26 research outputs found

    Diamond-based models for scientific visualization

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    Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

    Embedding a complete binary tree into a faulty supercube

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    [[abstract]]The supercube is a novel interconnection network that is derived from the hypercube. Unlike the hypercube, the supercube can be constructed for any number of nodes. That is, the supercube is incrementally expandable. In addition, the supercube retains the connectivity and diameter properties of the corresponding hypercube. In this paper, we consider the problem of embedding and reconfiguring binary tree structures in a faulty supercube. Further more, for finding the replaceable node of the faulty node, we allow 2-expansion such that we can show that up to (n-2) faults can be tolerated with congestion 1 and dilation 4 that is (n-1) is the dimension of a supercube[[notice]]èŁœæ­ŁćźŒç•ą[[conferencetype]]朋際[[conferencedate]]19971210~19971212[[iscallforpapers]]Y[[conferencelocation]]Melbourne, Australi

    Stellar Double Coronagraph: a multistage coronagraphic platform at Palomar observatory

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    We present a new instrument, the "Stellar Double Coronagraph" (SDC), a flexible coronagraphic platform. Designed for Palomar Observatory's 200" Hale telescope, its two focal and pupil planes allow for a number of different observing configurations, including multiple vortex coronagraphs in series for improved contrast at small angles. We describe the motivation, design, observing modes, wavefront control approaches, data reduction pipeline, and early science results. We also discuss future directions for the instrument.Comment: 25 pages, 12 figures. Correspondence welcome. The published work is open access and differs trivially from the version posted here. The published version may be found at http://iopscience.iop.org/article/10.1088/1538-3873/128/965/075003/met

    Finding hamiltonian cycles on incrementally extensible hypercube graphs

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    [[abstract]]The existence of a Hamiltonian cycle is the premise of usage in an interconnection network. A novel interconnection network, the incrementally extensible hypercube (IEH) graph, has been proposed. The IEH graphs are derived from hypercubes and also retain most of the properties of hypercubes. Unlike hypercubes without incremental extensibility, IEH graphs can be constructed in any number of nodes. In this paper, we present an algorithm to find a Hamiltonian cycle or path and prove that there exists a Hamiltonian cycle in all IEH graphs except for those containing exactly 2n-1 nodes.[[notice]]èŁœæ­ŁćźŒç•ą[[conferencetype]]朋際[[conferencedate]]19970428~19970502[[iscallforpapers]]Y[[conferencelocation]]Seoul, KORE

    Simplicial Methods for Solving Selected Problems in General Relativity Numerically: Regge Calculus and the Finite-Element Method

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    In der vorliegenden Arbeit werden zwei numerische Verfahren betrachtet, welche spezielle Probleme der Allgemeine RelativitĂ€tstheorie nĂ€herungsweise berechnen können. Dies ist zum einen die Finite-Element-Methode und zum anderen das Regge-KalkĂŒl. Beide Verfahren basieren auf einer Zerlegung des betrachteten Gebietes in Simplizes. Zahlreiche dieser Simplizialzerlegungen und ihre Anwendbarkeit auf beide Verfahren wurden in dieser Arbeit eingehend untersucht bevor diese zur Lösung des ProblemsĂ€ verwendet wurden. Um Probleme aus der Allgemeinen RelativitĂ€tstheorie numerisch zu berechnen, wird in dieser Arbeit die 3+1-Zerlegung angewendet. Diese unterteilt die Lösung des Problems in zwei Teilschritte. Im ersten Schritt werden Anfangsdaten bestimmt mit Hilfe derer man im zweiten Schritt ein Zeitentwicklungsschema anwenden kann. Der erste Teil dieser Arbeit demonstriert, wie man das Anfangsdaten-Problem fĂŒr spezielle Probleme unter Verwendung der Finiten-Element-Methode lösen kann. Der zweite Teil der Arbeit widmet sich der Aufgabe, Anfangsdaten mit Hilfe des Regge-KalkĂŒls zu entwickeln. WĂ€hrend viele Formulierungen in der Allgemeinen RelativitĂ€tstheorie koordinatenabhĂ€ngig sind und somit eine Vielzahl an Lösungen ein und dasselbe Problem beschreiben, verwendet das Regge-KalkĂŒl KantenlĂ€ngenquadrate als Variablen. Die LĂ€nge einer Kante ist unabhĂ€ngig von dem zugrundeliegenden Koordinatensystem. Die Lösung eines Problems wird somit durch genau einen Satz an KantenlĂ€ngenquadraten reprĂ€sentiert. Dass man auf das Quadrat dieser LĂ€nge zugreift, liegt daran, dass die vierdimensionale Raumzeit nicht euklidisch ist, sondern Minkowski-Signatur besitzt. AbhĂ€ngig vom Vorzeichen des KantenlĂ€ngenquadrates ergibt sich eine rĂ€umliche Ausdehnung oder eine Zeitdifferenz. Anhand vieler Beispiele werden beide Verfahren untersucht. FĂŒr die Anfangsdaten wurde ein statisches und ein sich rotierendes schwarzes Loch sowie zwei sich aufeinander zubewegende schwarze Löcher betrachtet. FĂŒr die Zeitentwicklung wurden Beispiele der Apples-With-Apples-Testsuite, das Kasner-Universum und ein statisches schwarzes Loch untersucht. Es zeigt sich, das beide Verfahren auf einfache Probleme der Numerischen RelativitĂ€tstheorie anwendbar sind. Die Finite-Element-Methode liefert Anfangsdaten auf einer Excision-DomĂ€ne, wobei hier einer selbst konstruierten Triangulierung einer unstrukturierten der Vorzug zu geben ist. Im Regge-KalkĂŒl ist es erstmals gelungen, unstrukturierte Gitter, welche von externen Gittergeneratoren erstellt werden, als Grundlage fĂŒr Zeitentwicklungen im Regge-KalkĂŒl zu benutzen. Damit können auch komplexe Gebiete schnell modelliert werden. Des weiteren zeigen die Ergebnisse dieser Arbeit, dass das QR-Verfahren einem sonst ĂŒblichen LU-Verfahren vorzuziehen ist. Vor allem in fast flachen Raumzeiten und bei der Zeitentwicklung von unstrukturierten Gittern zeigt sich, das erst durch die Anwendung des QR-Verfahrens eine stabile Simulation möglich ist. Durch den Verzicht auf die Anwendung einer simplizialen Bianchi-IdentitĂ€t gelingt es entsprechende Probleme zu lösen und die Ergebnisse mit bestehenden Resultaten aus Finite-Differenzen-Verfahren zu vergleichen. Erstmals wurde die Konvergenz des Regge-Kalkžls anhand integraler Normen der Metrik untersucht. Bisher wurden nur Abweichungen von KantenlĂ€ngen diskutiert oder das Residuum der Regge-Gleichungen betrachtet. Mittels des Linear-Wellen-Tests aus der Apples-With-Apples-Testsammlung wird das Verhalten der numerischen Lösung in den neuen Normen eingehend untersucht. Hierbei wurde auch eine aus der KausalitĂ€t abgeleitete Courant-Friedrichs-Levi-Bedingung numerisch bestĂ€tigt. Simulationen des Kasner-Unviersums und des Gowdy-Universums zeigen, dass analytisch bekannte Lösungen qualitativ und quantitativ erfolgreich numerisch approximiert werden können. Im ersten Fall stimmt die zeitentwickelte Lösung mit der analytischen bis auf einen relativen Fehler in der GrĂ¶ĂŸenordnung von 0,001% ĂŒberein. Auch im Kasner-Universum wird die theoretisch ermittelte Courant-Friedrichs-Levi-Bedingung numerisch bestĂ€tigt. Zudem ist es auch erstmals gelungen, Probleme auf DomĂ€nen mit rĂ€umlichen Rand zu lösen, wobei geeignete Bedingungen an Randkanten ausschlaggebend fĂŒr die StabilitĂ€t sind. Hiermit wurden auf unstrukturierten Gittern die gestörte flache Raumzeit und die Schwarzschild-Raumzeit zeitentwickelt. Es zeigt sich, das mit besseren Winkeln des Gitters auch die Zeitentwicklung stabiler wird. Das Regge-KalkĂŒl wie auch die Finite-Element-Methode sind vielversprechende und wie in dieser Arbeit gezeigt wurde funktionierende LösungsansĂ€tze fĂŒr einfache Probleme der Numerischen RelativitĂ€tstheorie. Durch die höhere FlexibilitĂ€t dieser Simplizialmethoden sind sie interessante Alternativen zu bisherigen, auf Finiten Differenzen basierenden AnsĂ€tzen. WeiterfĂŒhrende Arbeiten auf diesem Gebiet könnten beide Methoden dahingehend weiterentwickeln komplexere Probleme, wie das Einspiralen zweier schwarzer Löcher, zu lösen. Solche alternativen Lösungen könnten bestehende Verfahren verifizieren und erweitern

    On the Effect of Quantum Interaction Distance on Quantum Addition Circuits

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    We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any Ω(log⁥n)\Omega(\log n)-depth quantum adder circuit for two nn-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates. Unfortunately, on the chosen kk-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer Ω(log⁥n)\Omega(\log {n}), but Ω(nk)\Omega(\sqrt[k]{n}). This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing System

    Entropic Bonding in Nanoparticle and Colloidal Systems

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    Scientists and engineers will create the next generation of materials by precisely controlling their microstructure. One of the most promising and effective methods to control material microstructure is self-assembly, in which the properties of constituent “particles” guide their assembly into the desired structure. Self- assembly mechanisms rely on both inherent interactions between particles and emergent interactions resulting from the collective effects of all particles in the system. These emergent effects are of interest as they provide minimal mechanisms to control self-assembly, and thus can be used in conjunction with other assembly methods to create novel materials. Literature shows that complex phases can be obtained solely from hard, anisotropic particles, which are attracted via an emergent Directional Entropic Force. This thesis shows that this force gives rise to the entropic bond, a mesoscale analog to the chemical bond. In Chapter 3 I investigate the self- assembly of a system from a random tiling into an ordered crystal. Analysis of the emergent directional entropic forces reveal the importance of shape in the final self-assembled system as well as the ability for shape manipulation to control the final self-assembled structure. In Chapter 4, I investigate three-dimensional analogs of two-dimensional systems in Chapter 3, explaining the self-assembly behavior of these systems via understanding of the emergent directional entropic forces. In Chapter 5 I investigate the nature of the entropic bond, investigating two-dimensional systems of hexagonal nanoplatelets. The Entropic bond is quantified, and the ability to manipulate the bonds to produce similar self- assembly behavior to chemically-functionalized nanoparticles is demonstrated. Finally, Chapter 6 investigates the phase transitions of the general class of particle studied in Chapter 5, showing the ability for particle shape to change the type of phase transition present in a system of nanoparticles as well as stabilize phases otherwise not found. As a whole, this work details the nature of the entropic bond and its use in directing the self-assembly of systems of non- interacting anisotropic particles.PHDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144096/1/harperic_1.pd

    Multi-objective mixed-integer evolutionary algorithms for building spatial design

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    Multi-objective evolutionary computation aims to find high quality (Pareto optimal) solutions that represent the trade-off between multiple objectives. Within this field there are a number of key challenges. Among others, this includes constraint handling and the exploration of mixed-integer search spaces. This thesis investigates how these challenges can be handled at the same time, and in particular how they can be applied in the multi-objective optimisation algorithms. These algorithms are developed in the context of the optimisation of building spatial designs, which describe the exterior shape of a building, and the internal division into different spaces. Spatial designs are developed early in the design process, and thus have a large impact on the final building design, and in turn also on the quality of the building. Here the structural and thermal performance of a building are optimised to reduce resource consumption. The main contributions of this thesis are as follows. Firstly, a representation for building spatial designs in is introduced. Secondly, specialised search operators are designed to ensure only feasible solutions will be explored. Thirdly, data about the discovered solutions is analysed to explain the results to domain experts. Finally, a general purpose multi-objective mixed-integer evolutionary algorithm is developed. This work is part of the TTW-Open Technology Programme with project number 13596, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).Computer Science
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