QC 20110616

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Millions of Canadians rely on private groundwater wells to access drinking water, which presents many challenges including a lack of government regulations, and limited resources for maintenance, monitoring, management, and protection. These challenges result in an increased risk of acute gastrointestinal illness in private well users. The goal of this work is to improve the understanding of drivers of E. coli fate and transport in groundwater using a data-driven approach to better inform well owners and policy makers. Specifically, the objectives include: exploratory analysis of the physical and human drivers of private well contamination; advancing the understanding of the relationships between land use-land cover and E. coli presence in wells; assessment of rainfall intermittency patterns as a driver of contamination, as an alternative to standard lag times; and, the development of data-driven explanatory models for E. coli contamination in private wells that move towards a novel coupled-systems approach. This research utilizes a large dataset with 795,023 contamination observations, 253,136 unique wells, and over 33 variables (i.e., microbiological, hydrogeological, well characteristic, meteorological, geographical, and testing behaviour) across Ontario, Canada between 2010 and 2017. Data used includes the Well Water Information Database, Well Water Information System, Daymet, Provincial Digital Elevation Model, Ontario Land Cover Compilation, Southern Ontario Land Resource Information System, and Roads Network. Data analysis methods range from univariate and bivariate analyses to supervised and unsupervised machine learning techniques, including regression, clustering, and classification. This work has contributed important understandings of the relationships between E. coli contamination and well and aquifer characteristics, seasonality, weather, and human behaviour. Specifically, increased well depth reduced, but did not eliminate, likelihood of contamination; wells completed in consolidated material increased likelihood of contamination; the most significant driver of contamination was identified as land use - land cover, which was categorized into four classes of E. coli contamination potential for wells, ranging from very high to low; latitude was found to drive seasonality and consequent weather patterns, leading to the creation of geographically-based seasonal models; liquid water (i.e., rainfall, snow melt) was a key driver of contamination, where increased water generally increased presence of E.coli while causing decreasing prevalence; time of year, not habit, drove user testing, generally peaking in July; and, a surrogate measure of well user stewardship was identified as driving time to closest drop-off location. Further, this work has contributed methodological advancements in identifying drivers of groundwater contamination including: utilizing literature confidence ratings alongside regression analyses to supply strategic direction to policy makers; demonstrating the value of large datasets in combination with innovative machine learning techniques, and subject matter expertise, to identify improved physically-based understandings of the system; and, highlighting the need for coupled-systems approaches as physical models alone do not capture human behaviour-based factors of contamination. / Thesis / Doctor of Engineering (DEng) / There are millions of people globally relying on private groundwater to access drinking water. Unfortunately, these wells come with many challenges including a lack of government regulations, and limited resources for maintenance, management, and protection. These challenges also result in an increased risk of illness in private well users. Groundwater research is often limited by lack of numerical data, making it extremely difficult to understand how groundwater and contaminants are transported. This research utilizes a large dataset with 795,023 contamination observations, 253,136 unique wells, and over 33 variables (i.e., well and aquifer characteristics, human behaviours, weather-related) across Ontario, Canada between 2010 and 2017. The work in this thesis utilizes a data-driven approach, using various machine learning techniques combined with subject matter expertise, to uncover trends and insights into when and how contamination events occur in private wells, to inform policy makers and empower well users.

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In soil and rock mechanics, coupling effects between geomechanics field and fluid-flow field are important to understand many physical phenomena. Coupling effects in fluid-saturated porous media comes from the interaction between the geomechanics field and the fluid flow. Stresses subjected on the porous material result volumetric strains and fluid diffusion in the pores. In turn, pore pressure change cause effective stresses change that leads to the deformation of the geomechanics field. Coupling effects have been neglected in traditional geotechnical engineering and petroleum engineering however, it should not be ignored or simplified to increases reliability of the results. The coupling effect in porous media was theoretically established in the poroelasticity theory developed by Biot, and it has become a powerful theory for modeling three-dimensional consolidation type of problem. The analysis of the porous media with fully-coupled simulations based on the Biot's theory requires intensive computational effort due to the large number of interacting fields. Therefore, advanced computational techniques need to be exploited to reduce computational time. In order to solve the coupled problem, several techniques are currently available such as one-way coupling, partial-coupling, and full-coupling. The fully-coupled approach is the most rigorous approach and produces the most correct results. However, it needs large computational efforts because it solves the geomechanics and the fluid-flow unknowns simultaneously and monolithically. In order to overcome this limitation, staggered solution based on the Biot's theory is proposed and implemented using a modular approach. In this thesis, Biot's equations are implemented using a Finite Element method and/or Finite Difference method with expansion of nonlinear stress-strain constitutive relation and multi-phase fluid flow. Fully-coupled effects are achieved by updating the compressibility matrix and by using an additional source term in the conventional fluid flow equation. The proposed method is tested in multi-phase FE and FD fluid flow codes coupled with a FE geomechanical code and numerical results are compared with analytical solutions and published results. / Ph. D.

Quantum chemical methods to predict experimental chiroptical properties by solving the time-dependent Schrödinger equation are useful in the assignment of absolute configurations. Chiroptical properties, being very sensitive to the electronic structure of the system, require highly-accurate methods on the one hand and on the other, need to be able to be computed with limited computational resources. The calculation of the optical rotation in the solution phase is complicated by solvent effects. In order to capture those solvent effects, we present a study that uses conformational averaging and time-dependent density functional theory calculations that incorporate solvent molecules explicitly in the quantum mechanical region. While considering several controllable parameters along which the system's optical rotation varies, we find that the sampling of the dynamical trajectory and the density functional chosen have the largest impact on the value of the rotation. In order to eliminate the arbitrariness of the choice of density functional, we would prefer to use coupled cluster theory, a robust and systematically improvable method. However, the high-order polynomial scaling of coupled cluster theory makes it intractable for numerous large calculations, including the conformational averaging required for optical rotation calculations in solution. We therefore attempt to reduce the scaling of a linear response coupled cluster singles and doubles (LR-CCSD) calculation via a perturbed pair natural orbital (PNO++) local correlation approach which uses an orbital space created using a perturbed density matrix. We find that by creating a "combined PNO++" space, incorporating a set of orbitals from the unperturbed pair natural orbital (PNO) space into the PNO++ space, we can obtain well-behaved convergence behavior for both CCSD correlation energies and linear response properties, including dynamic polarizabilities and optical rotations, for the small systems considered. The PNO++ and combined PNO++ methods require aggressive truncation to keep the computational cost low, due to an expensive two-electron integral transformation at the beginning of the calculation. We apply the methods to larger systems than previously studied and refine them for more aggressive truncation by exploring an alternative form of the perturbed density and a perturbation-including weak pair approximation. / Doctor of Philosophy / Theoretical chemistry attempts to provide connections between the structure of molecules and their observable properties. One such family of observables are chiroptical properties, or the effect of the medium on the light which passes through it. These properties include the scattering, absorption and change in polarization of light. Light being classically an electromagnetic field, chiroptical properties can be derived by treating molecules quantum mechanically and the light classically. The prediction of chiroptical properties on computers using the principles of quantum mechanics is still a growing field, being very sensitive to the method used, and requiring considerations of factors such as conformations and anharmonic corrections. Matching experimental properties is an important step in the creation of a reliable method of predicting properties of systems in order to provide more information than can be obtained through experimental observation. This work begins by addressing the problem of matching experimentally obtained quantities. Our results show that current time-intensive methods still fall short in the matching of experimental data. Thus, we then move on to approximating a more robust but computationally expensive method in order to be able to use a more accurate method on a larger scale than is currently possible. On obtaining positive results for small test systems, we test the new method on larger systems, and explore possible improvements to its accuracy and efficiency.

This thesis is a numerical study of the coupled Burgers equation. The coupled Burgers equation is motivated by the Boussinesq equations that are often used to model the thermal-fluid dynamics of air in buildings. We apply Finite Element Methods to the coupled Burgers equation and conduct several numerical experiments. Based on these results, the Group Finite Element method (GFE) appears to be more stable than the standard Finite Element Method. The design and implementation of controllers heavily relies on rapid solutions to complex models such as the Boussinesq equations. Thus, we further examine the feasibility and efficiency of the Proper Orthogonal Decomposition (POD) for the coupled Burgers equation. Using POD, we reduce the system to a "minimal" number of ODE's and conduct numerous numerical studies comparing the POD and GFE method. Further numerical experiments consider an application where the dynamics are projected on a POD basis and then the governing parameters of the system are varied. / Master of Science

In research environments, many soft switching inverters have been conceived, simulated, designed, implemented and proven to have advantages over hard switched inverters. To date however, no soft-switching inverters have reached commercial production for various reasons. The fixed timing coupled inductor soft-switching inverter is of interest because in simulation and previous implementation it exhibits load and source adaptability using simple RC timer circuitry and can be implemented with low cost active auxiliary devices. During the course of this implementation, it is noted that attempting to use excessively small/inexpensive active auxiliary devices has reliability ramifications related to device packaging. The issue of auxiliary active device reliability is conjectured upon by referencing available datasheet information, application specific requirements, device pulse testing and secondary research findings related to semiconductor failure characteristics. It is also noted that aspects of the simple fixed timing circuitry operation, in conjunction with coupled inductor and saturable inductor design, can lead to coupled inductor saturation if not properly addressed. Simulation is performed and validates various causes for this non-ideal behavior. / Master of Science

Translational and rotational motion are coupled for spacecraft performing formation flying missions. This motion is coupled because orbital control is dependent on the spacecraft attitude for vectored thrust. Formation flying spacecraft have a limited mass and volume for propulsion systems. We want to maximize the efficiency of the spacecraft, which leads to minimizing the error introduced by thrusting in the wrong direction. This thrust direction error leads to the need for a coupled attitude and orbital control strategy. In this thesis a coupled control system is developed using a nonlinear Lyapunov attitude controller and a nonlinear Lyapunov-based orbital controller. A nonlinear Lyapunov attitude controller is presented for a spacecraft with three-axis momentum wheel control. The nonlinear Lyapunov-based orbital controller is combined with a mean motion control strategy to provide a globally asymptotically stable controller. The attitude and orbit control laws are verified separately using numerical simulation, and then are integrated into a coupled control strategy. The coupled system simulations verify that the coupled control strategy is able to correct for an initial relative position error between two spacecraft. / Master of Science

