双嵌段共聚物薄膜介观结构的耗散粒子动力学模拟

采用耗散粒子动力学(Dissipative Particle Dynamics, DPD)方法模拟两平行平板间的双嵌段共聚物体系的介观结构. 模拟结果表明, 随板间距的增大, 体系分层数量的增加是不连续的, 在分层数量的增加过程中, 出现不规则结构的过渡区；聚合物链末端距随板间距的增大呈周期性振荡, 振荡幅度逐渐减小. 对模拟结果的分析表明：层状结构转变点与分层数量之间存在近似线性关系；层状结构转变点近似与共聚物链长的2/3次方成正比.     

PSRK: A Group Contribution Equation of State Based on UNIFAC

A group contribution equation of state called PSRK (Predictive Soave-Redlich-Kwong) which is based on the Soave-Redlich-Kwong equation (Soave, 1972) has been developed. It uses the UNIFAC method to calculate the mixture parameter a and includes all already existing UNIFAC parameters. This concept makes use of recent developments by Michelsen (1990b) and has the main advantage, that vapor-uquid-equilibria (VLB) can be predicted for a large number of systems without introducing new model parameters that must be fitted to experimental VLB-data. The PSRK equation of state can be used for VLB-predictions over a much larger temperature and pressure range than the UNIFAC γ--approach and is easily extended to mixtures containing supercritical compounds. Additional PSRK parameters, which allow the calculation of gas/gas and gas/alkane phase equilibria, are given in this paper. In addition to those mixtures covered by UNIFAC, phase equilibrium calculations may also include gases like CH₄ C₂H₆, C₃H₆, c₄H₁₀, CO₂, N₂, H₂ and CO.     

Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

Fluctuating hydrodynamics and principal oscillation pattern analysis

Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series x_i(t) produced by systems whose dynamics are described by a linear Markov process x=Bx + . The matrixB gives the deterministic feedback and is a white noise vector with covariances (t) _j (t*Q _ij (t–t. The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) as given by Landau-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Bénard convection.     

High-density properties of hard spheres within a modified Percus-Yevick theory: The role of thermodynamic consistency

Using an integral-equation approach based upon an approximation for the tail function, the equilibrium properties of a system of hard spheres are studied with special concern for the behavior in the region of close packing. The closure adopted is such that full, internal consistency is ensured in the thermodynamics of the model with respect to both the two zero-separation theorems as well as to the more standard virial and fluctuation routes to the equation of state. The scheme also makes use of the continuity properties of the tail function and of the cavity distribution function at contact. These properties are explictly tested in the low-density limit up to the fourth derivative. The theory generates an equilibrium branch bounded on the high-density side by a point corresponding to a packing fraction0.78, a value which closely matches Rogers' least upper bound for the densest packing of spheres. The pair structure of the fluid in the state of random close packing is also compared to the type of local order predicted by the theory at similar densities.     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

Exact solution of the Boltzmann equation in the homogeneous color conductivity problem

An exact solution of the Boltzmann equation for a binary mixture of colored Maxwell molecules is found. The solution corresponds to a nonequilibrium homogeneous steady state created by a nonconservative external force. Explicit expressions for the moments of the distribution function are obtained. By using information theory, an approximate velocity distribution function is constructed, which is exact in the limits of small and large field strengths. Comparison is made between the exact energy flux and the one obtained from the information theory distribution.     

Transport phenomena in a plane shock wave

With the use of the nonpolynomial closure 1/ _z in the Mott-Smith approximation of the solution of the Boltzmann equation, we obtain a value of the density gradient in the limit of a very weak shock wave that is close to the correct value. For the determination of the transverse temperature gradient we calculated the _x ² / _z moment of the Mott-Smith collision integral. The effective values of viscosity and thermal conductivity in the limit of a very weak shock wave were calculated for inverse-power potentials and found to agree almost exactly with the Chapman-Enskog values. Such a comparison can serve as a criterion for the evaluation of different bimodal theories. Various bimodal theories give different values of viscosity and thermal conductivity, but all of them give 33 % too high a value of the Eucken ratio.     

Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term

Necessary and sufficient conditions are established in this paper for the existence of positive- and/or negative-definite solutions to the algebraic Riccati equation with indefinite coefficient. An iterative procedure is also given for computing such a solution.Project supported by the National Science Foundation of China and by the special program of the State Education Commission of China under grant 9033507.