Turbulent flows occur in various fields and are a central, yet an extremely complex, topic in fluid dynamics. Understanding the behaviour of fluids is vital for multiple research areas including, but not limited to: biological models, weather prediction, and engineering design models for automobiles and aircraft. In this thesis, we study a number of fundamental problems that arise in 2D turbulent flows, using the 2D Navier-Stokes system. Introducing optimization techniques for systems described by partial differential equations (PDE), we frame these problems such that they can be solved using computational methods. We utilize adjoint calculus to build the computational framework to be implemented in an iterative gradient flow procedure, using the "optimize-then-discretize" approach. Pseudospectral methods are employed for solving PDEs in a numerically efficient manner. The use of optimization methods together with computational mathematics in this work provides an illuminating perspective on fluid mechanics. We first apply these techniques to better understand enstrophy dissipation in 2D Navier-Stokes flows, in the limit of vanishing viscosity. By defining an optimization problem to determine optimal initial conditions, multiple branches of local maximizers were obtained each corresponding to a different mechanism producing maximum enstrophy dissipation. Viewing this quantity as a function of viscosity revealed quantitative agreement with an analytic bound, demonstrating the sharpness of this bound. We also introduce an extension of this problem, where enstrophy dissipation is maximized in the context of kinetic theory using the Boltzmann equation. Secondly, these PDE-constrained optimization techniques were used to probe the fundamental limitations on the performance of the Leith eddy-viscosity closure model for 2D Large-Eddy Simulations of the Navier-Stokes system. Obtained by solving an optimization problem with a non-standard structure, the results demonstrate the optimal eddy viscosities do not converge to a well-defined limit as regularization and discretization parameters are refined, hence the problem of determining an optimal eddy viscosity is ill-posed. Further extending the problem of finding optimal eddy-viscosity closures, we consider imposing an additional nonlinear constraint on the control variable in the problem, in the form of requiring the time-averaged enstrophy be preserved. To address this problem in a novel way, we employ adjoint calculus to characterize a subspace tangent to the constraint manifold, which allows one to approximately enforce the constraint. Not only do we demonstrate that this produces better results when compared to the case without constraints, but this also provides a flexible computational framework for approximate enforcement of general nonlinear constraints. Lastly in this thesis, we introduce an optimization problem to study the Kolmogorov-Richardson energy cascade, where a pathway towards solutions is outlined. / Thesis / Doctor of Philosophy (PhD)

The focus of Location-Aware Adaptive Vehicle Dynamics System (LAAVDS) research is to develop a system to avoid situations in which the vehicle exceeds its handling capabilities. The proposed method is predictive, estimating the ability of the vehicle to successfully navigate upcoming terrain, and it is assumed that the future vehicle states and local driving environment is known. An Intervention Strategy must be developed such that the vehicle is navigated successfully along a road via modest changes to the driver's commands and do so in a manner that is in harmony with the driver's intentions and not in a distracting or irritating manner. Clearly this research relies on the numerous new technologies being developed to capture and convey information about the local driving environment (e.g., bank angle, elevation changes, curvature, and friction coefficient) to the vehicle and driver. / Ph. D.

This dissertation explores approaches to the satisfiability problem, focusing on local search methods. The research endeavours to better understand how and why some local search methods are effective. At the root of this understanding are a set of metrics that characterize the behaviour of local search methods. Based on this understanding, two new local search methods are proposed and tested, the first, SDF, demonstrating the value of the insights drawn from the metrics, and the second, ESG, achieving state-of-the-art performance and generalizing the approach to arbitrary 0-1 integer linear programming problems. This generality is demonstrated by applying ESG to combinatorial auction winner determination. Further augmentations to local search are proposed and examined, exploring hybrids that incorporate aspects of backtrack search methods.

