Dimensional Analysis is a technique that has allowed engineering evaluation of complex objects by scaling analysis results of representative simpler models. The original premise of the procedure stems from the idea of developing non-dimensional parameters to relate physical events and underlying analytical basis. Extending the process to incorporate non-linear and time variant behavior has led to development of a novel process of similitude called the Empirical Similitude Method (ESM) where experimental data of test specimen is combined to produce the required prediction values. Using the original motivation and hypothesis of ESM, this research has expanded the experimental similitude process by using adapted matrix representations and continuous functional mapping of test results. This new approach has provided more rigorous mathematical definitions for similarity and prediction estimations based on an innovative error minimization algorithm. Shape factors are also introduced and integrated into ESM to obtain comprehensive evaluation of specimen choices. A detailed overview is provided summarizing methods, principles and laws of traditional similitude (TSM) and systems that satisfy extension into ESM. Applicability of ESM in different systems is described based on the limitations of TSM in the evaluation of complex structures. Several examples and ideas spanning aerodynamic, thermal, mechanical and electro-magnetic domains are illustrated to complement inherent technical analysis. For example, the new ESM procedure is shown to be considerably more accurate than earlier methods in predicting the values of drag coefficient of an airfoil. A final foray into the regime of \design evaluation by similarity" is made to elucidate applicability and efficiency of developed techniques in practical systems and products. A thorough methodology is also presented highlighting pertinent procedures and processes in usage of this method. / text

Traumatic skeletal muscle injuries that include loss of large amounts of muscle mass are becoming more common in today’s warfare. Traditional treatments often do not prevent long term functional impairments. Using a decellularized extracellular matrix (ECM) as scaffolding to replace lost muscle tissue allows for transmission of force through the injury site, and provides a suitable microenvironment receptive to myofiber growth. Seeding the ECM with progenitor cells improves cellular content in the defect area. Exercise exposes the muscle to improved blood flow as well as higher than normal loading. This results in increased blood vessel density as well as higher levels of cellular content, and near complete restoration of function. / text

Matrix metalloproteinase-2 (MMP-2, gelatinase A, type IV collagenase) is a member of a family of zinc-dependent metalloendopeptidases that functions in the degradation of elastin, collagens, and other components of extracellular matrix (ECM). Both secretion and activation of MMP-2 are elevated in human atherosclerotic lesions and abdominal aortic aneurysms (AAA). In this dissertation project, we sought to test the hypothesis that MMP-2 plays a critical role in both atherosclerosis and AAA. We also sought to determine the detailed mechanism. We first examined the atherosclerosis and AngII-induced AAAs development in MMP-2-/- x apolipoprotein (apoE)-/- mice in vivo. It was surprising that MMP-2 deficiency did not reduce the incidence of AngII-induced AAAs or the size of atherosclerosis in apoE-/- mice. However, the cellular and ECM content of atherosclerotic plaques were modified in MMP-2-/- x apoE-/- mice as compared to MMP-2+/+ x apoE-/- control mice. To explain the apparent paradox between this result and the hypothesis, we investigated the morphological characteristics of the aortic wall of MMP-2-/- mice. We detected an enhanced MMP-9 level in the aortic wall of MMP-2-/- x apoE-/- mice compared with MMP-2+/+ x apoE-/- mice. Interestingly, we also observed more branching of the elastin fibers in aortic wall of MMP-2-/- mice as compared with aorta of wild type mice. We also examined the behavior of macrophages from MMP-2-/- mice. Reduced adhesion, migration, and expression of integrin beta 3 were detected in MMP-2 deficient macrophages compared with wild type macrophages. Lastly, we examined whether MMP-2 deficiency in bone marrow-derived cells may influence AAAs and atherosclerosis using bone marrow transplantation technique. There was a significant reduction of both atherosclerosis development and AAAs formation in mice that were reconstituted MMP-2-/- bone marrow cells. In conclusion, the findings in this dissertation suggest that MMP-2 might play an important role in atherosclerosis and aneurysm through influencing inflammatory cell infiltration.

There are many scientific applications in which there is a need to solve very large linear systems. The preconditioned Krylove subspace methods are considered the preferred methods in this field. The preconditioners employed in the preconditioned iterative solvers usually determine the overall convergence rate. However, choosing a good preconditioner for a specific sparse linear system arising from a particular application is the combination of art and science, and presents a formidable challenge for many design engineers and application scientists who do not have much knowledge of preconditioned iterative methods. We tackled the problem of choosing suitable preconditioners for particular applications from a nontraditional point of view. We used the techniques and ideas in knowledge discovery and data mining to extract useful information and special features from unstructured sparse matrices and analyze the relationship between these features and the solving status of the spearse linear systems generated from these sparse matrices. We have designed an Intelligent Preconditioner Recommendation System, which can provide advice on choosing a high performance preconditioner as well as suitable parameters for a given sparse linear system. This work opened a new research direction for a very important topic in large scale high performance scientific computing. The performance of the various data mining algorithms applied in the recommendation system is directly related to the set of matrix features used in the system. We have extracted more than 60 features to represent a sparse matrix. We have proposed to use data mining techniques to predict some expensive matrix features like the condition number. We have also proposed to use the combination of the clustering and classification methods to predict the solving status of a sparse linear system. For the preconditioners with multiple parameters, we may predict the possible combinations of the values of the parameters with which a given sparse linear system may be successfully solved. Furthermore, we have proposed an algorithm to find out which preconditioners work best for a certain sparse linear system with what parameters.

