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The capillary surface formed within a symmetric annular tube is analyzed. Assuming identical contact angles along each boundary, we consider surfaces u(x,y) that satisfy the capillary problem on an annular region. Several qualitative properties of u are determined and in particular, the behaviour of u is examined in the limiting cases of the annular domain approaching a disk as well as a thin ring. The iterative method of Siegel is also applied to the boundary value problem and convergence is demonstrated under conditions which include a contact angle of zero. Moreover, some geometries still yield interleaving iterates, allowing for upper and lower bounds to be placed on the boundary values of u. However, the interleaving properties no longer hold universally and for other geometries, another more complex behaviour is described. Finally, a numerical method is designed to approximate the iterative scheme.

Low back pain is highly prevalent in the developed world, with 80% of the population being affected at some point in their lives. Herniation, a common injury to the intervertebral disc, is characterized as the posterior migration of the nucleus pulposus through the layers of the annulus fibrosus. Various risk factors have been associated with the development of disc herniation, but the mechanisms are largely not understood. For example, exposure to vibration has been linked to the occurrence of herniation, yet our understanding of this association is not clear. It is hypothesized that vibration cyclically loads the tissues of the intervertebral disc until failure occurs as a result of fatigue. Tissues at risk of fatigue failure may include the intra-lamellar matrix, the connective tissue found between collagen fibres within a single lamella, and the inter-lamellar matrix, the connective tissue found between adjacent lamellae. In order to determine the mechanistic link between vibration and herniation, a firm understanding of the properties of the intervertebral disc as well as the intra and inter-lamellar matrices are of utmost importance. Further, it is important to determine these properties under physiological loading scenarios. This thesis consists of five studies, which have each provided a unique piece to the intervertebral disc herniation puzzle in order to better understand this mechanistic link. First, it was discovered that annular tissue is subject to significantly higher stresses and is stiffer under biaxial strain as compared to uniaxial strain. Biaxial strain is more representative of the in vivo loading scenario and provides more accurate information regarding scenarios that the annulus can tolerate and those that can result in injury. It was also revealed that, when strained at physiological strain rates (up to 4%/sec), these mechanical properties do not change such that they are independent of strain rate. Therefore, when strained at varying rates akin to voluntary movement, the annulus is not subject to higher stresses or altered stiffness. Second, the effect of vibration, an acknowledged risk factor for herniation, was examined on the mechanical properties of the intra and inter-lamellar matrices. It was discovered that vibration altered these matrices such that they were more extensible and strained to greater magnitudes, yet did not reach higher stresses before failing. It was hypothesized that this increased extensibility was due to damage to elastin, as elastin assists in minimizing tissue deformation and helps tissues recover from tensile strain. The final study assessed the effect of exposure to vibration on the development of disc herniation. The initiation of herniation was observed in a significantly greater number of intervertebral discs exposed to vibration as compared to a control condition. Although epidemiological studies had documented a correlation between exposure to vibration and herniation, this was the first study to conclude that exposure to vibration is in fact a mechanical risk factor for the development of herniation and increases the incidence of herniation. Further, based on the findings of the mechanical properties of the intra and inter-lamellar matrices, and in particular the observed 15-20 times greater failure strength of the intra as compared to inter-lamellar matrix, it would appear that the inter-lamellar matrix, and thus delamination, may be the weakest link in the herniation pathway. This thesis has uncovered new information regarding physiological mechanical properties of the annulus. Further, new information regarding the intra and inter-lamellar matrices was obtained, improving our understanding of the healthy disc. Last, by subjecting the disc to a known risk factor for herniation, hypotheses were generated regarding the initiation and progression of disc herniation, specifically related to the roles of the intra and inter-lamellar matrices.

The capillary surface formed within a symmetric annular tube is analyzed. Assuming identical contact angles along each boundary, we consider surfaces u(x,y) that satisfy the capillary problem on an annular region. Several qualitative properties of u are determined and in particular, the behaviour of u is examined in the limiting cases of the annular domain approaching a disk as well as a thin ring. The iterative method of Siegel is also applied to the boundary value problem and convergence is demonstrated under conditions which include a contact angle of zero. Moreover, some geometries still yield interleaving iterates, allowing for upper and lower bounds to be placed on the boundary values of u. However, the interleaving properties no longer hold universally and for other geometries, another more complex behaviour is described. Finally, a numerical method is designed to approximate the iterative scheme.

