This thesis is centered upon the published A Novel Method and Exoskeletons for Whole-arm Gravity Compensation (Turner, Hull 2020), and includes a novel concept for supporting the weight of a person's arm or robotic linkage. The design is capable of supporting weights held near the hand, and provides support regardless of position. This support is provided with a pantograph. The upper-arm and forearm bars are mirrored by smaller copies. Force applied to a pull point on the scaled copy of the arm is flipped and applied at a support point on the forearm or to a tool near the hand. Two exoskeletons, using different linkages make use of the pantograph design. These include the Panto-Arm Exo, which uses it's slim, reduced size to comfortably assist users in lifting their arm, and the Panto-Tool Exo which is designed for a support point that coincides with a mass representing a heavy tool. The differing topologies and purposes of these two devices resulted in different qualities regarding their ability to lift weight. The Panto-Arm Exo was specifically used in human subject testing, in which fourteen users wore electromyography electrodes and performed simple arm movements and holding tasks. While the Panto-Arm Exo did not undergo stringent design improvements or user-specific optimization, the device was shown to reduce muscle use in the measured upper-arm muscles for certain arm positions. / Master of Science / This thesis is centered upon the published A Novel Method and Exoskeletons for Whole-arm Gravity Compensation (Turner, Hull 2020), includes a new way to lift a person's arm or robotic linkage. The design can lift weights close to the hand regardless of arm placement. This support is provided with a pantograph. The pantograph design is based on a mirrored, smaller copy of the upper-arm and forearm bars, which is pulled downwards to create an upwards support force at chosen support point. This point is based underneath the forearm or at a heavy tool. The concept is similar to pushing down on a teeter-totter in order to prevent the other end from dropping. Two exoskeletons, using different linkages make use of this pantograph design. The Panto-Arm Exo is slim and light. It is made to help users in lift their arm by supporting its weight. The Panto-Tool Exo has a support point that located where a mass representing a heavy tool sits. The changes between both devices means that they display different lifting qualities. The Panto-Arm Exo was worn by 14 people, also wearing electrodes that measured muscle activation. These users held weights and moved their arms around while muscle activation was recorded. While the Panto-Arm Exo wasn't fine-tuned or adjusted for individual people, it was shown to reduce muscle activation in the measured upper-arm muscles for some of the arm placements.

We present and analyze two arm exoskeletons based on a pantograph linkage that allow for the support of 89~N (20~pounds) at the user's hand. Using a pantograph linkage allows for a constant force to be created at the hand in any orientation when a constant vertical force is supplied to the other side of the pantograph. We present several topologies and analyze them based on feasibility of manufacture and ability to provide a near vertical force to the pantograph linkage. Simulations are created using the best topologies and the resulting forces at the hand are reported. The mechanical design of an unpowered (passive) exoskeleton which uses a gas spring mechanism is presented. Additionally, simulations and block-CAD of a powered (active) exoskeleton which uses a motor for the supply of force are presented. The performance of the passive exoskeleton is qualitatively compared with simulations. / Master of Science / A wearable device or exoskeleton is presented which is designed to help a user support a weight of 20 pounds (89~N) at their hand. A pantograph linkage arm exoskeleton provides forces to the hand which are equal to the force provided to the linkage divided by the linkage's ratio. Providing a force to the linkage that is purely vertical will result in a purely vertical force at the hand. Layouts of the exoskeleton components which produce a near-vertical force for the linkage are explored. The more promising layouts are simulated and the forces are compared based on how vertical the forces are. The design of an unpowered exoskeleton is also presented, which uses a gas spring mechanism to provide force. Additionally, simulation results for the unpowered exoskeleton and the basic design and analysis of a powered exoskeleton are presented.

