A new derivation of the averaged heat and mass transport equations for two-phase flows is presented. A volume averaging technique is used in which averaging is perform over both phases simultaneously in order to derive equations that describe transport the mixture, rather than transport in each phase. The derivation is particularly applicable to incompressible liquid/solid systems in which the two phases are tightly coupled. An example of the numerical solution of the equations is then presented in which a thermally convecting suspension is modelled. It is seen that large-scale instability can result from the interaction of thermal and compositional density gradients.

A model for bushfire spread is proposed, in which radiative heat transfer, species consumption and flammable gas production are taken into account. It is shown that fire propagation in this model does not occur as a one-dimensional travelling wave, except for smouldering combustion of wet bushland. Numerical solutions for the evolution of a line fire are obtained using a diagonally implicit finite difference scheme, and the effects of firebreaks and uncleared combustible debris are studied. An energy theorem is presented for the case of a spreading two-dimensional fire, and numerical results are illustrated.

How to obtain a workable initial guess to start an optimal control (control parametrization) algorithm is an important question. In particular, for a system of multi-link vertical planar robot arms moving under the effect of gravity and applied torques (which can exhibit chaotic behaviour), a non-workable initial guess of torques may cause integration failure regardless of what numerical packages are used. In this paper, we address this problem by introducing a simple and intuitive “Blind Man” algorithm. Theoretical justification as well as a numerical example is provided.

Two coupled nonlinear evolution equations correct to fourth order in wave steepness are derived for a three-dimensional wave packet in the presence of a thin thermocline. These two coupled equations are reduced to a single equation on the assumption that the space variation of the amplitudes takes place along a line making an arbitrary fixed angle with the direction of propagation of the wave. This single equation is used to study the stability of a uniform wave train. Expressions for maximum growth rate of instability and wave number at marginal stability are obtained. Some of the results are shown graphically. It is found that a thin thermocline has a stabilizing influence and the maximum growth rate of instability decreases with the increase of thermocline depth.

We study differential game problems in which the players can select different maximal monotone operators for the governing evolution system. Setting up our problem on a real Hilbert space, we show that the Elliott-Kalton upper and lower value of the game are viscosity solution of some Hamilton-Jacobi-Isaacs equations. Uniqueness is obtained by assuming condition analogous to the classical Isaacs condition, and thus the existence of value of the game follows.

The paper contains mainly three theorems involving generating functions expressed in terms of single and double Laplace and beta integrals. The theorems, in turn, yield, as special cases, a number of bilinear and bilateral generating functions of generalized functions particularly general double and triple hypergeometric series. One variable special cases of the generalized functions are important in several applied problems.

Fluid withdrawn through a line sink from a layered fluid in a vertically confined porous medium is considered. A hodograph method is used to obtain the shape of the interface for a given sink position at the critical flow rate. The analytical solution is compared with a more general numerical solution developed in earlier work. It was found that the surface profiles obtained by the two methods are in close agreement. However, the present work has the advantage that it gives a fully explicit solution.

In this paper we present an Extended Linear-Quadratic Programming method for the minimax problem. We show that the Extended Linear-Quadratic Programming method for the minimax problem is equivalent to the Josephy-Newton method for generalized equation, and establish the local convergence result. Furthermore, we obtain the global convergence result for the minimax problem by means of the equivalence relation between the generalized equation and the normal equation.