Aggregate strength, gradation, and shape play a vital role in controlling asphalt mixture performance. Many studies have demonstrated the effects of these factors on asphalt mixture performance in terms of resistance to fatigue cracking and rutting. This study introduces numerical and analytical approaches supported with imaging techniques for studying the interrelated effects of aggregate strength, gradation, and shape on resistance of asphalt mixtures to fracture. The numerical approach relies on the discrete element method (DEM). The main advantage of this approach is the ability to account for the interaction between the internal structure distribution and aggregate properties in the analysis of asphalt mixture response and performance. The analytical approach combines aggregate strength variability and internal force distribution in an asphalt mixture to predict the probability of aggregate fracture. The numerical and analytical approaches were calibrated and verified using laboratory tests on various aggregate types and mixtures. Consequently these approaches were used to: (1) determine the resistance of various mixture types with different aggregate properties to fracture, (2) study the effects of aggregate strength variability on fracture, (3) quantify the influence of blending different types of aggregate on mixture strength, (4) develop a mathematical expression for calculating the probability of aggregate fracture within asphalt mixture, and (5) relate cracking patterns (cohesive: aggregate - aggregate and matrix - matrix, and adhesive: aggregate - matrix) in an asphalt mixture to internal structure distribution and aggregate properties. The results of this dissertation established numerical and analytical techniques that are useful for developing a virtual testing environment of asphalt mixtures. Such a virtual testing environment would be capable of relating the microscopic response of asphalt mixtures to the properties of the mixture constituents and internal structure distribution. The virtual testing environment would be an inexpensive mean to evaluate the influence of changing different material and design factors on the mixture response.

This dissertation has four interrelated studies, namely (1) the characterization of milk purchase choices which included the purchase of organic milk, both organic and conventional milk and conventional milk only; (2) the estimation of a single-equation household demand function for organic and conventional milk; (3) the assessment of binary choice models for organic milk using the Brier Probability score and Yates partition, and (4) the estimation of demand systems that addresses the censoring issue through the use of econometric techniques. In the first paper, the study utilized the estimation of both multinomial logit and probit models in examining a set of causal socio-demographic variables in explaining the purchase of three outcome milk choices namely organic milk, organic and conventional milk and conventional milk only. These crucial variables include income, household size, education level and employment of household head, race, ethnicity and region. Using the 2004 Nielsen Homescan Panel, the second study used the Heckman two-step procedure in calculating the own-price, cross-price, and income elasticities by estimating the demand relationships for both organic and conventional milk. Results indicated that organic and conventional milk are substitutes. Also, an asymmetric pattern existed with regard to the substitution patterns of the respective milk types. Likewise, the third study showed that predictive outcomes from binary choice models associated with organic milk can be enhanced with the use of the Brier score method. In this case, specifications omitting important socio-demographic variables reduced the variability of predicted probabilities and therefore limited its sorting ability. The last study estimated both censored Almost Ideal Demand Systems (AIDS) and Quadratic Almost Ideal Demand System (QUAIDS) specifications in modeling nonalcoholic beverages. In this research, five estimation techniques were used which included the usage of Iterated Seemingly Unrelated Regression (ITSUR), two stage methods such as the Heien and Wessells (1990) and the Shonkwiler and Yen (1999) approaches, Generalized Maximum Entropy and the Dong, Gould and Kaiser (2004a) methods. The findings of the study showed that at various censoring techniques, price elasticity estimates were observed to have greater variability in highly censored nonalcoholic beverage items such as tea, coffee and bottled water.

Neural networks (NNs) are widely used to investigate the relationship among variables in complex multivariate problems. In cases of limited data, the network behavior strongly depends on factors such as the choice of network activation function and network initial weights. In this study, I investigated the use of neural networks for multivariate analysis in the case of limited data. The analysis shows that special attention should be paid when building and using NNs in cases of limited data. The linear activation function at the output nodes outperforms the sigmoidal and Gaussian functions. I found that combining network predictions gives less biased predictions and allows for the assessment of the prediction variability. The NN results, along with conventional statistical analysis, were used to examine the effects of folding, bed thickness, structural position, and lithology on the fracture properties distributions in the Lisburne Formation, folded and exposed in the northeastern Brooks Range of Alaska. Fracture data from five folds, representing different degrees of folding, were analyzed. In addition, I modeled the fracture system using the discrete fracture network approach and investigated the effects of fracture properties on the flow conductance of the system. For the Lisburne data, two major fracture sets striking north/south and east/west were studied. Results of the NNs analysis suggest that fracture spacing in both sets is similar and weakly affected by folding and that stratigraphic position and lithology have a strong effect on fracture spacing. Folding, however, has a significant effect on fracture length. In open folds, fracture lengths in both sets have similar averages and variances. As the folds tighten, both the east/west and north/south fracture lengths increase by a factor of 2 or 3 and become more variable. In tight folds, fracture length in the north/south direction is significantly larger than in the east/west direction. The difference in length between the two fracture sets creates a strong anisotropy in the reservoir. Given the same fracture density in both sets, the set with the greater length plays an important role for fluid flow, not only for flow along its principal direction but also in the orthogonal direction.

