Viral infections, such as HIV, are often treated with orally administered antiviral medications that are dosed at particular intervals, leading to periodic drug levels and hence periodic inhibition of viral replication. These drugs generally bind to viral proteins and inhibit particular steps in the viral lifecycle, and resistance often evolves due to point mutations in the virus that prevent the drug from binding its target. However, it has been proposed (Wahl \& Nowak, Proc Roy Soc B, 2000) that a completely different ``cryptic'' mechanism for resistance could exist: the virus population may evolve towards synchronizing its lifecycle with the pattern of drug treatment. If the lifecycle of the virus is a multiple of the dosing interval, it is possible that over time the bulk of the virus population will replicate during trough concentrations of the drug. In this thesis, we use stochastic mathematical models of viral dynamics to demonstrate that cryptic resistance could plausibly provide a powerful fitness advantage to a wide variety of viral strains whose expected lifecycle times are slightly less than the expected time between doses of an antiviral drug, allowing them to survive drug regimes that would otherwise drive infected cell populations to extinction. This in turn suggests that continuously-administered antiviral drug treatments may be significantly more effective than periodically-administered treatments in combatting viral infections. / Applied Mathematics

We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility (for expansion) K and the thickness 2ht of the hydrophobic part of the bilayer. The model is a lattice model which incorporates stress relaxation, and considers the nucleation of pores at constant area, constant temperature, and constant particle number. The particle number is conserved by allowing multiple occupancy of the sites. A value for the rigidity of the phopholipid tails in the Lalpha liquid phase are found for saturated and unsaturated lipids, and long diblock copolymers. An equilibrium "phase diagram" is constructed as a function of temperature and strain with the pores total surface and distribution as the order parameters. With parameters relevant to saturated phosphatidylcholine (PC) lipid membranes, well defined regions of "no pores", "protopores (non-critical pores)", "rupture" are found. The model also reproduces recent results on super-thick membranes, and on membranes in presence of peptides. Free energy curves as a function of total pore surface are presented for various values of tension and temperature, and the fractal dimension of the pore edge is evaluated.

The purpose of the present investigation was to determine the net passive elastic joint moment and the angular damping coefficient of the human knee joint in full range flexion-extension. A secondary purpose was to develop regression equations to predict the measured passive properties from anthropometric data. The passive elastic moments increased exponentially as the limits of either flexion or extension were approached. The midrange of joint motion was a low moment (5 N$\cdot$m), low stiffness region. Considerable variability in the magnitudes of the passive elastic moments existed across subjects. At 140$\sp\circ$ of flexion, between about 5 N$\cdot$m and 86 N$\cdot$m was measured while the range at full extension (0$\sp\circ$) was about 6 N$\cdot$m to 22 N$\cdot$m. The angular damping coefficient was a nonlinear function (approximately quadratic) of the knee joint angle. The variability was not quite as high compared to the elastic component. Application of the data to the late swing phase of walking indicated that, for some subjects, the passive moments may contribute (or oppose) significantly to the net joint moment. (Abstract shortened by UMI.)

The study makes use of a variation of the Finite-Difference Time-Domain (FDTD) method as first proposed by Yee to simulate electromagnetic field distribution and propagation in an open waveguide structure. In order to prove that this new method is valid, a reflection coefficient is calculated with simulation data and compared to measurements. The agreement between measurement and simulation data, while not exact, is enough to establish the veracity of the new method. This study contains a detailed discussion of the discrepancies which were observed. Also presented are colour images of the simulation which give the reader an idea as to the nature and level of detail of the information which can be obtained from the simulation.

This thesis addresses the problem of analytical determination of the response behaviour of fibre reinforced composite materials, under both quasi-static and dynamic loadings. In the first part of the thesis (Chapters 2 and 3), the effects of microstructural parameters, such as fibre aspect ratio, fibre off-axis angle and fibre volume fraction, on the damping and stiffness of a fibre-composite system are examined. Quasi-static models are, then, developed by using a "Forced Balance Approach" to define mechanical response properties of discontinuous fibre reinforced composite materials. Subsequently, simultaneous optimization of damping, stiffness and weight is carried out by using the so-called "Inverted Utility Function Method". The obtained results show that discontinuous fibre-reinforced composites have superior design flexibility and higher damping properties as compared with those pertaining to continuous fibre-reinforced composites of the same material. In the second part of the thesis (Chapters 4 and 5), the determination of the impact response of laminated composite plates is dealt with. In this context, the "First Shear Deformation Theory (FSDT)" is employed to deal with the so called "Transient Wave Propagation Phenomenon". In this, the "Correspondence Principle" is, then, utilized to extend the obtained elastic solutions to corresponding viscoelastic problems. Here, the closed form displacement solutions are obtained first in the frequency-domain, then, the "Fast Fourier Transformation (FFT)" is applied to invert numerically the dealt-with solutions from frequency-domain to time-domain. The obtained results emphasize the importance of including viscoelastic effects in the analysis, for the prediction of the mechanical response of laminated composites under impact loading.

