ON VULNERABILITY MEASURES OF NETWORKS

As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication networks are discussed including the connectivities, fault diameters, and measures based on Hosoya-Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved

ON VULNERABILITY MEASURES OF NETWORKS

As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication networks are discussed including the connectivities, fault diameters, and measures based on Hosoya-Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved

Modeling single-phase flow and solute transport across scales

textFlow and transport phenomena in the subsurface often span a wide range of length (nanometers to kilometers) and time (nanoseconds to years) scales, and frequently arise in applications of CO₂ sequestration, pollutant transport, and near-well acid stimulation. Reliable field-scale predictions depend on our predictive capacity at each individual scale as well as our ability to accurately propagate information across scales. Pore-scale modeling (coupled with experiments) has assumed an important role in improving our fundamental understanding at the small scale, and is frequently used to inform/guide modeling efforts at larger scales. Among the various methods, there often exists a trade-off between computational efficiency/simplicity and accuracy. While high-resolution methods are very accurate, they are computationally limited to relatively small domains. Since macroscopic properties of a porous medium are statistically representative only when sample sizes are sufficiently large, simple and efficient pore-scale methods are more attractive. In this work, two Eulerian pore-network models for simulating single-phase flow and solute transport are developed. The models focus on capturing two key pore-level mechanisms: a) partial mixing within pores (large void volumes), and b) shear dispersion within throats (narrow constrictions connecting the pores), which are shown to have a substantial impact on transverse and longitudinal dispersion coefficients at the macro scale. The models are verified with high-resolution pore-scale methods and validated against micromodel experiments as well as experimental data from the literature. Studies regarding the significance of different pore-level mixing assumptions (perfect mixing vs. partial mixing) in disordered media, as well as the predictive capacity of network modeling as a whole for ordered media are conducted. A mortar domain decomposition framework is additionally developed, under which efficient and accurate simulations on even larger and highly heterogeneous pore-scale domains are feasible. The mortar methods are verified and parallel scalability is demonstrated. It is shown that they can be used as “hybrid” methods for coupling localized pore-scale inclusions to a surrounding continuum (when insufficient scale separation exists). The framework further permits multi-model simulations within the same computational domain. An application of the methods studying “emergent” behavior during calcite precipitation in the context of geologic CO₂ sequestration is provided.Petroleum and Geosystems Engineerin

Atomistic Simulations of Defect Nucleation and Intralayer Fracture in Molybdenum Disulphide During Nanoindentation

Molybdenum disulphide (MoS2) is a layered, hexagonal crystal that has a very low coefficient of friction. Due to this low coefficient of friction, MoS2 has become a well-known solid lubricant and liquid lubricant additive. As such, nanoparticles of MoS2 have been proposed as an additive to traditional liquid lubricants to provide frictional properties that are sensitive to different temperature and pressure regimes. However, to properly design these MoS2 nanoparticles to be sensitive to different temperature and pressure regimes, it is necessary to understand the mechanical response of crystalline MoS2 under mechanical loading. Specifically, the fundamental mechanism associated with the nucleation and interaction of defects as well as intralayer fracture. This thesis addressed the mechanical response of crystalline MoS2 via contact deformation (nanoindentation) simulations, which is representative of the loading conditions experienced by these nanoparticles during synthesis and application. There are two main tasks to this thesis. First, a Mo-S interatomic potential (a combination of the reactive empirical bond-order (REBO) interatomic potential and the Lennard-Jones 12-6 interatomic potential) that has been parameterized specifically to investigate the tribological properties of MoS2 was implemented into the classical molecular simulation package, LAMMPS, and refined to provide improved predictions for the mechanical properties of MoS2 via molecular statics calculations. Second, using this newly implemented interatomic potential, molecular statics calculations were performed to investigate the mechanical response of MoS2 via nanoindentation with specific focus on the nucleation of defects. Nanoindentation force - displacement curves were compared to the Hertzian contact theory prediction. It was shown that MoS2 does not follow the Hertzian prediction due it anisotropic nature. In addition, it was shown that the initial sudden force drop event in the force - displacement curves corresponds to plastic deformation. It was hypothesized that the mechanism associated with plastic failure of MoS2 was the occurrence of broken bonds. However, it was proven that this initial plastic yield does not correspond to the occurrence of broken bonds in the MoS2 lattice; instead, a permanent slip occurred within or between the MoS2 layers

