Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 24, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Thesis advisor: Dr. Kannapan Palaniappan. Includes bibliographical references.

Thesis (M.S.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 70-74). Also available on the World Wide Web.

The objects studied in geoscience are often not man-made objects, but rather the spatial distribution of three-dimensional continuous geographical phenomena such as the salinity of a body of water, the humidity of the air or the percentage of gold in the rock (phenomena that tend to change over time). These are referred to as fields, and their modelling with geographical information systems is problematic because the structures of these systems are usually two dimensional and static. Raster structures (voxels or octrees) are the most popular solutions, but, as I argue in this thesis, they have several shortcomings for geoscientific fields. As an alternative to using rasters for representing and modelling three-dimensional fields, I propose using a new spatial model based the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT). I argue that constructing the VD/DT of the samples that were collected to study the field can be beneficial for extracting meaningful information from it. Firstly, the tessellation of space obtained with the VD gives a clear and consistent definition of neighbourhood for unconnected points in three dimensions, which is useful since geoscientific datasets often have highly anisotropic distributions. Secondly, the efficient and robust reconstruction of the field can be obtained with natural neighbour interpolation, which is entirely based on the properties of the VD. Thirdly, the tessellations of the VD and the DT make possible, and even optimise, several spatial analysis and visualisation operations. A further important consideration is that the VD/DT is locally modifiable (insertion, deletion and movement of points), which permits us to model the temporal dimension, and also to interactively explore a dataset, thus gaining insight by observing on the fly the consequences of manipulations and spatial analysis operations. In this thesis, the development of this new spatial model is from an algorithmic point of view, i.e. I describe in details algorithms to construct, manipulate, analyse and visualise fields represented with the VD/DT. A strong emphasis is put on the implementation of the spatial model, and, for this reason, the many degeneracies that arise in three-dimensional geometric computing are described and handled. A new data structure, the augmented quad-edge, is also presented. It permits us to store simultaneously both the VD and the DT, and helps in the analysis of fields. Finally, the usefulness of this Voronoi-based spatial model is demonstrated with a series of potential applications in geoscience.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 61-66). Also available in print.

Diplomarbeit - Technische Universität Berlin / Title from title screen (viewed on June 17, 2008). Abstract in German and English. Title from document title page. Includes bibliographical references. Available in PDF format via the World Wide Web.

published_or_final_version / Computer Science / Master / Master of Philosophy

In Voronoi-based nearest neighbor search, the Voronoi cell of every point p in a database can be used to check whether p is the closest to some query point q. We extend the notion of Voronoi cells to support uncertain objects, whose attribute values are inexact. Particularly, we propose the Possible Voronoi cell (or PV-cell). A PV-cell of a multi-dimensional uncertain object o is a region R, such that for any point p ∈ R, o may be the nearest neighbor of p. If the PV-cells of all objects in a database S are known, they can be used to identify objects that have a chance to be the nearest neighbor of q. However, there is no efficient algorithm for computing an exact PV-cell. We hence study how to derive an axis-parallel hyper-rectangle (called the Uncertain Bounding Rectangle, or UBR) that tightly contains a PV-cell. We further develop the PV-index, a structure that stores UBRs, to evaluate probabilistic nearest neighbor queries over uncertain data. An advantage of the PV-index is that upon updates on S, it can be incrementally updated. Extensive experiments on both synthetic and real datasets are carried out to validate the performance of the PV-index. / published_or_final_version / Computer Science / Master / Master of Philosophy

Title page, abstract and table of contents only. The complete thesis in print form is available from the University of Adelaide Library. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1274742 / Thesis (Ph.D.) -- University of Adelaide, School of Psychology, 2007

Thesis (M.S.)--State University of New York at Binghamton, Department of Computer Science, 2005. / Includes bibliographical references.

The development and numerical implementation of a three-dimensional Particle-In-Cell (PIC) methodology on unstructured Voronoi-Delauney tetrahedral grids is presented. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints for three-dimensional unstructured grids. The algorithms for particle motion, particle tracing, particle injection, and loading are discussed. Solution to Poisson's equation is based on a finite-volume formulation that takes advantage of the Voronoi-Delauney dual. The PIC methodology and code are validated by application to the problem of current collection by cylindrical Langmuir probes in stationary and moving collisionless plasmas. Numerical results are compared favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. A methodology for evaluation of the heating, slowing-down and deflection times in 3D PIC simulations is presented. An extensive parametric evaluation is performed and the effects of the number of computational particles per cell, the ratio of cell-edge to Debye length, and timestep are investigated. The unstructured PIC code is applied to the simulation of Field Emission Array (FEA) cathodes. Electron injection conditions are obtained from a Field Emission microtip model and the simulation domain includes the FEA cathode and anode. Currents collected by the electrodes are compared to theoretical values. Simulations show the formation of the virtual cathode and three-dimensional effects under certain injection conditions. The unstructured PIC code is also applied to the simulation of a micro-Retarding Potential Analyzer. For simple cases the current at the collector plate is compared favorably with theoretical predictions. The simulations show the complex structure of the potential inside the segmented microchannel, the phase space of plasma species and the space-charge effects not captured by the theory.