Dynamic frictionless contact with adhesion

A model for the dynamic, adhesive, frictionless contact between a viscoelastic body and a deformable foundation is described. The adhesion process is modeled by a bonding field on the contact surface. The contact is described by a modified normal compliance condition. The tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field. The existence of a unique weak solution for the problem is established, together with a partial regularity result. The existence proof proceeds by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space.     

Inventory Lot Size Models with Vanishing Market

The paper is concerned with equipment which is being phased out because it is superseded by a technologically more advanced product. It nevertheless still requires efficient handling for the rest of its life span.An inventory lot size model without backlogs for a single commodity with a vanishing market is used. The vanishing market is represented by- a demand function that decreases with time and eventually reaches zero, implying that the planning horizon is finite and known. It is assumed that there is no lead time for replenishments. The problem is to devise an optimal management scheme for this inventory system, namely, to determine the number of replenishments and their schedule over the predicted survival time horizon of the product.The problem is completely solved for the class of demand functions which can be approximated to by positive powers of time. The solution is given in a nearly closed form and is proven to be unique.     

Interval optimal control problem in a Hilbert space

An optimal control problem for a system involving an interval parameter is considered. The concepts of a universal optimal state and a universal optimal control are introduced. The existence and uniqueness of a universal solution to the interval optimal control problem is proved, and an algorithm for its determination is presented. The interval optimal control problem for a system described by the boundary value problem for a second-order ordinary differential equation is solved as an example.     

Determining modes and almost periodic integrals for cocycles

Cocycles of general form on an arbitrary metric space are considered. The notion of determining modes for cocycles on a Hilbert space is introduced, and a theorem on the existence of finitely many determining modes for such cocycles is proved. The existence of a B-pullback attractor in the problem of microwave heating of a material is proved. The notion of almost periodic integral for a cocycle is introduced, and the existence of such an integral for a certain class of cocycles is proved.     

Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials

This paper deals with inventory models that unify the decisions for raw materials and the finished product for a single product manufacturing system. The product is manufactured in batches and raw materials are jointly replenished from outside suppliers. The system is assumed to deteriorate during the production process. As a result, some proportion of nonconforming items is produced. The objective is to minimize the total variable cost for the system. A solution procedure is developed to find a near optimal solution for the basic model. The analysis for the basic model is extended to cases where the proportion of defective items is not constant or the defective rate is a function of production setup cost.     

Approximate analytic solutions to Radulet equations for the analysis of electromagnetic transients in single-phase power transmission lines

In this work, an analytic development for a transmission line with a corona effect for simulating an electromagnetic transient is presented. The asymptotic solution for the Radulet equations in which a nonlinear term is presented is obtained. The study is carried out for a single-phase transmission line. The electrical parameters for an overhead line are defined and several formulations for their calculation are presented. The frequency dependence of the electrical parameters is considered. In the first part, the linear problem solution is found; the Fourier and Laplace transforms are applied with respect to distance and time respectively. After finding the solution in the Fourier–Laplace domain, which is expressed in terms of a Green’s function integral, an approximate analytical solution is obtained in the distance–time domain by means of asymptotic methods. Finally, the nonlinear solution is found using as a first approach the linear solution. The results obtained show an attenuation in the voltage wave due to the corona effect.     

Improved vehicle scheduling in public transport through systematic changes in the time-table

Vehicle scheduling for a fixed time-table is easy to formulate and solve as a minimal-cost-flow problem. Normally, however, there is considerable flexibility in the time-table. We propose here a method for exploiting this flexibility in order to improve the vehicle scheduling.A given set of trips must be assigned to a fleet of identical vehicles, starting from a common garage. Each trip is characterized by initial stop, final stop, duration, earliest departure time, and latest departure time.The problem is to decide which vehicle should be assigned to each individual trip and when the trip should start, so that a generalized cost is minimized.The minimum-cost-flow problem is first solved for the ‘kernels’ of every trip in order to make clear when the critical time-periods occur and obtain a lower bound for the solution. The kernel is defined as a trip that starts at the latest possible departure time and finishes at the earliest possible arriving time.The departure time for each trip is then chosen, thereby increasing the chances of obtaining a good schedule. The minimum-cost-flow problem is then solved for this fixed time-table.Finally, the departure times for each vehicle are adjusted (blocked) so that each vehicle (and driver) is efficiently used. This method is used as an integral part of the Volvo Traffic Planning Package.     

A cellular-automata method for studying porous media properties

A cellular-automata (CA) approach for investigating properties of porous media with tortuous channels and different smoothness of pore walls is proposed. This approach is aimed at combining two different CA models: the first one is intended for constructing the morphology of a porous material; the second, for simulating a fluid flow through it. The porous media morphology is obtained as a result of evolution of a cellular automaton, forming a “steady pattern.” The result is then used for simulating a fluid flow through a porous medium by applying the Lattice Gas CA model. The method has been tested on a small fragment of a porous material and implemented for investigating a carbon electrode of a hydrogen fuel cell on a multiprocessor cluster.     

The Clique Complex and Hypergraph Matching

The width of a hypergraph is the minimal for which there exist such that for any , for some . The matching width of is the minimal such that for any matching there exist such that for any , for some . The following extension of the Aharoni-Haxell matching Theorem [3] is proved: Let be a family of hypergraphs such that for each either or , then there exists a matching such that for all . This is a consequence of a more general result on colored cliques in graphs. The proofs are topological and use the Nerve Theorem. Received June 14, 1999     

Ordered Site Access and Optimal Forest Rotation

The ordered-site-access model of forest harvesting formulated for once-and-for-all forests in [7] is extended to the case of ongoing forests. The economic content of the corresponding optimal harvest schedule is delineated. For an infinite harvest sequence, the optimal schedule is shown to include the classical Faustmann rotation as a special case, and the effect of net revenue functions changing with harvest is studied. For the practically more important case of planning for a finite sequence of [INLINEEQUATION] harvests, the optimal harvest schedule is determined for a Faustmann environment with limited, and unlimited harvesting capacity, and its rapid convergence to the Faustmann rotation is shown for the case of unlimited harvesting capacity. The case of harvest cost functions varying with harvest rate is discussed. The existence of a steady-state optimal harvesting schedule (involving a pathwise uniform age distribution) for the more realistic Heaps-Neher environment and its relation to the Faustmann rotation are analyzed. The evolution of the optimal harvest schedule for a finite harvest sequence in a Heaps-Neher environment toward this steady-state (Faustmann type) rotation is demonstrated.