[pt] Quando se analisa a distribuição de tensões e de formações em tubos cilíndricos circulares submetidos à pressão interna ou externa, resultados são facilmente encontrados; se o tubo for considerado de comprimento infinito e a pressão uniformemente distribuída ao longo de todo o seu comprimento. Neste caso, o estado de tensões pode ser considerado plano. Entretanto se o tubo for infinito e a pressão estiver aplicada em parte de seu comprimento, o estado de tensões deverá ser estudado com tridimensional. Advém daí uma maior complexibilidade do problema, acarretando soluções matemáticas bastante elaboradas. Uma solução para cilindros circulares de comprimento foi desenvolvida neste trabalho. Nos casos analisados, o carregamento constitui em um anel de pressão uniforme, interna ou externa, aplicado simetricamente em relação à secção transversal média do tubo. Procura-se assinalar a importância que assume a tensão axial para certas dimensões do tubo e posição do carregamento. Indicou-se também a discrepância existente entre os valores calculados, considerando o problema como plano e como tridimensional. Os resultados gráficos mostram as distribuições de tensão na secção transversal média referentes a cilindros curtos de parede espessa com razões entre dinâmico interno e comprimento de .. 0,25, 0,50, e 0,75 e com razões entre comprimento do anel de pressão e do tubo de 0,5 e 1,0, embora outras relações tenham sido estudadas. Devido à solução encontrada, as condições de fronteira incluem flanges nas extremidades do tubo, exercendo tensões cisalhantes sobre as secções transversais externas e tendo características de flexibilidade às deformações axiais e rigidez às deformações radias. Muitos problemas de computação surgiram na obtenção dos resultados numéricos, tais como as limitações nas sub-rotinas usadas no cálculo das funções de Beesel. A resolução do problema para o caso de tubos com extremidades livres pode ser alcançada através da utilização de métodos matemáticos mais sofisticados. / [en] Stress and strain distributions on circular hollow cylindres, can easily be found for infinite length and uniform surface pressure. In such case, for a finite length, the stress-state must be considered triaxial. Thus, involving more elaborate mathematical solutions. A solution to the finite circular hollow cylinder problem is developed in this thesis. In all the cases that were analyzed external load consisted of a uniform pressure ring applied to the external or internal cylinder surfaces. This load was applied symmetrically with respect to the midle transverse section of the tube. The importance assumed by the axial component of stress under certain conditions of stress under certain conditions of tube geometry and external load positions is analyzed. Bisagreement between determined values of stress, whe considered as biaxial or triaxial independently, is also shown. Graphs of stress distribution on the middle transverse section of short thick walled cylinders are presented for internal diamenter and tube length ratios of 0.25, 0,50, and 0,75 and pressure ring and tube length rations of 0,5 and 1,0, although other of end flanges having caracteristics of infinite flexibility for axial deformations and infinite stiffness for radial deformations. Many computational problems arose when obtaining numerical results, such as limitations in the subroutines udes for evaluation of Bessel functions. Also, for the case of free end tubes more sophisticated mathematical methods must be applied. These troubles can be overcome throungh more advanced studies of the problem.

A CFD model to simulate two-phase flow in refrigerant ejectors is described. This work is part of an effort to develop the ejector expansion refrigeration cycle, a device which increases performance of a standard vapor compression cycle by replacing the throttling valve with a work-producing ejector. Experimental results have confirmed the performance benefit of the ejector cycle, but significant improvement can be obtained by optimally designing the ejector. The poorly understood two-phase, non-equilibrium flow occuring in the ejector complicates this task. The CFD code is based on a parabolic two-fluid model. The applicable two-phase flow conservation equations are presented. Also described are the interfacial interaction terms, important in modelling non-equilibrium effects. Other features of the code, such as a mixing length turbulence model and wall function approximation, are discussed. Discretization of the equations by the control volume method and organization of the computer program is described. Code results are shown and compared to experimental data. It is shown that experimental pressure rise through the mixing section matches well against code results. Variable parameters in the code, such as droplet diameter and turbulence constants, are shown to have a large influence on the results. Results are shown in which an unexpected problem, separation in the mixing section, occurs. Also described is the distribution of liquid across the mixing section, which matches qualitative experimental observations. From these results, conclusions regarding ejector design and two-phase CFD modelling are drawn. / Ph. D.

