equilibrium pair-correlation function.     

On the enumeration of parking functions by leading terms

Let x=(x₁,…,x_n) be a sequence of positive integers. An x-parking function is a sequence (a₁,…,a_n) of positive integers whose non-decreasing rearrangement b₁b_n satisfies b_ix₁++x_i. In this paper we give a combinatorial approach to the enumeration of (a,b,…,b)-parking functions by their leading terms, which covers the special cases x=(1,…,1), (a,1,…,1), and (b,…,b). The approach relies on bijections between the x-parking functions and labeled rooted forests. To serve this purpose, we present a simple method for establishing the required bijections. Some bijective results between certain sets of x-parking functions of distinct leading terms are also given.     

Isotope effects on resonance cross sections in predissociation/preassociation

Isotope effects on the resonance cross sections of preassociative scattering are explicitly studied for the O₂, OH and OD systems, based on a semiclassical theory similar to Stückelberg's theory of inelastic scattering. It is found that there are significant isotopic differentiations for the systems studied, which may be exploited in the laboratory for selective photodissociations of the molecules.     

Generalized hydrodynamic theory of shock waves: Mach-number dependence of inverse shock width for nitrogen gas

A generalized hydrodynamic theory of shock wave structures is presented for rigid diatomic gases. The theory yields shock solutions for all Mach numbers. The accuracy of the theory is examined for nitrogen gas as an example. Excellent agreement with experiment is obtained for the inverse shock widths for the entire range of Mach number studied by experiment. The comparison made shows that we are now in possession of a successful continuum theory of shock waves in molecular gases for all Mach numbers.     

超薄膜磁头滑块气动力特性

采用有限差分法对广义润滑方程进行数值求解,计算出计算机磁头滑块压强场的分布情况。分析、研究了其稳态和动态气动力特性,并将计算结果分别与求解一阶、二阶修正雷诺方程所得到的结果进行了比较,得到如下三个结论:(1)当飞行高度很小,飞行速度较低时,必须采用广义润滑方程进行磁头滑块的气动力计算,(2)与广义润滑方程结果比较,求解一阶修正雷诺方程所得到的计算结果总是偏高,而求解二阶修正雷诺方程所得到的计算结果总是偏低。此外,还解决了大压缩数下数值失稳问题,使得压缩数可以计算到120万,足以适应任何实际工程的需要。     

Application and limitations on thermal and spectroscopic methods for shelf-life prediction

In medical products, shelf-life after thermoplastic processing and sterilization is important, and ionizing radiation has become a preferred sterilization mode for medical devices. We have employed successfully thermal analytical methods to predict shelf-life for many polyolefin materials. However, as the material of construction becoming more sophisticated: multiphase alloys and blends, multi-layer constructions etc., issues existed that require clarification as to what extent these methodologies are applicable. We have employed thermal analytical methods in conjunction with spectroscopic and morphological methods to study the applicability and limitation of these techniques. Results were combined with real life and simulated aging experiments and presented in this article.     

The Topkis-Veinott algorithm for solving nonlinear programs with lower and upper bounded variables

In this paper we consider a nonlinear programming problem of the form to minimize f(x) subject to a x b, where f is a differentiable function on E_n and a and b are fixed vectors in E_n. We develop a variation of the feasible direction algorithm of Topkis and Veinott for solving the above problem and provide explicit expressions of the optimal directions for a family of direction-finding problems using different normalization constraints. We show that the algorithm converges to a Kuhn-Tucker point. The reported computational results indicate efficiency of the algorithm. It also indicates the strong effect of the form of the normalization constraint on convergence properties.     

A stochastic theory of collision phenomena: one-dimensional atom-diatom collision model

A stochastic model of one-dimensional atom—diatom collisions is explicitly solved and studied in this paper. By treating the translational motion as an irrelevant variable, a second order partial differential equation is obtained for which the energy conservation is strictly satisfied. This equation is shown to be solvable in terms of Mathieu functions. It is shown that when certain further approximations are made in the equation, it leads to the equations studied by other authors in the stochastic model of collision phenomena. Various approximate but analytic distribution functions are obtained for the distribution of the observables and some aspects of the model are discussed in terms of the solutions obtained.