Since fluids flow under completely different conditions in basin modelling and reservoir simulation, a modified 3-D three-phase (water, oil, gas) black-oil model for basin modelling has been presented in this paper. The main challenge in solving this model is how to ensure the stability and convergence. To tackle this problem, a practical approach to determine the allowable maximum timestep ∆ t max has been proposed. The detailed case study in the Kuqa Depression of the Tarim Basin in western China shows that the simulation results and predictions agree well with field evaluations, which suggests that the key to deal with the problem is to correctly select ∆ t max for a given application. In the calculations, we employ some techniques such as the finite volume method based on PEBI (perpendicular and bisection) gridcells, and the fully implicit solution based on the Newton iteration and the ORTHOMIN (orthogonal minimum) algorithm.

This paper presents a simple, two-stage method, implemented in the commonly available Excel spreadsheet program, for quickly finding high quality solutions to larger, more difficult instances of the capacitated task allocation problem (CTAP) than have been previously reported. In Stage 1, an innovative modification of the approximation method of Griffith and Stewart is used to reformulate CTAP and find a near-integer solution. Based on the partial solution from Stage 1, the remaining tasks are allocated in a greatly reduced quadratic CTAP solved in Stage 2. Our results show that this approach yields very good solutions relatively quickly to very large problems (1,000 binary variables and 49,500 quadratic terms in the objective function). Ours is the first paper to modify the continuous approximation method of Griffith and Stewart to solve 0/1 problems and the first article to demonstrate the successful use of an Excel-based approach for solving very large CTAP problems.

By deriving an upper bound of the so-called 'price of anarchy', this paper analyses the efficiency of oligopolistic games in networks with non-separable and asymmetric cost functions, splittable flows and fixed demands. The new bound is determined by the optimal objective function values of some optimisation problems. In particular, for some special cases, the bound turns out to be explicit in the sense that it is representable explicitly by the number of players, and the constants measuring the degree of asymmetry and non-linearity of the cost function. Copyright © 2010 Inderscience Enterprises Ltd.

Decay estimates like a negative power of t are studied in some general Sobolev spaces for a solution of the one-dimensional semi-linear wave equation with power-like damping term and Dirichlet homogeneous boundary conditions. Upper estimates of this kind are valid for smooth initial data, and we establish also weaker estimates from below on the time-derivative which differ from the above upper estimates by a 3/2 factor with respect to the power of t.