Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Tight-Binding Approximations in 1D and 2D Coupled-Cavity Photonic Crystal Structures

Light confinement and controlling an optical field has numerous applications in the field of telecommunications for optical signals processing. When the wavelength of the electromagnetic field is on the order of the period of a photonic microstructure, the field undergoes reflection, refraction, and coherent scattering. This produces photonic bandgaps, forbidden frequency regions or spectral stop bands where light cannot exist. Dielectric perturbations that break the perfect periodicity of these structures produce what is analogous to an impurity state in the bandgap of a semiconductor. The defect modes that exist at discrete frequencies within the photonic bandgap are spatially localized about the cavity-defects in the photonic crystal. In this thesis the properties of two tight-binding approximations (TBAs) are investigated in one-dimensional and two-dimensional coupled-cavity photonic crystal structures We require an efficient and simple approach that ensures the continuity of the electromagnetic field across dielectric interfaces in complex structures. In this thesis we develop \textrm{E} -- and \textrm{D} --TBAs to calculate the modes in finite 1D and 2D two-defect coupled-cavity photonic crystal structures. In the \textrm{E} -- and \textrm{D} --TBAs we expand the coupled-cavity \overrightarrow{E} --modes in terms of the individual \overrightarrow{E} -- and \overrightarrow{D} --modes, respectively. We investigate the dependence of the defect modes, their frequencies and quality factors on the relative placement of the defects in the photonic crystal structures. We then elucidate the differences between the two TBA formulations, and describe the conditions under which these formulations may be more robust when encountering a dielectric perturbation. Our 1D analysis showed that the 1D modes were sensitive to the structure geometry. The antisymmetric \textrm{D} mode amplitudes show that the \textrm{D} --TBA did not capture the correct (tangential \overrightarrow{E} --field) boundary conditions. However, the \textrm{D} --TBA did not yield significantly poorer results compared to the \textrm{E} --TBA. Our 2D analysis reveals that the \textrm{E} -- and \textrm{D} --TBAs produced nearly identical mode profiles for every structure. Plots of the relative difference between the \textrm{E} and \textrm{D} mode amplitudes show that the \textrm{D} --TBA did capture the correct (normal \overrightarrow{E} --field) boundary conditions. We found that the 2D TBA CC mode calculations were 125-150 times faster than an FDTD calculation for the same two-defect PCS. Notwithstanding this efficiency, the appropriateness of either TBA was found to depend on the geometry of the structure and the mode(s), i.e. whether or not the mode has a large normal or tangential component.

Towards Mapping of Rock Walls Using a UAV-Mounted 2D Laser Scanner in GPS Denied Environments

In geotechnical engineering, the stability of rock excavations and walls is estimated by using tools that include a map of the orientations of exposed rock faces. However, measuring these orientations by using conventional methods can be time consuming, sometimes dangerous, and is limited to regions of the exposed rock that are reachable by a human. This thesis introduces a 2D, simulated, quadcopter-based rock wall mapping algorithm for GPS denied environments such as underground mines or near high walls on surface. The proposed algorithm employs techniques from the field of robotics known as simultaneous localization and mapping (SLAM) and is a step towards 3D rock wall mapping. Not only are quadcopters agile, but they can hover. This is very useful for confined spaces such as underground or near rock walls. The quadcopter requires sensors to enable self localization and mapping in dark, confined and GPS denied environments. However, these sensors are limited by the quadcopter payload and power restrictions. Because of these restrictions, a light weight 2D laser scanner is proposed. As a first step towards a 3D mapping algorithm, this thesis proposes a simplified scenario in which a simulated 1D laser range finder and 2D IMU are mounted on a quadcopter that is moving on a plane. Because the 1D laser does not provide enough information to map the 2D world from a single measurement, many measurements are combined over the trajectory of the quadcopter. Least Squares Optimization (LSO) is used to optimize the estimated trajectory and rock face for all data collected over the length of a light. Simulation results show that the mapping algorithm developed is a good first step. It shows that by combining measurements over a trajectory, the scanned rock face can be estimated using a lower-dimensional range sensor. A swathing manoeuvre is introduced as a way to promote loop closures within a short time period, thus reducing accumulated error. Some suggestions on how to improve the algorithm are also provided.

A solution to the three disjoint path problem on honeycomb meshes

Recently honeycomb meshes have been considered as alternative candidates for interconnection networks in parallel and distributed computer systems. This paper presents a solution to one of the open problems about honeycomb meshes—the so-called three disjoint path problem. The problem requires minimizing the length of the longest of any three disjoint paths between 3-degree nodes. This solution provides information on the re-routing of traffic along the network in the presence of faults.

Fast 2D/3D object representation with growing neural gas

This work presents the design of a real-time system to model visual objects with the use of self-organising networks. The architecture of the system addresses multiple computer vision tasks such as image segmentation, optimal parameter estimation and object representation. We first develop a framework for building non-rigid shapes using the growth mechanism of the self-organising maps, and then we define an optimal number of nodes without overfitting or underfitting the network based on the knowledge obtained from information-theoretic considerations. We present experimental results for hands and faces, and we quantitatively evaluate the matching capabilities of the proposed method with the topographic product. The proposed method is easily extensible to 3D objects, as it offers similar features for efficient mesh reconstruction.

