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We investigate the asymptotic behaviour of the wetting front arising from unsaturated flow in porous media wherein the liquid saturation θ obeys a nonlinear diffusion equation having moisture diffusivity that is an exponential function D(θ) = Do exp(βθ). For values of the physical parameters corresponding to actual porous media, the diffusivity at the(More)
The motion of exible bres suspended in an incompressible uid is of interest to researchers in a wide variety of elds, including reinforced composite materials, biotechnology and the pulp and paper industry. In this work, we concentrate on the application to pulp bres and demonstrate how the complex hydrodynamic interaction between a exible bre and the(More)
The immersed boundary method is known to exhibit a high degree of numerical stiiness, which is associated with the interaction of immersed elastic bres with the surrounding uid. We perform a linear analysis of the underlying equations of motion for immersed bres, and identify a discrete set of bre modes which are associated solely with the presence of the(More)
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A linear stability analysis is performed on a two-dimensional version of the \immersed ber problem", formulated by C. Peskin to model the ow of uid in the presence of a mesh of moving, elastic bers. The purpose of the analysis is to isolate the modes in the solution which are associated with the ber, and thereby determine the eeect of the presence of a ber(More)
The Gaussian plume model is a standard approach for studying the transport of airborne contaminants due to turbulent diffusion and advection by the wind. This paper reviews the assumptions underlying the model, its derivation from the advection-diffusion equation, and the key properties of the plume solution. The results are then applied to solving an(More)
We accept this thesis as conforming to the required standard In presenting this thesis in partial fullllment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive c o p ying of this thesis for scholarly(More)
In this paper, we investigate a traffic model similar to the Lighthill–Whitham– Richards model, consisting of a hyperbolic conservation law with a discontinuous, non-convex, piecewise-linear flux. Using Dias and Figueira's mollification framework, analytical solutions to the corresponding Riemann problem are derived. For certain initial data, these Riemann(More)