Non-equilibrium systems have no set method of analysis, and a wide array of dynamics can be present in such systems. In this work we present three very different non-equilibrium models, inspired by biological systems and phenomena, that we analyze through computational means to showcase both the range of dynamics encompassed by these systems, as well as various techniques used to analyze them. The first system we model is a surface plasmon resonance (SPR) cell, a device used to determine the binding rates between various species of chemicals. We simulate the SPR cell and compare these computational results with a mean-field approximation, and find that such a simplification fails for a wide range of reaction rates that have been observed between different species of chemicals. Specifically, the mean-field approximation places limits on the possible resolution of the measured rates, and such an analysis fails to capture very fast dynamics between chemicals. The second system we analyzed is an avalanching neural network that models cascading neural activity seen in monkeys, rats, and humans. We used a model devised by Lombardi, Herrmann, de Arcangelis et al. to simulate this system and characterized its behavior as the fraction of inhibitory neurons was changed. At low fractions of inhibitory neurons we observed epileptic-like behavior in the system, as well as extended tails in the avalanche strength and duration distributions, which dominate the system in this regime. We also observed how the connectivity of these networks evolved under the effects of different inhibitory fractions, and found the high fractions of inhibitory neurons cause networks to evolve more sparsely, while networks with low fractions maintain their initial connectivity. We demonstrated two strategies to control the extreme avalanches present at low inhibitory fractions through either the random or targeted disabling of neurons. The final system we present is a sparsely encoding convolutional neural network, a computational system inspired by the human visual cortex that has been engineered to reconstruct images inputted into the network using a series of "patterns" learned from previous images as basis elements. The network attempts to do so "sparsely," so that the fewest number of neurons are used. Such systems are often used for denoising tasks, where noisy or fragmented images are reconstructed. We observed a minimum in this denoising error as the fraction of active neurons was varied, and observed the depth and location of this minimum to obey finite-size scaling laws that suggest the system is undergoing a second-order phase transition. We can use these finite-size scaling relations to further optimize this system by tuning it to the critical point for any given system size. / Doctor of Philosophy / Non-equilibrium systems have no set method of analysis, and a wide array of dynamics can be present in such systems. In this work we present three very different non-equilibrium models, inspired by biological systems and phenomena, that we analyze through computational means to showcase both the range of dynamics encompassed by these systems, as well as various techniques used to analyze them. The first system we model is a surface plasmon resonance (SPR) cell, a device used to determine the binding rates between various species of chemicals. We simulate the SPR cell and compare these computational results with a mean-field approximation, and find that such a simplification fails for a wide range of reaction rates that have been observed between different species of chemicals. Specifically, the mean-field approximation places limits on the possible resolution of the measured rates, and such an analysis fails to capture very fast dynamics between chemicals. The second system we analyzed is an avalanching neural network that models cascading neural activity seen in monkeys, rats, and humans. We used a model devised by Lombardi, Herrmann, de Arcangelis et al. to simulate this system and characterized its behavior as the fraction of inhibitory neurons was changed. At low fractions of inhibitory neurons we observed epileptic-like behavior in the system, as well as extended tails in the avalanche strength and duration distributions, which dominate the system in this regime. We also observed how the connectivity of these networks evolved under the effects of different inhibitory fractions, and found the high fractions of inhibitory neurons cause networks to evolve more sparsely, while networks with low fractions maintain their initial connectivity. We demonstrated two strategies to control the extreme avalanches present at low inhibitory fractions through either the random or targeted disabling of neurons. The final system we present is a sparsely encoding convolutional neural network, a computational system inspired by the human visual cortex that has been engineered to reconstruct images inputted into the network using a series of “patterns” learned from previous images as basis elements. The network attempts to do so “sparsely,” so that the fewest number of neurons are used. Such systems are often used for denoising tasks, where noisy or fragmented images are reconstructed. We observed a minimum in this denoising error as the fraction of active neurons was varied, and observed the depth and location of this minimum to obey finite-size scaling laws that suggest the system is undergoing a second-order phase transition. We can use these finite-size scaling relations to further optimize this system by tuning it to the critical point for any given system size.

