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Variational method is used to investigate, at zero temperature, the deformed- Fermi-surfaces mechanism for solving the problem of superconducting pairing of two species of fermions (i.e., spin-up and -down) of mismatched Fermi surfaces due to the existence of a uniform exchange or Zeeman field. After analyzing the depairing regions in the whole three-dimensional parameter space, we obtain a trial groundstate wave-function as a function of the three variational parameters, one of which is the gap function. Then within the frame work of the weak-coupling BCS theory, the expectation value of the Hamiltonian of a conductor under an exchange or Zeeman field is derived, from which a gap equation is derived by differentiation. The influence of deformed Fermi surfaces on the chemical potential is then calculated. Computer programing is finally used to solve the gap equation, and find the minimum-energy state with respect to the remaining two variational parameters (δµ and z). These two parameters are better than the original parameters used in the trial Hamiltonian when compared with the FF state. And we also found if we keep the total number of electrons fixed, the system prefers an unchanged chemical potential and the ground state energy of the deformed-Fermi-surfaces state, which is found to be an angle dependent case of Sarma’s solution III, is no better than that of the unpolarized BCS state.

Variational method is used to investigate, at zero temperature, the deformed- Fermi-surfaces mechanism for solving the problem of superconducting pairing of two species of fermions (i.e., spin-up and -down) of mismatched Fermi surfaces due to the existence of a uniform exchange or Zeeman field. After analyzing the depairing regions in the whole three-dimensional parameter space, we obtain a trial groundstate wave-function as a function of the three variational parameters, one of which is the gap function. Then within the frame work of the weak-coupling BCS theory, the expectation value of the Hamiltonian of a conductor under an exchange or Zeeman field is derived, from which a gap equation is derived by differentiation. The influence of deformed Fermi surfaces on the chemical potential is then calculated. Computer programing is finally used to solve the gap equation, and find the minimum-energy state with respect to the remaining two variational parameters (δμ and z). These two parameters are better than the original parameters used in the trial Hamiltonian when compared with the FF state. And we also found if we keep the total number of electrons fixed, the system prefers an unchanged chemical potential and the ground state energy of the deformed-Fermi-surfaces state, which is found to be an angle dependent case of Sarma's solution III, is no better than that of the unpolarized BCS state.

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The risks posed by rapidly evolving RNA viruses to human and animal health are well recognized. Epidemics in managed and wildlife populations can lead to considerable economic and biodiversity losses. Yet, we lack understanding of the ecological and evolutionary factors that promote disease emergence. Host-switching viruses may be a particular threat to species important for human welfare, such as pollinating bees. Both honeybees and wild bumblebees have faced sharp declines in the last decades, with high winter mortality seen in honeybees. Infectious and emerging diseases are considered one of the key drivers of declines, acting in synergy with habitat loss and pesticide use. Here I focus on multihost viruses that pose a risk to wild bumblebees. I first identify the risk factors driving viral spillover and emergence from managed honeybees to wild bumblebees, by synthesising current data and literature. Biological factors (i.e. the nature of RNA viruses and ecology of social bees) play a clear role in increasing the risk of disease emergence, but anthropogenic factors (trade and transportation of commercial honeybees and bumblebees) creates the greatest risk of viral spillover to wild bees. Basic knowledge of the pathogenic effect of many common pollinator viruses on hosts other than A. mellifera is currently lacking, yet vital for understanding the wider impacts of infection at a population level. Here, I provide evidence that a common bumblebee virus, Slow bee paralysis virus (SBPV), reduces the longevity of Bombus terrestris under conditions of nutrition stress. The invasion of Varroa destructor as an ectoparasitic viral vector in European honeybees has dramatically altered viral dynamics in honeybees. I test how this specialist honeybee vector affects multi-host pathogens that can infect and be transmitted by both honeybees and wild bumblebees. I sampled across three host species (A. mellifera, B. terrestris and B. pascuorum) from Varroa-free and Varroa-present locations. Using a combination of molecular and phylogenetic techniques I find that this specialist honeybee vector increases the prevalence of four multi-host viruses (deformed wing virus (type A and B), SBPV and black queen cell virus) in sympatric wild bumblebees. Furthermore, wild bumblebees are currently experiencing a DWV epidemic driven by the presence of virus-vectoring Varroa in A. mellifera. Overall this thesis demonstrates that wild bumblebees are at high risk of viral disease emergence. My research adds to the ever-expanding body of evidence indicating that stronger disease controls on commercial bee operations are crucial to protect our wild bumblebees.

