Are upwind techniques in multi-phase flow models necessary?

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.     

Para‐hydrogen induced polarization of Si‐29 NMR resonances as a potentially useful tool for analytical applications

Para‐hydrogen–induced polarization effects have been observed in the ²⁹Si NMR spectra of trimethylsilyl para‐hydrogenated molecules. The high signal enhancements and the long T₁ values observed for the ²⁹Si hyperpolarized resonances point toward the possibility of using ²⁹Si for hyperpolarization applications. A method for the discrimination of multiple compounds and/or complex mixtures of hydroxylic compounds (such as steroids), consisting of the silylization of alcoholic functionalities with an unsaturated silylalkyl moiety and subsequent reaction with para‐H₂, is proposed. Copyright © 2012 John Wiley & Sons, Ltd.     

An improvement on the positivity results for 2-stage explicit Runge-Kutta methods

In this paper, we investigate the positivity property for a class of 2-stage explicit Runge-Kutta (RK2) methods of order two when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We also pay particular attention to monotonicity property. We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.     

理科大学物理实验课课程体系的研究与实验

通过对80年代以来物理实验课改革的研究与实践，提出了理科大学物理实验课课程体系的建设意见。     

A survey of retrial queues

We present a survey of the main results and methods of the theory of retrial queues, concentrating on Markovian single and multi-channel systems. For the single channel case we consider the main model as well as models with batch arrivals, multiclasses, customer impatience, double connection, control devices, two-way communication and buffer. The stochastic processes arising from these models are considered in the stationary as well as the nonstationary regime. For multi-channel queues we survey numerical investigations of stationary distributions, limit theorems for high and low retrial intensities and heavy and light traffic behaviour.     

Probabilistically induced domain decomposition methods for elliptic boundary-value problems

Monte Carlo as well as quasi-Monte Carlo methods are used to generate only few interfacial values in two-dimensional domains where boundary-value elliptic problems are formulated. This allows for a domain decomposition of the domain. A continuous approximation of the solution is obtained interpolating on such interfaces, and then used as boundary data to split the original problem into fully decoupled subproblems. The numerical treatment can then be continued, implementing any deterministic algorithm on each subdomain. Both, Monte Carlo (or quasi-Monte Carlo) simulations and the domain decomposition strategy allow for exploiting parallel architectures. Scalability and natural fault tolerance are peculiarities of the present algorithm. Examples concern Helmholtz and Poisson equations, whose probabilistic treatment presents additional complications with respect to the case of homogeneous elliptic problems without any potential term and source.     

Runge–Kutta Methods for Monotone Differential and Delay Equations

Classes of Runge–Kutta methods preserving the monotonicity of ordinary and delay differential equations are identified. Essentially, the vector b and the matrix A from the Butcher tableau should be such that all components of b are positive and all components of the matrix B(r)A, where B(r) is the inverse of the matrix I+rA, are nonnegative for sufficiently small positive r. The latter is satisfied by all explicit, diagonally-implicit and fully implicit Runge–Kutta methods for which all of the components of the matrix A, except those that are zero by definition, are positive.     

Bifurcations of a Thin Plate-Strip Excited Transversally and Axially

The complex vibrations and bifurcations of plates modeled as systemswith infinite degrees-of-freedom are considered. Both theBubnov–Galerkin with high-order approximations and finite differencemethods with approximation O(h ⁴)are applied. In addition, the calculation ofthe Lyapunov exponents of the system is performed, and the results arecompared to those derived by Bennetin's method. Some examples of newnonlinear phenomena exhibited by the considered systems are reported.     

Spectral/hp least-squares finite element formulation for the Navier–Stokes equations

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier–Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier–Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton’s method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L₂ least-squares functional and L₂ error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier–Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation.