For a long time topological relationships between spatial objects have been a focus of research in a number of disciplines like artificial intelligence, cognitive science, linguistics, robotics, and spatial reasoning. Especially as predicates they support the design of suitable query languages for spatial data retrieval and analysis in spatial databases and geographical information systems (GIS). Unfortunately, they have so far only been defined for and applicable to simplified abstractions of spatial objects like single points, continuous lines, and simple regions. With the introduction of complex spatial data types an issue arises regarding the design, definition, and number of topological relationships operating on these complex types. This article closes this gap and first introduces definitions of general and versatile spatial data types for complex points, complex lines, and complex regions. Based on the well known 9-intersection model, it then determines the complete sets of mutually exclusive topological relationships for all type combinations. Completeness and mutual exclusion are shown by a proof technique called proof-by-constraint-and-drawing. Due to the resulting large numbers of predicates and the difficulty of handling them, the user is provided with the concepts of topological cluster predicates and topological predicate groups, which permit one to reduce the number of predicates to be dealt with in a user-defined and/or application-specific manner.

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With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatio-temporal databases. In this paper we consider the following problem: Given a set of moving object trajectories D and a query trajectory mq, find the k nearest neighbors to mq within D for any instant of time within the life time of mq. We assume D is indexed in a 3D-R-tree and employ a filter-and-refine strategy. The filter step traverses the index and creates a stream of so-called units (linear pieces of a trajectory) as a superset of the units required to build the result of the query. The refinement step processes an ordered stream of units and determines the pieces of units forming the precise result.To support the filter step, for each node p of the index, in preprocessing a time dependent coverage function C p (t) is computed which is the number of trajectories represented in p present at time t. Within the filter step, sophisticated data structures are used to keep track of the aggregated coverages of the nodes seen so far in the index traversal to enable pruning. Moreover, the R-tree index is built in a special way to obtain coverage functions that are effective for pruning. As a result, one obtains a highly efficient k-NN algorithm for moving data and query points that outperforms the two competing algorithms by a wide margin.Implementations of the new algorithms and of the competing techniques are made available as well. Algorithms can be used in a system context including, for example, visualization and animation of results. Experiments of the paper can be easily checked or repeated, and new experiments be performed.

In axial turbine the tip clearance flow occurring in rotor blade rows is responsible for about one third of the aerodynamic losses in the blade row and in many cases is the limiting factor for the blade lifetime. The tip leakage vortex forms when the leaking fluid crosses the gap between the rotor blade tip and the casing from pressure to suction side and rolls up into a vortex on the blade suction side. The flow through the tip gap is both of high velocity and high temperature, with the heat transfer to the blade from the hot fluid being very high in the blade tip area. In order to avoid blade tip burnout and a failure of the machine, blade tip cooling is commonly used. This paper presents the physical study and an improved design of a recessed blade tip for a highly loaded axial turbine rotor blade with application in high pressure axial turbines in aero engine or power generation. With use of three-dimensional Computational Fluid Dynamics (CFD), the flow field near the tip of the blade for different shapes of the recess cavities is investigated. Through better understanding and control of cavity vortical structures, an improved design is presented and the differences to the generic flat tip blade are highlighted. It is observed that by an appropriate profiling of the recess shape, the total tip heat transfer Nusselt Number was significantly reduced, being 15% lower than the flat tip and 7% lower than the baseline recess shape. Experimental results also showed an overall improvement of 0.2% in the one-and-1/2-stage turbine total efficiency with the improved recess design compared to the flat tip case. The CFD analysis conducted on single rotor row configurations predicted a 0.38% total efficiency increase for the rotor equipped with the new recess design compared to the flat tip rotor.