Browsing by Subject "Stability"

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Analysis of Ricci flow on noncompact manifolds
(2013-05) Wu, Haotian, active 2013; Knopf, Dan, 1959-
In this dissertation, we present some analysis of Ricci flow on complete noncompact manifolds. The first half of the dissertation concerns the formation of Type-II singularity in Ricci flow on [mathematical equation]. For each [mathematical equation] , we construct complete solutions to Ricci flow on [mathematical equation] which encounter global singularities at a finite time T such that the singularities are forming arbitrarily slowly with the curvature blowing up arbitrarily fast at the rate [mathematical equation]. Near the origin, blow-ups of such a solution converge uniformly to the Bryant soliton. Near spatial infinity, blow-ups of such a solution converge uniformly to the shrinking cylinder soliton. As an application of this result, we prove that there exist standard solutions of Ricci flow on [mathematical equation] whose blow-ups near the origin converge uniformly to the Bryant soliton. In the second half of the dissertation, we fully analyze the structure of the Lichnerowicz Laplacian of a Bergman metric g[subscript B] on a complex hyperbolic space [mathematical equation] and establish the linear stability of the curvature-normalized Ricci flow at such a geometry in complex dimension [mathematical equation]. We then apply the maximal regularity theory for quasilinear parabolic systems to prove a dynamical stability result of Bergman metric on the complete noncompact CH[superscript m] under the curvature-normalized Ricci flow in complex dimension [mathematical equation]. We also prove a similar dynamical stability result on a smooth closed quotient manifold of [mathematical symbols]. In order to apply the maximal regularity theory, we define suitably weighted little Hölder spaces on a complete noncompact manifold and establish their interpolation properties.
Behavior of steel tub girders with optimized bracing layouts
(2019-09-11) Armijos Moya, Stalin Vinicio; Helwig, Todd Aaron, 1965-; Engelhardt, Michael D.; Clayton, Patricia M; Williamson, Eric B; Rodin, Gregory J
Composite steel tub girders are a popular alternative for straight and horizontally curved bridges due to their high torsional stiffness and aesthetic appearance. While the closed girder in the finished bridge has a high torsional stiffness, prior to curing of the concrete deck the steel girder alone is relatively flexible. Consequently, steel tub girders require extensive amounts of bracing to avoid instability and cross section distortion due to the relatively low torsional stiffness during construction. The primary bracing systems include a top flange lateral truss as well as internal and external cross frames. The quasi-closed shape that results with the added bracing, results in a stiff girder system capable of resisting significant torsional moments and deformations. However, current design and detailing practices for steel tub girders commonly include several aspects that may lead to unnecessary fabrication costs and structural inefficiencies. The top flange lateral truss is commonly installed along the entire length of steel tub girders to increase the girder torsional stiffness. However, the horizontal truss is mainly effective near the ends of the girders where the shear deformations are the largest. Thus, partial top lateral bracing systems can be an alternative for straight and mildly horizontally curved bridge applications. Additionally, the internal K-frame braces are usually installed at every panel point to control cross-sectional distortion of the girders. However, the amount of internal K-frames can be significantly reduced with little impact on the structural performance. By optimizing the amount of bracing depending on the application, steel tub girders can be more cost-effective without undermining their structural integrity. In addition to modifications in the bracing, current AASHTO Specifications have several geometric restrictions for the section geometry of steel tub girders that may not be warranted. AASHTO restricts the web slope not to exceed the limit of 1 Horizontal to 4 Vertical. Tub girders with flatter web slopes can result in girders with higher tributary widths that could potentially reduce the number of girder lines on a bridge. In addition, top flanges are required to be centered on the top of the webs. If the top flanges are permitted to offset towards inside of the tub, more space would be available to connect directly the horizontal truss and avoid undesired eccentricities due to large gusset plates. Since these cross-sectional and bracing details are not currently allowed by AASHTO Specifications, a TxDOT-sponsored research project was performed to evaluate the impact of the aforementioned details using large-scale experimental tests and parametric finite element analyses. This dissertation evaluates the feasibility of optimized bracing layouts for straight and horizontally curved steel tub girders, in addition to analyzing the impact of modified cross-sectional geometries in the ultimate flexural capacity of steel tub girders.
Behavior of systems under conflicting commands : results and case studies
(1995) Anvar, Mahmood; Baughman, Martin L.; Driga, Mircea D.
Two different types of systems under conflicting commands are considered: linear time invariant dynamical systems with multiple input channels and a particular type of nonlinear systems with two conflicting inputs. The common features of these are the existence of multiple input channels to the systems where the channels are not always under central control. In the setting of linear time invariant systems under conflicting commands, the states and the output may be found by superposition. This, however, does not provide any insight into the problem of controllability of such systems. The structure of linear systems may be utilized to derive a decomposition algorithm that allows one to identify those states of a system that can be controlled by any individual or group of the inputs, regardless of the inputs to the system from other channels. These states are shown to form subspaces in the state space of the system. In this context, Pontryagin’s solution to the game of pursuit and evasion is adopted to show that under certain conditions each player is capable of preventing the state of the system from reaching an arbitrary state. Decomposition of a general N area interconnected electric power system along the above lines shows that as long as the network is connected, regardless of the number and location of the tie lines and implemented control, all states of each area, except the input mechanical power in that area, also are in the controllable spaces of all other areas. In view of this result, it is argued that in a highly competitive electricity market, if economically independent, electrically interconnected areas are to be provided with full local control over their areas, decoupling of the dynamics of those areas is necessary. This decoupling is also shown to be possible through the use of flexible transmission lines. Results concerning the relationship of the outcome to set-points, in a particular type of nonlinear system with two conflicting inputs, are also presented. It is shown that under certain conditions, the higher set-point, while under other conditions, the lower set-point, determines the output. It is also shown that a two area electric power system controlled using the signals collected from erroneous sensors may be modeled and analyzed as such a nonlinear system
Cross-frame forces in a straight bridge with normal supports
(2018-05) Moore, Matthew Eric; Helwig, Todd Aaron, 1965-; Engelhardt, Michael D.
Cross-frame and diaphragm systems are important structural elements in steel I-girder bridges. These members enhance the lateral-torsional buckling resistance in straight girder systems by reducing the unbraced length. The critical stage for the braces from a stability perspective often occurs during construction of the concrete bridge deck when the non-composite steel girders must resist the entire construction load. The braces not only enhance the lateral-torsional buckling resistance of the girders, but are also necessary to resist the torsion applied to the girders due to the deck overhang construction, and distribute lateral loads across the structure from sources such as wind. In horizontally curved bridges, the braces are primary structural elements in the superstructure and engage the girders across the width of the bridge to behave as a structural system to resist the torsion that develops as a result of the curved geometry. For straight girder systems, the specifications of the American Association of State Highway and Transportation Officials (AASHTO) have generally provided little guidance in the sizing of the braces other than recommended connection plate (web stiffener) details or slenderness limits. While there have been many advances in recent years towards improving the understanding of the behavior of cross-frame systems, there has not been sufficient research carried out on the proper loading conditions for assessing the fatigue performance of cross-frames. The work outlined in this thesis is part of a larger study on the behavior of cross-frames in steel bridge system. The study is funded by the National Cooperative Highway Research Program (NCHRP 12-113). The fundamental goals of the research investigation are to produce methodologies and design guidelines for the following: evaluation of fatigue design stresses in cross-frames in straight and horizontally curved steel I-girder bridges; calculation of minimum cross-frame strength and stiffness requirements for stability bracing of I-girders during construction and in-service; development of improved methods to account for the influence of end connection details on cross-frame stiffness that extend beyond and improve upon the suggested guidance currently provided in Article C4.6.3.3.4 of the AASHTO LRFD Bridge Design Specifications. This work includes field monitoring and parametric FEA studies. The field studies are focused on three bridges: 1) a straight bridge with normal supports, 2) a straight bridge with skewed supports, and 3) a horizontally curved bridge. The field studies include rainflow monitoring of fatigue induced stresses in select cross-frames and the girders for a period of approximately 1 month as well as live load tests using trucks of known weights. This thesis focuses on some of the background studies, a survey of bridge owners around the United States, as well as the instrumentation and live load tests on the straight bridge with normal supports
Database of planar and three-dimensional periodic orbits and families near the moon
(2021-08-20) Franz, Carter Joseph; Russell, Ryan Paul, 1976-; Jones, Brandon
The renewed interest in Lunar exploration prompts a need to better understand the dynamics of spacecraft in the vicinity of the moon. Here, a detailed survey is conducted via a broad grid search to find, characterize, and archive periodic orbits. The resulting database contains over 13 million planar and three-dimensional solutions in the circular restricted three body problem. The work is a direct follow-on to previous periodic orbit grid searches, with a focus on the Earth-Moon mass ratio, the addition of x-z symmetric orbits, and family clustering. Each periodic orbit successfully identified is evaluated for stability properties, perilune distance, number and center of revolutions, and other defining properties. DBSCAN, an unsupervised learning clustering algorithm, is used to isolate family curves in phase space and group orbits into family or sub-family clusters. The clustered orbits are then sorted to form smooth, ordered curves in phase space, allowing for arbitrary data resolution and improved labeling of the discrete grid solutions. A custom cluster confidence measure is introduced and applied. Over 80% of 3D data and over 62% of planar data are clustered with high confidence, with better results at lower revolutions. Approximately 4.25% of 3D solutions and less than 0.5% of planar solutions are classified as outliers. The resulting database is an extension of several recent lunar periodic orbit studies, and can be considered a modern update to Broucke's seminal database of planar cislunar periodic orbits. This new public database is a tool for future mission design and has potential use in a variety of catalogue maintenance space situational awareness applications
Design synthesis of multistable equilibrium systems
(2004) King, Carey Wayne; Beaman, Joseph J.; Campbell, Matthew I.
Mechanical systems are often desired to have features that can adapt to changing environments. Ideally these systems have a minimum number of parts and consume as little power as possible. Unfortunately many adaptable systems either have a large number of heavy parts and/or continuous actuation of smart materials to provide the adaptive capabilities. For systems where both adaptability and power conservation are desired characteristics, adaptability can be limited by power consumption. Multistable equilibrium (MSE) systems aim to provide a type of adaptable system that can have multiple mechanical configurations, or states, that require no power to maintain each stable configuration. Power is only needed to move among the stable states, and a level of adaptability is maintained. The stable equilibrium configurations are defined by a system potential energy being at a minimum. The design of a MSE system is based around locally shaping a potential energy curve about desired equilibrium configurations, both stable and unstable, such that the basic design goals of position, linearized natural frequency, and transition energy can be specified for the MSE system. By mapping the performance space from the design space in tandem with stochastic numerical optimization methods, the designer determines if a certain system topology can be designed as a MSE system. Qualitative and quantitative mapping procedures enable the designer to decide whether or not the desired design lies near the center or periphery of a performance space. The performance space is defined by the desired design criteria (i.e. locations of the equilibria, natural frequency at the equilibria, etc.) that the designer deems important. If the desired design lies near the periphery of the performance space, a series of optimization trials is performed. This series shows the tendency of the problem to be solved as the desired MSE system characteristics are varied within the performance space from a location where the solution is known to exist to the true desired location where the solution is not guaranteed to exist. Upon analysis of the resulting optimization trends, the designer is able to determine whether or not a feasible limit in the system performance has been reached.
Development of a hydrate-gas-water static equilibrium model and analysis of three-phase stability
(2018-05) Leung, Ryan Wai-Hung; Daigle, Hugh
Recent evidence suggests that a three-phase stability zone exists at the base of gas hydrate stability (BGHS), where hydrate and gas may coexist due to the pore size distribution. We develop a three-phase stability zone model at static equilibrium based on the idea of minimizing interfacial energy. We use this model to produce three-phase saturations and study the effects of three-phase stability for two applications. The first application is related to the migration of gas from beneath sealing hydrate layers to the seafloor. A proposed mechanism for this upwards gas migration is the generation of fractures through the sealing hydrate sediment due to overpressures caused by the accumulation of gas on geologic timescales. Our study focuses on how the fracturing potential of a three-phase stability zone differs from a discrete BGHS, where hydrate is separated from gas by a sharp boundary. We model gas overpressures at Blake Ridge, Hydrate Ridge, and the Kumano Basin by incorporating mercury intrusion capillary pressure data with our three-phase stability model. Our results show that the overpressures in the three-phase stability model are smaller, reducing the potential for gas-driven fracturing. We also find that hydrate-bearing basins with shallower seafloor depths modeled with three-phase stability need much more methane to generate the overpressures that will initiate fractures. The second application of three-phase stability relates to the bottom-simulating reflection (BSR), which is a common negative polarity reflection in marine sediments that often follows the contour of the seafloor. Recent literature suggests that the BSR indicates the shallowest presence of gas, not the BGHS. This three-phase stability model has an impact on the seismic response of the BSR, and we study this effect by developing 1-D rock physics models of Blake Ridge. By varying the methane quantity and performing fluid substitution with three-phase saturation profiles, we generate synthetic seismograms and analyze the difference in two way travel time (TWTT). For comparison, we use the workflow for a parameter sensitivity model and an original-resolution model. Through this analysis, we find a relationship between the TWTT width of the BSR’s peaks and the methane abundance at the BGHS
