In this thesis, we mainly investigate the application of a nodal discontinuous Galerkin spectral element method (DGSEM) for simulating processes in column liquid chromatography. Additionally, we investigate the effectiveness of a total variation diminishing in the mean (TVDM) limiter in controlling spurious oscillations related to the Gibbs phenomenon. With an order-of-accuracy test, we demonstrated that our nodal DGSEM achieved and, in multiple instances, even exceeded theoretical convergence rates, especially with an increased number of elements, validating the use of high-order basis functions for achieving high-order accuracy. We also demonstrated how setup parameters could affect process outcomes, which suggests that numerical simulations can help guide the development of experimental methods since they can explore the solution space of an optimization problem much faster than experimental procedures by leveraging computational speed. Finally, we showed that the TVDM limiter successfully eliminated severe oscillations and negative concentrations near shock regions but introduced significant smearing of the shocks. These findings validate the nodal DGSEM as a highly accurate and reliable tool for detailed modeling of column liquid chromatography, which is essential for improving efficiency, yield, and product quality in biopharmaceutical manufacturing.

The applicability and adequacy of three modeling approaches to describe and predict breakthough curves (BTCs) for non-reactive solutes in statistically homogeneous porous media were numerically and experimentally investigated. Modeling approaches were: the convection-dispersion equation (CDE) with scale-dependent dispersivity, mobile-immobile model (MIM), and the fractional convection-dispersion equation (FCDE). In order to test these modeling approaches, a prototype laboratory column system was designed for conducting miscible displacement experiments with a free-inlet boundary. Its performance and operating conditions were rigorously evaluated. When the CDE with scale-dependent dispersivity is solved numerically for generating a BTC at a given location, the scale-dependent dispersivity can be specified in several ways namely, local time-dependent dispersivity, average time-dependent dispersivity, apparent time-dependent dispersivity, apparent distance-dependent dispersivity, and local distance-dependent dispersivity. Theoretical analysis showed that, when dispersion was assumed to be a diffusion-like process, the scale-dependent dispersivity was locally time-dependent. In this case, definitions of the other dispersivities and relationships between them were directly or indirectly derived from local time-dependent dispersivity. Making choice between these dispersivities and relationships depended on the solute transport problem, solute transport conditions, level of accuracy of the calculated BTC, and computational efficiency The distribution of these scale-dependent dispersivities over scales could be described as either as a power-law function, hyperbolic function, log-power function, or as a new scale-dependent dispersivity function (termed as the LIC). The hyperbolic function and the LIC were two potentially applicable functions to adequately describe the scale dependent dispersivity distribution in statistically homogeneous porous media. All of the three modeling approaches described observed BTCs very well. The MIM was the only model that could explain the tailing phenomenon in the experimental BTCs. However, all of them could not accurately predict BTCs at other scales using parameters determined at one observed scale. For the MIM and the FCDE, the predictions might be acceptable only when the scale for prediction was very close to the observed scale. When the distribution of the dispersivity over a range of scales could be reasonably well-defined by observations, the CDE might be the best choice for predicting non-reactive solute transport in statistically homogeneous porous media. / Ph. D.

Increasing interest, from the U.S. Army Corps of Engineers (USACE) and other agencies, in using deep-mixing methods (DMM) to improve the stability of levees constructed on soft ground is driven by the need to reduce levee footprints and environmental impacts and to allow for more rapid construction. Suitable methods for analysis and design of these systems are needed to ensure that the DMM technology is properly applied. DMM shear walls oriented perpendicular to the levee alignment are an effective arrangement for supporting unbalanced lateral loads. Shear walls constructed by overlapping individual DMM columns installed with single-axis or multiple axis equipment include vertical joints caused by the reduced width of the wall at the overlap between adjacent columns. These joints can be made weaker by misalignment during construction, which reduces the efficiency of the overlap. Depending on the prevalence and strength of these joints, complex failure mechanisms, such as racking due to slipping along vertical joints between adjacent installations in the shear walls, can occur. Ordinary limit equilibrium analyses only account for a composite shearing failure mode; whereas, numerical stress-strain analyses can account for other failure modes. Five case studies provided by the USACE were analyzed to evaluate the behavior of levee and floodwall systems founded on soft ground stabilized with DMM shear walls. These identified and illustrated potential failure mechanisms of these types of systems. Two-dimensional numerical stability and settlement analyses were performed for the case studies using the FLAC computer program. The key findings and conclusions for the individual case studies were assessed and integrated into general conclusions about design of deep-mixing support for levees and floodwalls. One of the significant findings from this research was to identify the potential for a partial depth racking failure, which can control design when the DMM shear walls are socketted into a relatively strong bearing layer. The potential for partial depth racking failure is not discussed in the literature and represents a new failure mode identified by this research. This discovery also highlights the importance of adapting suitable methods for analysis and design of these systems to address all potential failure modes. / Ph. D.