In this dissertation, we study iterative methods for computing eigenvalues and exponentials of large matrices. These types of computational problems arise in a large number of applications, including mathematical models in economics, physical and biological processes. Although numerical methods for computing eigenvalues and matrix exponentials have been well studied in the literature, there is a lack of analysis in inexact iterative methods for eigenvalue computation and certain variants of the Krylov subspace methods for approximating the matrix exponentials. In this work, we proposed an inexact inverse subspace iteration method that generalizes the inexact inverse iteration for computing multiple and clustered eigenvalues of a generalized eigenvalue problem. Compared with other methods, the inexact inverse subspace iteration method is generally more robust. Convergence analysis showed that the linear convergence rate of the exact case is preserved. The second part of the work is to present an inverse Lanczos method to approximate the product of a matrix exponential and a vector. This is proposed to allow use of larger time step in a time-propagation scheme for solving linear initial value problems. Error analysis is given for the inverse Lanczos method, the standard Lanczos method as well as the shift-and-invert Lanczos method. The analysis demonstrates different behaviors of these variants and helps in choosing which variant to use in practice.

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

Data-mining has become a hot topic in recent years. It consists of extracting relevant information or structures from data such as: pictures, textual material, networks, etc. Such information or structures are usually not trivial to obtain and many techniques have been proposed to address this problem, including Independent Component Analysis, Latent Sematic Analysis, etc. Nonnegative Matrix Factorization is yet another technique that relies on the nonnegativity of the data and the nonnegativity assumption of the underlying model. The main advantage of this technique is that nonnegative objects are modeled by a combination of some basic nonnegative parts, which provides a physical interpretation of the construction of the objects. This is an exclusive feature that is known to be useful in many areas such as Computer Vision, Information Retrieval, etc. In this thesis, we look at several aspects of Nonnegative Matrix Factorization, focusing on numerical algorithms and their applications to different kinds of data and constraints. This includes Tensor Nonnegative Factorization, Weighted Nonnegative Matrix Factorization, Symmetric Nonnegative Matrix Factorization, Stochastic Matrix Approximation, etc. The recently proposed Rank-one Residue Iteration (RRI) is the common thread in all of these factorizations. It is shown to be a fast method with good convergence properties which adapts well to many situations.

Lattice simulations are a popular tool for studying the non-perturbative physics of nonlinear field theories. To perform accurate lattice simulations, a careful account of the discretization error is necessary. Spatial discretization error as a result of lattice spacing dependence in Langevin simulations of anisotropic (2 + 1)-dimensional classical scalar field theories is studied. A transfer integral operator (TIO) method and a one-loop renormalization (1LR) procedure are used to formulate effective potentials. The effective potentials contain counterterms which are intended to suppress the lattice spacing dependence. The two effective potentials were tested numerically in the case of a phi-4 model. A high accuracy modified Euler method was used to evolve a phenomenological Langevin equation. Large scale Langevin simulations were performed in parameter ranges determined to be appropriate. Attempts at extracting correlation lengths as a means of determining effectiveness of each method were not successful. Lattice sizes used in this study were not of a sufficient size to obtain an accurate representation of thermal equilibrium. As an alternative, the initial behaviour of the ensemble field average was observed. Results for the TIO method showed that it was successful at suppressing lattice spacing dependence in a mean field limit. Results for the 1LR method showed that it performed poorly.

Cardiovascular disease, often induced by hypertension, represents a serious health threat, is a primary cause of death worldwide, and results in altered cardiovascular function and ECM composition. Hypertension and related cardiovascular diseases are associated with immune dysfunction. This dissertation investigated the role of T-lymphocytes in modulating cardiovascular function and ECM composition as a possible therapeutic for the treatment of cardiovascular disease. Study one investigated the role of TCR peptide in the development of hypertension and subsequent cardiovascular changes in Balb/C mice. The coadminstration of TCR and L-NAME/8% NaCl reduced the effects of L-NAME/8% NaCl, decreasing blood pressure and crosslinked collagen compared to L-NAME/8% NaCl alone. Study two examined the effects of T-lymphocyte function on cardiovascular structure and function. Adoptive transfer of T-lymphocytes from C57BL/6 WT mice into C57BL/6 SCID mice induced changes in the SCID so that it resembled the WT donor, with increased percent crosslinked collagen and LOX activity. Hemodynamics in the SCID recipient resembled that of the WT and were significantly different from the sham injected SCID. Study three combined aspects of both previous studies. T-lymphocytes were adoptively transferred from hypertensive WT donors into naïve SCID recipients, who developed hypertension and cardiovascular function resembling the hypertensive donor, as well as changes in the ECM, including increased collagen crosslinking. Study four investigated the effect of strain specific T-lymphocyte polarization on hypertension induced cardiac ECM remodeling. Balb/C, C57BL/6 WT, and C57BL/6 SCID had divergent responses to L-NAME induced hypertension. Ventricular stiffness increased in Balb/C, decreased in C57 SCID and did not change in C57 WT; LOX activity changed correspondingly in all groups. The final study examined the effect of TCR administration on LOX activity and collagen crosslinking. Th1 polarization increased LOX activity and crosslinked collagen with corresponding changes in cardiovascular function. In conclusion, modulation of T-lymphocyte function alters cardiovascular function and ECM composition in pathologic and non-pathologic conditions. Immune modulation should be further investigated as a therapeutic for cardiovascular disease.

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