Modeling interstitial fluid flow involves processes such as fluid diffusion, convective transport in the extracellular matrix, and extravasation from blood vessels. In all of these processes, computational fluid dynamics can play a crucial role in elucidating the mechanisms of fluid flow in solid tumors and surrounding tissues. To date, microvasculature flow modeling has been most extensively studied with simple tumor shapes and their capillaries at different levels and scales. With our proposed numerical model, however, more complex and realistic tumor shapes and capillary networks can be studied. First, a mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, the interstitial pressure distribution results in a non-uniform distribution of drug particles. Pressure distribution for different values of necrotic radii is examined, and two new parameters, the critical tumor radius and critical necrotic radius, are defined. In specific ranges of these critical dimensions the interstitial fluid pressure is relatively lower, which in turn leads to a diminished opposing force against drug movement and a subsequently higher drug concentration and potentially enhanced therapeutic effects. In this work, the numerical model of fluid flow in solid tumors is further developed to incorporate and investigate non-spherical tumor shapes such as prolate and oblate ones. Using this enhanced model, tumor shape and size effects on drug delivery to solid tumors are then studied. Based on the assumption that drug particles flow with the interstitial fluid, the pressure and velocity maps of the latter are used to illustrate the drug delivery pattern in a solid tumor. Additionally, the effects of the surface area per unit volume of the tissue, as well as vascular and interstitial hydraulic conductivity on drug delivery efficiency, are investigated. Using a tumor-induced microvasculature architecture instead of a uniform distribution of vessels provides a more realistic model of solid tumors. To this end, continuous and discrete mathematical models of angiogenesis were utilized to observe the effect of matrix density and matrix degrading enzymes on capillary network formation in solid tumors. Additionally, the interactions between matrix-degrading enzymes, the extracellular matrix and endothelial cells are mathematically modeled. Existing continuous and discrete models of angiogenesis were modified to impose the effect of matrix density on the solution. The imposition has been performed by a specific function in movement potential. Implementing realistic boundary and initial conditions showed that, unlike in previous models, the endothelial cells accelerate as they migrate toward the tumor. Now, the tumor-induced microvasculature network can be applied to the model developed in Chapters 2 and 3. Once the capillary network was set up, fluid flow in normal and cancerous tissues was numerically simulated under three conditions: constant and uniform distribution of intravascular pressure in the whole domain, a rigid vascular network, and an adaptable vascular network. First, governing equations of sprouting angiogenesis were implemented to specify the different domains for the network and interstitium. Governing equations for flow modeling were introduced for different domains. The conservation laws for mass and momentum, Darcy’s equation for tissue, and a simplified Navier Stokes equation for blood flow through capillaries were then used for simulating interstitial and intravascular flows. Finally, Starling’s law was used to close this system of equations and to couple the intravascular and extravascular flows. The non-continuous behavior of blood and the adaptability of capillary diameter to hemodynamics and metabolic stimuli were considered in blood flow simulations through a capillary network. This approach provided a more realistic capillary distribution network, very similar to that of the human body. This work describes the first study of flow modeling in solid tumors to realistically couple intravascular and extravascular flow through a network generated by sprouting angiogenesis, consisting of one parent vessel connected to the network. Other key factors incorporated in the model for the first time include capillary adaptation, non-continuous viscosity blood, and phase separation of blood flow in capillary bifurcation. Contrary to earlier studies which arbitrarily assumed veins and arteries to operate on opposite sides of a tumor network, the present approach requires the same vessel to run and from the network. Expanding the earlier models by introducing the outlined components was performed in order to achieve a more-realistic picture of blood flow through solid tumors. Results predict an almost doubled interstitial pressure and are in better agreement with human biology compared to the more simplified models generally in use today.