In recent years a new interesting research avenue has emerged in non-equilibrium statistical physics, namely studies of collective responses in spatially inhomogeneous systems. Whereas substantial progress has been made in understanding the origins and the often universal nature of cooperative behavior in systems far from equilibrium, it is still unclear whether it is possible to control their global collective stochastic dynamics through local manipulations. Therefore, a comprehensive characterization of spatially inhomogeneous non-equilibrium systems is required. In the first system, we explore a variant of the Katz–Lebowitz–Spohn (KLS) driven lattice gas in two dimensions, where the lattice is split into two regions that are coupled to heat baths with distinct temperatures T > T_c and T_c respectively, where T_c indicates the critical temperature for phase ordering. The geometry was arranged such that the temperature boundaries are oriented perpendicular or parallel to the external particle drive and resulting net current. For perpendicular orientation of the temperature boundaries, in the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. This blockage is induced by extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high- and low-temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_c, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power-law density decay near the interfaces into the cooler region. For parallel orientation of the temperature boundaries, we have explored the changes in the dynamical behavior of the hybrid KLS model that are induced by our choice of the hopping rates across the temperature boundaries. If these hopping rates at the interfaces satisfy particle-hole symmetry, the current difference across them generates a vector flow diagram akin to an infinite flat vortex sheet. We have studied the finite-size scaling of the particle density fluctuations in both temperature regions, and observed that it is controlled by the respective temperature values. If the colder subsystem is maintained at the KLS critical temperature, while the hotter subsystem's temperature is set much higher, the interface current greatly suppresses particle exchange between the two regions. As a result of the ensuing effective subsystem decoupling, strong fluctuations persist in the critical region, whence the particle density fluctuations scale with the KLS critical exponents. However, if both temperatures are set well above the critical temperature, the particle density fluctuations scale according to the totally asymmetric exclusion process. We have also measured the entropy production rate in both subsystems; it displays intriguing algebraic decay in the critical region, while it saturates quickly at a small but non-zero level in the hotter region. The second system is a lattice gas that simulates the spread of COVID-19 epidemics using the paradigmatic stochastic Susceptible-Infectious-Recovered (SIR) model. In our effort to control the spread of the infection of a lattice, we robustly find that the intensity and spatial spread on the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak). / Doctor of Philosophy / In recent years a new interesting research avenue has emerged in far-from-equilibrium statistical physics, namely studies of collective behavior in spatially non-uniform systems. Whereas substantial progress has been made in understanding the origins and the often universal nature of cooperative behavior in systems far from equilibrium, it is still unclear whether it is possible to control their global collective and randomly determined dynamics through local manipulations. Therefore, a comprehensive characterization of spatially non-uniform systems out of equilibrium is required. In the first system, we explore a variant of the two-dimensional lattice gas with completely biased diffusion in one direction and attractive particle interactions. By lattice gas we mean a lattice filled with particles that can hop on nearest-neighbor empty sites. The system we are considering is a lattice that is split into two regions, which in turn are maintained at distinct temperatures T > T_c and T_c, respectively, with T_c indicating the critical temperature for the second-order phase transition. The geometry of the lattice was arranged such that the temperature boundaries are oriented perpendicular or parallel to the external particle drive that is responsible for a completely biased diffusion. When the temperature boundaries are oriented perpendicular to the drive, in the hotter region with temperature T > T_c, the system evolves as if there are no attractive interactions between the particles, and experiences particle blockage in front of the temperature boundary from the hotter region held at T>T_c to the critical region held at T_c. This accumulation of particles at the temperature boundary is induced by elongated collections of particle, i.e., particle clusters in the critical region. We observe the particle density profiles (ρ(x) vs x plots) in both high-and low-temperature subsystems to be