This dissertation addresses the development of enhanced formulations for minimax and mixed-integer programming models for certain industrial and logistical systems, along with the design and implementation of efficient algorithmic strategies. We first examine the general class of minimax mixed-integer 0-1 problems of the type that frequently arise in decomposition approaches and in a variety of location and scheduling problems. We conduct an extensive polyhedral analysis of this problem in order to tighten its representation using the Reformulation-Linearization/Convexification Technique (RLT), and demonstrate the benefits of the resulting lifted formulations for several classes of problems. Specifically, we investigate RLT-enhanced Lagrangian dual formulations for the class of minimax mixed-integer 0-1 problems in concert with deflected/conjugate subgradient algorithms. In addition, we propose two general purpose lifting mechanisms for tightening the mathematical programming formulations associated with such minimax optimization problems. Next, we explore novel continuous nonconvex as well as lifted discrete formulations for the notoriously challenging class of job-shop scheduling problems with the objective of minimizing the maximum completion time (i.e., minimizing the makespan). In particular, we develop an RLT-enhanced continuous nonconvex model for the job-shop problem based on a quadratic formulation of the job sequencing constraints on machines. The tight linear programming relaxation that is induced by this formulation is then embedded in a globally convergent branch-and-bound algorithm. Furthermore, we design another novel formulation for the job-shop scheduling problem that possesses a tight continuous relaxation, where the non-overlapping job sequencing constraints on machines are modeled via a lifted asymmetric traveling salesman problem (ATSP) construct, and specific sets of valid inequalities and RLT-based enhancements are incorporated to further tighten the resulting mathematical program. The efficacy of our enhanced models is demonstrated by an extensive computational experiment using classical benchmark problems from the literature. Our results reveal that the LP relaxations produced by the lifted ATSP-based models provide very tight lower bounds, and directly yield a 0\% optimality gap for many benchmark problems, thereby substantially dominating other alternative mixed-integer programming models available for this class of problems. Notably, our lifted ATSP-based formulation produced a 0\% optimality gap via the root node LP relaxation for 50\% of the classical problem instances due to Lawrence. We also investigate enhanced model formulations and specialized, efficient solution methodologies for applications arising in four particular industrial and sports scheduling settings. The first of these was posed to us by a major trucking company (Volvo Logistics North America), and concerns an integrated assembly and routing problem, which is a unique study of its kind in the literature. In this context, we examine the general class of logistical systems where it is desirable to appropriately ascertain the joint composition of the sequences of vehicles that are to be physically connected along with determining their delivery routes. Such assembly-routing problems occur in the truck manufacturing industry where different models of vehicles designed for a network of customers need to be composed into compatible groups (assemblies) and subsequently dispatched via appropriately optimized delivery routes that are restricted by the particular sequence in which the trucks are connected. A similar structure is exhibited in the business of shipping goods via boat-towed barges along inland waterways, or via trains through railroad networks. We present a novel modeling framework and column generation-based optimization approach for this challenging class of joint vehicle assembly-routing problems. In addition, we suggest several extensions to accommodate particular industrial restrictions where assembly sequence-dependent delivery routes are necessary, as well as those where limited driver- and equipment-related resources are available. Computational experience is provided using large-scale realistic data to demonstrate the applicability of our suggested methodology in practice. The second application addressed pertains to a production planning problem faced by a major motorcycle manufacturing firm (Harley-Davidson Motor Company). We consider the problem of partitioning and sequencing the production of different manufactured items in mixed-model assembly lines, where each model has various specific options and designated destinations. We propose a mixed-integer programming formulation (MPSP1) for this problem that sequences the manufactured goods within production batches in order to balance the motorcycle model and destination outputs as well as the load demands on material and labor resources. An alternative (relaxed) formulation (MPSP2) is also presented to model a closely related case where all production decisions and outputs are monitored within a common sequence of batches, which permits an enhanced tighter representation via an additional set of hierarchical symmetry-defeating constraints that impart specific identities amongst batches of products under composition. The latter model