Of all the trace elements emitted during coal combustion, mercury is most problematic. Mercury from the atmosphere enters into oceanic and terrestrial waters. Part of the inorganic Hg in water is converted into organic Hg (CH3Hg), which is toxic and bioaccumulates in human and animal tissue. The largest source of human-caused mercury air emissions in the U.S is from combustion coal, a dominant fuel used for power generation. The Hg emitted from plants primarily occurs in two forms: elemental Hg and oxidized Hg (Hg2+). The coal chlorine content and ash composition, gas temperature, residence time and presence of different gases will decide the speciation of Hg into Hg0 and Hg2+. For Wyoming coal the concentrations of mercury and chlorine in coal are 120ppb and 140ppb. In order to understand the basic process of formulation of HgCl2 and Hg0 a numerical model is developed in the current work to simulate in the detail i) heating ii) transient pyrolysis of coal and evolution of mercury and chlorine, iii) gas phase oxidation iv) reaction chemistry of Hg and v) heterogeneous oxidation of carbon during isolated coal particle combustion. The model assumes that mercury and chlorine are released as a part of volatiles in the form of elemental mercury and HCl. Homogenous reaction are implemented for the oxidation of mercury. Heterogeneous Hg reactions are ignored. The model investigates the effect of different parameters on the extent of mercury oxidation; particle size, ambient temperature, volatile matter, blending coal with high chlorine coal and feedlot biomass etc,. Mercury oxidation is increased when the coal is blended with feedlot biomass and high chlorine coal and Hg % conversion to HgCl2 increased from 10% to 90% when 20% FB is blended with coal. The ambient temperature has a negative effect on mercury oxidation, an increase in ambient temperature resulted in a decrease in the mercury oxidation. The percentage of oxidized mercury increases from 9% to 50% when the chlorine concentration is increased from 100ppm to 1000ppm. When the temperature is decreased from 1950 K to 950 K, the percentage of mercury oxidized increased from 3% to 27%.

A combination of in situ sampling and numerical modeling was used to investigate the effects of mesoscale (<50 km) circulation patterns and stratification on the evolution of hypoxia on the Louisiana Shelf. Temperature, salinity, and dissolved oxygen concentrations records reveal the presence of an alongshelf meander, which is manifested vertically and horizontally as a wave-like distribution of the properties in the water column. The observations suggest the meander is a ubiquitous characteristic of the shelf with alongshore spatial scale approximately 50 km and less, which is consistent with the locations of sandy shoals along the coast and the local deformation radius. Twelve numerical experiments using an idealized three-dimensional shelf circulation model were performed to evaluate the relative importance of the variable bottom topography and freshwater forcing on the development, evolution, and scales of the dynamic instabilities. The inclusion of the shoals into the bottom topography showed the development of the dynamic instabilities as the flow passed over the shoals and downstream. Introduction of fresh water onto the shelf resulted in greater salinity differences, and, as a consequence in the formation of the dynamically unstable salinity fronts along the plume edge. The combination of the freshwater forcing and shoaling topography produced competing and complex interactions. Six numerical experiments were analyzed in order to investigate the effect of dynamic instabilities on spatial and temporal patterns of dissolved oxygen concentrations along the shelf. Although a linear relationship between Brunt-Väisälä frequency and dissolved oxygen deficit was expected, a nonlinear loop-like relationship was discovered that reflects the response of biochemical properties to the alongshelf variability of the density field. Comparison of the numerical modeling runs to observations of density and dissolved oxygen concentrations on the Louisiana Shelf reinforces the importance of physical processes such as topographic steering and/or freshwater forcing on the alongshore distribution of physical and biochemical properties. It suggests that the time scales of respiration (~3 days) and buoyancy transfer processes (~5-7 days), associated with the physical processes that are responsible for water column stability and ventilation, are similar to the time scales associated with the benthic respiration rates.

Carbon Dioxide (CO₂) sequestration requires that the injected CO₂ be permanently trapped in the subsurface and not leak from the target location. To accomplish this, it is important to understand the main mechanisms associated with CO₂ flow and transport in the subsurface once CO₂ is injected. In this work CO₂ seeps at the Crystal Geyser site were studied using modeling and simulation to determine how CO₂ geochemically reacts with formation brines and how these interactions impact the migration of CO₂. Furthermore different scenarios for CO₂ migration and seepage along the Grand Wash fault are studied and the possible outcomes for these different scenarios are documented. The GEM (Generalized Equation-of-State Model) from CMG Ltd. was used to perform the simulation studies. A 2-D model was built without geochemical reactions to mainly study the mechanism associated with dissolution of CO₂ gas. The process of CO₂ release from the brine as the fluid mixture flows up along the fault was modeled. Then, 3-D models with geochemical reactions were built for CO₂ migration corresponding to two different sources of CO₂ - deep crustal ₂ and CO₂-dissolved in groundwater. In both these cases, CO₂ reacted with the aqueous components and minerals of the formation and caused carbonate mineralization. In the case of deep crustal CO₂ source, there were vertical patterns of calcite mineralization simulated along the fault that indicated that calcite mineralization might be localized to isolated vertical flow paths due to vertical channeling of CO₂ from the crust. In the case of CO₂-dissolved groundwater flowing along the sandstone layers, calcite mineralization is spread over the entire fault surface. In this case, the groundwater flow is interrupted by the fault and there is vertical flow along the fault until a permeable sandstone layer is encountered on the other side of the fault. This vertical migration of CO₂-saturated brine causes a release in pressure and subsequent ex-solution of CO₂. As a result, modeling allowed us to establish difference in surface expression of CO₂ leakage due to two different CO₂ migrations scenarios along the fault and helped develop a scheme for selecting appropriate model for CO₂ leakage based on surface observation of travertine mounds. A key observation at the Crystal Geyser site is the lateral migration of CO₂ seep sites over time. These migrations have been confirmed by isotope studies. In this modeling study, the mechanism for migration of seep sites was studied. A model for permeability reduction due to precipitation of calcite was developed. It is shown using percolation calculations that flow re-routing due to permeability alterations can result in lateral migration of CO₂ seeps at rates comparable to those established by isotope dating. / text

