This thesis presents a three-dimensional groundwater modeling of Wekia springshed in central Florida using a numerical model, WASH123D. Springs have historically played an important role in Florida's history. The Wekiva River is a spring-fed system associated with about 19 springs connected to the Floridan aquifer. With increased urbanization and population growth in this region, there has been an increased strain on the water levels of Floridan aquifer which is a major source of potable water. Maintaining groundwater recharge to the aquifer is a key factor of the viability of the regional water supply as well as Wekiva ecosystem. Hence, the first-principle, physics-based watershed model WASH123D has been applied to conduct the study of Wekiva "springshed", which is the recharge area and watershed contributing groundwater and surface water to the spring. In this work, the hydrogeologic conditions of the Wekiva springshed are discussed followed by the modeling details such as mathematical background, domain discretization and initial and boundary conditions considered. Finally, the results from the model are discussed. The Wekiva WASH123D model was run to evaluate the average, steady state 1995 hydrological conditions. The distribution of simulated Floridan aquifer system groundwater levels using WASH123D shows very good agreement with the field observations at corresponding locations.

Rivers are considered as one of the most important surface water resources on the earth. During the time, most of the rivers on the earth experienced evolution and changes. River bends and confluences are one of the common cases in most rivers. There is a significant impact of the flow on the cross-sectional profile of river bends and confluences. Secondary currents are one of the important features that characterize flow in river bends and confluences. In such currents, fluid particles follow a helical path instead of moving nearly parallel to the axis of the channel. The local imbalance between the vertically varying centrifugal force and the cross-stream pressure gradient results in generating the secondary flow and raising a typical motion of the helical flow. Several studies, including experimental or mathematical, have been conducted to examine flow characteristics in curved open channels, river meanders, or confluences. In this research, the influence of secondary currents is studied on the elevation of water surface and the hydraulic structures in channel bends and confluences by employing a 3D OpenFOAM numerical model. The research implements a 3D OpenFOAM numerical model to simulate the horizontal distribution of the flow. In addition, the progress in unraveling and understanding the bend and confluent dynamics is discussed. The finite volume method in OpenFOAM software is used to simulate and examine the behavior of the secondary current. Thereafter, a comparison between the experimental data and a numerical model is conducted. Two sets of experimental data are used as the dataset for these two experiments are complete and validated; the data provided by Rozovskii (1961) for a sharply curved channel, and the dataset provided by Shumate (1998) for a confluent channel. Two solvers in OpenFOAM software were selected to solve the problem regarding the experiment: InterFoam and PisoFoam. InterFoam is a transient solver for incompressible flow that is used with open channel flow with Free Surface Model. PisoFoam is a transient solver for incompressible flow that is used with closed channel flow and Rigid-Lid Model. Various turbulence models (i.e., Standard k-ε, Realizable k-ε) are applied in the numerical model to assess the accuracy of turbulence models in predicting the behavior of the flow. The accuracies of various turbulence models are examined and discussed.

<p>The local corrosion of refractories at the slag/gas interface is a serious problem that limits the life of the refractories.Although, there have been several studies focused on understanding the Marangoni effect on the refractory dissolution process, there is little quantifiable analysis available. The aim of this study is to establish a better fundamental understanding of refractory dissolution mechanisms, and develop appropriate models for predicting the extent and rate of slag-line dissolution.</p> <p>In the first part of this research, experimental studies using a high temperature dip technique were performed: MgO refractory in SiO₂-CaO-FeO_x-MgO slag and Al₂O₃- SiO₂-CaO-FeO_x-MgO. The experiments were conducted at varies temperature. There was significant evidence of a spinel phase formed at the slag/refractory interface for slags containing 20wt.% Al₂O₃. This existence of the spinel seems to have retarded the dissolution of the refractory. The decrease in erosion rate in the presence of spinel is in proportion to the decrease in the equilibrium MgO concentration at the slag/solid interface. The activation energy is calculated from the relationship of effective mass transfer coefficient vs. temperature and found in the range of mass transfer activation energy.</p> <p>The second part of this search is developing a numerical model to predict the slag-line dissolution. An effective algorithm for analysis of unsteady Marangoni convection in refractory slag line dissolution has been developed. The results show that the Marangoni effect plays a very important role in slag-line erosion at this condition; both the moving boundary condition and curved surface condition have significant effects on the slag-line erosion rate. The comparison of experimental and numerical results shows that the model can predict the refractory maximum corrosion distance caused by Marangoni flow at the slag line. However, the eroded material volume was predicted within 20~30% deviation</p> / Doctor of Philosophy (PhD)

The electronic band structure of a semiconductor is an essential property to determine most of its optical characteristics. The complexity of the energy band structure calculations makes analytical calculations impossible. Any calculation leading to electronic band structures has to utilize numerical methods. In this thesis, two solvers were developed to calculate the energy band structure of 1D Kronig-Penney lattice, 30 diamond lattice-structure and silicon lattice. In this thesis, many of the important methods of calculating the energy band structures were discussed. Through comparisons among different methods, we have determined that Self-Consistent Pseudopotential Method, SCPM, is the most suitable method for calculating the energy band structures when self-sufficiency and accuracy are of special importance. The SCPM is an iterative method which was utilized in this thesis by using efficient numerical methods. Instead of using conventional numerical methods such as Finite Difference Method or Finite Element Method which cause inefficiency, this thesis calculates the energy band structure by utilizing Orthogonal Plane-Wave expansion of the potentials. The 1D electronic band structure solver was developed as a foundation for the implementation of the 30 electronic band structure solver. It uses a minimal number of Fourier coefficients to calculate the energy band structure of the 1D Lattices without compromising accuracy. The 30 electronic band structure solver development needs multiple changes and modifications to the 1D solver. As the 30 solver is essentially made using the 10 solver platform, it is also efficient and needs a minimal number of Fourier coefficients for accurate results. The 30 solver can be used for either Nearly Free Electron Method, NFEM, or SCPM calculations. The NFEM calculations were done on the diamond lattice structure. The results were shown to be the same as the benchmarks of [28, 80]. The silicon lattice energy band structure was also calculated with the 30 solver using SCPM with LOA. The results were in the same range as the four sets of data gathered from three benchmarks [58, 81, 82], showing good agreement. Based on the two comparisons made for the 30 solver, it was shown that it is a reliable and efficient program to calculate energy band structures of the 30 lattices. / Thesis / Master of Applied Science (MASc)

Yes / In this study, the evolution process of the swallow-tailed flip bucket water nappe entering into the plunge pool is simulated by using the standard 𝑘-𝜀 turbulence model and the volume of fluid method. The effects of the upstream opening width ratio and downstream bucket angle on the flow pattern, the unit discharge distribution and the impact pressure distribution are studied. Based on the numerical results, the inner and outer jet trajectories are proposed by using the data. Results show that the longitudinal stretching length decreases with the increase of the upstream opening width ratio, and increases with the increase of the downstream bucket angle. The water nappe enters the plunge pool in a long strip shape. Thus, the unit discharge distribution of water nappe entry is consistent with the pressure distribution at the plunge pool bottom. The upstream opening width ratio and downstream bucket angle should be chosen as their intermediate values in order to have a uniform discharge distribution and to reduce the pressure peak at the plunge pool floor, which is effectively to avoid instability and destruction of plunge pool floor. / National Science Fund for Distinguished Young Scholars (No. 51625901) and National Nature Science Foundation of China (No: 51579165).

The importance of precise values for the parameters used in heat and mass transfer models has been demonstrated by many research studies. Thermal conductivity values used in previous models are usually empirical and fluctuate. Theoretical analysis and estimations of wood thermal conductivities in the radial and tangential directions were conducted with the geometric models built up from the macro- and micro-structure observations. Theoretically, thermal conductivity in the radial direction is about 1.5 to 2.5 times of the tangential direction for softwood species with moisture content (MC) below Fiber Saturation Point (FSP). When MC is over the FSP, tangential radial thermal conductivity both increase dramatically and are linear function of MC. The two thermal conductivity values are close with a ratio of near one estimated by the model for MC above the FPS. In hardwood species, radial thermal conductivity estimated by the model is 1.5 times of the tangential thermal conductivity. Validation tests for model estimations of thermal conductivities in the radial and tangential directions for three wood species showed the reliability of the geometric models developed in this project. Correlations between the wood thermal conductivity and structure parameters, such as latewood percentage and cell wall percentage, were examined. Linear relationships for the thermal conductivity and average temperature in wood were established in both radial and tangential directions of three wood species. A two-dimensional transient heat conduction model was developed utilizing thermal conductivity values derived from geometric models. The anisotropic material property affect on heat transport in radial and tangential directions was discussed using an assumed situation. The simulation run showed slightly faster heat flow in the radial direction than in the tangential direction due to higher thermal conductivity in the radial direction. Validation tests on practical wood blocks showed the 2D model with the use of theoretical thermal conductivity values can predict good temperature distribution in wood during the heating process. However, in the practical wood samples with curved rings on the cross section, no significant difference was found in the two transverse directions. Mathematica software was introduced in this study for the intense and complicated math calculations and model programming. Mathematica was found to be a powerful technique for solving sophisticated math problems. It had abundant and flexible plotting options for providing optimized presentations for the results. These advantages make Mathematica popular for engineering modeling research. / Ph. D.

