Numerical solutions of a model for the propagation of a surface-catalysed flame in a tube

Numerical simulations of a surface-catalysed flame in a tubeare performed, corresponding to an experiment where a premixedfuel is fed into a tube whose inner surface is coated with acatalyst. In these experiments, subsequent to ignition, a reactionwave can be seen as a red-hot region which propagates back alongthe tube towards the inlet, and is due to low temperature combustionoccurring only on the inner surface of the tube where the catalystis present. The solutions of a mathematical model for this behaviourshow that initial-value problems do indeed result in such steadilypropagating waves. The numerically obtained wave speeds andsteady solution are compared to a previous large Damköhlernumber (D_a) asymptotic analysis using a simple reaction ratemodel, and agreement is very good even for moderately largevalues of D_a. However, for such Damköhler numbers, thewave speeds are found to be much larger than observed experimentally.Indeed, the simulations show that O(1) values of D_a are requiredto obtain the lower experimental wave speeds. Nevertheless,the wave speeds as a function of flow rate through the tubedo not agree well with the preliminary experimental resultsfor any choice of the parameters. A more realistic, Arrheniusreaction rate model is then considered. The Arrhenius modelpredicts a rapid change in temperature at the wave front, inmuch better agreement with the experiments than for the simplerreaction model.     

On the sign-stability of numerical solutions of one-dimensional parabolic problems

The preservation of the qualitative properties of physical phenomena in numerical models of these phenomena is an important requirement in scientific computations. In this paper, the numerical solutions of a one-dimensional linear parabolic problem are analysed. The problem can be considered as a altitudinal part of a split air pollution transport model or a heat conduction equation with a linear source term. The paper is focussed on the so-called sign-stability property, which reflects the fact that the number of the spatial sign changes of the solution does not grow in time. We give sufficient conditions that guarantee the sign-stability both for the finite difference and the finite element methods.     

A numerical solution for the simultaneous disturbance decoupling and row-by-row decoupling problem

The numerical computation of the simultaneous disturbance decoupling and row-by-row decoupling problem is considered. Based on a condensed form for the system matrices the solvability of the simultaneous disturbance decoupling and row-by-row decoupling problem is reduced to the verification of an integer equality and the nonsingularity of a lower-dimensional constant matrix. The condensed form we use is computed using only orthogonal transformations, which can be implemented in a numerically stable way. Hence, it leads directly to an effective numerical method for solving the disturbance decoupling and row-by-row decoupling problem using existing tools such as LAPACK and Matlab. Our result complements existing geometric and structural approaches which are of a theoretical nature and are not suitable for numerical computation.     

Fixed-bed drying simulation of agricultural products using a new backward finite difference scheme

This work is concerned with the numerical simulation of fixed-bed corn drying using MSU (Michigan State University) drying model. The classical numerical procedure for MSU model relies on an explicit method of finite differences which requires certain stability conditions between the step sizes of the time and space variables. The objective of the present paper is to establish a stable implicit method based on backward finite differences, in both time and space variables, which takes into account some specific empirical aspects of the problem. Computational results illustrate the efficiency and the flexibility of method.     

Calculation of the critical point for mixtures using mixture models based on Helmholtz energy equations of state

This paper mainly focuses on refrigerant mixtures with relatively simple critical behavior, and presents a practical and useful method for the critical point calculation for the mixtures using mixture models based on Helmholtz energy equations of state. The expression for critical point criterion suitable for this objective is derived first. Numerical manipulations to obtain a physically correct solution are described in detail. For four binary refrigerant mixtures of difluoromethane (R-32) + pentafluoroethane (R-125), R-125 + 1,1,1,2-tetrafluoroethane (R-134a), R-125 + 1,1,1-trifluoroethane (R-143a), and R-32 + propane (R-290), the critical temperatures and critical molar volumes are calculated applying the presented method. The calculation results are compared with experimental values, and the capabilities of the mixture models for the mixtures in the critical region are discussed.     

The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions

In this paper a spectral method and a numerical continuation algorithm for solving eigenvalue problems for the rectangular von Kármán plate with different boundary conditions (simply supported, partially or totally clamped) and physical parameters are introduced. The solution of these problems has a postbuckling behaviour. The spectral method is based on a variational principle (Galerkin’s approach) with a choice of global basis functions which are combinations of trigonometric functions. Convergence results of this method are proved and the rate of convergence is estimated. The discretized nonlinear model is treated by Newton’s iterative scheme and numerical continuation. Branches of eigenfunctions found by the algorithm are traced. Numerical results of solving the problems for polygonal and ferroconcrete plates are presented. Communicated by A. Zhou.     

Computation of direct intensity and medium intensity by using the discrete ordinates method

On the basis of the discrete ordinate scheme with (an) infinitely small weight(s), an easy-to-use and comprehensive method, named multi-rays method, is developed to calculate total, direct and medium intensities in arbitrarily specified directions. In doing this, for each of the specified directions, three identical discrete directions with infinitely small weights are employed to represent the three intensities. The new method is verified with two standard test problems, and is used to compute the intensities in two anisotropically scattering problems.     

Persistence in financial markets

Persistence is studied in a financial context by mapping the time evolution of the values of the shares quoted on the London Financial Times Stock Exchange 100 index (FTSE 100) onto Ising spins. By following the time dependence of the spins, we find evidence for power law decay of the proportion of shares that remain either above or below their 'starting' values. As a result, we estimate a persistence exponent for the underlying financial market to be θ_f∼0.5.     

不可压缩流动的移动粒子半隐式法数值模拟

介绍了一种新的移动粒子半隐式方法。该方法采用Lagrange描述,用一系列离散粒子代替流体,通过半隐式求解和时间推进法来进行计算,弥补了传统网格法对复杂形状、大变形、高速撞击等情况下网格划分和重构过于繁琐的缺点,在模拟不可压缩流动问题中得到了较好的效果。