A method is described for setting revised target scores for the team batting second when a limited-overs cricket match has been forcibly shortened after it has commenced. It is designed so that neither team bene®ts or suffers from the shortening of the game and so is totally fair to both. It is easy to apply, requring nothing more than a single table of numbers and a pocket calculator, and is capable of dealing with any number of interruptions at any stage of either or both innings.The method is based on a simple model involving a two-factor relationship giving the number of runs which can be scored on average in the remainder of an innings as a function of the number of overs remaining and the number of wickets fallen. It is shown how the relationship enables the target score in an interrupted match to be recalculated to re¯ect the relative run scoring resources available to the two teams, that is overs and wickets in combination. The method was used in several international and domestic one-day competitions and tournaments in 1997.
We present a new model reduction approach to fluid simulation, enabling large, real-time, detailed flows with continuous user interaction. Our reduced model can also handle moving obstacles immersed in the flow. We create separate models for the velocity field and for each moving boundary, and show that the coupling forces may be reduced as well. Our results indicate that surprisingly few basis functions are needed to resolve small but visually important features such as spinning vortices.
We report on a fast, easily implemented method to determine all the geometrical alignment errors of a laser tracker, to high precision. The technique requires no specialist equipment and can be performed in less than an hour. The technique is based on the determination of parameters of a geometric model of the laser tracker, using measurements of a set of fixed target locations, from multiple locations of the tracker. After fitting of the model parameters to the observed data, the model can be used to perform error correction of the raw laser tracker data or to derive correction parameters in the format of the tracker manufacturer's internal error map. In addition to determination of the model parameters, the method also determines the uncertainties and correlations associated with the parameters. We have tested the technique on a commercial laser tracker in the following way. We disabled the tracker's internal error compensation, and used a five-position, fifteen-target network to estimate all the geometric errors of the instrument. Using the error map generated from this network test, the tracker was able to pass a full performance validation test, conducted according to a recognized specification standard (ASME B89.4.19-2006). We conclude that the error correction determined from the network test is as effective as the manufacturer's own error correction methodologies.
We present an implementation of an absolute distance measurement system which uses frequency scanning interferometry (FSI). The technique, referred to as dynamic FSI, uses two frequency scanning lasers, a gas absorption cell and a reference interferometer to determine the unknown optical path length difference (OPD) of one or many measurement interferometers. The gas absorption cell is the length reference for the measurement system and is traceable to international standards through knowledge of the frequencies of its absorption features. The OPD of the measurement interferometers can vary during the measurement and the variation is measured at the sampling rate of the system (2.77 MHz in the system described here). The system is shown to measure distances from 0.2 m to 20 m with a combined relative uncertainty of 0.41 × 10⁻⁶ at the two sigma level (k = 2). It will be shown that within a scan the change in OPD of the measurement interferometer can be determined to a resolution of 40 nm.
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