Applied Visualization in the Neurosciences and the Enhancement of Visualization through Computer Graphics

The complexity and size of measured and simulated data in many fields of science is increasing constantly. The technical evolution allows for capturing smaller features and more complex structures in the data. To make this data accessible by the scientists, efficient and specialized visualization techniques are required. Maximum efficiency and value for the user can only be achieved by adapting visualization to the specific application area and the specific requirements of the scientific field. Part I: In the first part of my work, I address the visualization in the neurosciences. The neuroscience tries to understand the human brain; beginning at its smallest parts, up to its global infrastructure. To achieve this ambitious goal, the neuroscience uses a combination of three-dimensional data from a myriad of sources, like MRI, CT, or functional MRI. To handle this diversity of different data types and sources, the neuroscience need specialized and well evaluated visualization techniques. As a start, I will introduce an extensive software called \"OpenWalnut\". It forms the common base for developing and using visualization techniques with our neuroscientific collaborators. Using OpenWalnut, standard and novel visualization approaches are available to the neuroscientific researchers too. Afterwards, I am introducing a very specialized method to illustrate the causal relation of brain areas, which was, prior to that, only representable via abstract graph models. I will finalize the first part of my work with an evaluation of several standard visualization techniques in the context of simulated electrical fields in the brain. The goal of this evaluation was clarify the advantages and disadvantages of the used visualization techniques to the neuroscientific community. We exemplified these, using clinically relevant scenarios. Part II: Besides the data preprocessing, which plays a tremendous role in visualization, the final graphical representation of the data is essential to understand structure and features in the data. The graphical representation of data can be seen as the interface between the data and the human mind. The second part of my work is focused on the improvement of structural and spatial perception of visualization -- the improvement of the interface. Unfortunately, visual improvements using computer graphics methods of the computer game industry is often seen sceptically. In the second part, I will show that such methods can be applied to existing visualization techniques to improve spatiality and to emphasize structural details in the data. I will use a computer graphics paradigm called \"screen space rendering\". Its advantage, amongst others, is its seamless applicability to nearly every visualization technique. I will start with two methods that improve the perception of mesh-like structures on arbitrary surfaces. Those mesh structures represent second-order tensors and are generated by a method named \"TensorMesh\". Afterwards I show a novel approach to optimally shade line and point data renderings. With this technique it is possible for the first time to emphasize local details and global, spatial relations in dense line and point data.In vielen Bereichen der Wissenschaft nimmt die Größe und Komplexität von gemessenen