Low back pain is highly prevalent in the developed world, with 80% of the population being affected at some point in their lives. Herniation, a common injury to the intervertebral disc, is characterized as the posterior migration of the nucleus pulposus through the layers of the annulus fibrosus. Various risk factors have been associated with the development of disc herniation, but the mechanisms are largely not understood. For example, exposure to vibration has been linked to the occurrence of herniation, yet our understanding of this association is not clear. It is hypothesized that vibration cyclically loads the tissues of the intervertebral disc until failure occurs as a result of fatigue. Tissues at risk of fatigue failure may include the intra-lamellar matrix, the connective tissue found between collagen fibres within a single lamella, and the inter-lamellar matrix, the connective tissue found between adjacent lamellae. In order to determine the mechanistic link between vibration and herniation, a firm understanding of the properties of the intervertebral disc as well as the intra and inter-lamellar matrices are of utmost importance. Further, it is important to determine these properties under physiological loading scenarios. This thesis consists of five studies, which have each provided a unique piece to the intervertebral disc herniation puzzle in order to better understand this mechanistic link. First, it was discovered that annular tissue is subject to significantly higher stresses and is stiffer under biaxial strain as compared to uniaxial strain. Biaxial strain is more representative of the in vivo loading scenario and provides more accurate information regarding scenarios that the annulus can tolerate and those that can result in injury. It was also revealed that, when strained at physiological strain rates (up to 4%/sec), these mechanical properties do not change such that they are independent of strain rate. Therefore, when strained at varying rates akin to voluntary movement, the annulus is not subject to higher stresses or altered stiffness. Second, the effect of vibration, an acknowledged risk factor for herniation, was examined on the mechanical properties of the intra and inter-lamellar matrices. It was discovered that vibration altered these matrices such that they were more extensible and strained to greater magnitudes, yet did not reach higher stresses before failing. It was hypothesized that this increased extensibility was due to damage to elastin, as elastin assists in minimizing tissue deformation and helps tissues recover from tensile strain. The final study assessed the effect of exposure to vibration on the development of disc herniation. The initiation of herniation was observed in a significantly greater number of intervertebral discs exposed to vibration as compared to a control condition. Although epidemiological studies had documented a correlation between exposure to vibration and herniation, this was the first study to conclude that exposure to vibration is in fact a mechanical risk factor for the development of herniation and increases the incidence of herniation. Further, based on the findings of the mechanical properties of the intra and inter-lamellar matrices, and in particular the observed 15-20 times greater failure strength of the intra as compared to inter-lamellar matrix, it would appear that the inter-lamellar matrix, and thus delamination, may be the weakest link in the herniation pathway. This thesis has uncovered new information regarding physiological mechanical properties of the annulus. Further, new information regarding the intra and inter-lamellar matrices was obtained, improving our understanding of the healthy disc. Last, by subjecting the disc to a known risk factor for herniation, hypotheses were generated regarding the initiation and progression of disc herniation, specifically related to the roles of the intra and inter-lamellar matrices.

Septins are a family of guanine nucleotide-binding proteins that function in eukaryotic cell division, where they form a high-order cortical structure at the site of division, which is essential in most eukaryotes. Expanded roles have evolved for septins in metazoans, where they also have essential functions in terminally-differentiated cell types, such as neurons and spermatozoa. Specific details of septin function are lacking in most roles described, due at least in part to the limited number of characterized binding partners. In this work, yeast two-hybrid screens and pull-downs from tissue homogenate were used to identify novel septin binding partners for subsequent characterization. The neuron-enriched septin, SEPT5, interacted directly with SUMO E3 ligases of the PIAS family. However, I was not able to demonstrate endogenous sumoylation of SEPT5 and SUMO isoforms did not concentrate with the septins during cytokinesis. SEPT5 also interacted with a novel septin, SEPT12, which I further characterized to be testis-specific and localized to the annulus in mature spermatozoa. Further, using SEPT12-specific reagents, I determined that the annulus forms via sequestration and subsequent segregation from the Golgi during spermiogenesis. SEPT9 pull-downs identified another novel testis-specific septin, SEPT14. Reagents specific to SEPT2 and SEPT9 also revealed a septin-rich structure in the seminiferous epithelium in close association with the ectoplasmic specialization. The specific role of septins in this structure awaits further characterization. Several other intriguing candidate septin-interaction partners were identified and the further study of their possible in vivo interaction with septins may provide substantial insight into the mechanisms of septin function in eukaryotes.

Septins are a family of guanine nucleotide-binding proteins that function in eukaryotic cell division, where they form a high-order cortical structure at the site of division, which is essential in most eukaryotes. Expanded roles have evolved for septins in metazoans, where they also have essential functions in terminally-differentiated cell types, such as neurons and spermatozoa. Specific details of septin function are lacking in most roles described, due at least in part to the limited number of characterized binding partners. In this work, yeast two-hybrid screens and pull-downs from tissue homogenate were used to identify novel septin binding partners for subsequent characterization. The neuron-enriched septin, SEPT5, interacted directly with SUMO E3 ligases of the PIAS family. However, I was not able to demonstrate endogenous sumoylation of SEPT5 and SUMO isoforms did not concentrate with the septins during cytokinesis. SEPT5 also interacted with a novel septin, SEPT12, which I further characterized to be testis-specific and localized to the annulus in mature spermatozoa. Further, using SEPT12-specific reagents, I determined that the annulus forms via sequestration and subsequent segregation from the Golgi during spermiogenesis. SEPT9 pull-downs identified another novel testis-specific septin, SEPT14. Reagents specific to SEPT2 and SEPT9 also revealed a septin-rich structure in the seminiferous epithelium in close association with the ectoplasmic specialization. The specific role of septins in this structure awaits further characterization. Several other intriguing candidate septin-interaction partners were identified and the further study of their possible in vivo interaction with septins may provide substantial insight into the mechanisms of septin function in eukaryotes.