At present, most of the energy power consumed in the world is produced by fossil fuel combustion, which has raised increasing interest in renewable energy technologies, non-conventional oil and gas reservoirs, and nuclear power. Innovative nuclear fuels and reactors depend on the economical and environmental impacts of waste management. Disposals in mined geological formations are viewed as potential consolidated storage facilities before final disposition. Different stress paths during construction result in different kinds of failure mechanisms, which alter rock strength and induce anisotropy of rock elastic properties. Crack propagation in rock can be originated by these engineering activities (excavation, drilling, mining, building overburden), or by changes of the natural environment (tectonic processes, erosion or weathering). Damage is a mathematical variable that can represent a variety of microstructure changes, such as crack density, length, aspect ratio and orientation. The framework of Continuum Damage Mechanics allows modeling the resulting reduction in strength and stiffness, as well as the associated stress-induced anisotropy and irreversible deformation. This work presents a modeling framework for anisotropic crack propagation in rock, in conditions of stress typical of geological storage and oil and gas extraction. Emphasis is put on the prediction of the damage zone around cavities and ahead of pressurized fracture tips. An original model of anisotropic damage, the Differential Stress Induced Damage (DSID) model, is explained. The Drucker-Prager yield function is adapted to make the damage threshold depend on damage energy release rate and to distinguish between tension and compression strength. Flow rules are derived with the energy release rate conjugate to damage, which is thermodynamically consistent. The positivity of dissipation is ensured by using a non-associate flow rule for damage, while nonelastic deformation due to damage is computed by an associate flow rule. Stress paths simulated at the material point illustrate damaged stiffness and deformation variations in classical rock mechanics tests. The maximum likelihood method was employed to calibrate and verify the DSID model against stress-strain curves obtained during triaxial compression tests and uniaxial compression tests performed on clay rock and shale. Logarithmic transformation, normalization and forward deletion allowed optimizing the formulation of the DSID model, and reduce the number of damage constitutive parameters from seven to two for clay rock. The DSID model was implemented in ABAQUS Finite Element (FE) software. The iterative scheme was adapted in order to account for the non-linearities induce both by damage and damage-induced deformation. FE simulations of laboratory tests capture size an intrinsic anisotropy effects on the propagation of damage in rock. Smeared DSID zones representing shale delamination planes avoid some convergence problems encountered when modeling discontinuities with debonded contact surface elements. FE simulations of tunnel excavation, fracture propagation and borehole pressurization were performed to illustrate the evolution of the damage zone and the impact on energy dissipation, anisotropy of deformation, and loss of stiffness. Future work will focus on coupling the propagation of fractures with the evolution of the damage process zone, and on the transition from continuum damage to discrete fracture upon crack coalescence.

