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Even though first order LWR models have many limitations, they are still widely used in many engineering applications. Second-order models, on the other hand, address many of those limitations. Among second-order models, the inhomogeneous Aw-Rascle-Zhang (ARZ) model is well-received as its structure generates characteristic waves that make physical sense. The ARZ model --- and other $2\times 2$ hyperbolic systems with a relaxation term --- possess a critical phase transition: whenever the sub-characteristic condition (SCC) is violated, uniform traffic flow is unstable, and small perturbations grow into nonlinear traveling waves, called jamitons. The case where the SCC is satisfied has been studied extensively. However, what is essentially unstudied is the question: which jamiton solutions are dynamically stable? To understand which stop-and-go traffic waves can arise through the dynamics of the model, this question is critical. This dissertation first outlines the mathematical foundations of the ARZ model and its solutions, then presents a computational study demonstrating which types of jamitons are dynamically stable, and which are not. After that, a procedure is presented that characterizes the stability of jamitons. The study reveals that a critical component of this analysis is the proper treatment of the perturbations to the shocks, and of the neighborhood of the sonic points. The insight gained from answering the question regarding the dynamical stability of jamitons has many applications. One particular application presented here is deriving an averaged model for the ARZ model. Such a model is as simple to solve (analytically and numerically) as the LWR model, but nevertheless captures the cumulative effects of jamitons regarding fuel consumption, total flow, and braking events. / Mathematics

In sufficient dimension reduction (Li, 1991; Cook, 1998b), original predictors are replaced by their low-dimensional linear combinations while preserving all of the conditional information of the response given the predictors. Sliced inverse regression [SIR; Li, 1991] and principal Hessian directions [PHD; Li, 1992] are two popular sufficient dimension reduction methods, and both SIR and PHD estimators involve all of the original predictor variables. To deal with the cases when the linear combinations involve only a subset of the original predictors, we propose a Bayesian model averaging (Raftery et al., 1997) approach to achieve sparse sufficient dimension reduction. We extend both SIR and PHD under the Bayesian framework. The superior performance of the proposed methods is demonstrated through extensive numerical studies as well as a real data analysis. / Statistics

The primary objective of this research is to develop and verify a methodology for modeling three dimensional discrete crack growth in concrete and reinforced concrete structures. Two main sources of damage, considered in this work, include the mechanical loading and the chemical interaction. The behavior of concrete is brittle in tension and becomes ductile behavior under compressive loading. At the same time, the chemical interaction triggers a progressive degradation of strength parameters. The main focus in this research is on numerical analysis of localized damage that is associated with formation of macrocracks. The specific form of chemical interaction examined here involves the alkali-silica reaction (ASR). The approach used in this work for describing the propagation of macrocraks is based on the volume averaging technique. This scheme represents a simplified form of strong discontinuity approach (SDA). It incorporates the notion of a ‘characteristic length’, which is defined as the ratio of area of the crack surface to the considered referential volume. It is demonstrated, based on an extensive numerical study, that this approach gives mesh-independent results which are consistent with the experimental evidence. The accuracy of the solutions is virtually the same as that based on SDA and/or the Extended Finite Element Method (XFEM), while the computational effort is significantly smaller. In order to describe the behavior of the fractured zone, a traction velocity discontinuity relation is formulated that is representative of different modes of damage propagation, including crack opening in tensile regime as well as shear band formation under compression. For tracing the discontinuity within domain, crack smoothening algorithm is employed to overcome any numerical instabilities that may occur close to ultimate load of the structure. The general methodology, as outlined above, has been enhanced by incorporating the chemoplasticity framework to describe the damage propagation in concrete affected by chemical interaction, i.e. continuing ASR. The latter is associated with progressive expansion of the silica gel that is coupled with degradation of strength properties. An implicit scheme has been developed, incorporating the return mapping algorithm, for the integration of the governing constitutive relations. The framework has been implemented in Abaqus software to examine the crack propagation pattern in structural elements subjected to continuing ASR. Another major topic addressed in this thesis is the ‘size effect’ phenomenon. The existing experimental studies, conducted primarily on various concrete structures, clearly show that the ultimate strength is strongly affected by the size of the structure. This phenomenon stems primarily from the effect of localized damage that accompanies the structural failure. The quantitative response depends on the geometry of the structure, type of loading and the material properties. The size effect has been investigated here for a number of notched and un-notched concrete beams, of different geometries, subjected to three-point bending. Both mechanical loading and the chemical interaction have been considered. The next topic considered in this study deals with analysis of localized fracture in 3D reinforced concrete structures. Here, a mesoscale approach is employed whereby the material is perceived as a composite medium comprising two constituents, i.e. concrete matrix and steel reinforcement. The response at the macroscale is obtained via a homogenization procedure that incorporates again the volume averaging. The latter incorporates a set of static and kinematic constraints that are representative of the response prior to the onset of fracture. After the formation of macrocracks, a traction-separation law within the fractured zone is modified by incorporating the Timoshenko beam theory in order to assess the stiffness characteristics in the presence of reinforcement. A number of numerical examples are given that examine the crack pattern formation and the associated fracture mechanism in concrete beams at different intensity of reinforcement. The final chapter of this thesis provides an illustrative example of the application of the proposed methodology to the analysis of a large scale structure. The focus here is on the assessment of structural damage in a hydraulic structure subjected to ASR continuing over of period of a few decades. The results, in term of the predicted extent of damage as well as the displacement history at some specific locations, are compared with in-situ monitoring. / Thesis / Doctor of Philosophy (PhD)

