Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Ecological and evolutionary effects of dispersal on freshwater zooplankton

A recent focus on contemporary evolution and the connections between communities has sought to more closely integrate the fields of ecology and evolutionary biology. Studies of coevolutionary dynamics, life history evolution, and rapid local adaptation demonstrate that ecological circumstances can dictate evolutionary trajectories. Thus, variation in species identity, trait distributions, and genetic composition may be maintained among ecologically divergent habitats. New theories and hypotheses (e.g., metacommunity theory and the Monopolization hypothesis) have been developed to understand better the processes occurring in spatially structured environments and how the movement of individuals among habitats contributes to ecology and evolution at broader scales. As few empirical studies of these theories exist, this work seeks to further test these concepts. Spatial and temporal dispersal are the mechanisms that connect habitats to one another. Both processes allow organisms to leave conditions that are suboptimal or unfavorable, and enable colonization and invasion, species range expansion, and gene flow among populations. Freshwater zooplankton are aquatic crustaceans that typically develop resting stages as part of their life cycle. Their dormant propagules allow organisms to disperse both temporally and among habitats. Additionally, because a number of species are cyclically parthenogenetic, they make excellent model organisms for studying evolutionary questions in a controlled environment. Here, I use freshwater zooplankton communities as model systems to explore the mechanisms and consequences of dispersal and to test these nascent theories on the influence of spatial structure in natural systems. In Chapter one, I use field experiments and mathematical models to determine the range of adult zooplankton dispersal over land and what vectors are moving zooplankton. Chapter two focuses on prolonged dormancy of one aquatic zooplankter, Daphnia pulex. Using statistical models with field and mesocosm experiments, I show that variation in Daphnia dormant egg hatching is substantial among populations in nature, and some of that variation can be attributed to genetic differences among the populations. Chapters three and four explore the consequences of dispersal at multiple levels of biological organization. Chapter three seeks to understand the population level consequences of dispersal over evolutionary time on current patterns of population genetic differentiation. Nearby populations of D. pulex often exhibit high population genetic differentiation characteristic of very low dispersal. I explore two alternative hypotheses that seek to explain this pattern. Finally, chapter four is a case study of how dispersal has influenced patterns of variation at the community, trait and genetic levels of biodiversity in a lake metacommunity.

Quantitative characterization of physico-chemical properties of the active layers of reverse osmosis and nanofiltration membranes, and their relation to membrane performance

The main objectives of this dissertation were: (i) to develop experimental and analytical procedures to quantify different physico-chemical properties of the ultra-thin (~ 100 nm) active layers of reverse osmosis (RO) and nanofiltration (NF) membranes and their interactions with contaminants; (ii) to use such procedures to evaluate the similarities and differences between the active layers of different RO/NF membranes; and (iii) to relate characterization results to membrane performance. Such objectives were motivated by the current limited understanding of the physico-chemical properties of active layers as a result of traditional characterization techniques having limitations associated with the nanometer-scale spatial resolution required to study these ultra-thin films. Functional groups were chosen as the main active layer property of interest. Specific accomplishments of this study include the development of procedures to quantify in active layers as a function of pH: (1) the concentration of both negatively and positively ionized functional groups; (2) the stoichiometry of association between ions (i.e., barium) and ionized functional groups (i.e., carboxylate and sulfonate); and (3) the steric effects experienced by ions (i.e., barium). Conceptual and mathematical models were developed to describe experimental results. The depth heterogeneity of the active layer physico-chemical properties and interactions with contaminants studied in this dissertation was also characterized. Additionally, measured concentrations of ionized functional groups in the polyamide active layers of several commercial RO/NF membranes were used as input in a simplified RO/NF transport model to predict the rejection of a strong electrolyte (i.e., potassium iodide) and a weak acid (i.e., arsenious acid) at different pH values based on rejection results at one pH condition. The good agreement between predicted and experimental results showed that the characterization procedures developed in this study serve as useful tools in the advancement of the understanding of the properties and structure of the active layers of RO/NF membranes, and the mechanisms of contaminant transport through them.

A path-based framework for analyzing large markov models

Reliability and dependability modeling can be employed during many stages of analysis of a computing system to gain insights into its critical behaviors. To provide useful results, realistic models of systems are often necessarily large and complex. Numerical analysis of these models presents a formidable challenge because the sizes of their state-space descriptions grow exponentially in proportion to the sizes of the models. On the other hand, simulation of the models requires analysis of many trajectories in order to compute statistically correct solutions. This dissertation presents a novel framework for performing both numerical analysis and simulation. The new numerical approach computes bounds on the solutions of transient measures in large continuous-time Markov chains (CTMCs). It extends existing path-based and uniformization-based methods by identifying sets of paths that are equivalent with respect to a reward measure and related to one another via a simple structural relationship. This relationship makes it possible for the approach to explore multiple paths at the same time,· thus significantly increasing the number of paths that can be explored in a given amount of time. Furthermore, the use of a structured representation for the state space and the direct computation of the desired reward measure (without ever storing the solution vector) allow it to analyze very large models using a very small amount of storage. Often, path-based techniques must compute many paths to obtain tight bounds. In addition to presenting the basic path-based approach, we also present algorithms for computing more paths and tighter bounds quickly. One resulting approach is based on the concept of path composition whereby precomputed subpaths are composed to compute the whole paths efficiently. Another approach is based on selecting important paths (among a set of many paths) for evaluation. Many path-based techniques suffer from having to evaluate many (unimportant) paths. Evaluating the important ones helps to compute tight bounds efficiently and quickly.