While several lines of evidence strongly hint at the biological importance of impact-induced hydrothermal systems during the impact cataclysm at ~3.9 Ga, these systems are not well understood. There is unambiguous evidence of hydrothermal activity at many terrestrial craters, but the available samples represent a very limited number of crater diameters and locations within the crater. Therefore, computer models are crucial for learning how impact-induced hydrothermal systems work, how long they last, and whether they provide suitable environments for thermophilic microorganisms. This dissertation presents detailed simulations of hydrothermal activity at the terrestrial craters Chicxulub and Sudbury, as well as at range of crater sizes on early Mars. A well-established computer code HYDROTHERM was used. The models for terrestrial craters were constrained by seismic, magnetic, and gravity surveys, as well as petrological, mineralogical, and chemical analyses of samples (by others).Sudbury crater is ~180 km in diameter, and 1.85 Ga. Simulation results indicate that a hydrothermal system at Sudbury crater remained active for several hundred thousand to several million years, depending on assumed permeability, and produced habitable volumes of up to ~20,000 km^3.Chicxulub crater is also ~180-km in diameter, but only 65 Ma. The lifetime of the hydrothermal system ranges from 1.5 Ma to 2.3 Ma depending on assumed permeability. The temperatures and fluxes observed in the model are consistent with alteration patterns observed by others in borehole samples.Another set of simulations modeled post-impact cooling of hypothetical craters with diameters of 30, 100, and 180 km in an early Martian environment. System lifetimes, averaged for all permeability cases examined, were 67,000 years for the 30-km crater, 290,000 years for the 100-km crater, and 380,000 for the 180-km crater. Also, an ap-proximation of the thermal evolution of a Hellas-sized basin (~2000 km) suggests poten-tial for hydrothermal activity for ~10 Myr after the impact. The habitable volume reached a maximum of ~6,000 km^3 in the 180-km crater model.Possible morphological and mineralogical signs of hydrothermal activity in Martian craters were observed, both in this work and by others. These observations, while by no means definitive, are generally consistent with model predictions.

The primary purpose of the current research was to implement a numerical model to investigate the interactions between the energy consumption in Heating, Ventilating, and Air Conditioning (HVAC) systems and occupants’ thermal comfort in commercial buildings. A numerical model was developed to perform a thermal analysis of a single zone and simultaneously investigate its occupants’ thermal sensations as a non-linear function of the thermal environmental (i.e. temperature, thermal radiation, humidity, and air speed) and personal factors (i.e. activity and clothing). The zone thermal analyses and thermal comfort calculations were carried out by applying the heat balance method and current thermal comfort standard (ASHRAE STANDARD 55-2004) respectively. The model was then validated and applied on a single generic zone, representing the perimeter office spaces of the Centre for Interactive Research on Sustainability (CIRS), to investigate the impacts of variation in occupants’ behaviors, building’s envelope, HVAC system, and climate on both energy consumption and thermal comfort. Regarding the large number of parameters involved, the initial summer and winter screening analyses were carried out to determine the measures that their impacts on the energy and/or thermal comfort were most significant. These analyses showed that, without any incremental cost, the energy consumption in both new and existing buildings may significantly be reduced with a broader range of setpoints, adaptive clothing for the occupants, and higher air exchange rate over the cooling season. The effects of these measures as well as their combination on the zone thermal performance were then studied in more detail with the whole year analyses. These analyses suggest that with the modest increase in the averaged occupants’ thermal dissatisfaction, the combination scenario can notably reduce the total annual energy consumption of the baseline zone. Considering the global warming and the life of a building, the impacts of climate change on the whole year modeling results were also investigated for the year 2050. According to these analyses, global warming reduced the energy consumption for both the baseline and combination scenario, thanks to the moderate and cold climate of Vancouver.

Photonic bandgap materials are periodic structures that exclude electromagnetic field propagation over frequency intervals known as bandgaps. These materials exhibit remarkable wave dispersion and have found use in many applications that require control over dynamic electromagnetic fields, as their properties can be tailored by design. The two principal objectives of this thesis are the development of a liquid crystal-based microwave photonic bandgap device whose bandgap could be tuned during operation and the design and implementation of a spectral transmission-line modeling method for band structure calculations. The description of computational methods comprises an overview of the implemented numerical routines, a derivation of the spectral properties of the transmission-line modeling method in periodic domains, and the development of an efficient sparse matrix eigenvalue algorithm that formed the basis of the spectral transmission-line modeling method. The discussion of experimental methods considers the use of liquid crystals in microwave applications and details the design and fabrication of several devices. These include a series of modified twisted nematic cells that were used to evaluate liquid crystal alignment and switching, a patch resonator that was used to measure liquid crystal permittivity, and the liquid crystal photonic bandgap device itself. Numerical experiments showed that the spectral transmission-line modeling method is accurate and substantially faster and less memory intensive than the reference plane wave method for problems of high dielectric contrast or rapidly varying spatial detail. Physical experiments successfully realized a microwave photonic bandgap structure whose bandgap could be continuously tuned with a bias voltage. The very good agreement between simulated and measured results validate the computational and experimental methods used, particularly the resonance-based technique for permittivity measurement. This work's results may be applied to many applications, including microwave filters, negative group velocity/negative refraction materials, and microwave permittivity measurement of liquid crystals.