inspires a third set partitioning-based formulation in concert with an efficient column generation approach that directly achieves the joint partitioning of jobs into batches along with ascertaining the sequence of jobs within each composed batch. Finally, we investigate a subgradient-based optimization strategy that exploits a non-differentiable optimization formulation, which is prompted by the flexibility in the production process as reflected in the model via several soft-constraints, thereby providing a real-time decision-making tool. Computational experience is presented to demonstrate the relative effectiveness of the different proposed formulations and the associated optimization strategies for solving a set of realistic problem instances. The third application pertains to the problem of matching or assigning subassembly parts in assembly lines, where we seek to minimize the total deviation of the resulting final assemblies from a vector of nominal and mean quality characteristic values. We introduce three symmetry-defeating enhancements for an existing assignment-based model, and highlight the critical importance of using particular types of symmetry-defeating hierarchical constraints that preserve the model structure. We also develop an alternative set partitioning-based formulation in concert with a column generation approach that efficiently exploits the structure of the problem. A special complementary column generation feature is proposed, and we provide insights into its vital role for the proposed column generation strategy, as well as highlight its benefits in the broader context of set partitioning-based formulations that are characterized by columns having relatively dense non-zero values. In addition, we develop several heuristic procedures. Computational experience is presented to demonstrate the relative effectiveness of the different adopted strategies for solving a set of realistic problem instances. Finally, we analyze a doubles tennis scheduling problem in the context of a training tournament as prompted by a tennis club in Virginia, and develop two alternative 0-1 mixed-integer programming models, each with three different objective functions that attempt to balance the partnership and the opponentship pairings among the players. Our analysis and computational experience demonstrate the superiority of one of these models over the other, and reflect the importance of model structure in formulating discrete optimization problems. Furthermore, we design effective symmetry-defeating strategies that impose certain decision hierarchies within the models, which serve to significantly enhance algorithmic performance. In particular, our study provides the insight that the special structure of the mathematical program to which specific tailored symmetry-defeating constraints are appended can greatly influence their pruning effect. We also propose a novel nonpreemptive multi-objective programming strategy in concert with decision hierarchies, and highlight its effectiveness and conceptual value in enhancing problem solvability. Finally, four specialized heuristics are devised and are computationally evaluated along with the exact solution schemes using a set of realistic practical test problems. Aside from the development of specialized effective models and algorithms for particular interesting and challenging applications arising in different assembly, routing, and scheduling contexts, this dissertation makes several broader contributions that emerge from the foregoing studies, which are generally applicable to solving formidable combinatorial optimization problems. First, we have shown that it is of utmost importance to enforce symmetry-defeating constraints that preserve the structure of mathematical programs to which they are adjoined, so that their pruning effects are most efficiently coupled with the branch-and-bound strategies that are orchestrated within mathematical programming software packages. In addition, our work provides the insight that the concept of symmetry compatible formulations plays a crucial role in the effectiveness of implementing any particular symmetry-defeating constraints. In essence, if the root node LP solution of the original formulation does not conform relatively well with the proposed symmetry-defeating hierarchical constraints, then a significant branching effort might be required to identify a good solution that is compatible with the pattern induced by the selected symmetry-defeating constraints. Therefore, it is advisable to enforce decision hierarchies that conform as much as possible with the problem structure as well as with the initial LP relaxation. Second, we have introduced an alternative concept for defeating symmetry via augmented objective functions. This concept prompts the incorporation of objective perturbation terms that discriminate amongst subsets of originally undistinguishable solution structures and, in particular, leads to the development of a nonpreemptive multiobjective programming approach based on, and combined with, symmetry-defeating constraints. Interestingly, nonpreemptive multiobjective programming approaches that accommodate symmetry-defeating hierarchical objective terms induce a root node solution that is compatible with the imposed symmetry-defeating constraints, and hence affords an automated alternative to