High-Frequency Variations in the Rotation of the Earth

We report here observational results demonstrating that a three-station network of properly distributed VLBI observatories can routinely determine UT1 with a formal standard error of ±0.05 ms of time, in an observing period of 24 h. We also report the results of a three-month series of daily observing sessions of only 1-h duration with a single interferometer, which produced estimates of UT1 with standard errors of ±0.1 ms. The UT1 values obtained from the 1-h observing sessions track smoothly between the points of the 24-h time series, and the combined time series shows that it is not unusual for UT1 to vary by 1-2 ms in periods of several days. Preliminary results of reprocessing the 24-h observing sessions in 2-h segments suggest that variations of 0.4 ms may occur on time scales of only 6-8 h.     

Flotation machine design: impeller—stator interaction

The separate contributions of impellers and stators to suction are studied by means of interaction models. From these, suction can be predicted when interchangeable components are used in any combination, and in either direction of impeller rotation. Methods are devised by which numerical values of the impeller and stator terms can be simply assigned. The resulting model provides good agreement with experiment. The influence of variability in component geometry is reflected in the model parameters. Possible applications of the model are suggested.     

Adaptive cell division for ray tracing

In ray tracing the two most commonly used data structures are the octree and uniform cell division. The octree structure allows efficient adaptive subdivision of space, while taking care of the spatial coherence of the objects in it; however, the tree structure locating the next node in the path of a ray is complex and time consuming. The cell structure, on the other hand, can be stored in a three-dimensional array, and each cell can be efficiently accessed by specifying three indices. However, such a uniform cell division does not take care of object coherence. The proposed data structure combines the positive features of the above data structures while minimising their disadvantages. The entire object space is implicitly assumed to be a three-dimensional grid of cells. Initially, the entire object space is a single voxel which later undergoes “adaptive cell division.” But, unlike in the octree structure, where each voxel is divided exactly at the middle of each dimension, in adaptive cell division, each voxel is divided at the nearest cell boundary. The result is that each voxel contains an integral number of cells along each axis. Corresponding to the implicit cell division we maintain a three-dimensional array, with each array element containing the voxel number which is used to index into the voxel array. The voxel array is used to store information about the structure of each voxel, in particular, the objects in each voxel. While a ray moves from one voxel to another we always keep track of the cell through which the ray is currently passing. Since only arrays are involved in accessing the next voxel in the path of the ray, the operation is very efficient.     

A broad line n.m.r. study of oriented poly(vinylidene fluoride)

Broadline nuclear magnetic resonance measurements have been carried out for the proton resonance in oriented poly(vinylidene fluoride). The spectra in general show two component lines with distinctly different line widths. The broad component shows a high degree of molecular orientation and can be satisfactorily assigned to the crystalline regions of the polymer. The narrow component corresponds to an oriented non crystalline phase which is sufficiently constrained to allow motion about the chain axis only. An appreciable decrease in the value of the rigid mass fraction was observed in both of the samples over the temperature range examined. Our calculations indicate that this could play an important role in the temperature dependence of the pyroelectric response of this material.     

Generalisations of Heyman's and Foulkes' theorems using dual formulation

Existing duality principles in structural optimisation are briefly reviewed and then they are extended to structures with segment-wise constant cross-sections. All theories are discussed in the particular context of optimal plastic beam design with symmetric convex specific cost functions and are confirmed by independent calculations on illustrative examples. It is shown that the optimal solution is always associated with a displacement field in which the mean absolute curvature value for each segment equals the subgradient of the specific cost function, with respect to the maximum absolute moment value for that segment. Moreover, the dual problem consists of the maximisation of the difference of two terms: the first one is the integral of the product of load and deflection (external work), and the second is the sum of products of segment lengths and the mean complementary cost values (taken with respect to the mean absolute curvature for that segment). Finally, some tentative proposals for a class of non-convex optimisation problems are presented. For special cases, the proposed general statements reduce to theorems by Heyman, Foulkes and Hemp.     

Combining multiple knowledge bases

Combining knowledge present in multiple knowledge base systems into a single knowledge base is discussed. A knowledge based system can be considered an extension of a deductive database in that it permits function symbols as part of the theory. Alternative knowledge bases that deal with the same subject matter are considered. The authors define the concept of combining knowledge present in a set of knowledge bases and present algorithms to maximally combine them so that the combination is consistent with respect to the integrity constraints associated with the knowledge bases. For this, the authors define the concept of maximality and prove that the algorithms presented combine the knowledge bases to generate a maximal theory. The authors also discuss the relationships between combining multiple knowledge bases and the view update problem