Topological Stability of Kinetic kk-Centers

We study the $k$-center problem in a kinetic setting: given a set of continuously moving points $P$ in the plane, determine a set of $k$ (moving) disks that cover $P$ at every time step, such that the disks are as small as possible at any point in time. Whereas the optimal solution over time may exhibit discontinuous changes, many practical applications require the solution to be stable: the disks must move smoothly over time. Existing results on this problem require the disks to move with a bounded speed, but this model is very hard to work with. Hence, the results are limited and offer little theoretical insight. Instead, we study the topological stability of $k$-centers. Topological stability was recently introduced and simply requires the solution to change continuously, but may do so arbitrarily fast. We prove upper and lower bounds on the ratio between the radii of an optimal but unstable solution and the radii of a topologically stable solution---the topological stability ratio---considering various metrics and various optimization criteria. For $k = 2$ we provide tight bounds, and for small $k > 2$ we can obtain nontrivial lower and upper bounds. Finally, we provide an algorithm to compute the topological stability ratio in polynomial time for constant $k$

Solid rocket booster thermal radiation model, volume 1

A solid rocket booster (SRB) thermal radiation model, capable of defining the influence of the plume flowfield structure on the magnitude and distribution of thermal radiation leaving the plume, was prepared and documented. Radiant heating rates may be calculated for a single SRB plume or for the dual SRB plumes astride the space shuttle. The plumes may be gimbaled in the yaw and pitch planes. Space shuttle surface geometries are simulated with combinations of quadric surfaces. The effect of surface shading is included. The computer program also has the capability to calculate view factors between the SRB plumes and space shuttle surfaces as well as surface-to-surface view factors

Geometrically-Complex Magnetic Field Distributions Enabled By Bulk, Laser-Micromachined Permanent Magnets At The Submillimeter Scale

High-energy-product permanent magnets (PM) are utilized in many industrial, research, consumer, and commercial applications. Indeed, there are many potential applications that can utilize sub-mm PM to create miniaturized versions of motors, generators, energy harvesters, undulators, sensors, actuators, and other microelectromechanical systems (MEMS) devices. Magnets in MEMS are both important and useful because they can provide a strong force at a distance within a compact package; however, there exists a gap in magnet technologies today where magnets have little to no presence between bottom-up microfabricated PM and top-down machined bulk PM. Thus, there is a need for a form of PM that can be 100–500��m thick with lateral dimensions of the same order to fill this gap and provide the advantageous magnetic properties of bulk PM at this scale. This dissertation presents the development of laser micromachining as a fabrication technology that enables the microfabrication of PM to generate geometrically complex magnetic fields at the sub-mm scale. Generating geometrically complex magnetic fields at the sub-mm scale opens up new possibilities in medical technology, energy generation, and many other applications. Models simulating magnetic properties and the effects of laser machining are presented and compared to measurements. The fabrication technology discussed here allows sub-mm, geometrically complex magnetic fields to be achieved while maintaining the characteristics of bulk PM. The utility of this advance in fabrication technology is demonstrated through multiple research vehicles, including undulators for radiation generation and multipole energy harvesters operable at low frequency. Such vehicles represent a small sample of the potential applications for this work

Vision-Based Autonomous Robotic Floor Cleaning in Domestic Environments

Fleer DR. Vision-Based Autonomous Robotic Floor Cleaning in Domestic Environments. Bielefeld: Universität Bielefeld; 2018

Atomic Scale Investigation of Pressure Induced Phase Transitions in the solid State