the aforementioned concept of symmetry compatible formulations. Third, we have proposed a new idea of complementary column generation in the context of column generation approaches that generally provide a versatile framework for analyzing industrial-related, integrated problems that involve the joint optimization of multiple operational decisions, such as assembly and routing, or partitioning and scheduling. In such situations, we have reinforced the insight that assignment-related problems that involve collections of objects (production batches, final assemblies, etc.) whose permutation yields equivalent symmetric solutions may be judiciously formulated as set partitioning models. The latter can then be effectively tackled via column generation approaches, thereby implicitly obviating the foregoing combinatorial symmetric reflections through the dynamic generation of attractive patterns or columns. The complementary column generation feature we have proposed and investigated in this dissertation proves to be particularly valuable for such set partitioning formulations that involve columns having relatively dense non-zero values. The incorporation of this feature guarantees that every LP iteration (involving the solution of a restricted master program and its associated subproblem) systematically produces a consistent set of columns that collectively qualify as a feasible solution to the problem under consideration. Upon solving the problem to optimality as a linear program, the resultant formulation encompasses multiple feasible solutions that generally include optimal or near-optimal solutions to the original integer-restricted set partitioning formulation, thereby yielding a useful representation for designing heuristic methods as well as exact branch-and-price algorithms. In addition, using duality theory and considering set partitioning problems where the number of patterns needed to collectively compose a feasible solution is bounded, we have derived a lower bound on the objective value that is updated at every LP phase iteration. By virtue of this sequence of lower bounds and the availability of upper bounds via the restricted master program at every LP phase iteration, the LP relaxation of the set partitioning problem is efficiently solved as using a pre-specified optimality tolerance. This yields enhanced algorithmic performance due to early termination strategies that successfully mitigate the tailing-off effect that is commonly witnessed for simplex-based column generation approaches. / Ph. D.

When an embankment is to be constructed over ground that is too soft or compressible to adequately support the embankment, columns of strong material can be placed in the soft ground to provide the necessary support by transferring the embankment load to a firm stratum. This technology is known as column-supported embankments (CSEs). A geosynthetic-reinforced load transfer platform (LTP) or bridging layer may be constructed immediately above the columns to help transfer the load from the embankment to the columns. There are two principal reasons to use CSEs: 1) accelerated construction compared to more conventional construction methods such as prefabricated vertical drains (PVDs) or staged construction, and 2) protection of adjacent facilities from distress, such as settlement of existing pavements when a roadway is being widened. One of the most significant obstacles limiting the use of CSEs is the lack of a standard design procedure which has been properly validated. This report and the testing described herein were undertaken to help resolve some of the uncertainty regarding CSE design procedures in light of the advantages of the CSE technology and potential for significant contributions to the Strategic Highway Research Program, which include accelerated construction and long-lived facilities. Twelve design/analysis procedures are described in this report, and ratings are assigned based on information available in the literature. A test facility was constructed and the facility, instrumentation, materials, equipment, and test procedures are described. A total of 5 CSE tests were conducted with 2 ft diameter columns in a square array. The first test had a column center-to-center spacing of 10 ft and the remaining four tests had center-to-center spacings of 6 ft. The Adapted Terzaghi Method of determining the vertical stress on the geosynthetic reinforcement and the Parabolic Method of determining the tension in the geosynthetic reinforcement provide the best agreement with the test results. The tests also illustrate the importance of soft soil support in CSE performance and behavior. A generalized formulation of the Adapted Terzaghi Method for any column/unit cell geometry and two layers of embankment fill is presented, and two new formulations of the Parabolic Method for triangular arrangements is described. A recommended design procedure is presented which includes use of the GeogridBridge Excel workbook described by Filz and Smith (2006, 2007), which was adapted for both square and triangular column arrangements. GeogridBridge uses the Adapted Terzaghi Method and the Parabolic Method in a load-displacement compatibility design approach. For completeness, recommended quality control and quality assurance procedures are also provided, and a new guide specification is presented. / Ph. D.

