Geometry optimization is a fundamental step in the numerical modelling of chemical reactions. Many thermodynamic and kinetic properties are closely related to the structure of the reactant, product, and the transition states connecting them. Different from the reaction and product, which are local minima on the potential energy surface, a transition state is the first-order saddle point with only one negative curvature. Over years, many methods have been devised to tackle the problem. Locating stable structures is relatively easy with a reliable algorithm and high accuracy. One can follow the gradient descent direction to pursuit the local minimum until convergence is reached. But for the transition state, the determination is more challenging as either the up-hill or down-hill direction is allowed in the process. Motivated by the difficulty, many well-designed optimization algorithms are elaborated specifically to stress the problem. The performance of geometry optimization is affected by various aspects: the initial guess structure, the coordinate system representing the molecule, the accuracy of the initial Hessian matrix, the Hessian update schemes, and the step-size control of each iteration. In this thesis, we propose a new geometry optimization algorithm considering all the important components. More specifically, in Chapter 2, a new set of robust dihedral and redundant internal coordinates is introduced to effectively represent the molecular structures, as well as a computational efficient transformation method to generate a guess structure. In Chapter 3 and 5, a sophisticated robust algorithm is presented and tested to solve intricate transition state optimization problems. In Chapter 4, a new algorithm to exploring reaction pathways based on redundant internal coordinates is illustrated with real chemical reactions. Last but not least, in Chapter 6, a systematic test to explore the optimal methods in each procedure is presented. A well-performed combination of optimization methods is drawn for generic optimization purposes. All the methods and algorithms introduced in this thesis is included in our forth-coming open-source Python package named GOpt. It's a general-purpose library that can work in conjunction with major quantum chemistry software including Gaussian. More features are under development and await to be released in the coming update. / Thesis / Doctor of Science (PhD)

This dissertation addresses the problem of approximating, in floating-point arithmetic, all real roots (simple, clustered, and multiple) over the unit interval of polynomials in Bernstein form with real coefficients.

As surprising as it may seem, accurate north finding, with an error of only several milli-radian, is still a very difficulttask and has been achieved only with very expensive systems. On the contrary, there are very simple systems that give theazimuth with an angular error five times superior but for a price a hundred times inferior. Moreover, these systems generally arenon-autonomous (i.e. they are environment dependent and can lose their precision in many situations). This assessment leads tothe following relevant question: Is it possible to design a north finding system with good precision, for a moderated cost and thatworks in any situation?This report presents and evaluates a solution which attempts to answer this problem. This solution is based on a gyrocompassingprinciple: a gyro measures the earth’s angular velocity in order to find the azimuth. This solution can be implementedfollowing several methods, this report presents and compares two of these implementations: Maytagging and Carouseling. Thecomparison is made thanks to a theoretical study, a computer simulation and tests on a real model designed for this report.Carouseling allows us, in theory, to reach an accurate azimuth, but puts mechanical constraints on the system. Maytaggingimplementation seems adapted considering trade-off between precision and cost. Further improvements on gyros will certainlymake systems based on gyro-compassing the most efficient autonomous systems for north finding.In this report, precisions reached by the different implementations are not made explicit for confidentiality reasons.

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Tensegrity structures consist of isolated compression members (rigid bars) suspended by a continuous network of tension members (cables). Tensegrity structures can be used as variable geometry truss (VGT) mechanisms by actuating links to change their length. This paper will present a new method of position finding for tensegrity structures that can be used for actuation as VGT mechanisms. Tensegrity structures are difficult to understand and mathematically model. This difficulty is primarily because tensegrity structures only exist in specific stable tensegrity positions. Previous work has focused on analysis based on statics, dynamics, and virtual work approaches. This work considers tensegrity structures from a kinematic viewpoint. The kinematic approach leads to a better understanding of the conditions under which tensegrity structures exist in the stable positions. The primary understanding that comes from this kinematic analysis is that stable positions for tensegrity structures exist only on the boundaries of nonassembly of the structure. This understanding also allows the tensegrity positions to be easily found. This paper presents a method of position finding based on kinematic constraints and applies that method to several example tensegrity structures. / Master of Science

The Range Limited Antenna (RLA) has the ability to track and pin-point RF devices operating within a certain accepted range. Using two antenna arrays, each made up of several elements, direction-finding algorithms such as MUSIC and Modified Root Pisarenko (MRP) are used to estimate the angles of arrival of incoming signals. Using the estimated angles of arrival, a range estimation algorithm is used to estimate the distance of the emitter from the antenna array. The aim of this thesis is to check the sensitivity of the range estimation and to form a statistical analysis for such conditions. Conditions of error are introduced into the system and several extensive Monte Carlo simulations are run for both MUSIC and MRP. Upon simulating physical errors in the antenna set-up, it is realized that the range estimation algorithm is sensitive to the slightest of phase shift differences, cable loss differences, mixer mismatches, and antenna mismatches. / Master of Science

We have created an eight-element antenna array system for evaluating various Angle of Arrival (AOA) Position Location (PL) algorithms, such as MUltiple SIgnal Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance Techniques ESPRIT algorithms. Since using delay of arrival information can improve AOA estimates and classical PL algorithms do not incorporate Delay of Arrival (DOA) information, the performance of these algorithms is not optimal. Recently proposed Joint AOA and DOA Estimation (JADE) algorithms, though more complicated, potentially have higher resolutions in both space and time domains. Our investigation shows that by using bandlimited known signals it is possible to resolve the DOA within a fraction of the sample period using JADE algorithms. Joint AOA and DOA algorithms can provide high resolution DSP-based channel measurement using low bandwidth hardware. / Master of Science

This PhD Thesis has been immersed in investigating the holistic experience of way-finding in buildings by people who have a range of visual ability. Previous research studies, spanning across a broad spectrum of disciplines, have focused on various characteristics of human way-finding (Arthur and Passini, 1992;Lynch, 1960;Downs and Stea, 1973). It is specifically recognised that the built environment is failing people with visual loss (Barker et al., 1995) and the strategic task and skill of way-finding within a building is a particular problem (Arthur and Passini, 1992). Under the social model of disability (Oliver, 1990) this is recognised as a form of architectural disablement (Goldsmith, 1997). There are few evidence-based studies of way-finding in a building. Furthermore, there are no studies of real-life experiences of way-finding undertaken by real-life participants who have a range of visual ability within the context of a real-life building. This leads to a research question: What are the design issues revealed by participants who have a range of visual ability as they way-find in a large public building? This doctoral research, based within the discipline of architecture, focuses on the holistic experiential components of a Journey (Myerson, 2001;Harper and Green, 2000). It coins and defines the term Way-finding Hot-spot as it explores the events [positive and negative] which are experienced and therefore impact on a Way-finding Journey around a building. To fill an important gap in the current knowledge a research enquiry, based on a user-centred design approach, was implemented. Exploratory in nature, the methodology was inductive and it evolved throughout the study. A series of Research Principles, borrowed from the established methodologies of Grounded Theory (Glaser, 1968) and Case Study (Yin, 2003a;Yin, 2003b), guided this study. Ten participants [with varying degrees of visual ability, different ages and other forms of disability] undertook a Way-finding Scenario designed to evaluate both existing memories of way-finding and present way-finding experience. This was composed of a Purposeful Conversation (Burgess, 1982) and a context specific Way-finding Task. The study has produced a large amount of data based on user experience in a real-world way-finding context – this has not been done before. Participant data contributed to a new Theory of Way-finding – The Experiential Charting of a Way-finding Journey – which derived from experiential data, was found to be composed of three elements: Journey Stages, Tasks Components and Communication Requirements. This thesis presents detailed findings which generate dialogue in the design of way-finding systems suitable for a diverse range of way-finders. It provides a research-based foundation to open the problem area and provide an insight into the issues people with different visual abilities encounter as they undertake a Way-finding Journey around a building. It generates a greater understanding of the problems and joys of way-finding in a building which will be of use in professional practice across disciplines of architecture and design as well as in areas of rehabilitation, policy-making and academia. This research is a start, but it is not the end. Future research questions have been revealed and these, combined with further reviews of literature and creative use of method, will further explore the phenomenon of way-finding within the context of buildings.

Passive wireless sensor networks (WSNs) are quickly becoming popular for many applications such as article tracking, position location, temperature sensing, and passive data storage. Passive tags and sensors are unique in that they collect their electrical energy by harvesting it from the ambient environment. Tags with charge pumps collect their energy from the signal they receive from the transmitting source. The efficiency of converting the received signal to DC power is greatly enhanced using a power-optimized waveform (POW). Measurements in the first part of this dissertation show that a POW can provide efficiency gains of up to 12 dB compared to a sine-wave input. Tracking the real-time location of these passive tags is a specialized feature used in some applications such as animal tracking. A passive WSN that uses POWs for the improvement of energy-harvesting may also estimate the range to a tag by measuring the time delay of propagation from the transmitter to the tag and back to the transmitter. The maximum-likelihood (ML) estimator is used for estimating this time delay, which simplifies to taking the cross-correlation of the received signal with the transmitted signal. This research characterizes key aspects of performing range estimations in passive WSNs using POWs. The shape of the POW has a directly-measurable effect on ranging performance. Measurements and simulations show that the RMS bandwidth of the waveform has an inversely proportional relationship to the uncertainty of a range measurement. The clutter of an environment greatly affects the uncertainty and bias exhibited by a range estimator. Random frequency-selective environments with heavy clutter are shown to produce estimation uncertainties more than 20 dB higher than the theoretical lower bound. Estimation in random frequency-flat environments is well-behaved and fits the theory quite nicely. Nonlinear circuits such as the charge pump distort the POW during reflection, which biases the range estimations. This research derives an empirical model for predicting the estimation bias for Dickson charge pumps and verifies it with simulations and measurements.