The approaches for discretizing the direction variable in particle transport calculations are the discrete-ordinates method and function-expansion methods. Both approaches are limited if the transport solution is not smooth. Angular discretization errors in the discrete-ordinates method arise from the inability of a given quadrature set to accurately perform the needed integrals over the direction ("angular") domain. We propose that an adaptive discrete-ordinate algorithm will be useful in many problems of practical interest. We start with a "base quadrature set" and add quadrature points as needed in order to resolve the angular flux function. We compare an interpolated angular-flux value against a calculated value. If the values are within a user specified tolerance, the point is not added; otherwise it is. Upon the addition of a point we must recalculate weights. Our interpolatory functions map angular-flux values at the quadrature directions to a continuous function that can be evaluated at any direction. We force our quadrature weights to be consistent with these functions in the sense that the quadrature integral of the angular flux is the exact integral of the interpolatory function (a finite-element methodology that determines coefficients by collocation instead of the usual weightedresidual procedure). We demonstrate our approach in two-dimensional Cartesian geometry, focusing on the azimuthal direction The interpolative methods we test are simple linear, linear in sine and cosine, an Abu-Shumays â baseâ quadrature with a simple linear adaptive and an Abu-Shumays â baseâ quadrature with a linear in sine and cosine adaptive. In the latter two methods the local refinement does not reduce the ability of the base set to integrate high-order spherical harmonics (important in problems with highly anisotropic scattering). We utilize a variety of one-group test problems to demonstrate that in all cases, angular discretization errors (including "ray effects") can be eliminated to whatever tolerance the user requests. We further demonstrate through detailed quantitative analysis that local refinement does indeed produce a more efficient placement of unknowns. We conclude that this work introduces a very promising approach to a long-standing problem in deterministic transport, and we believe it will lead to fruitful avenues of further investigation.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematical Sciences." Includes bibliographical references (p. 52-53).

This thesis proposes and tests a recursive, adpative, and computationally inexpensive method for partitioning real-number spaces. When tested for proof-of-concept on both one- and two- dimensional classification and control problems, the Fern algorithm was found to work well in one dimension, moderately well for two-dimensional classification, and not at all for two-dimensional control. Testing ferns as pure discretizers - which would involve a secondary discrete learner - has been left to future work. / text

Some problems of' statistical inference for discrete-valued time series are investigated in this study. New statistical theories and methods are developed which may aid us in gaining more insight into the understanding of discrete-valued time series data. The first part is concerned with the measurement of the serial dependence of binary time series. In early studies the classical autocorrelation function was used, which, however, may not be an effective and informative means of revealing the dependence feature of a binary time series. Recently, the autopersistence function has been proposed as an alternative to the autocorrelation function for binary time series. The theoretical autopersistence functions and their sample analogues, the autopersistence graphs, are studied within a binary autoregressive model. Some properties of the autopcrsistencc functions and the asymptotic properties of the autopersistence graphs are discussed, justifying that the antopersistence graphs can be used to assess the dependence feature. Besides binary time series, intcger-vall1ed time series arc perhaps the most commonly seen discrete-valued time series. A generalization of the Poisson autoregression model for non-negative integer-valued time series is proposed by imposing an additional threshold structure on the latent mean process of the Poisson autoregression. The geometric ergodicity of the threshold Poisson autoregression with perburbations in the latent mean process and the stochastic stability of the threshold Poisson autoregression are obtained. The maximum likelihood estimator for the parameters is discussed and the conditions for its consistency and asymptotic normally are given as well. Furthermore, there is an increasing need for models of integer-valued time series which can accommodate series with negative observations and dependence structure more complicated than that of an autoregression or a moving average. In this regard, an integer-valued autoregressive moving average process induced by the so-called signed thinning operator is proposed. The first-order model is studied in detail. The conditions for the existence of stationary solution and the existence of finite moments are discussed under general assumptions. Under some further assumptions about the signed thinning operators and the distribution of the innovation, a moment-based estimator for the parameters is proposed, whose consistency and asymptotic normality are also proved. The problem of conducting one-step-ahead forecast is also considered based on hidden Markov chain theory. Simulation studies arc conducted to demonstrate the validity of the theories and methods established above. Real data analysis such as the annual counts of major earthquakes data are also presented to show their potential usefulness in applications. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

Modeling and simulation of fluid flow in subsurface fractured systems has been steadily a popular topic in petroleum industry. The huge potential hydrocarbon reserve in naturally and hydraulically fractured reservoirs has been a major stimulant for developments in this field. Although several models have found limited applications in studying fractured reservoirs, still more comprehensive models are required to be applied for practical purposes. A recently developed Embedded Discrete Fracture Model (EDFM) incorporates the advantages of two of the well-known approaches, the dual continuum and the discrete fracture models, to investigate more complex fracture geometries. In EDFM, each fracture is embedded inside the matrix grid and is discretized by the cell boundaries. This approach introduces a robust methodology to represent the fracture planes explicitly in the computational domain. As part of this research, the EDFM was implemented in two of The University of Texas in-house reservoir simulators, UTCOMP and UTGEL. The modified reservoir simulators are capable of modeling and simulation of a broad range of reservoir engineering applications in naturally and hydraulically fractured reservoirs. To validate this work, comparisons were made against a fine-grid simulation and a semi-analytical solution. Also, the results were compared for more complicated fracture geometries with the results obtained from EDFM implementation in the GPAS reservoir simulator. In all the examples, good agreements were observed. To further illustrate the application and capabilities of UTCOMP- and UTGEL-EDFM, a few case studies were presented. First, a synthetic reservoir model with a network of fractures was considered to study the impact of well placement. It was shown that considering the configuration of background fracture networks can significantly improve the well placement design and also maximize the oil recovery. Then, the capillary imbibition effect was investigated for the same reservoir models to display its effect on incremental oil recovery. Furthermore, UTCOMP-EDFM was applied for hydraulic fracturing design where the performances of a simple and a complex fracture networks were evaluated in reservoirs with different rock matrix permeabilities. Accordingly, it was shown that a complex network is an ideal design for a very low permeability reservoir, while a simple network results in higher recovery when the reservoir permeability is moderate. Finally, UTGEL-EDFM was employed to optimize a conformance control process. Different injection timings and different gel concentrations were selected for water-flooding processes and their impact on oil recovery was evaluated henceforth. / text

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