Time-resolved dosimetric verification of respiratory-gated radiotherapy exposures using a high-resolution 2D ionisation chamber array

The aim of this work was to track and verify the delivery of respiratory-gated irradiations, performed with three versions of TrueBeam linac, using a novel phantom arrangement that combined the OCTAVIUS® SRS 1000 array with a moving platform. The platform was programmed to generate sinusoidal motion of the array. This motion was tracked using the real-time position management (RPM) system and four amplitude gating options were employed to interrupt MV beam delivery when the platform was not located within set limits. Time-resolved spatial information extracted from analysis of x-ray fluences measured by the array was compared to the programmed motion of the platform and to the trace recorded by the RPM system during the delivery of the x-ray field. Temporal data recorded by the phantom and the RPM system were validated against trajectory log files, recorded by the linac during the irradiation, as well as oscilloscope waveforms recorded from the linac target signal. Gamma analysis was employed to compare time-integrated 2D x-ray dose fluences with theoretical fluences derived from the probability density function for each of the gating settings applied, where gamma criteria of 2%/2 mm, 1%/1 mm and 0.5%/0.5 mm were used to evaluate the limitations of the RPM system. Excellent agreement was observed in the analysis of spatial information extracted from the SRS 1000 array measurements. Comparisons of the average platform position with the expected position indicated absolute deviations of  <0.5 mm for all four gating settings. Differences were observed when comparing time-resolved beam-on data stored in the RPM files and trajectory logs to the true target signal waveforms. Trajectory log files underestimated the cycle time between consecutive beam-on windows by 10.0  ±  0.8 ms. All measured fluences achieved 100% pass-rates using gamma criteria of 2%/2 mm and 50% of the fluences achieved pass-rates  >90% when criteria of 0.5%/0.5 mm were used. Results using this novel phantom arrangement indicate that the RPM system is capable of accurately gating x-ray exposure during the delivery of a fixed-field treatment beam.

The dynamics of neutrino-driven supernova explosions after shock revival in 2D and 3D

We study the growth of the explosion energy after shock revival in neutrino-driven explosions in two and three dimensions (2D/3D) using multi-group neutrino hydrodynamics simulations of an 11.2 M⊙ star. The 3D model shows a faster and steadier growth of the explosion energy and already shows signs of subsiding accretion after one second. By contrast, the growth of the explosion energy in 2D is unsteady, and accretion lasts for several seconds as confirmed by additional long-time simulations of stars of similar masses. Appreciable explosion energies can still be reached, albeit at the expense of rather high neutron star masses. In 2D, the binding energy at the gain radius is larger because the strong excitation of downward-propagating g modes removes energy from the freshly accreted material in the downflows. Consequently, the mass outflow rate is considerably lower in 2D than in 3D. This is only partially compensated by additional heating by outward-propagating acoustic waves in 2D. Moreover, the mass outflow rate in 2D is reduced because much of the neutrino energy deposition occurs in downflows or bubbles confined by secondary shocks without driving outflows. Episodic constriction of outflows and vertical mixing of colder shocked material and hot, neutrino-heated ejecta due to Rayleigh–Taylor instability further hamper the growth of the explosion energy in 2D. Further simulations will be necessary to determine whether these effects are generic over a wider range of supernova progenitors.

Few-layer, large-area, 2D covalent organic framework semiconductor thin films.

In this work, we synthesize large-area thin films of a conjugated, imine-based, two-dimensional covalent organic framework at the solution/air interface. Thicknesses between ∼2-200 nm are achieved. Films can be transferred to any desired substrate by lifting from underneath, enabling their use as the semiconducting active layer in field-effect transistors.

Creazione di una costmap 2D per la navigazione di un rover terrestre

L’obiettivo di questa tesi è riuscire ad elaborare una point cloud 3D proveniente dal laser scanner per individuare possibili ostacoli e creare con essa, successivamente, una mappa che permetta la navigazione di un rover.

Análisis, diseño y desarrollo de un videojuego en 2D vista lateral

[ES]En este proyecto se ha desarrollado un prototipo de un videojuego en 2D con perspectiva lateral. El juego es fundamentalmente un juego de peleas en el que se usa una pelota para combatir. El objetivo es derrotar al rival, consiguiendo que la pelota le golpee y evitando recibir golpes mediante el uso de los controles apropiados. Está ambientado en un mundo futurista y los combates tienen lugar en naves espaciales o planetas alienígenas. Para el desarrollo de este juego se ha empleado el motor de videojuegos Unity 5, además de recursos creados por la propia autora u obtenidos de diversas fuentes de contenido open-source.

Resources Grabbing and Human Rights: Building a Triangular Relationship Between States, Indigenous Peoples and Corporations

This is a pre-copyedited, author-produced PDF of a chapter accepted for publication in Angelica Bonfanti, Francesca Romanin Jacur, Francesco Seatzu (eds), Natural Resources Grabbing: Natural Resources Grabbing: An International Law Perspective, (Brill, 2016). The version of record is available at: http://www.brill.com/products/book/natural-resources-grabbing

A domain decomposition based algorithm for non-linear 2D inverse heat conduction problems

Inverse heat conduction problems (IHCPs) appear in many important scientific and technological fields. Hence analysis, design, implementation and testing of inverse algorithms are also of great scientific and technological interest. The numerical simulation of 2-D and –D inverse (or even direct) problems involves a considerable amount of computation. Therefore, the investigation and exploitation of parallel properties of such algorithms are equally becoming very important. Domain decomposition (DD) methods are widely used to solve large scale engineering problems and to exploit their inherent ability for the solution of such problems.