The stomatal network in plants is a well-characterized biological system that hypothetically solves the constrained optimization problem of maximizing CO2 uptake from the air while constraining evaporative water loss during the process of photosynthesis. There are numerous such constrained optimization problems present in the real world as well as in computer science. This thesis work attempts to solve one such constrained optimization problem in a distributed manner by taking a cue from the dynamics of stomatal networks. The problem considered here is Dynamic Thermal Management (DTM) in a multi-processing element system in computing. There have been several approaches in the past that tried to solve the problem of DTM by varying the frequency of operation of blocks in the computing system. The selection of frequencies for DTM such that overall performance is maximized while temperature is constrained is a non-deterministic polynomial-time (NP) hard problem. In this thesis, a distributed approach to solve the problem of DTM using a cellular neural network is proposed. A cellular neural network is used to mimic the stomatal network with slight variations based on the problem considered.

Due to the increasing demand for high dimensional data analysis from various applications such as electrocardiogram signal analysis and gene expression analysis for cancer detection, dimensionality reduction becomes a viable process to extracts essential information from data such that the high-dimensional data can be represented in a more condensed form with much lower dimensionality to both improve classification accuracy and reduce computational complexity. Conventional dimensionality reduction methods can be categorized into stand-alone and hybrid approaches. The stand-alone method utilizes a single criterion from either supervised or unsupervised perspective. On the other hand, the hybrid method integrates both criteria. Compared with a variety of stand-alone dimensionality reduction methods, the hybrid approach is promising as it takes advantage of both the supervised criterion for better classification accuracy and the unsupervised criterion for better data representation, simultaneously. However, several issues always exist that challenge the efficiency of the hybrid approach, including (1) the difficulty in finding a subspace that seamlessly integrates both criteria in a single hybrid framework, (2) the robustness of the performance regarding noisy data, and (3) nonlinear data representation capability. This dissertation presents a new hybrid dimensionality reduction method to seek projection through optimization of both structural risk (supervised criterion) from Support Vector Machine (SVM) and data independence (unsupervised criterion) from Independent Component Analysis (ICA). The projection from SVM directly contributes to classification performance improvement in a supervised perspective whereas maximum independence among features by ICA construct projection indirectly achieving classification accuracy improvement due to better intrinsic data representation in an unsupervised perspective. For linear dimensionality reduction model, I introduce orthogonality to interrelate both projections from SVM and ICA while redundancy removal process eliminates a part of the projection vectors from SVM, leading to more effective dimensionality reduction. The orthogonality-based linear hybrid dimensionality reduction method is extended to uncorrelatedness-based algorithm with nonlinear data representation capability. In the proposed approach, SVM and ICA are integrated into a single framework by the uncorrelated subspace based on kernel implementation. Experimental results show that the proposed approaches give higher classification performance with better robustness in relatively lower dimensions than conventional methods for high-dimensional datasets.

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Using derivative based numerical optimization routines to solve optimization problems governed by partial differential equations (PDEs) with uncertain coefficients is computationally expensive due to the large number of PDE solves required at each iteration. In this thesis, I present an adaptive stochastic collocation framework for the discretization and numerical solution of these PDE constrained optimization problems. This adaptive approach is based on dimension adaptive sparse grid interpolation and employs trust regions to manage the adapted stochastic collocation models. Furthermore, I prove the convergence of sparse grid collocation methods applied to these optimization problems as well as the global convergence of the retrospective trust region algorithm under weakened assumptions on gradient inexactness. In fact, if one can bound the error between actual and modeled gradients using reliable and efficient a posteriori error estimators, then the global convergence of the proposed algorithm follows. Moreover, I describe a high performance implementation of my adaptive collocation and trust region framework using the C++ programming language with the Message Passing interface (MPI). Many PDE solves are required to accurately quantify the uncertainty in such optimization problems, therefore it is essential to appropriately choose inexpensive approximate models and large-scale nonlinear programming techniques throughout the optimization routine. Numerical results for the adaptive solution of these optimization problems are presented.

This dissertation explores approaches to the satisfiability problem, focusing on local search methods. The research endeavours to better understand how and why some local search methods are effective. At the root of this understanding are a set of metrics that characterize the behaviour of local search methods. Based on this understanding, two new local search methods are proposed and tested, the first, SDF, demonstrating the value of the insights drawn from the metrics, and the second, ESG, achieving state-of-the-art performance and generalizing the approach to arbitrary 0-1 integer linear programming problems. This generality is demonstrated by applying ESG to combinatorial auction winner determination. Further augmentations to local search are proposed and examined, exploring hybrids that incorporate aspects of backtrack search methods.

In recent years, demands on all kinds of wireless communications become heavier due to the developments of new services and devices. At the same time, future wireless networks are expected to provide services with high quality and data rate. A possible solution which can attain these objectives is wireless communication systems that use multiple-input multiple-output (MIMO) antennas along with Alamouti¡¦s space-time block code and direct-sequence code division multiple access (DS-CDMA) modulation technique. In such systems, spatial diversity rendered by multiple antennas as well as coding in spatial and time domains are the keys to improve quality of transmission. Many multiuser detection techniques for the space-time block coded CDMA systems have been investigated. In [8], the blind Capon receiver was proposed, which consists of a two-branch filterbank followed by the blind Capon channel estimator. The design of blind Capon receiver is based on linearly constrained minimum variance (LCMV) criterion, which is known to be sensitive to inaccuracies in the acquisition or tracking of the desired user's timing, referred to as mismatch effect. In other words, the LCMV-based receiver may perform undesirably under mismatch effect. In this thesis, we propose a new blind adaptive MIMO-CDMA receiver based on the linearly constrained constant modulus (LCCM) criterion. This work is motivated by the robustness of LCCM approach to the mismatch effect. To reduce the complexity of receiver design, framework of the generalized sidelobe canceller (GSC) associated with the recursive least squares (RLS) algorithm is adopted for implementing the adaptive LCCM MIMO-CDMA filterbank. Based on the GSC-RLS structure, we derive the proposed MIMO CM-GSC-RLS algorithm. For the purpose of comparison, an adaptive implementation of the blind Capon receiver proposed in [8] is also derived, which is referred to as the MIMO MV-GSC-RLS algorithm. We note that the signal model in [8] was constructed under assumption of frequency-flat channels. To obtain a more practical and realistic signal model, in this thesis we extend the system and channel model by including multipath effects in the beginning of our work. In completing this extension, inter-symbol interference (ISI) caused by the special coding scheme of ST-BC will be specifically analyzed. Finally, a full discussion of the multipath signal model will be provided, including necessity of truncating the received signals as well as modifications in the signal model when considering time-varying channels. Via computer simulations, advantages of the proposed scheme will be verified. Compared to the conventional blind Capon receiver, we will show that the performance of the proposed CM-GSC-RLS algorithm is better. This is especially true when mismatch problem is considered in the MIMO-CDMA systems of interest. The proposed scheme show more robustness against the mismatch effects than the conventional blind Capon receiver. Moreover, the benefit resulted by truncating the received signals is also demonstrated, especially for binary phase-shift-keying (BPSK) modulated source symbol. Finally, simulations considering time-varying channels are provided to reveal that our proposed scheme can adapt itself to the time-varying environments appropriately.

In this thesis, we present a new hybrid pre-coded direct-sequence code division multiple access (DS-CDMA) system framework that use the multiple-input multiple-output (MIMO) antennas along with Alamouti¡¦s space-time block code (ST-BC). In the transmitter, the idea of hybrid pre-coded is exploited. It not only used to counteract the inter-symbol interference (ISI) introduced by the channel fading duo to multipath propagation but also very useful for exacting the phase of channel by appropriate design, which is not adopted in the conventional blind receiver. Under this structure, we propose a new blind adaptive MIMO-CDMA receiver based on the linearly constrained constant modulus (LCCM) criterion. To reduce the complexity of receiver design, framework of the generalized sidelobe canceller (GSC) associated with the recursive least square (RLS) algorithm is adopted for implementing the LCCM MIMO-CDMA receiver, and use gradient method to track the desired user¡¦s amplitude, simultaneously. Via computer simulations, advantages of the proposed scheme will be verified. Compared to the conventional blind Capon receiver, we will show that the performance of the proposed scheme is more robust against inaccuracies in the acquisition of the desired user¡¦s timing.