Development of efficient, stable organic-inorganic hybrid solar cells
(2012-08) Jayan, Baby Reeja; Manthiram, Arumugam
Developing a fundamental understanding of photocurrent generation processes at organic-inorganic interfaces is critical for improving hybrid solar cell efficiency and stability. This dissertation explores processes at these interfaces by combining data from photovoltaic device performance tests with characterization experiments conducted directly on the device. The dissertation initially focuses on exploring how morphologically and chemically modifying the organic-inorganic interface, between poly(3-hexylthiophene) (P3HT) as the electron donating light absorbing polymer and titanium dioxide (TiO₂) as the electron acceptor, can result in stable and efficient hybrid solar cells. Given the heterogeneity which exists within bulk heterojunction devices, stable interfacial prototypes with well-defined interfaces between bilayers of TiO₂ and P3HT were developed, which demonstrate tunable efficiencies ranging from 0.01 to 1.6 %. Stability of these devices was improved by using Cu-based hole collecting electrodes. Efficiency values were tailored by changing TiO₂ morphology and by introducing sulfide layers like antimony trisulfide (Sb₂S₃) at the P3HT-TiO₂ interface. The simple bilayer device design developed in this dissertation provides an opportunity to study the precise role played by nanostructured TiO₂ surfaces and interfacial modifiers using a host of characterization techniques directly on a working device. Examples introduced in this dissertation include X-ray photoelectron spectroscopy (XPS) depth profiling analysis of metal-P3HT and P3HT-TiO₂ interfaces and Raman analysis of bonding between interface modifiers like Sb₂S₃ and P3HT. The incompatibility of TiO₂ with P3HT was significantly reduced by using P3HT derivatives with -COOH moieties at the extremity of a polymer chain. The role of functional groups like -COOH in interfacial charge separation phenomena was studied by comparing the photovoltaic behavior of these devices with those based on pristine P3HT. Finally, for hybrid solar cells discussed in this dissertation to become commercially viable, high temperature processing steps of the inorganic TiO₂ layer must be avoided. Accordingly, this dissertation demonstrates the novel use of electromagnetic radiation in the form of microwaves to catalyze growth of anatase TiO₂ thin films at temperatures as low as 150 °C, which is significantly lower than that used in conventional techniques. This low temperature process can be adapted to a variety of substrates and can produce patterned films. Accordingly, the ability to fabricate TiO₂ thin films by the microwave process at low temperatures is anticipated to have a significant impact in processing devices based on plastics.
Effects of multi-joint stiffness on the stable, Cartesian workspace for dexterous manipulation with the anatomically correct testbed hand
(2022-10-06) Shafer, Anna J.; Deshpande, Ashish D.
Human hands perform amazingly complex dexterous in-hand manipulation tasks stably through modulation of musculotendon stiffness, setting a high standard for the capabilities of robotic manipulators. Applying passive stiffness boundary analysis to quantify human-like stiffness modulation properties on a human-like physical simulation platform, the Anatomically Correct Testbed (ACT) hand, has the potential to further our understanding of the human stiffness parameter modulation that enables this manipulation performance. In this work, a model of human-like index finger endtip stiffness is developed to quantify the passively stable region within a 3D workspace for stable manipulation. The stiffness model shows that biomechanical properties vary throughout the workspace with the greatest stiffness volume at proximal postures enabling efficient opposition of the anatomical thumb for precision grasping tasks. Using biomechanically informed control principles on the ACT hand index finger increased the stable manipulation region and trajectory tracking performance. Finally, the effect of external forces on the stable region was characterized as an inverse linear relationship to the magnitude of the applied force and the direction of the applied force highlighted the observed biomechanical constraints which make the positive ulnar axis ideal for opposing the thumb. The resulting method has the potential for general optimization of tendon-driven system stability on a task basis in 3D space, bringing robotic manipulators closer to human levels of dexterity.
Energy storage sizing for low-inertia microgrids, and lessons learned from a potential microgrid
(2016-05) Toliyat, Amir; Baldick, Ross; Kwasinski, Alexis; Arapostathis, Aristotle; Hallock, Gary; Uriarte, Fabian
The coordinated control of multiple distributed generators in a microgrid and the preservation of adequate system inertia in real-time operations are some of the principal technical challenges for stable microgrid operation. One issue in particular pertains to grid-tied inverters, which, as mandated by present standards, are only permitted to operate at unity power factor, thereby requiring the microgrid’s synchronous generators to operate at a low power factor. This behavior accordingly introduces ramifications by limiting the generator’s active power output, which would compromise frequency and voltage stability margins. Consideration is also given to the effect of line impedances, since interconnecting microgrid lines can be described by a variety of X/R ratios that affect the control and flow of active and reactive power. Moreover, the absence of a stiff grid presents control challenges for grid-tied inverters due to the inverters’ tendency to regulate the voltage at the point of common coupling. These same inverters also jeopardize microgrid stability due to their low equivalent inertia as traditional forms of generation (i.e., spinning sources) become displaced by inertia-less inverters. Because of this low microgrid inertia, fluctuations in the output power of renewable energy sources or changes in local load levels may lead to power quality or frequency/voltage stability concerns. Therefore, energy storage sizing is investigated in this dissertation, as it is closely related to the stability analysis of microgrids. Furthermore, an existing residential community (in Austin, TX) described by a moderate penetration of photovoltaic sources and electric vehicle charging is considered, and the implications of said community being retrofitted to a microgrid are examined.
Estimating the minimum bit-width precision for stable deep neural networks utilizing numerical linear algebra
(2019-06-20) Maheshwari, Naman; Kulkarni, Jaydeep P.
Understanding the bit-width precision is critical in compact representation of a Deep Neural Network (DNN) model with minimal degradation in the inference accuracy. While DNNs are resilient to small errors and noise as pointed out by many prior sources, there is a need to develop a generic mathematical framework for evaluating a given DNN’s sensitivity to input bit-width precision. In this work, we derive a bit-width precision estimator which incorporates the sensitivity of DNN inference accuracy to round-off errors, noise, or other perturbations in inputs. We use the tools of numerical linear algebra, particularly stability analysis, to establish the general bounds that can be imposed on the precision. Random perturbations and ‘worst-case’ perturbations, via adversarial attacks, are applied to determine the tightness of the proposed estimator. The experimental results on AlexNet and VGG-19 showed that minimum 11 bits of input bit-width precision is required for these networks to remain stable. The proposed bit-width precision estimator can enable compact yet highly accurate DNN implementations
Experimental evaluation of partial depth precast concrete deck panels subjected to shear loading
(2017-05-03) Kintz, John Robert; Helwig, Todd Aaron, 1965-
Horizontally curved girder bridges are often utilized for highway interchanges and other projects with restricted right-of-way. The large torsional demands caused by the girder geometry often require these systems to have extensive bracing, typically in the form of cross frames or diaphragms, to increase the torsional stiffness of the girder system during the construction phase. The most critical stage for the bracing is during the deck placement, when the noncomposite girders must resist the full construction load. Partial depth precast concrete panels (PCPs) are prestressed concrete panels used primarily as stay-in-place (SIP) formwork for straight girder systems. They are placed on full-length extruded bedding strips epoxied to the girder top flange, and the remaining depth of the deck is cast above. This is a time-efficient method of construction, and has become an attractive option due to ease of constructability and deck longevity. Although the panels have not been used on horizontally curved girder systems, there is a desire by bridge owners and contractors to use the forms in some curved girder applications. In addition to using the panels on curved girder applications, engaging the in-plane shear stiffness of the panels may lead to significant bracing in both straight and horizontally curved girder applications. A research investigation focused on measuring the behavior of PCPs acting as a shear diaphragm, as well as to develop an adequate connection between the PCPs and the girders was conducted at The University of Texas at Austin. Four PCP connection details were developed and tested at two different bedding strip heights. These connections were designed for a range of capacities, and in-plane shear load was applied until failure using a frame mechanism assembly. The experimental results showed that the connected PCPs had significant shear stiffness and strength, with the panels reaching shear capacities between 91 and 154 kips before failure depending on the connection detail that was utilized. A 46 to 70 percent increase in shear stiffness was also observed when the bedding strip height was reduced from 4 inches to ½ inch. All panels greatly exceeded the design capacity using the ACI design predictions, with 7 of 8 panels eventually failing due to concrete side face breakout. The eighth PCP failed from weld rupture in which the weld connecting the WT and the girder flange began to unzip.
Exploring new varieties and applications of trophic cascades using pond species interaction experiments and theory
(2023-05-01) Rakowski, Chase J.; Leibold, Mathew A.; Farrior, Caroline E.; Manning, Schonna R; Jha, Shalene; Theriot, Edward C
Global change is altering the diversity, composition, and interactions of predator species even more rapidly than those of lower trophic levels. While many of the most important ecosystem functions and services such as primary production are provided by bottom trophic levels, we know from the classic trophic cascade concept that these ecosystem properties can be strongly impacted by predators via chains of species interactions. However, the relationships between changing attributes of predator communities and these key ecosystem properties at the base of the food web remain unclear. I identify three ways that the trophic cascade concept can be expanded to help fill this knowledge gap. First, ecologists can assess cascading consequences of changes in predator diversity or interactions rather than the less realistic addition or removal of entire top trophic levels. Second, trophic cascade research can move away from an equilibrium approach to incorporate the food web dynamics that determine ecosystem stability. Third, there is understudied potential for the application of trophic cascade theory to improving environmental technologies involving the cultivation of microalgae. In Chapter One I experimentally test the effects of insect predator diversity on the central tendency and variability of pond plankton biomass. I find that the insect species better suppress their collective zooplankton prey when together, leading to less variable phytoplankton biomass. In Chapter Two I analyze a food web model to explore the influence of the degree of intraguild predation on the variability of biomass of lower trophic levels. I show that stronger intraguild predation is associated with biomass fluctuations throughout the food web. Finally, in Chapter Three I experimentally show that fish can provide effective biological control in wastewater algal raceway ponds, increasing algal biomass though not necessarily improving nutrient removal from the wastewater. Overall, the present dissertation describes two novel varieties of trophic cascades and expands upon a new application. These links between the top and bottom ends of food webs predict consequential effects of changes in predator communities, and they also suggest strategies for ecosystem management in pursuit of reliable ecosystem services.
Formulation, bioprocessing, and manufacturing of viral vectors in unique dosage forms
(2024-05) Le, Matthew Dinh Kien ; Croyle, Maria A.; David Lechuga; Mohammed Maniruzzaman; Debadyuti Ghosh; Hugh Smyth
Though the market for biological drugs has rapidly expanded in recent years, most formulations still require the cold chain for sufficient thermostability, making these therapies costly. When looking to improve the overall shelf-life stability profile of biological therapeutics, solid-state stabilization techniques are commonly used. These techniques have long been dominated by dry preparations like lyophilization and spray drying, where low residual moisture (RM) content is necessary for stability. However, these techniques are generally expensive, requiring long development and processing times, and are typically inaccessible to low-income countries. Our lab has developed a film technology that can stabilize biologics at ambient temperatures, with relatively high RM, especially when compared to existing lyophilization and spray dried preparations. Here, we investigate the importance of the film drying parameters and storage relative humidity (RH) on the resulting film’s RM, and how this impacts the thermostability profile of the film. When evaluating Adenovirus (Ad) and Adeno-Associated Virus Serotype 9 (AAV9), we found that a controlled equilibrium drying at high RH (52.5% RH) was optimal for long-term thermostability. We also found that Ad was sensitive to both drying and storage RH, while AAV9 was less sensitive in comparison. After investigating the film matrix stability, we determined that the amorphous film matrix itself was relatively stable, and that virus degradation in the film matrix could be due to aggregation and chemical degradation of virus within the microenvironment of the film. Lastly, another method to improve to biological therapies is PEGylation. This technique aims to improve the stability of a product in vivo, as it typically increases the half-life of biologics in the body. However, to properly characterize a successful PEGylation, assays are needed to monitor and verify the conjugation to ensure consistency and repeatability. Here, we have outlined a small-scale PEGylation process that can be easily implemented at the bench scale, which allows researchers to quickly conjugate and evaluate their given biologic for efficacy. To this end, the goal is to provide a blueprint for efficiently developing a PEGylated biologic to be evaluated in preclinical studies. Furthermore, we have outlined the minimum protein or vector requirements needed to characterize the PEGylation process, in the event that material restraints are an issue.
A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method
(2010-05) Leger, Nicholas Matthew; Vasseur, Alexis F.; Arbogast, Todd J.; Gamba, Irene M.; Vishik, Mikhail M.; Raman, Venkatramanan
We present a mathematical study of two conservative systems in fluid mechanics. First, we study a fragmentation model for sprays. The model takes into account the break-up of spray droplets due to drag forces. In particular, we establish the existence of global weak solutions to a system of incompressible Navier-Stokes equations coupled with a Boltzmann-like kinetic equation. We assume the particles initially have bounded radii and bounded velocities relative to the gas, and we show that those bounds remain as the system evolves. One interesting feature of the model is the apparent accumulation of particles with arbitrarily small radii. As a result, there can be no nontrivial hydrodynamical equilibrium for this system. Next, with an interest in understanding hydrodynamical limits in discontinuous regimes, we study a classical model for shock waves. Specifically, we consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L² perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show that up to a time-dependent translation of the shock, the L² norm of a perturbed solution relative to the shock wave is bounded above by the L² norm of the initial perturbation. Finally, we include some preliminary relative entropy estimates which are suitable for a study of shock wave solutions to n x n systems of conservation laws having a convex entropy.
Hierarchical control of dc microgrids with constant power loads
(2017-08) Srinivasan, Mahesh; Baldick, Ross; Kwasinski, Alexis; Arapostathis, Aristotle; Hallock, Gary; Hebner, Robert
This dissertation proposes general methodologies for designing hierarchical control schemes for dc microgrids loaded by constant power loads (CPLs). CPLs form a major proportion of the system loads in many microgrids. Without proper control, CPLs present destabilizing effect at the dc microgrid. In addition to stable operation of microgrid, proper current sharing among paralleled sources is essential. The proposed hierarchical control strategy consists of two control levels. The lower level consists of droop-based primary controllers which enables current-sharing among paralleled sources and also damps limit cycle oscillations due to CPLs. The higher level consists of secondary controller which compensates for voltage deviations due to primary controller. This higher level is implemented either as autonomous controllers or as a centralized controller. In the case of autonomous secondary controllers, they operate alongside of primary controllers in each of the paralleled converters. In the case of centralized secondary controller, a remote secondary controller uses a high speed communication link to communicate to local controllers. Interfacing sources with different characteristics and voltage ranges necessitates the use of complex converter topologies. As an initial step towards implementing hierarchical control scheme for such microgrids with CPLs, a linear controller is proposed for dc microgrids with standalone SEPIC, Cuk and Zeta converters. During the first stage of the two stage controller, limit cycle oscillations are damped by inserting a virtual resistance in series with the converter input inductor. During the second stage, an integral controller is added to the first stage to compensate for voltage deviations. For microgrids containing different converter topologies, stability of equilibrium points is examined and stability conditions are derived and explained. Experiments performed on a prototype microgrid are used to verify the proposed control laws. Expanding study on stability of microgrids, the maximum real power load in a dc microgrid bus is traced geometrically. The generalized circle diagram approach used in a conventional power system is modified for this purpose. The different types of buses present in a dc microgrid are described and the locus of operating points is obtained. The proposed method is verified by simulations on an example dc microgrid.
High-order finite element methods for seismic wave propagation
(2009-05) De Basabe Delgado, Jonás de Dios, 1975-; Sen, Mrinal K.; Wheeler, Mary F. (Mary Fanett)
Purely numerical methods based on the Finite Element Method (FEM) are becoming increasingly popular in seismic modeling for the propagation of acoustic and elastic waves in geophysical models. These methods o er a better control on the accuracy and more geometrical exibility than the Finite Di erence methods that have been traditionally used for the generation of synthetic seismograms. However, the success of these methods has outpaced their analytic validation. The accuracy of the FEMs used for seismic wave propagation is unknown in most cases and therefore the simulation parameters in numerical experiments are determined by empirical rules. I focus on two methods that are particularly suited for seismic modeling: the Spectral Element Method (SEM) and the Interior-Penalty Discontinuous Galerkin Method (IP-DGM). The goals of this research are to investigate the grid dispersion and stability of SEM and IP-DGM, to implement these methods and to apply them to subsurface models to obtain synthetic seismograms. In order to analyze the grid dispersion and stability, I use the von Neumann method (plane wave analysis) to obtain a generalized eigenvalue problem. I show that the eigenvalues are related to the grid dispersion and that, with certain assumptions, the size of the eigenvalue problem can be reduced from the total number of degrees of freedom to one proportional to the number of degrees of freedom inside one element. The grid dispersion results indicate that SEM of degree greater than 4 is isotropic and has a very low dispersion. Similar dispersion properties are observed for the symmetric formulation of IP-DGM of degree greater than 4 using nodal basis functions. The low dispersion of these methods allows for a sampling ratio of 4 nodes per wavelength to be used. On the other hand, the stability analysis shows that, in the elastic case, the size of the time step required in IP-DGM is approximately 6 times smaller than that of SEM. The results from the analysis are con rmed by numerical experiments performed using an implementation of these methods. The methods are tested using two benchmarks: Lamb's problems and the SEG/EAGE salt dome model.