One of the central problems limiting the application of accurate {em ab initio} methods to large molecular systems is their high computational costs, i.e., their computing and storage requirements exhibit polynomial scaling with the size of the system. For example, the coupled cluster singles and doubles method with the perturbative inclusion of triples: the CCSD(T) model, which is considered to be the ``gold standard'' of quantum chemistry scales as 𝑂(N⁷) in its canonical formulation, where $N$ is a measure of the system size. However, the steep scaling associated with these methods is unphysical since the property of dynamic electron correlation or dispersion (for insulators) is local in nature and decays as R⁻⁶ power of distance. Different reduced-scaling techniques which attempt to exploit this inherent sparsity in the wavefunction have been used in conjunction with the coupled cluster theory to calculate ground-state properties of molecular systems with hundreds of heavy atoms in reasonable computational time. However, efforts towards extension of these methods for describing response properties like polarizabilities, optical rotations, etc., which are related to the derivative of the wavefunction with respect to external electric or/and magnetic fields, have been fairly limited and conventional reduced-scaling algorithms have been shown to yield large and often erratic deviations from the full canonical results. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different chiral drug candidates. In this work, we identify the reasons behind the unsatisfactory performance of the pair natural orbital (PNO) based reduced-scaling approach for calculating linear response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}) that can provide the necessary accuracy at significantly lower computational costs. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. {em J. Phys. Chem. A}, 2017, 121(3), pp 708 716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, {em manuscript in preparation}). The essence of these modified schemes (FVNO++ and PNO++) lie in finding suitable field perturbed one-electron densities to construct ``perturbation aware" virtual spaces which, by construction, are much more compact for describing response properties, making them ideal for applications on large molecular systems. / Ph. D. / Since its inception, quantum mechanics has been widely used by theoretical chemists to study, model and predict a variety of molecular properties and reactions accurately and reliably. Central to the field of quantum mechanics is the Schr¨odinger equation, whose exact solution is only known for one electron systems. As such, numerous quantum mechanical models have been proposed over the years which attempt to solve the many body Schrodinger equation approximately. A very good example in this regard is the coupled cluster (CC) family of methods wherein the CCSD(T) model is considered as the “gold standard” of quantum chemistry due to its high accuracy. However, one major bottleneck which prevents the use of accurate CC models to study biological systems which routinely involve hundreds of atoms, is the issue of high computational expenses. For example, doubling the system size in a CCSD(T) calculation can lead to more than a hundred-fold increase in the computational costs, which limits the application of this model to systems with 10 to 20 atoms. However, this unfavorable scaling with respect to system size is unphysical for large molecules as inter-electron interactions decay rapidly with distance, or are in other words, a local phenomenon. Reduced-scaling methods attempt to exploit this property of locality by finding a compact representation of the wavefunction. Various reduced-scaling approaches like pair natural orbitals (PNOs), projected atomic orbitals (PAOs) have been proposed and developed over the years which have extended the applicability of the CC methods to systems as large as proteins and DNA fragments. While these methods have been shown to be quite reliable for calculating properties like molecular energies, much more work needs to be done to guarantee similar levels of accuracy and computational cost for describing molecular response properties like polarizabilities and optical rotations. As the name suggests, response properties are related to the response or the change induced in the wavefunction in the presence of external electromagnetic fields like visible light. Accurate simulation of response properties like optical rotation is highly desirable as it can help the experimental chemists in understanding the structure-activity relationship of different drug candidates, an important part of the drug discovery process. However, limited applications of the reduced-scaling algorithms to these properties have been shown to yield large and often erratic errors. In this work, we identify the reasons behind the unsatisfactory performance of the PNO based reduced-scaling approach for calculating response properties at the coupled cluster level of theory and propose novel modifications, which we refer to as PNO++, (A. Kumar and T. D. Crawford. Perturbed Pair Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, manuscript in preparation) which can provide the desired accuracy reliably at significantly lower computational costs than the regular PNO method. The motivation behind the PNO++ approach came from our works on the (frozen) virtual natural orbitals (FVNO), which can be seen as a precursor to the concept of PNOs (A. Kumar and T. D. Crawford. Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory. J. Phys. Chem. A, 2017, 121(3), pp 708-716) and the improved FVNO++ method (A. Kumar and T. D. Crawford. Perturbed Natural Orbitals for Coupled-Cluster Linear-Response Theory. 2018, manuscript in preparation). The essence of these modified schemes (FVNO++ and PNO++) lie in choosing a “field aware” representation of the wavefunction, which by construction, is much more compact than their conventional counterparts for calculating response properties. Thus, these schemes are ideal for applications to larger and chemically interesting systems like molecules in solutions, biomolecules, etc.