Characterizing and preserving available groundwater resources within crystalline rocks is pertinent to understanding and predicting resources for ecosystems worldwide. Crystalline-rock aquifers, with favorable structure and climate, can be pumped year-round to meet local domestic demand. The Ploemeur hydrogeologic site, near the southern coast of Brittany, France, is characterized by a structurally complex fractured mica-schist and granite confined aquifer system. A contact zone, which acts as the main localized flow path through the aquifer, separates the two crystalline units, and a sub-vertical permeable fault zone cross-cuts the crystalline bedrock and contact zone. Using field observations, recharge estimates, and a calibrated three-dimensional numerical multi-zone MODFLOW 6 model, we present preferential flow paths of recharge infiltrating the complex geology of the Ploemeur hydrogeological site during pumping conditions. Using MODPATH to track groundwater and recharge path lines, we determine that water extracted from the aquifer originates from higher elevation areas west of the pumping site. Particle tracking analyses indicate that precipitation simulated over the pumping zone takes a minimum of two years to reach the pumping wells and travels up to 100 m in distance. Analyses of the water budget of the aquifer system using Zonebudget show that storage contributes significantly to the productivity of the system. Based on these analyses, we determine that recharge mechanisms such as piston flow and preferential flow play important roles in the Ploemeur hydrogeologic site. Though the Ploemeur site is unique in its composition and geometry, the methods used to characterize and monitor the aquifer can be applied to fractured crystalline-rock aquifers globally. Fractured crystalline-rock aquifers make up 10% of the region's freshwater sources, thus understanding their flow mechanisms contributes greatly to the management of freshwater resources. / Master of Science / Groundwater aquifers are a common source of freshwater worldwide as groundwater makes up 30% of Earth's freshwater resources. Porous, sedimentary aquifers, made of materials such as sand or gravel, are well studied; however, the less understood aquifers found in crystalline bedrock are also found all over the world. Generally, igneous and metamorphic crystalline rocks are not porous and have low permeabilities, but fractures and faults in the crystalline rock can increase the ability for water to travel through the system. The Ploemeur hydrogeologic site, located on the southern coast of Brittany, France, is a productive fractured crystalline-rock groundwater aquifer producing freshwater year round. The productivity of this aquifer is attributed to the increased hydraulic conductivity associated with the intersection of two permeable features: a subvertical fault zone and a sub-horizontal contact zone. Despite the aquifer's output, recharge travels very slowly into the system due to the depth, heterogeneity, and clay content in an overlying layer of weathered rock fragments and soil. In this study, we create a three-dimensional numerical model using MODFLOW to simulate precipitation in different locations to see how it travels through the aquifer to the site of groundwater pumping. We see that the recharge prefers to travel topographically from regions of higher elevation to lower elevation. The recharge preferentially travels through the geologic features with higher permeabilities, including the fault zone, regolith, and contact zone, but it does still travel through the less permeable, crystalline bedrock units. Even in the features with the higher permeabilities, simulated recharge requires a minimum of 2 years to travel from the land surface to the pumping wells. The pumping wells extract significant water from storage, as seen in our water budget calculations of each geologic unit. We see two recharge mechanisms present in the hydrogeologic site: piston flow, where young water displaces older water from the storage, and preferential flow, where recharge prefers to travel through regions with higher hydraulic conductivity. Understanding the recharge mechanisms in crystalline aquifers is pertinent to our knowledge of freshwater resources as crystalline aquifers make up approximately 10% of all groundwater supplies.

In this thesis we study modeling and simulation approaches for multiscale biochemical systems. The thesis addresses both modeling methods and simulation strategies. In the first part, we propose modeling methods to study the behavior of the insulin secretion pathway. We first expand the single cell model proposed by Bertram et. al. to model multiple cells. Synchronization among multiple cells is observed. Then an unhealthy cell model is proposed to study the insulin secretion failure caused by weakening of mitochondria function. By studying the interaction between the healthy and unhealthy cells, we find that the insulin secretion can be reinstated by increasing the glucokinase level. This new discovery sheds light on antidiabetic medication. In order to study the stochastic dynamics of the insulin secretion pathway, we first apply the hybrid method to model the discrete events in the insulin secretion pathway. Based on the hybrid model, a probability based measurement is proposed and applied to test the new antidiabetic remedy. In the second part, we focus on different simulation schemes for multiscale biochemical systems. We first propose a partitioning strategy for the hybrid method which leads to an efficient way of building stochastic cell cycle models. Then different implementation methods for the hybrid method are studied. A root finding method based on inverse interpolation is introduced to implement the hybrid method with three different ODE solvers. A detailed discussion of the performance of these three ODE solvers is presented. Last, we propose a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. The efficiency is demonstrated by applying this new strategy on a stiff decaying dimerization model and a heat shock protein regulation model. / Ph. D.

The 2010-2011 Canterbury, New Zealand, Earthquake Sequence (CES) resulted in 185 fatalities and approximately $NZ40 billion in damage, much of which was due to liquefaction and related phenomena. As a result, an extensive soil improvement field testing program was initiated and Rammed Aggregate Piers� (RAP) were shown to be a feasible method to mitigate the risk from liquefaction during future events. To better design and more fully assess the efficacy of reinforcement techniques against liquefaction, pre- and post-treatment in-situ test data are compiled, to include results from cone penetration tests (CPT), direct-push crosshole tests, and vibroseis (T-Rex) shaking tests. The data are used to evaluate the capabilities of numerical tools to predict the liquefaction response of unimproved and improved sites. A finite difference (FD) numerical model is developed in a FLAC platform and a coupled analysis using the Finn model with Byrne (1991) formulation is conducted. The FD model calibrated for top-down shakings similar to the vibroseis tests succeeded in qualitatively reproducing the general observed behavior without quantitatively matching the in-situ values for shear strains and excess pore pressure ratios. The introduction of the RAP elements to the FD model reduced the shear strain, but slightly overestimated that reduction. Considering more advanced constitutive models that better simulate the complexity of the soil behavior under dynamic loading would likely increase the accuracy of the predicted response. / MS / During earthquakes, a significant loss of strength in soil can occur. This phenomenon, known as liquefaction, can have a devastating impact on the area affected. The 2010-2011 Canterbury, New Zealand, Earthquake Sequence (CES) resulted in 185 fatalities and approximately $NZ40 billion in damage, much of which was due to liquefaction and related phenomena. Consequently, the New Zealand Earthquake Commission implemented a field testing program in order to investigate the efficiency of ground improvement techniques in reducing soil liquefaction potential. One of the tested techniques was Rammed Aggregate Piers™ (RAP) and was shown to be a feasible method in mitigating the risk from liquefaction during future events. The focus of this study is to develop a numerical model capable of predicting the liquefaction response of unimproved and RAP-improved sites. Pre- and post-treatment test data are therefore compiled and used to calibrate the model. The numerical model calibrated for shakings similar to the on-site tests succeeded in qualitatively, but not quantitatively, reproducing the behavior observed in the field. The introduction of the RAP elements to the model revealed an improvement against liquefaction hazard; however, the improvement was overestimated compared to the field results. Considering more advanced numerical features that better simulate the complexity of the soil behavior under dynamic loading would likely increase the accuracy of the predicted response.

Thesis (PhD (Civil Engineering))--Stellenbosch University, 2008. / The velocity, density and turbulence profiles of a horizontal, saline gravity current were measured experimentally. Stable stratfication damped the turbulence and prevented the gravity current from becoming self-similar. The velocity and density prfiles were measured simultaneously and non-intrusively with particle image velocimetry scalar (PIV-S) technology. The application of the PIV-S technology had to be extended in order to measure the continuously stratified gravity current. Measurement of the Reynolds fluxes and Reynolds stresses revealed the anisotropic turbulent transport of mass and momentum within the gravity current body. These measurements also allowed the interaction between turbulence and stratification to be studied. The measured profiles were used to evaluate the accuracy of a gravity current model which did not assume self-similarity. The gravity current model was based on a Reynolds-averaged Navier-Stokes (RANS) multispecies mixture model. The Reynolds flux and Reynolds stress profiles did not show self-similarity with increasing downstream distance. Comparison of the vertical and horizontal Reynolds fluxes showed that gravity strongly damped the vertical flux. At a downstream location, where the bulk Richardson number was supercritical, the shear production profile had a positive inner (near bed) peak and a positive outer peak, while the buoyancy production pro le had a negative outer peak. Further downstream, where the bulk Richardson number was near-critical, the outer shear and buoyancy production peaks disappeared, due to the continuous damping of the turbulence intensities by the stable stratification. However, near bed shearing allowed the inner shear production peak to remain. Sensitivity analyses of different turbulence models for the gravity current model showed that the standard k -e turbulence model, as well as the Renormalization Group theory (RNG) k -e turbulence model, generally underpredicted the mean streamwise velocity profile and overpredicted the excess density pro le. The flux-gradient hypothesis, used to provide closure for the Reynolds uxes, modelled the vertical Reynolds ux reasonably, but not the horizontal flux. This did not compromise the results, since the horizontal gravity current had the characteristics of a boundary-layer ow, where the horizontal flux does not contribute significantly to the flow structure. It was shown that the gravity current model, implementing the standard k -e turbulence model with a constant turbulent Schmidt number of ot = 1;3, produced profiles which were within 10% - 20% of the measured profiles.