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Doctor of Philosophy / Department of Mathematics / Zongzhu Lin / For any given quiver [Gamma], there is a preprojective algebra and deformed preprojective algebras associated to it. If the ground field is of characteristic 0, then there are no finite dimensional representations of deformed preprojective algebras with special weight 1. However, if the ground field is of characteristic p, there are many dimension vectors with nonempty representation spaces of that deformed preprojective algebras. In this thesis, we study the representation category of deformed preprojective algebra with weight 1 over field of characteristic p > 0. The motivation is to count the number of rational points of the numbers X[subscript [lambda]] =[mu]⁻¹([lambda]) of moment maps at the special weights [lambda] [element of] K[superscript x] over finite fields, and to study the relations of the Zeta functions of these algebraic varieties X[subscript [lambda]] which are defined over integers to Betti numbers of the manifolds X[subscript [lambda]](C). The first step toward counting is to study the categories of representations of the deformed preprojective algebras [Pi][superscript [lambda]]. The main results of this thesis contain two types of quivers. First result shows that over finite field, the category of finite dimensional representations of deformed preprojective algebras [Pi]¹ associated to type A quiver with weight 1 is closely related to the category of finite dimensional representations of the preprojective algebra associated to two different type A quivers. Moreover, we also give the relations between their Zeta functions. The second result shows that over algebraically closed field of characteristic p > 0, the category of finite dimensional representations of deformed preprojective algebras [Pi]¹ associated to Jordan quiver with weight 1 has a close relationship with the category of finite dimensional representations of preprojective algebra associated to Jordan quiver.

<p> Metagreywackes of the Goldenville Formation, Nova Scotia, possess a well developed penetrative cleavage. Measurement of strain, based on quartz grain shape, indicates that much of the strain has been achieved by pressure solution of detrital quartz grains. Strain ratios in the system range from X/Z = 3.8 in cleavage zones, through 2.0 in intermediate areas, to 1.6 in lithons. The volume lost from cleavage zones ranges from 60 to 70 percent, while loss of volume to the system as a whole is 40 percent or greater. Strain due to plastic deformation is minimal, relative to the strain due to volume loss. The strain within the system is not homogeneous on a centimeter scale, but rather range from low values in mid-lithon zones to much higher values in cleavage zones. Lithon and intermediate areas are representative of the deformation history of the cleavage.</p> / Thesis / Bachelor of Science (BSc)

This thesis presents a robust real-time active tracking system with a pan-tilt camera. The proposed visual servo framework is able to track a deformed object and maintain the target always inside the field of view. For the image processing, an efficient template matching and searching method using the mean-shift theory is developed. The robustness is achieved by appending the ratio histogram, a kernel function, and the template update to the framework when the target is deformed. Then the pan-tilt unit turns towards the target and keeps the target inside the field of view of the camera by feeding back the position information to a Kalman filter. Experimental results show that the presented scheme works successfully when the target is vague or concealed or deformed. The visual tracking task can also be accomplished even when a similar object crosses over the target. In addition, the refreshing rate can be up to 60 frames per second.