During an earthquake, columns in a one-story building must support vertical gravity loads while undergoing large lateral drifts associated with deflections of the vertical seismic force resisting system and deflections of the flexible roof diaphragm. Analyzing the behavior of these gravity columns is complex since not only is there an interaction between compression and bending, but also the boundary conditions are not perfectly pinned or fixed. In this research, the behavior of steel columns that are square hollow structural sections (HSS) is investigated for stability using three design methods: elastic design, plastic hinge design, and pinned base design. First, for elastic design, the compression and flexural strength of the HSS columns are calculated according to the AISC specifications, and the story drift ratio that causes the interaction equation to be violated for varying axial force demands is examined. Then, a simplified design procedure is proposed; this procedure includes a modified interaction equation applicable to HSS column design based on a parameter, Pnh/Mn, and a set of design charts are provided. Second, a plastic hinge design is grounded in the concept that a stable plastic hinge makes the column continue to resist the gravity load while undergoing large drifts. Based on the available test data and the analytical results from finite element models, three limits on the width to thickness ratios are developed for steel square HSS columns. Lastly, for pinned base design, the detailing of a column base connection is schematically described. Using FE modeling, it is shown that it is possible to create rotational stiffness below a limit such that negligible moment develops at the column base. All the design methods are demonstrated with a design example / Master of Science / One-story buildings are one of the most economical types of structures built for industrial, commercial, or recreational use. During an earthquake, columns in a one-story building must support vertical gravity loads while undergoing large lateral displacements, referred to as story drift. Vertical loads cause compression forces, and lateral drifts produce bending moments. The interaction between these forces makes it more complex to analyze the behavior of these gravity columns. Moreover, since the column base is not perfectly fixed to the ground, there are many boundary conditions applicable to the column base depending on the fixity condition. For these reasons, the design for columns subjected to lateral drifts while supporting axial compressive forces has been a growing interest of researchers in the field. However, many researchers have focused more on wide-flange section (I-shape) steel columns rather than on tube section columns, known as hollow structural section (HSS) steel columns. In this research, the behavior of steel square tube section columns is investigated for stability using three design methods: elastic design, plastic hinge design, and pinned base design. First, for elastic design, the compression and flexural strength of the HSS columns are calculated according to current code equations, and the story drift that causes failure for varying axial force demands is examined. Then, a simplified design procedure is proposed including design charts. Second, a plastic hinge design is grounded in the concept that controlled yielding at the column base makes the column continue to resist the gravity load while undergoing large drifts. Based on the available test data and results from computational models, three limits on the width to thickness ratios of the tubes are developed. Lastly, for pinned base design, concepts for detailing a column base connection with negligible bending resistance is schematically described. Using a computational model, it is shown that the column base can be detailed to be sufficiently flexible to allow rotation. All the design methods are demonstrated with a design example.

Between 1970 and 2010 almost one-third of drinking water related waterborne disease outbreaks reported to the US Centers for Disease Control and Prevention were associated with systems dependent on untreated groundwater (i.e., most commonly, household wells). This is unsurprising, given that numerous past efforts to monitor household well water quality have indicated a high prevalence of fecal coliforms and/or E. coli at the point of use. Non-point sources of pollution, including septic tank leakages and poorly constructed drain fields, have been identified as the leading risk factors associated with outbreaks in households dependent on groundwater. Ideally, the integration of emerging source tracking (ST) analyses in well monitoring programs could be used to identify whether the presence of fecal indicator bacteria (FIB) is associated with human or non-human sources in order to inform remediation strategies. However, the application of ST to groundwater has been limited, and the interpretation of data is consequently difficult. This research compares the fate and transport of FIB (E. coli and enterococci) with a chemical (optical brighteners, OB) and a molecular (Bacteroides HF183) ST target in order to evaluate their potential use as indicators of water quality issues in private drinking water systems. Eighteen PVC soil columns were constructed in an outdoor soil column facility to represent small-scale septic drainfield models; they received synchronized doses of primary-treated wastewater twice daily and were monitored bi-weekly over a 7-month period. Columns were subject to variable influent loading rates of wastewater effluent, and differing degrees of soil compromisation (i.e. synthetic solution channels). Results show that while column effluent volume and constituent levels were related to dosage, they were not always related to soil compromisation (ANOVA, p < 0.05). E. coli and enterococci concentrations were associated with effluent volume and OB levels (Spearman's rank, p < 0.05). The presence of Bacteroides HF183 was not strongly associated with the other measured ST target levels (Point-biserial correlation, p < 0.05). Findings from this study suggest surface water ST methodologies may have a role in groundwater quality monitoring efforts. Quantifying the relative recovery of ST targets and FIB from controlled groundwater simulations will assist in the development of strategies to identify non-point sources of human wastewater pollution efficiently and effectively to inform remediation. / Master of Science