This study presents a strategy for position feedback control, a so-called self-adjusting adaptive sliding mode controller, to obtain a desired steady state error for a DC-motor servo in the presence of Coulomb friction and stiction. Sliding mode controllers are of the type of nonlinear controllers which have been studied extensively by Russian scientists, including V. I. Utkin and V. Itkis. The self adjusting sliding mode control method that this thesis is focused on is an adaptive discontinuous controller with an approximated sliding mode trajectory. The study is concerned with both analytical and experimental performances of such a class of control strategy and a PID (proportional integral and derivative) controller in the presence of dry friction for the purpose of comparison. The study also investigates the effect of nonlinear phenomenon such as torque saturation on the states of the variables of such a system. The result of the paper is finally based on the suitable performance of the suggested control methodology utilizing a new form of sliding mode controller for the second order class of systems, rather than the conventional forms from V. Itkis and V. I. Utkin.

This research examined three different diving stances during the competitive grab start of swimming--that of the standard position, called the Toes-Over position, the Toes-Back position where the swimmers were not permitted to curl their toes over the edge of the $-$10 degree inclined starting block and the Level position where the platform was levelled. A starting position was being sought which would increase a swimmer's projection angle from the blocks and thus flight time before entry. Eight female swimmers were filmed using a stationary cinecamera while reaction forces were collected, simultaneously, by a force platform mounted on the starting block. Net forces and moments of force at the three leg joints were calculated using inverse dynamics (Winter, 1979). The powers produced by these net moments were then computed to determine which muscle groups contributed to the work done during the start. Based on the results of this study there were no significant differences in the performances of female swimmers using the grab start technique in terms of takeoff velocity, takeoff angle or horizontal distance for the dive when starting from a level surface or $-$10 degree inclined surface. The hip extensor muscles provided the greatest amount of power during the propulsive (thrust) phase of the swim start.

The effects of buoyancy forces on liquid-liquid displacement processes occurring in porous media are important in a variety of practical situations, in particular during the displacement of oil from partially-depleted underground reservoirs by means of aqueous solutions. Most previous studies involving the visualization of water/oil displacements in porous media have been undertaken in horizontal two-dimensional porous medium cells. The objective of this work was to determine the effects of buoyancy forces on the fingering pattern and oil recovery by conducting immiscible displacement experiments in two-dimensional porous medium cells aligned in the vertical plane. A consolidated porous medium cell was utilized to perform the displacements, which permitted a wide range of experiments to be carried out within an identical porous medium. In order to obtain a clear understanding of the effects of buoyancy forces (both favourable and unfavourable) experiments were carried out in three different modes, namely horizontal, vertical upward, and vertical downward. As the effects of buoyancy forces are almost negligible, in the horizontal mode, recoveries obtained in this mode are used as a reference and compared to those obtained in the other two modes. For the system studied in this work, as the displacing liquid in all cases had a higher density than the displaced liquid, buoyancy forces were always favourable in the vertical upward mode and always unfavourable in the vertical downward mode. The immiscible system employed consisted of heavy paraffin oil and glycerol solution as the displaced and displacing phases respectively. The viscosity ratio was varied by changing the concentration of the glycerol solution. Displacements with five different viscosity ratios were studied. Breakthrough time was measured and fractional oil recovery was calculated. The effects of buoyancy, viscous and capillary forces as well as the injection flow rate were also observed. The results obtained indicate that the buoyancy forces are highly effective at very low flow rates and low viscosity ratios (or high density ratios), and even with a slight increase in the flow rate, buoyancy forces lose their importance quickly.

It is the purpose of this thesis to review, and to evaluate to a degree, some of the current theories dealing with the effects of vibrations on foundations in contact with the earth. Basic parameters, the means of evaluating them, and their applications are discussed. Conditions leading to vibration and shock problems, the significance of these problems and various correctional methods are presented. The effects of vibrations on foundations, with particular regard to settlement, are considered by means of modifications to the soil characteristics as observed by other writers. Long term consolidation tests were carried out on undisturbed and remolded clay samples, both vibrated and unvibrated. These tests were conducted in order to secure a comparison between actual test results and the conclusions given by the above theory, for what may be considered an extreme case. Cohesive soil is known to be much less sensitive to vibration than cohesionless soil, thus very little work has been done on it in this regard. The degree of independence of cohesionless soil to vibration was investigated within the limits of these tests. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

This thesis derives the differential equation for the in plane extentionless buckling of a ring in an elastic foundation. The elastic foundation can exert forces proportional to radial and tangential displacements and a couple proportional to rotation. The external uniform load is always directed toward a fixed point on the initial radius. A special case of this is hydrostatic pressure where the load remains normal to the ring. In other cases the load may remain parallel to the initial radius or remain directed towards the initial centre. Complete solutions are presented for a full ring and several graphs of critical pressure versus foundation stiffness indicating the general behaviour. A full solution is given for a partial ring with hinged supports along with a number of graphs. A method is presented but no solutions are given for a partial ring with fixed supports. Finally, a solution is given for the case of a full ring under hydrostatic load with radial elastic supports having a different spring constant for inward and outward displacements. This solution, presented graphically for all combination of spring constants, can represent the buckling of a culvert under a high fill. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate