The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part of this work focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. Beyond the region of exponential growth, the instability waves evolve into a periodic array of vortices. In the second part of this work, the weakly nonlinear theory is extended to heated (or nonisothermal mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbances is also studied by solving the initial value problem and then examining the behavior of the long-time solution. The excitation produces a wave packet which consists of a few oscillations and is convected downstream by the mean flow. The magnitude of the disturbance in the jet depends on the location of the excitation and there is an optimum position at which little energy input will produce large perturbations. It is found that in order to generate the largest perturbations at any point in the jet, the disturbance should be deposited into the flow at a point where the phase velocity of the most amplified wave equals the fluid velocity (of the base flow).

A finite element formulation for the shear-deformable analysis of beams, plates and shells, based on a strain energy expression defined in terms of total and flexural displacement components, is presented. The effects of transverse shear deformation are considered while the normal strain is neglected. The finite element representation requires independent descriptions of total and flexural displacement components. The flexural strain energy term involves second derivatives of flexural displacement component and thereby necessitates slope-compatible shape functions. This requirement is relaxed by adopting the 'discrete Kirchhoff' hypothesis for the flexural displacement component. An element of triangular shape is formulated for the analysis of laminated composite plates and shallow shells. Numerically exact integration is employed in the calculation of element stiffness matrix and corresponding load vectors. The resulting finite element possesses twelve degrees of freedom at each corner node of the triangle. Numerical results obtained for an extensive range of thickness and planform aspect ratios, laminate configurations, mesh sizes, edge conditions, types of loading and geometry of the structure demonstrate the efficacy of the finite element formulation. The element is applicable to a full range of thicknesss ratios. The present formulation is employed for dynamic and stability analysis of beams, as a precursor to the inclusion of these effects in the analysis of plates and shells.

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Factor VIII (FVIII) is an essential blood-clotting protein and mutations in the FVIII gene are the cause of hemophilia A, a severe inherited bleeding disorder. FVIII synthesis has been observed in discreet endothelial sub-populations including liver sinusoidal endothelial cells and in selected microvascular beds. The mechanistic basis for this differential expression is unknown. Differences in shear stress are believed to play an important role in determining endothelial heterogeneity. In this study, we have evaluated the effect of various shear stress conditions on FVIII expression in blood outgrowth endothelial progenitor cells (BOECs) with an in vitro flow system. Under static conditions, BOECs do not express FVIII. In contrast, after exposure to laminar shear stress for 48 hrs, a significant increase in FVIII expression was documented by qRT-PCR, regardless of the magnitude of shear stress studied (1, 5, 15 and 30 dynes/cm2). To determine the effect of prolonged shear stress, laminar flow was applied over 120 hrs and FVIII mRNA levels returned to static levels. Induction of gene expression by laminar shear stress followed by repression after longer durations is common to other pro-coagulant genes induced by non-laminar or oscillatory flow (eg. tissue factor). BOECs exposed to 15 dyne/cm2 of shear stress, oscillating every 0.5 sec for 120 hrs, had FVIII mRNA levels 4.7-fold that of cells in static conditions. This was significantly higher than FVIII expression in BOECs exposed to 15 dyne/cm2 of laminar shear stress for the same duration. Expression of KLF2, a transcription factor that suppresses endothelial pro-coagulant gene expression under laminar shear stress, was significantly reduced in BOECs exposed to oscillatory as opposed to laminar shear stress. Finally, in BOECs exposed to oscillatory shear stress, FVIII protein was synthesized and co-localizes with its carrier protein VWF in Weibel-Palade bodies. These studies show that shear stress is a significant regulator of FVIII expression in BOECs, that FVIII expression is inversely correlated with that of KLF2, and that FVIII protein co-localizes with VWF in these cells. / Thesis (Master, Pathology & Molecular Medicine) -- Queen's University, 2013-03-04 17:00:27.994