This thesis is embodied by the design of a new gravity flow winery on the eastern slopes of the Blue Ridge Mountains in Northern Virginia. The 100 acre site is home to an existing winery with grape vines aged over a decade. From its initial inception, this thesis has been in part a response to the rapidly growing wine industry in Virginia and the typical ad hoc architecture associated with the wineries serving the state. The swelling interest in the culture of wine has sparked an evolution of the role of wineries. The winery of today is both an establishment for the production of wine as well as a venue for the enjoyment of its product and the delight of its natural setting. Creating a dialogue between site and visitor via thoughtful engagement of earth, air and sky is key for establishing a sense of place. The winery at the heart of this thesis is the quintessence of these ideals. The architecture of this winery embraces the steps of gravity flow winemaking, which aims to preserve the integrity of the grapes by utilizing gravity instead of electric pumps. The design seeks to make these steps perceivable and understandable, taking a visitor from the wind swept heights of the mountainside to the cool air of the winery's subterranean vaults and back again. From vine to glass and from layperson to student of wine, this shared journey engenders a transformation of both grape and visitor. / Master of Architecture / This thesis is embodied by the design of a new gravity flow winery on the eastern slopes of the Blue Ridge Mountains in Northern Virginia. The 100 acre site is home to an existing winery with grape vines aged over a decade. From its initial inception, this thesis has been a response and possible solution to the rapidly growing wine industry in Virginia and the typical ad hoc architecture--which is to say additions are made without acknowledging or responding to the existing buildings--associated with the wineries serving the state. The winery of today is both an establishment for the production of wine as well as a venue for the enjoyment of its product and the delight of its natural setting. Creating a dialogue between site and visitor via thoughtful engagement of earth, air and sky is key for establishing a sense of place. The winery at the heart of this thesis is the quintessence of these ideals. The architecture of this winery embraces the steps of gravity flow winemaking, which aims to preserve the integrity of the grapes by utilizing gravity instead of electric pumps. The design seeks to make these steps perceivable and understandable, taking a visitor from the wind swept heights of the mountainside to the cool air of the winery’s subterranean vaults and back again. From vine to glass and from layperson to student of wine, this shared journey engenders a transformation of both grape and visitor.

This thesis concerns a range of aspects of theoretical physics. It is composed of two parts. In the first part we motivate our line of research, and introduce and discuss the relevant concepts. In the second part, four research papers are collected. The first paper deals with a possible extension of general relativity, namely the recently discovered classically consistent bimetric theory. In this paper we study the behavior of perturbations of the metric(s) around cosmologically viable background solutions. In the second paper, we explore possibilities for particle physics with low-scale supersymmetry. In particular we consider the addition of supersymmetric higher-dimensional operators to the minimal supersymmetric standard model, and study collider phenomenology in this class of models. The third paper deals with a possible extension of the notion of Lie algebras within category theory. Considering Lie algebras as objects in additive symmetric ribbon categories we define the proper Killing form morphism and explore its role towards a structure theory of Lie algebras in this setting. Finally, the last paper is concerned with the computation of string amplitudes in four dimensional models with reduced supersymmetry. In particular, we develop general techniques to compute amplitudes involving gauge bosons and gravitons and explicitly compute the corresponding three- and four-point functions. On the one hand, these results can be used to extract important pieces of the effective actions that string theory dictates, on the other they can be used as a tool to compute the corresponding field theory amplitudes. / Over the last twenty years there have been spectacular observations and experimental achievements in fundamental physics. Nevertheless all the physical phenomena observed so far can still be explained in terms of two old models, namely the Standard Model of particle physics and the ΛCDM cosmological model. These models are based on profoundly different theories, quantum field theory and the general theory of relativity. There are many reasons to believe that the SM and the ΛCDM are effective models, that is they are valid at the energy scales probed so far but need to be extended and generalized to account of phenomena at higher energies. There are several proposals to extend these models and one promising theory that unifies all the fundamental interactions of nature: string theory. With the research documented in this thesis we contribute with four tiny drops to the filling of the fundamental physics research pot. When the pot will be saturated, the next fundamental discovery will take place.

The phenomenon of scale dependent spectral dimension has attracted special interest in the quantum gravity community over the last eight years. It was first observed in computer simulations of the causal dynamical triangulation (CDT) approach to quantum gravity and refers to the reduction of the spectral dimension from 4 at classical scales to 2 at short distances. Thereafter several authors confirmed a similar result from different approaches to quantum gravity. Despite the contribution from different approaches, no analytical model was proposed to explain the numerical results as the continuum limit of CDT. In this thesis we introduce graph ensembles as toy models of CDT and show that both the continuum limit and a scale dependent spectral dimension can be defined rigorously. First we focus on a simple graph ensemble, the random comb. It does not have any dynamics from the gravity point of view, but serves as an instructive toy model to introduce the characteristic scale of the graph, study the continuum limit and define the scale dependent spectral dimension. Having defined the continuum limit, we study the reduction of the spectral dimension on more realistic toy models, the multigraph ensembles, which serve as a radial approximation of CDT. We focus on the (recurrent) multigraph approximation of the two-dimensional CDT whose ensemble measure is analytically controlled. The latter comes from the critical Galton-Watson process conditioned on non-extinction. Next we turn our attention to transient multigraph ensembles, corresponding to higher-dimensional CDT. Firstly we study their fractal properties and secondly calculate the scale dependent spectral dimension and compare it to computer simulations. We comment further on the relation between Horava-Lifshitz gravity, asymptotic safety, multifractional spacetimes and CDT-like models.

This thesis is aimed at extending the spherical barotropic contour-advective semi-Lagrangian (CASL) Algorithm, written in 1996 by David Dritschel and Maarten Ambaum, to more complex test cases within the shallow-water context. This is an integral part for development of any numerical model and the accuracy obtained depends on many factors, including knowledge of the initial state of the atmosphere or ocean, the numerical methods applied, and the resolutions used. The work undertaken throughout this thesis is highly varied and produces important steps towards creating a versatile suite of programs to model all types of flow, quickly and accurately. This, as will be explained in later chapters, impacts both public safety and the world economy, since much depends on accurate medium range forecasting. There shall be an investigation of a series of tests which demonstrate certain aspects of a dynamical system and its progression into more unstable situations - including the generation and feedback of freely propagating inertia-gravity waves (hereafter “gravity waves"), which transmit throughout the system. The implications for increasing forecast accuracy will be discussed. Within this thesis two main CASL algorithms are outlined and tested, with the accuracy of the results compared with previous results. In addition, other dynamical fields (besides geopotential height and potential vorticity) are analysed in order to assess how well the models deal with gravity waves. We shall see that such waves are sensitive to the presence, or not, of sharp potential vorticity gradients, as well as to numerical parameter settings. In particular, large time-steps (convenient for semi-Lagrangian schemes) may not only seriously affect gravity waves, but may also have an adverse impact on the primary fields of height and velocity. These problems are exacerbated by a poor resolution of potential vorticity gradients, which we shall attempt to improve.

published_or_final_version / Applied Geosciences / Master / Master of Science

In the first part of this thesis, we study the duality of Wilson loops and M2-branes in AdS₄/CFT₃. We focus on supersymmetric M-theory solutions on AdS₄xY₇ that have a superconformal dual description on S³ = ?AdS⁴. We will find that the Hamiltonian function h_M for the M-theory circle plays an important role in the duality. We show that an M2-brane wrapping the M-theory circle is supersymmetric precisely at the critical points of h_M, and moreover the value of this function at those points determines the M2-brane actions. Such a configuration determines the holographic dual of a Wilson loop for a Hopf circle in S³. We find agreement in large classes of examples between the Wilson loop and its dual M2-brane and also that the image h_M(Y₇) determines the range of support of the eigenvalues in the dual large N matrix model, with the critical points of h_M mapping to points where the derivative of the eigenvalue density is discontinuous. We will then move away from the three-sphere and construct gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localisation. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories defined on a general class of background three-manifold geometries. To further verify that our gravitational backgrounds are indeed dual to field theories on their boundaries, we compute Wilson loops and their M2-brane duals in this general setting. We find that the Wilson loop is given by a simple closed formula which depends on the background geometry only through the supersymmetric Killing vector field. The supergravity dual M2-brane precisely reproduces this large N field theory result. This constitutes a further check of AdS₄/CFT₃ for a very broad class of examples.