similar to the density profiles found for other well-characterized (T)ASEP models with open boundary conditions, which are in the coexistence and maximal-current phases, and which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_c, we detect marked corrections to the hyperbolic and trigonometric tangent-like density profiles due to fluctuations, e.g., we observe the algebraic power-law decay of the density near the interfaces into the cooler region with the critical KLS exponent. For a parallel orientation of the temperature boundaries, we have explored the changes in the particle dynamics of the two-temperature KLS model that are induced by our choice of the particle hopping rates across the temperature boundaries. If these particle hopping rates at the temperature interfaces satisfy particle-hole symmetry (i.e. remain unchanged when particles are replaced with holes and vice versa), the particle current difference across them generates a current vector flow diagram akin to an infinite flat vortex sheet. We have studied how the particle density fluctuations in both temperature regions scale with the system size, and observed that the scaling is controlled by the respective temperature values. If the colder subsystem is maintained at the KLS critical temperature T_cold = T_c, while the hotter subsystem's temperature is set much higher T_hot >> T_c, the particle currents at the interface greatly suppresses particle exchange between the two temperature regions. As a result of the ensuing effective subsystem separation from each other, strong fluctuations persist in the critical region, whence the particle density fluctuations scale with the KLS critical exponents. However, if both temperatures are set well above the critical temperature, the particle density fluctuations scale with different scaling exponents, that fall into the totally asymmetric exclusion process (TASEP) universality class. We have also measured the rate of the entropy production in both subsystems; it displays intriguing algebraic decay in the critical region, while it reaches quickly a small but non-zero value in the hotter region. The second system is a lattice filled with particles of different types that hop around the lattice and are subjected to different sorts of reactions. That process simulates the spread of the COVID-19 epidemic using the paradigmatic random-process-based Susceptible-Infectious-Recovered (SIR) model. In our effort to control the spread of the infection of a lattice, we robustly find that the intensity and spatial spread of the epidemic second wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak).

We investigate the properties of two distinct disordered systems: the two-species predator-prey Lotka-Volterra model with rate variability, and an elastic line model to simulate vortex lines in type-II superconductors. We study the effects of intrinsic demographic variability with inheritance in the reaction rates of the Lotka-Volterra model via zero-dimensional Monte Carlo simulations as well as two-dimensional lattice simulations. Individuals of each species are assigned inheritable predation efficiencies during their creation, leading to evolutionary dynamics and thus population-level optimization. We derive an effective subspecies mean-field theory and compare its results to our numerical data. Furthermore, we introduce environmental variability via quenched spatial reaction-rate randomness. We investigate the competing effects and relative importance of the two types of variability, and find that both lead to a remarkable enhancement of the species densities, while the aforementioned optimization effects are essentially neutral in the densities. Additionally, we collected extinction time histograms for small systems and find a marked increase in the stability of the populations against extinction due to the presence of variability. We employ an elastic line model to investigate the steady-state properties and non-equilibrium relaxation kinetics of magnetic vortex lines in disordered type-II superconductors. To this end, we developed a versatile and efficient Langevin molecular dynamics simulation code, allowing us to do a careful study of samples with or without vortex-vortex interactions or disorder allows us to disentangle the various complex relaxational features present in this system and investigate their origin. In particular, we compare disordered samples with randomly distributed point defects versus correlated columnar defects. We extract two-time quantities such as the mean-square displacement, the height and density correlations, to investigate the relaxation kinetics of the system of flux lines. Additionally, we compare the steady-state mean velocity and gyration radius as a function of an external driving current in the presence of point-like and columnar disorder. We validate our simulation algorithm by matching our results against a previously-used Monte Carlo algorithm, verifying that these microscopically quite distinct methods yield similar results even in out-of-equilibrium settings. / Ph. D.