und simulierten Daten zu. Die technische Entwicklung erlaubt das Erfassen immer kleinerer Strukturen und komplexerer Sachverhalte. Um solche Daten dem Menschen zugänglich zu machen, benötigt man effiziente und spezialisierte Visualisierungswerkzeuge. Nur die Anpassung der Visualisierung auf ein Anwendungsgebiet und dessen Anforderungen erlaubt maximale Effizienz und Nutzen für den Anwender. Teil I: Im ersten Teil meiner Arbeit befasse ich mich mit der Visualisierung im Bereich der Neurowissenschaften. Ihr Ziel ist es, das menschliche Gehirn zu begreifen; von seinen kleinsten Teilen bis hin zu seiner Gesamtstruktur. Um dieses ehrgeizige Ziel zu erreichen nutzt die Neurowissenschaft vor allem kombinierte, dreidimensionale Daten aus vielzähligen Quellen, wie MRT, CT oder funktionalem MRT. Um mit dieser Vielfalt umgehen zu können, benötigt man in der Neurowissenschaft vor allem spezialisierte und evaluierte Visualisierungsmethoden. Zunächst stelle ich ein umfangreiches Softwareprojekt namens \"OpenWalnut\" vor. Es bildet die gemeinsame Basis für die Entwicklung und Nutzung von Visualisierungstechniken mit unseren neurowissenschaftlichen Kollaborationspartnern. Auf dieser Basis sind klassische und neu entwickelte Visualisierungen auch für Neurowissenschaftler zugänglich. Anschließend stelle ich ein spezialisiertes Visualisierungsverfahren vor, welches es ermöglicht, den kausalen Zusammenhang zwischen Gehirnarealen zu illustrieren. Das war vorher nur durch abstrakte Graphenmodelle möglich. Den ersten Teil der Arbeit schließe ich mit einer Evaluation verschiedener Standardmethoden unter dem Blickwinkel simulierter elektrischer Felder im Gehirn ab. Das Ziel dieser Evaluation war es, der neurowissenschaftlichen Gemeinde die Vor- und Nachteile bestimmter Techniken zu verdeutlichen und anhand klinisch relevanter Fälle zu erläutern. Teil II: Neben der eigentlichen Datenvorverarbeitung, welche in der Visualisierung eine enorme Rolle spielt, ist die grafische Darstellung essenziell für das Verständnis der Strukturen und Bestandteile in den Daten. Die grafische Repräsentation von Daten bildet die Schnittstelle zum Gehirn des Menschen. Der zweite Teile meiner Arbeit befasst sich mit der Verbesserung der strukturellen und räumlichen Wahrnehmung in Visualisierungsverfahren -- mit der Verbesserung der Schnittstelle. Leider werden viele visuelle Verbesserungen durch Computergrafikmethoden der Spieleindustrie mit Argwohn beäugt. Im zweiten Teil meiner Arbeit werde ich zeigen, dass solche Methoden in der Visualisierung angewendet werden können um den räumlichen Eindruck zu verbessern und Strukturen in den Daten hervorzuheben. Dazu nutze ich ein in der Computergrafik bekanntes Paradigma: das \"Screen Space Rendering\". Dieses Paradigma hat den Vorteil, dass es auf nahezu jede existierende Visualiserungsmethode als Nachbearbeitunsgschritt angewendet werden kann. Zunächst führe ich zwei Methoden ein, die die Wahrnehmung von gitterartigen Strukturen auf beliebigen Oberflächen verbessern. Diese Gitter repräsentieren die Struktur von Tensoren zweiter Ordnung und wurden durch eine Methode namens \"TensorMesh\" erzeugt. Anschließend zeige ich eine neuartige Technik für die optimale Schattierung von Linien und Punktdaten. Mit dieser Technik ist es erstmals möglich sowohl lokale Details als auch globale räumliche Zusammenhänge in dichten Linien- und Punktdaten zu erfassen