In this work, atomic scale investigation of pressure-induced transformations in the solid state have been carried out. A series of compounds including GaN, ZnO, CaF2, and AgI, in addition to elemental phosphorus have been studied. The corresponding transition mechanisms have been elucidated with a clear description of atomic displacements and intermediate structures involved therein. In the first group of compounds, the long standing debate on the transition path of the wurtzite(WZ)-to-rocksalt(RS) transition in semiconductors, GaN and ZnO was resolved using geometrical modeling combined with molecular dynamics (MD) simulations conducted in the frame of transition path sampling (TPS) method. In GaN, a two-step mechanism through a metastable intermediate phase with a tetragonal structure iT has been revealed from simulations. In ZnO, the tetragonal intermediate structure was kinetically less stable, although still part of the real transition mechanism. It appeared at the interface between WZ and RS as consequence of a layers shearing. The transition regime in ZnO was characterized by a competition between iT structure and another hexagonal intermediate with hexagonal symmetry iH. Although possible, the latter is not functional for the transition. In both cases, GaN and ZnO, two points of agreement with experiments have been revealed. The tilting of structures after transition, and the phonon mode softening associated with atomic displacements leading to the tetragonal structure iT In the second group of compounds, the investigation of transitions in superionic conductors, CaF2 and AgI, demonstrated a different and particular behavior of atomic motion under pressure. The solid-solid reconstruction of CaF2 structure was shown to be initiated and precedented by high disorder of the anionic sublattice. The percolation of fluoride ions through voids in the fluorite structure created a thin interface of liquid like state. The sparce regions caused by the departure of anions facilitates the cation sublattice reconstruction. In AgI, ion diffusion during the wurtzite/zincnlende(ZB)$rocksalt transition was more pronounced due to the extended stacking disorder WZ/ZB. The Ag+ ions profited not only from the structure of the interface but used the combination of interstitial voids offered by both phases, WZ and ZB, to achieve long diffusion paths and cause the cation sublattice to melt. Clearly, a proper account for such phenomena cannot be provided by geometry-designed mechanisms based on symmetry arguments. In phosphorus, the question of how the stereochemically active lone pairs are reorganized during the orthorhombic (PI) to trigonal (PV) structural transition was answered by means of simulations. Computation was performed at different levels theory. First, the mechanism of the transition was obtained from TPS MD simulations. MD runs were performed within density functional tight binding method (DFTB). The analysis of atomic displacements along the real transformation path indicated a fast bond switching mechanism. In a second step, the nature of the interplay between orbitals of phosphorus during the bond switching was investigated. A simultaneous deformation of lone pair and P−P bond showed a mutual switching of roles during the transformation. This interplay caused a low dimensional polymerization of phosphorus under pressure. The corresponding structure formed as zigzag linear chain of fourfold coordinated phosphorus atoms (· · ·(P(P2))n · · ·) at the interface between PI and PV phases. A further result of this work was the development of a simulation strategy to incorporate defects and chemical doping to structural transformations. On top of the transition path sampling iterations, a Monte Carlo like procedure is added to stepwise substitute atoms in the transforming system. Introducing a chemically different dopant to a pure system represents a perturbation to the energy landscape where the walk between different phases is performed. Therefore, any change in the transition regime reflects the kinetic preference of a given structural motif at times of phase formation. This method was applied to the elucidation of WZ-RS transition mechanism in the series of semiconducting compounds AlN, GaN, and InN. Simulations showed that In atoms adopt the same transformation mechanism as in GaN and favor it, while Al atoms demonstrated a significant reluctance to the path going through tetragonal intermediate iT. The difference between transition regime in mixed systems InxGa1−xN and AlxGa1−xN is in agreement with experiments on high pressure behavior of AlN, GaN, and InN. While transitions in GaN and InN are reversible down to ambient conditions, AlN is stable. The work presented in this thesis constitutes the seed of new perspectives in the understanding of pressure-induced phase transformations in the solid state, where the physics and the chemistry are brought together by means of computer simulations

