To obtain better well performance and improved production from shale gas reservoirs, it is important to understand the behavior of shale gas wells and to identify different flow regions in them over a period of time. It is also important to understand best fracture and stimulation practice to increase productivity of wells. These objectives require that accurate production analysis be performed. For accurate production analysis, it is important to analyze the production behavior of wells, and field production data should be interpreted in such a way that it will identify well parameters. This can be done by performing a detailed analysis on a number of wells over whole reservoirs. This study is an approach that will lead to identifying different flow regions in shale gas wells that include linear and bilinear flow. Important field parameters can be calculated from those observations to help improve future performance. The detailed plots of several wells in this study show some good numbers for linear and bilinear flow, and some unique observations were made. The purpose of this work is to also manage the large amount of data in such a way that they can be used with ease for future studies. A program was developed to automate the analysis and generation of different plots. The program can also be used to perform the simple calculations to calculate different parameters. The goal was to develop a friendly user interface that would facilitate reservoir analysis. Examples were shown for each flow period, i.e. linear and bilinear flow. Different plots were generated (e.g; Bob Plot (square root of time plot) and Fourth Root of Time Plot, that will help in measuring slopes and thus reservoir parameters such as fracture permeability and drainage area. Different unique cases were also observed that show a different behavior of well in one type of plot from another.

Prompted by the desire to increase the industrial applicability range of self-tuning control, the objective of this work has been to extend the standard linear self-tuning framework to facilitate the design of self-tuning controllers for bilinear systems. Bilinear systems form a well structured class of non-linear systems within which linear systems coexist as a special subclass. They are, therefore, appropriate for modelling a wider range of processes and plant than the restrictive, yet convenient, linear model structures since such models are valid both within the linear subregion and beyond. In addition to extending the self-tuning framework for bilinear systems another significant contribution of the Thesis is the introduction of a cautious least squares estimation procedure which also enhances the existing linear self-tuning schemes.

The trace form gives a connection between the representation ring and the space of invariant bilinear forms of a Lie algebra $L$. This thesis reviews the definition of the trace of an endomorphism of a finitely generated projective module over a commutative ring $R$. We then use this to look at the trace form of a finitely generated projective representation of a Lie algebra $L$ over $R$ and its representation ring. While doing so, we prove a few trace formulas which are useful in the theory of the Dynkin index, an invariant introduced by Dynkin in 1952 to study homomorphisms between simple Lie algebras.

No description available.

Dynamical systems are widely used to model physical phenomena and, in many cases, these physical phenomena are parameter dependent. In this thesis we investigate three prominent problems related to the simulation of parametric dynamical systems and develop the analysis and computational framework to solve each of them. In many cases we have access to data resulting from simulations of a parametric dynamical system for which an explicit description may not be available. We introduce the parametric AAA (p-AAA) algorithm that builds a rational approximation of the underlying parametric dynamical system from its input/output measurements, in the form of transfer function evaluations. Our algorithm generalizes the AAA algorithm, a popular method for the rational approximation of nonparametric systems, to the parametric case. We develop p-AAA for both scalar and matrix-valued data and study the impact of parameter scaling. Even though we present p-AAA with parametric dynamical systems in mind, the ideas can be applied to parametric stationary problems as well, and we include such examples. The solution of a dynamical system can often be expressed in terms of an eigenvalue problem (EVP). In many cases, the resulting EVP is nonlinear and depends on a parameter. A common approach to solving (nonparametric) nonlinear EVPs is to approximate them with a rational EVP and then to linearize this approximation. An existing algorithm can then be applied to find the eigenvalues of this linearization. The AAA algorithm has been successfully applied to this scheme for the nonparametric case. We generalize this approach by using our p-AAA algorithm to find a rational approximation of parametric nonlinear EVPs. We define a corresponding linearization that fits the format of the compact rational Krylov (CORK) algorithm for the approximation of eigenvalues. The simulation of dynamical systems may be costly, since the need for accuracy may yield a system of very large dimension. This cost is magnified in the case of parametric dynamical systems, since one may be interested in simulations for many parameter values. Interpolatory model order reduction (MOR) tackles this problem by creating a surrogate model that interpolates the original, is of much smaller dimension, and captures the dynamics of the quantities of interest well. We generalize interpolatory projection MOR methods from parametric linear to parametric bilinear systems. We provide necessary subspace conditions to guarantee interpolation of the subsystems and their first and second derivatives, including the parameter gradients and Hessians. Throughout the dissertation, the analysis is illustrated via various benchmark numerical examples. / Doctor of Philosophy / Simulation of mathematical models plays an important role in the development of science. There is a wide range of models and approaches that depend on the information available and the goal of the problem. In this dissertation we focus on three problems whose solution depends on parameters and for which we have either data resulting from simulations of the model or a explicit structure that describes the model. First, for the case when only data are available, we develop an algorithm that builds a data-driven approximation that is then easy to reevaluate. Second, we embed our algorithm in an already developed framework for the solution of a specific kind of model structure: nonlinear eigenvalue problems. Third, given a model with a specific nonlinear structure, we develop a method to build a model with the same structure, smaller dimension (for faster computation), and that provides an accurate approximation of the original model.