How perceptions impact real estate decisions : an analysis of residential demand in Austin, Texas
(2015-12) Fulmer, Kristen Alyse; Atkinson, Simon, Ph. D.; Wegmann, Jacob
This thesis examines how social media trends create perceptions, which influence real estate decision-making within the Millennial generation, ultimately affecting their long-term investment and longevity in the city of Austin, Texas. To investigate the residential real estate market in Austin, specifically within the Millennial generation, I discuss decision factors with the residents and developers, known as stakeholders. By completing a mixed-methods analysis, I determine how Internet-based tendencies affect perceptions and economic realities of specific neighborhoods or the city, thereby affecting the residential real estate market as a whole. Approaching this research as a post-positivist, I hypothesize that the Millennial cohort is currently creating short-term demand for residential development with no long-term intentions of staying in the city. By discovering this future instability of sectors within the Millennial generation, especially in newcomers to the city, I question Austin’s plans, which seem to lack amenities to provide for this cohort’s residential longevity.
Hydraulic performance and stability of geosynthetic landfill cover systems with constrained drainage at the outlet
(2011-08) Yates, Trevor Butler; Zornberg, Jorge G.; Gilbert, Robert B. (Robert Bruce), 1965-; El Mohtar, Chadi
Sliding failures of landfill cover systems are common, and the slip surface is often at the interface between a geosynthetic drainage layer and an underlying textured geomembrane. In an effort to understand the sliding failures, the objectives of this research project are to summarize current regulation and practice in landfill cover design, use experimental methods to characterize the behavior of geosynthetic landfill materials in cover systems approaching failure, and develop models to evaluate the hydraulic performance and stability of landfill cover systems. Inclined plane tests were conducted to explore the behavior of a geosynthetic drainage material/textured geomembrane interface. The interface had effective normal stress dependent strain softening behavior, with more strain softening measured at higher effective normal stresses. A numerical model for confined flow in a drainage layer with a constrained outlet was developed. The model was used to evaluate how water fills and empties from a geosynthetic drainage layer for a variety of inflow conditions and constraints to flow at the outlet. The model was used to demonstrate that a drainage layer that effectively conveys water out of a cover system with a free flowing drainage outlet quickly fills with water when the outlet has a modest constraint to flow. An iterative, numerical model was developed to calculate stability solutions for landfill cover slopes that satisfy force equilibrium and strain compatibility while accounting for effective normal stress dependent strain softening and various pore water pressure conditions. Stability solutions reveal that depending on the water pressure in the drainage layer, the geosynthetic drainage material may experience tension at many points along the slope. It is crucial for the stability of the landfill cover system to maintain free-flowing conditions at the drainage layer outlet. A modest constraint to flow at the outlet has a significant adverse effect on the ability of the landfill cover drainage layer to convey water out of the system, which can lead to instability. The drainage layer outlet should be designed to ensure free flow of water out of the drainage layer.
Identifying mutations that enhance the evolutionary stability of fluorescent protein expression from a plasmid in Escherichia coli
(2014-05) Rodríguez Mendoz, Álvaro Eugenio; Barrick, Jeffrey E.; Harshey, Rasika
Synthetic biologists and metabolic engineers seek to design and create organisms with novel functions. A major difficulty with many designed genetic devices is that they lack evolutionary robustness. In this study, our aim was to identify mutations that could enhance the evolutionary stability of green fluorescent protein (GFP) expression from a plasmid in Escherichia coli. To achieve this goal, we created a mutagenized strain library and performed an evolution experiment. To enrich potential mutants with improved GFP stability, we periodically sorted for cells that remained highly fluorescent as this population was propagated for several hundred generations and less-robust strains accumulated inactivating mutations. Further testing of clones isolated from the final evolved population showed that GFP expression was more stable in these strains and suggested mutations in the chromosome were responsible. Re-sequencing the genomes of four of these strains found that, among other genetic differences from the ancestor, all had a mutation in either PolA or PolB. These two types of DNA polymerase mutations may enhance GFP stability by causing a lower point mutation rate in the E. coli host.