<p> CHF and Post-CHF tests were performed in water at 9.7 MPa using two vertical test assemblies having identical, internally heated annular flow channels, one heated directly, the other indirectly. Experiments were conducted to determine the effect of these methods of heating on CHF and Post-CHF heat transfer. </p> <p> For the range of the test conditions investigated, the results show that the direct and indirect heaters have similar CHF performance. At heat fluxes above CHF and mass fluxes of 2.0 and 3.5 Mg.s^-1 .m^-2 , the indicated maximum wall temperatures of the heaters were similar, but at the highest mass flux for the tests, 5.0 Mg.s^-1 .m^-2 , the indirect heater had lower indicated maximum wall temperatures than the direct heater for a given heat flux above CHF. </p> <p> A multi-fluid model, of the type used previously in the prediction of CHF, was derived and tested against the experimental data. The model, which considers droplet entrainment, deposition and evaporation in the annular flow regime, assumes dryout to occur when the liquid film flow on the inner rod approaches zero. The CHF predictions were in fairly good agreement with the experimental results. In general, the model under-predicted CHF at low inlet subcoolings and over-predicted CHF at high inlet subcooling. The error trend is consistent with that of the CHF prediction models of other researchers. </p> <p> In addition to the CHF prediction model, a Post-CHF model to predict the vapour temperatures, and hence, the heated wall temperature is also presented in the report. The theory is based on a physical model of heat transfer in the liquid deficient regime. In the model, heat in the dry region is assumed to transfer from the heated wall to superheat the steam and some of this heat, in turn, is used to evaporate the droplets which are entrained in the vapour core. Droplet entrainment and deposition at the shroud (outer tube) film-vapour interface are modelled. Heat transfer enhancement due to increased turbulence downstream of the rod centering spacers is incorporated through an empirical correlation. The predicted results were compared to the direct heater experiments. In general, the predicted wall temperatures were in agreement with those in the experiments. </p> / Thesis / Master of Engineering (MEngr)

O conhecido Teorema de Poincaré afirma: O número de rotação de homeomorfismo do círculo S^1 que preserva orientação é racional se, e somente se, o homeomorfismo possui um ponto periódico cujo período é igual ao denominador de tal racional. Na presente dissertação estudamos resultados análogos, ao resultado acima mencionado, para homeomorfismos do anel A=S^1 x I homotópicos à identidade. Mais precisamente, estudaremos o famoso Teorema de Poincaré - Birkhoff e algumas versões devidas a J. Franks. Isto será feito impondo algumas condições no conjunto de rotação, o qual é uma generalização do número de rotação para homeomorfismos do círculo. / The well known Poincaré's Theorem state: The rotation number of an orientation preserving circle homeomorphism is rational if, only if, the homeomorphism has a periodic point of period equal to denominator of the rational. In this monograph we study results analogous, to the result above mentioned, for homeomorphisms of A=S^1 x I homotophics to the identity. More precisely, we study the famous Poincaré - Birkhoff Theorem and some versions obtained by J. Franks. This it will be done imposing some conditions in the rotation set, which is generalization of the rotation number for circle homeomorphisms.

O conhecido Teorema de Poincaré afirma: O número de rotação de homeomorfismo do círculo S^1 que preserva orientação é racional se, e somente se, o homeomorfismo possui um ponto periódico cujo período é igual ao denominador de tal racional. Na presente dissertação estudamos resultados análogos, ao resultado acima mencionado, para homeomorfismos do anel A=S^1 x I homotópicos à identidade. Mais precisamente, estudaremos o famoso Teorema de Poincaré - Birkhoff e algumas versões devidas a J. Franks. Isto será feito impondo algumas condições no conjunto de rotação, o qual é uma generalização do número de rotação para homeomorfismos do círculo. / The well known Poincaré's Theorem state: The rotation number of an orientation preserving circle homeomorphism is rational if, only if, the homeomorphism has a periodic point of period equal to denominator of the rational. In this monograph we study results analogous, to the result above mentioned, for homeomorphisms of A=S^1 x I homotophics to the identity. More precisely, we study the famous Poincaré - Birkhoff Theorem and some versions obtained by J. Franks. This it will be done imposing some conditions in the rotation set, which is generalization of the rotation number for circle homeomorphisms.