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The purpose of this thesis is to study the problem of a low Reynolds number swimmer that is in very close proximity to a wall or solid boundary in a non- Newtonian fluid. We assume that it moves by propagating waves down its length in one direction, creating a thrust and therefore propelling it in the opposite direction. We model the swimmer as an infinite, inextensible waving sheet. We consider two main cases of this swimming sheet problem. In the first case, the type of wave being propagated down the length of the swimmer is specified. We compare the swimming speeds of viscoelastic shear thinning, shear thickening and Newtonian fluids for a fixed propagating wave speed. We then compare the swimming speeds of these same fluids for a fixed rate of work per wavelength. In the latter situation, we find that a shear thinning fluid always yields the fastest swimming speed regardless of the amplitude of the propagating waves. We conclude that a shear thinning fluid is optimal for the swimmer. Analytical results are obtained for various limiting cases. Next, we consider the problem with a Bingham fluid. Yield surfaces and flow profiles are obtained. In the second case, the forcing along the length of the swimmer is specified, but the shape of the swimmer is unknown. First, we solve this problem for a Newtonian fluid. Large amplitude forcing yields a swimmer shape that has a plateau region following by a large spike region. It is found that there exists an optimal forcing that will yield a maximum swimming speed. Next, we solve the problem for moderate forcing amplitudes for viscoelastic shear thickening and shear thinning fluids. For a given forcing, it is found that a shear thinning fluid yields the fastest swimming speed when compared to a shear thickening fluid and a Newtonian fluid. The difference in swimming speeds decreases as the bending stiffness of the swimmer increases.

I have used an analytic model of tidal interactions to predict the evolution of a substructure in a static dark matter halo. Given the initial conditions of the satellite and background halo, the model predicts with high accuracy the mass loss of the satellite and also its density evolution. The main phenomena taken into account in the model are tidal truncation at the tidal radius of the satellite and heating due to tidal shocks at the pericenter of its orbit. To calibrate and test the model, it has been compared with numerical simulations of a satellite orbiting in a static dark matter halo. The model predicts a set of tidal radii for the satellite in different stages of its evolution. The mass of the satellite is accurately calculated at each stage by truncating an NFW (Navarro, Frenk and White) profile at the tidal radius. The mass lost beyond the tidal limit is scaled by half the instantaneous orbital period of the satellite. The model can also be used to predict analytically the new density profile of the satellite. This new profile is given by a modification of the NFW density profile as a function of radius. The tidal radius is the only parameter going into this modification. The effect of numerical relaxation has been studied and quantified by performing the same simulations in lower resolutions. I find that substructures with less than 1000 particles are artificially relaxed and this process affects their mass loss and results in their premature disruptions. This underlines the utility of an analytic model predicting the evolution of substructures in minor mergers.