A Província Alcalina Rio Verde - Iporá, na borda norte da Bacia do Paraná é caracterizada pela presença de intrusões alcalinas com forte assinatura aeromagnética e gravimétrica, apresentando-se como anomalias quase circulares. O trabalho refinou o levantamento gravimétrico na região sudoeste de Goiás, incluindo um levantamento de detalhe sobre as intrusões de Morro do Engenho (ME) e uma intrusão a poucos quilômetros a NE de Morro de Engenho (A2), com informações gravimétricas e aeromagnéticas, e sobre a anomalia gravimétrica próxima à cidade de Britânia, sem informação de anomalia aeromagnética. As anomalias gravimétricas variam de 15 a 30 mGal com relação ao campo gravimétrico regional, enquanto que as anomalias aeromagnéticas são da ordem de ±3000nT. Foram feitas também medidas das propriedades petrofísicas de amostras da área. Os resultados da inversão 2D e 3D dos dados gravimétricos e 3D dos dados magnéticos indicam que os corpos alongam-se dentro da crosta superior até a profundidade máxima de 10 km e diâmetro da ordem de 8 km, com geometria aproximadamente cilíndrica. Os dados gravimétricos e aeromagnéticos de ME foram tratados de forma conjunta por modelamento direto (2,5D) onde foi incluída a magnetização remanescente, os resultados obtidos indicam que o volume do corpo anômalo é da ordem de 980 km3. / The Alkaline Province Rio Verde - Iporá, in the north border of the Paraná Basin is characterized by the presence of alkaline intrusions with strong gravity and magnetic signature. This project implemented a gravity survey in the Southwest of Goiás, including a detail one on Morro do Engenho Complex (ME), and one a few kilometers towards NE from ME over an aeromagnetic anomaly known as A2, and over a gravity anomaly close to Britânia city. ME and A2 have magnetic anomaly. The gravity anomalies vary from 15 to 30 mGal in relation to the regional gravity field, while the magnetic anomalies are of the order ±3000nT. Measurements of petrophysical properties of samples from the area were also done. The results present the inversion of the gravity and magnetic data, suggesting that the bodies are inside of the superior crust until the maximum depth of 10 km, in a cylindrical form with 8 to 10 km in diameter. 2.5D direct modeling was also done for ME including remanent magnetization and was performed at the two data sets together, the obtained results indicate that the close volume of the anomalous body it is 980 km3.

Exact solutions to the Einstein field equations are notoriously difficult to find. Most known solutions describe systems with unrealistically high degrees of symmetry. A notable example is the FLRW metric underlying modern cosmology: the universe is assumed to be perfectly homogeneous and isotropic, but in the late universe, this is only true on average and only at large scales. Where an exact solution is not available, discrete gravitational approaches can approximate the system instead. This thesis investigates several cosmological systems using two distinct discrete approaches. Closed, flat, and open ‘lattice universes’ are first considered where matter is distributed as a regular lattice of identical point masses in constant-time hypersurfaces. Lindquist and Wheeler’s Schwarzschild–cell method is applied where the lattice cell around each mass is approximated by a perfectly spherical cell with Schwarzschild space–time inside. The resulting dynamics and cosmological redshifts closely resemble those of the dust-filled FLRW universes, but with certain differences in redshift behaviour attributable to the lattice universe’s lumpiness. The application of Regge calculus to cosmology is considered next. We focus exclusively on the closed models developed by Collins, Williams, and Brewin. Their approach is first applied to a universe where an exact solution is already well-established, the vacuum Λ-FLRW model. The resulting models are found to closely reproduce the dynamics of the continuum model being approximated, though certain constraints on the applicability of the approach are also uncovered. Then using this knowledge, we next model the closed lattice universe. The resulting evolution closely resembles that of the closed dust-filled FLRW universe. Constraints on the placement of the masses in the Regge skeleton are also uncovered. Finally, a ‘lattice universe’ with one perturbed mass is modelled. The evolution is still stable and similar to that of the unperturbed model. The thesis concludes by discussing possible extensions of our work.