As part of the International Asteroid Warning Network's observational exercises, we conducted a campaign to observe near-Earth asteroid 2019 XS around its close approach to Earth on 2021 November 9. The goal of the campaign was to characterize errors in the observation times reported to the Minor Planet Center, which become an increasingly important consideration as astrometric accuracy improves and more fast-moving asteroids are observed. As part of the exercise, a total of 957 astrometric observations of 2019 XS during the encounter were reported and subsequently were analyzed to obtain the corresponding residuals. While the timing errors are typically smaller than 1 s, the reported times appear to be negatively biased, i.e., they are generally earlier than they should be. We also compared the observer-provided position uncertainty with the cross-track residuals, which are independent of timing errors. A large fraction of the estimated uncertainties appear to be optimistic, especially when <0.″2. We compiled individual reports for each observer to help identify and remove the root cause of any possible timing error and improve the uncertainty quantification process. We suggest possible sources of timing errors and describe a simple procedure to derive reliable, conservative position uncertainties.

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The occurrence of high temperatures in combustion chambers of jet engines and gas turbines has led to the demand for new technologies and new materials for the manufacture of one of the most critical elements of these systems - the turbine blades. These elements have to withstand extreme temperatures for extended periods without loss of mechanical strength, conditions under which many alloys fail. Such failure is ascribed to the combination of high temperatures and high centrifugal forces, resulting in creep. This is especially prevalent in multi-crystalline structures in which grain boundaries present weaknesses in the structure. High temperature resistant alloys formed as single crystal (SX) structures offer the necessary material properties for safe performance under such extreme conditions. Modelling and simulation techniques were first used to study the directional solidification (DS) of crystal structures during vacuum investment casting. These models allowed the study of the dendritic growth rate, the formation of new grains ahead of the solid/liquid interface and the morphology of the dendritic microstructure. These studies indicated the opportunity to optimise the velocity of the solidification front (solidification rate) for single crystal structures. The aim of this study was therefore to investigate the effect of the solidification rate on the quality of SX castings. The investigations were carried out for nickel-based superalloy CMSX-4 turbine blade casts and rods using the Bridgman process for vacuum investment casting.

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The two most widely used error estimators for adaptive mesh re®nement are discussed and developed in the context of non-linear elliptic problems. The ®rst is based on the work of Babuska and Rheinboldt (1978) where the error norm is a function of the residual and the inter-element discontinuity of the stress ®eld. The discontinuous stress ®eld arises in the Finite Element formulation where C 0 continuity of the velocity ®eld is assumed.The second error estimator is based on the work of Zienkiewicz and Zhu (1987). This method also uses the discontinuous stress ®eld to measure the error, but results in a more simpli®ed expression for the error norm. In fact, the equivalence between the two error norms has been shown by Zienkiewicz.Finally, an error estimator which is based on the approximation velocity space only is proposed. This estimator has the advantage in that it does not require the a posteriori calculation of the pressure (or stress) ®eld. The method is applied to non-Newtonian Stokes¯ow which has a similar formulation to non-linear elasticity problems.