This thesis addresses the topic of local bond behaviour in RC structures. The mechanism of bond refers to the composite action between deformed steel reinforcing bars and the surrounding concrete. Bond behaviour is an open research topic with a wide scope, particularly because bond it is such a fundamental concept to structural engineers. However, despite many bond-related research findings having wide applications, the primary contribution of this research is an experimental evaluation of the prominent features of local bond behaviour and the associated implications for the seismic performance of RC structures. The findings presented in this thesis attempt to address some structural engineering recommendations made by the Canterbury Earthquakes Royal Commission following the 2010-2011 Canterbury (New Zealand) earthquake sequence. A chapter of this thesis discusses the structural behaviour of flexure-dominated RC wall structures with an insufficient quantity of longitudinal reinforcement, among other in situ conditions, that causes material damage to predominantly occur at a single crack plane. In this particular case, the extent of concrete damage and bond deterioration adjacent to the crack plane will influence the ductility capacity that is effectively provided by the reinforcing steel. As a consequence of these in situ conditions, some lightly reinforced wall buildings in Christchurch lost their structural integrity due to brittle fracture of the longitudinal reinforcement. With these concerning post-earthquake observations in mind, there is the underlying intention that this thesis presents experimental evidence of bond behaviour that allows structural engineers to re-assess their confidence levels for the ability of lightly reinforced concrete structures to achieve the life-safety seismic performance objective the ultimate limit state. Three chapters of this thesis are devoted to the experimental work that was conducted as the main contribution of this research. Critical details of the experimental design, bond testing method and test programme are reported. The bond stress-slip relationship was studied through 75 bond pull-out tests. In order to measure the maximum local bond strength, all bond tests were carried out on deformed reinforcing bars that did not yield as the embedded bond length was relatively short. Bond test results have been presented in two separate chapters in which 48 monotonic bond tests and 27 cyclic bond tests are presented. Permutations of the experiments include the loading rate, cyclic loading history, concrete strength (25 to 70 MPa), concrete age, cover thickness, bar diameter (16 and 20 mm), embedded length, and position of the embedded bond region within the specimen (close or far away to the free surface). The parametric study showed that the concrete strength significantly influences the maximum bond strength and that it is reasonable to normalise the bond stress by the square-root of the concrete compressive strength, √(f'c). The generalised monotonic bond behaviour is described within. An important outcome of the research is that the measured bond strength and stiffness was higher than stated by the bond stress-slip relationship in the fib Model Code 2010. To account for these observed differences, an alternative model is proposed for the local monotonic bond stress-slip relationship. Cyclic bond tests showed a significant proportion of the total bond degradation occurs after the loading cycle in the peak bond strength range, which is when bond slip has exceeded 0.5 mm. Subsequent loading to constant slip values showed a linear relationship between the amount of bond strength degradation and the log of the number of cycles that were applied. To a greater extent, the cyclic bond deterioration depends on the bond slip range, regardless of whether the applied load cycling is half- or fully-reversed. The observed bond deterioration and hysteretic energy dissipated during cyclic loading was found to agree reasonably well between these cyclic tests with different loading protocols. The cyclic bond deterioration was also found to be reasonably consistent exponential damage models found in the literature. This research concluded that the deformed reinforcing bars used in NZ construction, embedded in moderate to high strength concrete, are able to develop high local bond stresses that are mobilised by a small amount of local bond slip. Although the relative rib geometry was not varied within this experimental programme, a general conclusion of this thesis is that deformed bars currently available in NZ have a relative rib bearing area that is comparatively higher than the test bars used in previous international research. From the parametric study it was found that the maximum monotonic bond strength is significant enhanced by dynamic loading rates. Experimental evidence of high bond strength and initial bond stiffness generally suggests that only a small amount of local bond slip that can occur when the deformed test bar was subjected to large tension forces. Minimal bond slip and bond damage limits the effective yielding length that is available for the reinforcing steel to distribute inelastic material strains. Consequently, the potential for brittle fracture of the reinforcement may be a more problematic and widespread issue than is apparent to structural engineers. This research has provided information that improve the reliability of engineering predictions (with respect to ductility capacity) of maximum crack widths and the extent of bond deterioration that might occur in RC structures during seismic actions.