The purpose of this dissertation was to explore methods for generating neuroplastic changes in healthy individuals using transcutaneous spinal cord stimulation (TSCS) and perturbation-based training in order to improve balance performance. This was done to gain an understanding of their effects on healthy individuals, which could then be used in designing treatments for both healthy and motor-impaired subjects. Three studies were undertaken. First, we set out to show that the Robotic Upright Stand Trainer (RobUST) could generate improvements in balance after perturbation balance training (PBT). In this same study, we showed that the assist-as-needed support of RobUST generates postural control improvements. Balance performance metrics including (i) margin of stability (MOS), (ii) metrics based on the center of pressure (COP) and center of mass (COM) excursions, (iii) postural muscle activations, (iv) balance strategy selection (between ankle and hip strategies) were used in this study. Electromyographic data were also collected from 11 subjects who participated in this study. Subjects were split into a RobUST assisted group (FF) and a non-assisted group (NF). An analysis of variance (ANOVA) was carried out to identify the main effects of the two factors, i.e., training and grouping. We also studied the interaction effects between the two factors in the performance variables. After training, the threshold of the forces that destabilize balance increased for all participants. In addition, the area within which they could withstand perturbations without falling also increased. Muscle activation decreased in most muscles for subjects in both groups indicating that subjects improved balance while demonstrating more energetically efficient strategies. The post-training behavior of the two groups differed in the following way: the NF group adapted towards faster reactions to perturbations, greater use of the hip strategy, and more use of the erector spinae muscle, while the FF group adapted towards slower responses and less MOS. These results show that although balance adaptations with RobUST-assisted PBT are not the same as without RobUST, it is still a platform capable of improving balance performance. Second, the effect of TSCS as a means of boosting neuroplasticity and a replacement for epidural stimulation were tested. Eight subjects were given TSCS for 30 mins while lying supine, and their neurophysiological and balance performance measures were tested before and after the intervention. T-tests were used to assess the difference in performance, and it was found that TSCS caused hypopolarisation of the sensory neurons, which increased the synaptic efficacy of sensory afferent–motoneuron synapses. This change was evidenced by increased H-reflex recovery and a leftward shift of the H-reflex recruitment curve. No improvement in fall frequency was observed, although balance adjustments were made that reduced muscle activity. This experiment showed that TSCS could be used to modulate the excitability of the spinal cord in healthy subjects. Third, TSCS was combined with a training intervention in order to study how these two sources of plasticity interact. TSCS was applied to eleven subjects while they underwent a training intervention in which they played a game in virtual reality (VR) while their balance was perturbed by forces applied by RobUST. Balance characteristics were measured both with and without TSCS, before and after the intervention. It was found that TSCS initially caused an increase in muscle activity and an increase in fall frequency for perturbations in the forward direction. With more practice, though, muscle activity decreased. It was postulated that the CNS adjusted to the initial elevated levels of muscle activity caused by TSCS by suppressing muscle activity in order to ensure successful motor control. These results suggest that TSCS can be used to elevate the resting potential of neurons in the dorsal (close to the back of the body) root, making them more easily excited by cortical signals. These changes induced by TSCS can be beneficial to spinal cord injury patients.

<p> The melt equilibria of the system CaF2-CaMgSi2O6 has been studied at atmospheric pressure by using a modified quenching method. This system is characterized by a simple binary eutectic at CaF2 43.4, CaMgSi2O6 56.5 weight percent at 1082t 2°C; neither solid solution nor intermediate compound was found. Some special features have been discussed in detail. The results of the study of the system CaF2-CaMgSi2O6, together with suppositions regarding the system CaF2-CaMgSi2O6-CaCO3, have tentatively been applied to a hypothesis regarding the origin of certain skarns which are considered to be formed by differential melting of impure limestone in regional metamorphic terrains. The applications of this binary system to the theoretical chemistry of Portland cement burning is also incidentally considered. </p> / Thesis / Master of Science (MSc)