A continuum robotic platform for endoscopic non-contact laser surgery: design, control, and preclinical evaluation

The application of laser technologies in surgical interventions has been accepted in the clinical domain due to their atraumatic properties. In addition to manual application of fibre-guided lasers with tissue contact, non-contact transoral laser microsurgery (TLM) of laryngeal tumours has been prevailed in ENT surgery. However, TLM requires many years of surgical training for tumour resection in order to preserve the function of adjacent organs and thus preserve the patient’s quality of life. The positioning of the microscopic laser applicator outside the patient can also impede a direct line-of-sight to the target area due to anatomical variability and limit the working space. Further clinical challenges include positioning the laser focus on the tissue surface, imaging, planning and performing laser ablation, and motion of the target area during surgery. This dissertation aims to address the limitations of TLM through robotic approaches and intraoperative assistance. Although a trend towards minimally invasive surgery is apparent, no highly integrated platform for endoscopic delivery of focused laser radiation is available to date. Likewise, there are no known devices that incorporate scene information from endoscopic imaging into ablation planning and execution. For focusing of the laser beam close to the target tissue, this work first presents miniaturised focusing optics that can be integrated into endoscopic systems. Experimental trials characterise the optical properties and the ablation performance. A robotic platform is realised for manipulation of the focusing optics. This is based on a variable-length continuum manipulator. The latter enables movements of the endoscopic end effector in five degrees of freedom with a mechatronic actuation unit. The kinematic modelling and control of the robot are integrated into a modular framework that is evaluated experimentally. The manipulation of focused laser radiation also requires precise adjustment of the focal position on the tissue. For this purpose, visual, haptic and visual-haptic assistance functions are presented. These support the operator during teleoperation to set an optimal working distance. Advantages of visual-haptic assistance are demonstrated in a user study. The system performance and usability of the overall robotic system are assessed in an additional user study. Analogous to a clinical scenario, the subjects follow predefined target patterns with a laser spot. The mean positioning accuracy of the spot is 0.5 mm. Finally, methods of image-guided robot control are introduced to automate laser ablation. Experiments confirm a positive effect of proposed automation concepts on non-contact laser surgery.Die Anwendung von Lasertechnologien in chirurgischen Interventionen hat sich aufgrund der atraumatischen Eigenschaften in der Klinik etabliert. Neben manueller Applikation von fasergeführten Lasern mit Gewebekontakt hat sich die kontaktfreie transorale Lasermikrochirurgie (TLM) von Tumoren des Larynx in der HNO-Chirurgie durchgesetzt. Die TLM erfordert zur Tumorresektion jedoch ein langjähriges chirurgisches Training, um die Funktion der angrenzenden Organe zu sichern und damit die Lebensqualität der Patienten zu erhalten. Die Positionierung des mikroskopis chen Laserapplikators außerhalb des Patienten kann zudem die direkte Sicht auf das Zielgebiet durch anatomische Variabilität erschweren und den Arbeitsraum einschränken. Weitere klinische Herausforderungen betreffen die Positionierung des Laserfokus auf der Gewebeoberfläche, die Bildgebung, die Planung und Ausführung der Laserablation sowie intraoperative Bewegungen des Zielgebietes. Die vorliegende Dissertation zielt darauf ab, die Limitierungen der TLM durch robotische Ansätze und intraoperative Assistenz zu adressieren. Obwohl ein Trend zur minimal invasiven Chirurgie besteht, sind bislang keine hochintegrierten Plattformen für die endoskopische Applikation fokussierter Laserstrahlung verfügbar. Ebenfalls sind keine Systeme bekannt, die Szeneninformationen aus der endoskopischen Bildgebung in die Ablationsplanung und -ausführung einbeziehen. Für eine situsnahe Fokussierung des Laserstrahls wird in dieser Arbeit zunächst eine miniaturisierte Fokussieroptik zur Integration in endoskopische Systeme vorgestellt. Experimentelle Versuche charakterisieren die optischen Eigenschaften und das Ablationsverhalten. Zur Manipulation der Fokussieroptik wird eine robotische Plattform realisiert. Diese basiert auf einem längenveränderlichen Kontinuumsmanipulator. Letzterer ermöglicht in Kombination mit einer mechatronischen Aktuierungseinheit Bewegungen des Endoskopkopfes in fünf Freiheitsgraden. Die kinematische Modellierung und Regelung des Systems werden in ein modulares Framework eingebunden und evaluiert. Die Manipulation fokussierter Laserstrahlung erfordert zudem eine präzise Anpassung der Fokuslage auf das Gewebe. Dafür werden visuelle, haptische und visuell haptische Assistenzfunktionen eingeführt. Diese unterstützen den Anwender bei Teleoperation zur Einstellung eines optimalen Arbeitsabstandes. In einer Anwenderstudie werden Vorteile der visuell-haptischen Assistenz nachgewiesen. Die Systemperformanz und Gebrauchstauglichkeit des robotischen Gesamtsystems werden in einer weiteren Anwenderstudie untersucht. Analog zu einem klinischen Einsatz verfolgen die Probanden mit einem Laserspot vorgegebene Sollpfade. Die mittlere Positioniergenauigkeit des Spots beträgt dabei 0,5 mm. Zur Automatisierung der Ablation werden abschließend Methoden der bildgestützten Regelung vorgestellt. Experimente bestätigen einen positiven Effekt der Automationskonzepte für die kontaktfreie Laserchirurgie

Motion Planning

Motion planning is a fundamental function in robotics and numerous intelligent machines. The global concept of planning involves multiple capabilities, such as path generation, dynamic planning, optimization, tracking, and control. This book has organized different planning topics into three general perspectives that are classified by the type of robotic applications. The chapters are a selection of recent developments in a) planning and tracking methods for unmanned aerial vehicles, b) heuristically based methods for navigation planning and routes optimization, and c) control techniques developed for path planning of autonomous wheeled platforms

Bounds on distance measures in graphs and altered graphs

Abstract: Please refer to full text to view abstract.D.Phil. (Mathematics and Applied Mathematics