It was recently discovered by Joux [30] and Sakai, Ohgishi and Kasahara [47] that bilinear maps could be used to construct cryptographic schemes. Since then, bilinear maps have been used in applications as varied as identity-based encryption, short signatures and one-round tripartite key agreement. This thesis explains the notion of bilinear maps and surveys the applications of bilinear maps in the three main fields of cryptography: encryption, signature and key agreement. We also show how these maps can be constructed using the Weil and Tate pairings in elliptic curves.

It was recently discovered by Joux [30] and Sakai, Ohgishi and Kasahara [47] that bilinear maps could be used to construct cryptographic schemes. Since then, bilinear maps have been used in applications as varied as identity-based encryption, short signatures and one-round tripartite key agreement. This thesis explains the notion of bilinear maps and surveys the applications of bilinear maps in the three main fields of cryptography: encryption, signature and key agreement. We also show how these maps can be constructed using the Weil and Tate pairings in elliptic curves.

Abstract Attribute-Based Encryption (ABE) is a relatively new encryption technology which is similar to multi-receiver encryption but the privacy of ciphertext receivers is protected by a set of attributes such that no one, even the encryptor, knows the identities of the receivers. Although the identities of those receivers remain unknown, the encryptor can ensure that all of the receivers cannot decrypt the ciphertext except for those who match the restrictions on predefined attribute values associated with the ciphertext. However, maintaining the correctness of users¡¦ attributes will take huge cost because the interactions between all users and the key generation center (KGC) are required to renew all of their private keys whenever a user joins, leaves the group, or updates the value of any of his attributes. Since user joining, leaving, and attribute updating may occur frequently in real situations, membership management will become a quite important issue in an ABE system but no existing scheme can perfectly cope with this problem. In this manuscript, we will present an ABE scheme which aims at the issue on dynamic membership management. Our work keeps high flexibility of the constrains on attributes and makes it possible for the procedures of user joining, leaving, and attribute updating to be dynamic, that is, it is not necessary for those users who do not update their attribute statuses to renew their private keys when some user changes his status. Finally, we also formally prove the security of the proposed scheme.

The Pixel Router was developed at the University of Kentucky with the intent of supporting multi-projector displays by combining the scalability of commercial software solutions with the flexibility of commercial hardware solutions. This custom hardware solution uses a Look Up Table for an arbitrary input to output pixel mapping, but suffers from high memory latencies due to random SDRAM accesses. In order for this device to achieve marketability, the image interpolation method needed improvement as well. The previous design used the nearest neighbor interpolation method, which produces poor looking results but requires the least amount of memory accesses. A cache was implemented to support bilinear interpolation to simultaneously increase the output frame rate and image quality. A number of software simulations were conducted to test and refine the cache design, and these results were verified by testing the implementation on hardware. The frame rate was improved by a factor of 6 versus bilinear interpolation on the previous design, and by as much as 50% versus nearest neighbor on the previous design. The Pixel Router was also certified for FCC conducted and radiated emissions compliance, and potential commercial market areas were explored.

Thesis (M.S.)--University of North Carolina at Wilmington, 2004. / Includes bibliographical references (leaf : 32).