In this thesis we consider a set of mobile users that employ cloud-based computation offloading. In computation offloading, user energy consumption can be decreased by uploading and executing jobs on a remote server, rather than processing the jobs locally. In order to execute jobs in the cloud however, the user uploads must occur over a base station channel which is shared by all of the uploading users. Since the job completion times are subject to hard deadline constraints, this restricts the feasible set of jobs that can be remotely processed, and may constrain the users ability to reduce energy usage. The system is modelled as a competitive game in which each user is interested in minimizing its own energy consumption. The game is subject to the real-time constraints imposed by the job execution deadlines, user specific channel bit rates, and the competition over the shared communication channel. The thesis shows that for a variety of parameters, a game where each user independently sets its offloading decisions always has a pure Nash equilibrium, and a Gauss-Seidel method for determining this equilibrium is introduced. Results are presented which illustrate that the system always converges to a Nash equilibrium using the Gauss-Seidel method. Data is also presented which show the number of Nash equilibria that are found, the number of iterations required, and the quality of the solutions. We find that the solutions perform well compared to a lower bound on total energy performance. / Thesis / Master of Applied Science (MASc)

Page 39 was included twice in the thesis. / <p> This thesis describes reactions involving low valent technetium nitrosyl complexes. O-Substituted hydroxylamines were reacted with [TcOCl4]- in methanol producing [Tc(NO)Cl4]-. NMR studies have shown that two species are present besides the starting material during this reaction. One of these species was confirmed by NMR to be the corresponding alcohol of the O-substituted hydroxylamine. The other species is believed to be a hydroxylamine intermediate that is in equilibrium with the final product, [Tc(NO)Cl4]-. A plausible mechanism for this reaction was proposed that included an oxo group attack of the α-carbon of the O-substituted hydroxylamine which would lead to the formation of the corresponding alcohol. In an attempt to confirm the mechanism, O-18 labeled [TcOCl4]- was synthesized, however, there is no conclusive evidence that the label is transferred to the corresponding alcohol at the present time. Substitution reactions of [Tc(NO)Cl4]- with phenanthroline and bipyridyl ligands were also investigated. Reactions with these ligands produced [Tc^(II)(NO)Cl3phen] (4a) and [Tc^(II)(NO)Cl3bipy] (5), respectively. The crystal structures of these complexes showed that the meridonial isomer is produced with one nitrogen atom of the bidentate ligand trans to the nitrosyl moiety. EPR spectra of these compounds confirm the Tc(II) oxidation state of the metal. All of the chloride ligands of 4a and 5 can be displaced using AgBF4 in acetonitrile solvent, which, in the case of bipyridyl, produces [Tc^(I)(NO)(bipy)2(MeCN)]2+ (6). Other technetium nitrosyl containing complexes are formed in these reactions and are currently awaiting x-ray structure determination.</p> / Thesis / Master of Science (MSc)

<p> The effect of a C-7 substituent on the position of the cycloheptatriene/ norcaradiene equilibrium has been investigated. For this purpose a series of monosubstituted cycloheptatrienes was prepared in which the C-7 substituent was a carbonium ion grouping. From the spectral properties of these systems, it has been concluded that proportion of the norcaradiene valence tautomer present increases as the electron withdrawing ability of the carbonium ion substituent is enhanced.</p> <p> From a comparison of the pmr spectra of 7-norcaradienylmethyl cations with suitable model systems it is suggested that these norcaradienes are aromatic and that they support an induced diamagnetic ring current when in a magnetic field. It would appear that this type of cyclic delocalization is enhanced by the presence of an electron defficient substituent at C-7 of a norcaradiene and possible reasons for this are discussed.</p> <p> The 7-norcaradienylmethyl cations underwent a thermal isomerization to give benzenoid materials at relatively low temperatures. A mechanism for this rearrangement has been proposed and the implication of these results to the general pathways involved in the rearrangements of the C8H9+ family of cations discussed.</p> <p> Several synthetic routes to 9-substituted-3,4-homotropylidenes were investigated. A number of new compounds were isolated and a new synthetic approach to this class of compounds is suggested.</p> <p> Diamagnetic susceptibility exaltations of a series of substituted cycloheptatrienes were determined and used as a criterion of aromaticity. It was concluded that cycloheptatrienes are best regarded as homoaromatic molecules. Moreover it would appear that the substantial diamagnetic susceptibility exaltations observed with these compounds are related to the bulk of a C-7 substituent. One neutral norcaradiene was examined by this technique and was found to be nonaromatic.</p> / Thesis / Doctor of Philosophy (PhD)