An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

The influence of hyperpolarisability and field-gradient polarisability on field adsorption binding energies for He on W(111)

The effects of imaging-gas hyperpolarisability and field-gradient polarisabuity terms on field-adsorption binding energies have been explored. At best image fields for the noble imaging gases and molecular hydrogen, the correction to long-range binding energy is at most a few percent and may be neglected. At the tungsten evaporation field the correction is significant in the cases of Ar, Kr, H₂, and especially Xe. The system He on W(111) has been used as a paradigm in the investigation of short-range binding energy. The largest correction here is due to one of the field-gradient polarisabuity terms. In the field range of most relevance to the field-ion techniques the total correction is about 15–20%, and should not be neglected in detailed treatments.     

Cusp catastrophe in slowly varying equilibriums

Solutions of the equations v _x+v ³?tv+x=0 and v _xx=v ³? tv+x, which describe the nucleation of domain walls occurring in the neighborhood of cusps of slowly varying equilibriums, are analyzed. Examples related to the diffusion in smoothly inhomogeneous media are considered.     

Existence and multiplicity of solutions for a nonlinear Neumann problem

We consider a Neumann problem of the type -εΔu+F ^′(u(x))=0 in an open bounded subset Ω of R ⁿ , where F is a real function which has exactly k maximum points. Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them. Received: October 30, 1999 Published online: December 19, 2001     

Characterization of phospho-olivines as materials for Li-ion cell cathodes

Solid State Reaction was employed to prepare phospho-olivines LiMPO₄ (where M=Fe, Co) as pure phase and LiNiPO₄ in presence of foreign phases, as cathodic materials for lithiumions batteries. The relationship between structural, morphological and electrochemical properties were investigated in the case of LiFePO₄. Structural investigation has been carried out by means of X-ray powder diffraction (XRPD) and Rietveld refinement. The influence on the morphology of annealing temperature, different flowing gas mixture and addition of ascorbic acid during the synthesis, has been analysed via scanning electron microscopy. The electrochemical cycling performances on LiFePO₄ showed to be positively affected by the modifications of the experimental conditions. Cyclic voltammetry showed a good reversibility during insertion-extraction mechanism, in particular in presence of additives. LiCoPO₄ and LiNiPO₄ are interesting as high voltage cathode materials for Li-ion batteries and have been taken into account, but their electrochemical operating conditions are still to be optimised. In the case of LiNiPO₄ it is very difficult to obtain, by solid state synthesis, suitable purity powders, having a grain size small enough to exploit it usefully as cathodic material for Li-ion cells. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16 – 22, 2000.     

Assigning patients to nurses in neonatal intensive care

An intensive care nursery provides health care for critically ill newborn infants. During a typical shift, infants range from those needing only occasional care to those requiring constant attention. At the beginning of each shift, the head nurse groups the patients for assignment to staff nurses. Typically each nurse cares for one group of infants throughout the shift. The large variation in infant conditions along with several complicating side constraints makes it difficult to develop balanced nurse work loads. We develop a mathematical programming approach for achieving better workload balance. We first develop a detailed neonatal acuity system that quantifies the nursing workload of each patient. We then develop an integer linear program that assigns patients to nurses while balancing nurse workloads. Because this model is computationally intractable, we develop a heuristic that exploits the fact that most nurseries are divided into a number of physical zones. We use ten case studies taken from a major university hospital to benchmark the performance of this heuristic. We also perform a designed experiment using randomly generated problems that examines the effect of nursery parameters on heuristic performance.     

Fleet configuration subject to stochastic demand: an application in the distribution of liquefied petroleum gas

We study the problem of configuring a fleet, in which vehicles receive information on-line about the demand that they should fulfil while they are on the road. In each district it must be decided the number of vehicles and their capacity. The objective function is to minimise the operational cost subject to constraints for the minimum delivery capacity, the maximum vehicle size and the average waiting time for customers. The last constraint is modelled as a queuing system that is adjusted according to the simulation of the delivery process of a Chilean company that distributes liquefied petroleum gas in portable cylinders. We provide the analytical form of all the components of the model, so it can be solved using a standard non-linear programming package. We show that the fleet may increase its sales by 3% and reduce the waiting time of customers 10% by allowing a set of vehicles to share the buffer of orders rather than having vehicles to exclusively serve smaller sectors.