Feasible strategies for the control of a disk rolling on a moving horizontal plane

Let (X,Y,Z) be an inertial coordinate system and suppose that a horizontal plane is moving in a uniform velocity parallel to the (X,Y)-plane. A disk is rolling on the moving plane. Given two points A and B fixed in the (X,Y)-plane. Open-loop strategies are computed, for rolling the disk, on the moving plane, from A to B, during a given time interval [0, _f] and subject to state and control constraints.     

Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure

In this paper we prove the existence of a solution of a coupled system involving a two phase incompressible flow in the ground and the mechanical deformation of the porous medium where the porosity is a function of the global pressure. The model is strongly coupled and involves a nonlinear degenerate parabolic equation. In order to show the existence of a weak solution, we consider a sequence of related uniformly parabolic problems and apply the Schauder fixed point theorem to show that they possess a classical solution. We then prove the relative compactness of sequences of solutions by means of the Fréchet-Kolmogorov theorem; this yields the convergence of a subsequence to a weak solution of the parabolic system.     

The elixir of life: using a maintenance, repair and replacement model based on virtual and operating age in the water industry

Processing equipment in the water industry is subject to decayand requires maintenance, repair and eventual replacement. Thechallenge of competition within the water industry and the accompanyingregulatory regime requires that actions be integrated and costeffective. This is an industry, which has considerable dataon the failure of its equipment, but until recently very fewmodels of the maintenance process have been built. This paper describes the context of this problem for cleanwater processing where the equipment is that required to purifywater. It proposes a model based on the virtual and operatingage of the components. The operating age reflects the true ageof the equipment while the virtual age allows for the cumulativeeffect of maintenance actions performed on the equipment. Themodel also allows for different types of equipment by describingdegradation by Cox's proportional hazards model. Thus the specialfeatures of the equipment and environment in which the equipmentoperates are described by a set of characteristics, which modifythe hazard rate of the failure time of the equipment. This approachusing Cox's model with virtual and operating age can be appliedto other processing industries including the gas industry andthe ‘dirty water’ side of the water industry. The model is formulated as a stochastic dynamic programmingor Markov decision process and the form of the optimal policyis determined. This shows that repair and replacement shouldonly be performed when the equipment has failed and describesgeneral conditions when replacement is appropriate. The optimalpolicy is calculated numerically using the value iteration algorithmfor a specific example based on data on failure.