Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

Asymptotic expansion of the logistic midrange

Using the symbolic computation program MAPLE, we compute several terms of an asymptotic expansion for the distribution function of the logistic midrange.     

Two-fluid and population balance models for subcooled boiling flow

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUSIG (MUltiple-SIze-Group) model implemented in the computer code CFX4.4 is further developed to accommodate the wall nucleation at the heated wall and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison using empirical relationships for the active nucelation site density and local bubble diameter is also investigated. Good agreement is achieved with the local radial void fraction, bubble Sauter diameter and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency through the consideration of additional momentum equations or developing an algebraic slip model to account for bubble separation.     

Study on the possibilities of controlling the laser output beam properties by an intracavity deformable mirror

The possibilities of controlling the laser beam properties by a deformable mirror introduced into the laser optical cavity were studied theoretically and experimentally. The experiments were performed under conditions of an industrial high power transverse flow cw CO₂ laser operating with a stable resonator of a folded configuration. A deformable bimorph mirror of a surface profile controlled by the voltage applied to the mirror electrodes is implemented to the laser system as a back cavity mirror or as a one of the inner folding mirrors. The near-and far-field characteristics of the laser beam versus the resonator configuration controlled by the changes of the focal length of the deformable mirror are discussed in the paper. The analysis reveals that the resonator with an inner deformable mirror is much more sensitive to the mirror curvature variations than the resonator in which the deformable mirror is used as a back cavity mirror. The presented results show that dynamic and controllable changes in the resonator properties result in the controlled modification and optimisation of the laser output power and spatial parameters of the laser radiation.     

The flow of a variable viscosity fluid between parallel plates with shear heating

A model for the flow of a fluid through a channel with parallel plates is investigated. The channel is narrow, so that the lubrication approximation may be applied. The channel walls are maintained at a constant temperature. Shear heating effects are included and the fluid viscosity decreases exponentially with temperature. When the flow is driven solely by shear stress or imposed velocity at the top, analytical progress is possible. When pressure gradient also drives the flow the problem is solved numerically.     

Integration and propagation of a multi-criteria decision making model in constraint programming

In this paper we propose a general integration scheme for a Multi-Criteria Decision Making model of the Multi-Attribute Utility Theory in Constraint Programming. We introduce the Choquet integral as a general aggregation function for multi-criteria optimization problems and define the Choquet global constraint that propagates this function during the Branch-and-Bound search. Finally the benefits of the propagation of the Choquet constraint are evaluated on the examination timetabling problem.     

Dynamics of molybdenum nano structure formation on the TiO2(1 1 0) surface: A kinetic Monte Carlo approach

The rutile TiO₂(1 1 0) surface is a highly anisotropic surface exhibiting “channels” delimited by oxygen rows. In previous experimental and theoretical DFT works we could identify the molybdenum adsorption sites. They are located inside the channels. Moreover, experimental studies have shown that during subsequent annealing after deposition, special molybdenum nano structures can be formed, especially two monolayer high pyramidal chains of atoms.In order to better understand the dynamics of nano structure formation, we present a kinetic Monte Carlo study on diffusion and adsorption of molybdenum atoms on a TiO₂(1 1 0) surface. A quasi one-dimensional lattice gas model has been used which describes the possible adsorption sites of a Mo atom in a single channel of the surface. The atomic positions of a 1.5 monolayer thick Mo film formed of pyramidal chains define the lattice sites of the model. Thereby the formation of three-dimensional clusters could be studied. Here we have studied the cluster formation as a function of parameters that can be controlled in a growth experiment by physical vapor deposition: deposition and annealing temperature, flux and total amount of deposited Mo. Good qualitative agreement with recent experiments is obtained.