An impulsive differential equation model for Marek's disease

Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are referred to as impulsive differential equations, systems of differential equations coupled with discrete mappings in state space. In this thesis we employ impulsive differential equations to model disease transmission within an industrial livestock barn. In particular we focus on the poultry industry and a viral disease of poultry called Marek's disease. This system lends itself well to impulsive differential equations. Entire cohorts of poultry are introduced and removed from a barn concurrently. Additionally, Marek's disease is transmitted indirectly and the viral particles can survive outside the host for weeks. Therefore, depopulating, cleaning, and restocking of the barn are integral factors in modelling disease transmission and can be completely captured by the impulsive component of the model. Our model allows us to investigate how modern broiler farm practices can make disease elimination difficult or impossible to achieve. It also enables us to investigate factors that may contribute to virulence evolution. Our model suggests that by decrease the cohort duration or by decreasing the flock density, Marek's disease can be eliminated from a barn with no increase in cleaning effort. Unfortunately our model also suggests that these practices will lead to disease evolution towards greater virulence. Additionally, our model suggests that if intensive cleaning between cohorts does not rid the barn of disease, it may drive evolution and cause the disease to become more virulent.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.

The relationship between changes in cardiovascular function and changes in VO2peak following SIT

Background: It is well known that sprint interval training (SIT), induces significant increases in peak oxygen uptake (VO2peak) at the group level. However, there have been only a few studies that have addressed the variability of VO2peak response following SIT, and precise mechanism(s) that may explain individual magnitude of response are unknown. Purpose: Therefore, the purpose of this thesis was to: 1) examine the inter-individual variability of the VO2peak response following SIT, 2) to inspect the relationship between changes in both central and peripheral measures and changes in VO2peak, and 3) to assess if peripheral or central adaptations play a role in whether an individual is a high or low responder with respect to VO2peak. Subjects: Twenty-two young, recreationally active males (age: 20.4 1.7 years; weight: 78.4 10.2 kg; VO2peak: 3.7 0.62 L/min) Methods: VO2peak (L/min), peak cardiac output (Qpeak [L/min]), and peak deoxygenated hemoglobin (HHbpeak [mM]) were measured before and after 16 sessions of SIT (Tabata Protocol) over four weeks. Peak a-vO2diff was calculated using a derivation of the Fick equation. Results: Due to a systematic error, HHbpeak could not be used to differentiate between individual responses. There was a large range of VO2peak response from pre to post testing (-4.75 to 32.18% change) and there was a significant difference between the Low Response Group (LRG) (n=8) and the High Response Group (HRG) (n=8) [f(1, 14)= 64.27, p<0.001]. Furthermore, there was no correlation between delta () VO2peak and Qpeak (r=-0.18, p=0.46) for all participants, nor was there an interaction effect between the Low and High Response Groups [f(1,11)=0.572, p=0.47]. Lastly, there was a significant correlation between VO2peak and peak a-vO2diff [r=0.692, p<0.001], and a significant interaction effect with peak a-vO2diff [f(1, 14)= 13.27, p<0.004] when comparing the HRG to the LRG. Conclusions: There was inter-individual variability of VO2peak response following 4 weeks of SIT, but central adaptations did not influence this variation. This suggests that peripheral adaptations may be responsible for VO2peak adaptation.