Photonic bandgap materials are periodic structures that exclude electromagnetic field propagation over frequency intervals known as bandgaps. These materials exhibit remarkable wave dispersion and have found use in many applications that require control over dynamic electromagnetic fields, as their properties can be tailored by design. The two principal objectives of this thesis are the development of a liquid crystal-based microwave photonic bandgap device whose bandgap could be tuned during operation and the design and implementation of a spectral transmission-line modeling method for band structure calculations. The description of computational methods comprises an overview of the implemented numerical routines, a derivation of the spectral properties of the transmission-line modeling method in periodic domains, and the development of an efficient sparse matrix eigenvalue algorithm that formed the basis of the spectral transmission-line modeling method. The discussion of experimental methods considers the use of liquid crystals in microwave applications and details the design and fabrication of several devices. These include a series of modified twisted nematic cells that were used to evaluate liquid crystal alignment and switching, a patch resonator that was used to measure liquid crystal permittivity, and the liquid crystal photonic bandgap device itself. Numerical experiments showed that the spectral transmission-line modeling method is accurate and substantially faster and less memory intensive than the reference plane wave method for problems of high dielectric contrast or rapidly varying spatial detail. Physical experiments successfully realized a microwave photonic bandgap structure whose bandgap could be continuously tuned with a bias voltage. The very good agreement between simulated and measured results validate the computational and experimental methods used, particularly the resonance-based technique for permittivity measurement. This work's results may be applied to many applications, including microwave filters, negative group velocity/negative refraction materials, and microwave permittivity measurement of liquid crystals.

Part I of this thesis investigates current deformation in western British Columbia from northern Vancouver Island in the south to Haida Gwaii in the north. The area is characterized by transition from the Cascadia subduction zone to the Queen Charlotte transform fault. The tectonic setting involves interactions between the Pacific, North America, Juan de Fuca, and Explorer plates, and the Winona block, involving a number of plate boundaries: the mainly strike-slip Queen Charlotte, Revere-Dellwood-Wilson and Nootka faults, the Explorer ridge, and the Cascadia subduction zone. Using GPS campaign data from 1993 to 2008 I derive a new crustal velocity field for Northern Vancouver Island and the adjacent mainland, and integrate it with previous velocity fields developed for Haida Gwaii, southern Vancouver Island and the adjacent mainland. The northern limit of the subduction zone is confirmed to be at Brooks Peninsula, where the direction of the crustal motion changes abruptly from ENE to NNE. I use viscoelastic models to explore what percentage of the observed deformation is transient, related to the earthquake cycle, and how much is permanent ongoing deformation, distributed off the continental margin. Previous authors have developed two competing end-member models that can each explain how the Pacific/North America plate convergence is accommodated off Haida Gwaii. These models assume either internal crustal shortening or underthrusting of the Pacific plate. These new GPS data allow me to conclude that underthrusting does occur, and that a small component (<15%) of the observed data reflects long-term deformation. South of Haida Gwaii the distinction between transient and long-term deformation is not as clear; however, I conclude that transient deformation alone cannot fully explain the observed velocities, and so long-term deformation likely must also occur. Part II of the thesis investigates the updip and downdip limits of the seismogenic zone of the Sumatra megathrust fault. Temperature and downdip changes in formation composition are controls proposed for these limits. To examine the thermal control I developed 2-D finite element models of the Sumatra subduction zone with smoothly varying subduction dip, variable thermal properties of the rock units, frictional heating along the rupture plane, and an appropriate thermal state for the incoming plate. The common updip thermal limit for seismic behaviour of 100-150°C occurs close to or at the trench in agreement with the rupture limit of the 2004 earthquake. Off central Sumatra the common downdip thermal limit range of 350-450°C occurs at 30-60 km depth. The 350°C isotherm location is in agreement with the earthquake limits but 450°C is deeper. North of Sumatra, 350°C occurs ~14 km deeper than the earthquake rupture limit. The proposed composition control for the downdip limit, the intersection of the subduction thrust with the forearc mantle, is at a depth of ~30 km, 140-200 km from the trench, in good agreement with the earthquake limits. These results support the conclusion that the Sumatra updip seismogenic limit is thermally controlled, but the downdip limit is governed by the intersection of the downgoing plate with the forearc Moho. / Graduate