Structured meshes: composition and remeshing guided by the Curve-Skeleton

Virtual sculpting is currently a broadly used modeling metaphor with rising popularity especially in the entertainment industry. While this approach unleashes the artists' inspiration and creativity and leads to wonderfully detailed and artistic 3D models, it has the side effect, purely technical, of producing highly irregular meshes that are not optimal for subsequent processing. Converting an unstructured mesh into a more regular and struc- tured model in an automatic way is a challenging task and still open prob- lem. Since structured meshes are useful in different applications, it is of in- terest to be able to guarantee such property also in scenarios of part based modeling, which aim to build digital objects by composition, instead of modeling them from a scratch. This thesis will present methods for obtaining structured meshes in two different ways. First is presented a coarse quad layout computation method which starts from a triangle mesh and the curve-skeleton of the shape. The second approach allows to build complex shapes by procedural composition of PAM's. Since both quad layouts and PAMs exploit their global struc- ture, similarities between the two will be discussed, especially how their structure has correspondences to the curve-skeleton describing the topology of the shape being represented. Since both the presented methods rely on the information provided by the skeleton, the difficulties of using automat- ically extracted curve-skeletons without processing are discussed, and an interactive tool for user-assisted processing is presented

Structured meshes: composition and remeshing guided by the Curve-Skeleton

Virtual sculpting is currently a broadly used modeling metaphor with rising popularity especially in the entertainment industry. While this approach unleashes the artists' inspiration and creativity and leads to wonderfully detailed and artistic 3D models, it has the side effect, purely technical, of producing highly irregular meshes that are not optimal for subsequent processing. Converting an unstructured mesh into a more regular and struc- tured model in an automatic way is a challenging task and still open prob- lem. Since structured meshes are useful in different applications, it is of in- terest to be able to guarantee such property also in scenarios of part based modeling, which aim to build digital objects by composition, instead of modeling them from a scratch. This thesis will present methods for obtaining structured meshes in two different ways. First is presented a coarse quad layout computation method which starts from a triangle mesh and the curve-skeleton of the shape. The second approach allows to build complex shapes by procedural composition of PAM's. Since both quad layouts and PAMs exploit their global struc- ture, similarities between the two will be discussed, especially how their structure has correspondences to the curve-skeleton describing the topology of the shape being represented. Since both the presented methods rely on the information provided by the skeleton, the difficulties of using automat- ically extracted curve-skeletons without processing are discussed, and an interactive tool for user-assisted processing is presented

Cultural relationships in southern Ecuador 300 BC- AD 300: Excavations at the Guarumal and Punta Brava sites

Based upon an analysis of pottery excavated from the Guarumal and Punta Brava archaeological sites in south coastal Ecuador, the author seeks to place these sites into an overall cultural and chronological framework within the timescale 300 BC - AD 300, and to use some of the issues deriving from a discussion of the material and the occupation of the sites to assess the validity of the Jambeli culture, as defined by Estrada, Keggers and Evans (1964). "All Jambeli Phase sites are shell middens..." (ibld: 486) is one of the assertions questioned in this thesis, together with the question of using white-on-red decorated pottery as a distinguishing feature of the Ecuadorian Regional Developmental Period. Some of the material described as being of the Jambeli culture is likely to have been misidentified and wrongly ascribed pottery deriving from late Formative period cultures in the area, of which the most important is the Guayaquil phase, from the Gulf of Guayaquil. A clear sequence of development of pottery forms and styles can be demonstrated for the site Guarumal, from late Formative period Chorrera-like antecedents, exhibiting certain similarities with the Pechiche culture, through to those more typical of the Regional Developmental period - which is the Jambeli culture in this area - in the later phases of occupation. Stylistic parallels with several contemporary cultures in southern Ecuador (and parts of northern Peru) are also examined, for the insights or challenges they offer to questions of cultural relationships and interactions over a wider geographical area. It is increasingly clear that a re-evaluation of the Jambeli culture is necessary to take account of archaeological research of the last twenty years, research which has shown that the Jambeli culture was not merely a coastal adaptation of shell-fishing communities, but that it strecthed well into the interior and had Formative period roots