Resampling methods for spatial regression models under a class of stochastic designs

In this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a (possibly nonuniform) stochastic design and are irregularly spaced. It is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs. A variant of the blocking mechanism is proposed. It is shown that the proposed block bootstrap method provides a valid approximation to the distribution of a class of M-estimators of the spatial regression parameters. Finite sample properties of the method are investigated through a moderately large simulation study and a real data example is given to illustrate the methodology.Comment: Published at http://dx.doi.org/10.1214/009053606000000551 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Oil Blending: Mixing and Contamination

The Shell Company of Australia has a frequent need to blend lubricants. Blending, sometimes involving three lubricant oils and additives, takes place by jet mixing in large tanks of typically 45,000 titres capacity. The jets are driven by pumps with typical volume throughput of up to 1,000 titres per minute, and typical blending times may be as long as one or two hours. The jet blending process was investigated in a number of ways at the Study Group. These included: simple estimates for blending times, theoretical and experimental description of jet behaviour, development of a simple compartment model for the blending process, and several large scale computer simulations of the jet-induced motion using a commercial Computational Fluid Dynamics package. In addition, the sedimentation of contaminant particles in the tanks was investigated. This overall investigation, using a variety of approaches, gave a good knowledge of the blending process

Reduction of cogging torque in interior-magnet brushless machines

An investigation into the cogging torque in a four-pole interior-magnet brushless machines having either a six-slot stator and a short-pitched nonoverlapping winding or a 12-slot stator and a full-pitched overlapping winding is described. It is shown by finite-element analyses and measurements that, by appropriately defining the pole-arc to pole-pitch ratio, the optimal pole-arc to pole-pitch ratio for minimum cogging torque, which has been derived for surface-mounted magnet machines, is equally applicable to interior-magnet machines

Numerical simulations of negative-index refraction in wedge-shaped metamaterials

A wedge-shaped structure made of split-ring resonators (SRR) and wires is numerically simulated to evaluate its refraction behavior. Four frequency bands, namely, the stop band, left-handed band, ultralow-index band, and positive-index band, are distinguished according to the refracted field distributions. Negative phase velocity inside the wedge is demonstrated in the left-handed band and the Snell's law is conformed in terms of its refraction behaviors in different frequency bands. Our results confirmed that negative index of refraction indeed exists in such a composite metamaterial and also provided a convincing support to the results of previous Snell's law experiments.Comment: 18 pages, 6 figure