Three full-scale experimental tests were conducted to investigate the strength and stiffness of weak-axis moment end-plate connections. Each test consisted of two girders connected to a column web with four-bolt extended moment end-plates. Two tests were conducted with bare steel. One test included a composite concrete slab that confined the top extension of the end-plate. Finite element models of the tests were created with the commercial software SAP2000. A simplified modeling procedure was developed to overcome the contact problems between the end-plates and column web, and between the bolts and holes in the end-plates and web. The simplified modeling procedure accurately predicted the experimental elastic stiffness, in the form of column web rotations, of the connections. Yield line theory was used to investigate the plastic strength of the column web. Several yield line patterns were examined. Analytical plastic moment strengths were very conservative when compared to the observed behavior of the column web. The experimental stiffness of the test with the concrete slab confining the top extension of the end-plate was compared to the stiffness of a similar test without a slab. The slab increased the elastic stiffness of the connection; however, after the concrete began cracking and crushing around the connection, the stiffness was greatly decreased. / Master of Science

Instrument miniaturization is led by the desire to perform rapid diagnosis in remote areas with high throughput and low cost. In addition, miniaturized instruments hold the promise of consuming small sample volumes and are thus less prone to cross-contamination. Gas chromatography (GC) is the leading analytical instrument for the analysis of volatile organic compounds (VOCs). Due to its wide-ranging applications, it has received great attention both from industrial sectors and scientific communities. Recently, numerous research efforts have benefited from the advancements in micro-electromechanical system (MEMS) and nanotechnology based solutions to miniaturize the key components of GC instrument (pre-concentrator/injector, separation column, valves, pumps, and the detector). The purpose of this dissertation is to address the critical need of developing a micro GC system for various field- applications. The uniqueness of this work is to emphasize on the importance of integrating the basic components of μGC (including sampling/injection, separation and detection) on a single platform. This integration leads to overall improved performance as well as reducing the manufacturing cost of this technology. In this regard, the implementation of micro helium discharge photoionization detector (μDPID) in silicon-glass architecture served as a major accomplishment enabling its monolithic integration with the micro separation column (μSC). For the first time, the operation of a monolithic integrated module under temperature and flow programming conditions has been demonstrated to achieve rapid chromatographic analysis of a complex sample. Furthermore, an innovative sample injection mechanism has been incorporated in the integrated module to present the idea of a chip-scale μGC system. The possibility of using μGC technology in practical applications such as breath analysis and water monitoring is also demonstrated. Moreover, a nanotechnology based scheme for enhancing the adsorption capacity of the microfabricated pre-concentrator is also described. / Ph. D.

Computational fluid dynamics (CFD) modeling was used to predict the hydrodynamics of a column reactor. Bubble columns have applications across many engineering disciplines and improved modeling techniques help to increase the accuracy of numerical predictions. An Eulerian-Eulerian multi-fluid model was used to simulate fluidization and to capture the complex physics associated therewith. The commercial code ANSYS Fluent was used to study two-dimensional gas-liquid bubble columns. A comprehensive parameter study, including a detailed investigation of grid resolution was performed. Specific attention was paid to the bubble diameter, as it was shown to be related to cell size have significant effects on the characteristics of the flow. The parameters used to compare the two-dimensional (2D) cases to experimental results of Rampure, et. al. were then applied to a three-dimensional (3D) geometry. It was demonstrated that the increase in accuracy from 2D to 3D is negligible compared to the increase in CPU required to simulate the entire 3D domain. Additionally, the reaction chamber of a microbial fuel cell (MFC) was modeled and a preliminary parameter study investigating inlet velocity, temperature, and acetate concentration was conducted. MFCs are used in wastewater treatment and have the potential to treat water while simultaneously harvesting electricity. The spiral spacer and chemical reactions were modeled in a 3D geometry, and it was determined that inlet velocity was the most influential parameter that was simulated. There were also significant differences between the 2D and 3D geometries used to predict the MFC hydrodynamics. / Master of Science