No / The paper presents a 2-D large eddy simulation (LES) modelling approach to investigate the properties of the plunging waves. The numerical model is based on the smoothed particle hydrodynamics (SPH) method. SPH is a mesh-free Lagrangian particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The Smagorinsky model is used as the turbulence model due to its simplicity and effectiveness. The proposed 2-D SPH-LES model is applied to a cnoidal wave breaking and plunging over a mild slope. The computations are in good agreement with the documented data. Especially the computed turbulence quantities under the breaking waves agree better with the experiments as compared with the numerical results obtained by using the k- model. The sensitivity analyses of the SPH-LES computations indicate that both the turbulence model and the spatial resolution play an important role in the model predictions and the contributions from the sub-particle scale (SPS) turbulence decrease with the particle size refinement.

The standard methodology when building statistical models has been to use one of several algorithms to systematically search the model space for a good model. If the number of variables is small then all possible models or best subset procedures may be used, but for data sets with a large number of variables, a stepwise procedure is usually implemented. The stepwise procedure of model selection was designed for its computational efficiency and is not guaranteed to find the best model with respect to any optimality criteria. While the model selected may not be the best possible of those in the model space, commonly it is almost as good as the best model. Many times there will be several models that exist that may be competitors of the best model in terms of the selection criterion, but classical model building dictates that a single model be chosen to the exclusion of all others. An alternative to this is Bayesian model averaging (BMA), which uses the information from all models based on how well each is supported by the data. Using BMA allows a variance component due to the uncertainty of the model selection process to be estimated. The variance of any statistic of interest is conditional on the model selected so if there is model uncertainty then variance estimates should reflect this. BMA methodology can also be used for variable assessment since the probability that a given variable is active is readily obtained from the individual model posterior probabilities. The multivariate methods considered in this research are principal components analysis (PCA), canonical variate analysis (CVA), and canonical correlation analysis (CCA). Each method is viewed as a particular multivariate extension of univariate multiple regression. The marginal likelihood of a univariate multiple regression model has been approximated using the Bayes information criteria (BIC), hence the marginal likelihood for these multivariate extensions also makes use of this approximation. One of the main criticisms of multivariate techniques in general is that they are difficult to interpret. To aid interpretation, BMA methodology is used to assess the contribution of each variable to the methods investigated. A second issue that is addressed is displaying of results of an analysis graphically. The goal here is to effectively convey the germane elements of an analysis when BMA is used in order to obtain a clearer picture of what conclusions should be drawn. Finally, the model uncertainty variance component can be estimated using BMA. The variance due to model uncertainty is ignored when the standard model building tenets are used giving overly optimistic variance estimates. Even though the model attained via standard techniques may be adequate, in general, it would be difficult to argue that the chosen model is in fact the correct model. It seems more appropriate to incorporate the information from all plausible models that are well supported by the data to make decisions and to use variance estimates that account for the uncertainty in the model estimation as well as model selection. / Ph. D.