Formulation of linear time invariant (LTI) models of a nonlinear system about a periodic equilibrium using the harmonic domain representation of LTI model states has been studied in the literature. This thesis presents an alternative method and a computationally efficient scheme for implementation of the developed method for extraction of linear time invariant (LTI) models from a helicopter nonlinear model in forward flight. The fidelity of the extracted LTI models is evaluated using response comparisons between the extracted LTI models and the nonlinear model in both time and frequency domains. Moreover, the fidelity of stability properties is studied through the eigenvalue and eigenvector comparisons between LTI and LTP models by making use of the Floquet Transition Matrix. For time domain evaluations, individual blade control (IBC) and On-Blade Control (OBC) inputs that have been tried in the literature for vibration and noise control studies are used. For frequency domain evaluations, frequency sweep inputs are used to obtain frequency responses of fixed system hub loads to a single blade IBC input. The evaluation results demonstrate the fidelity of the extracted LTI models, and thus, establish the validity of the LTI model extraction process for use in integrated flight and rotor control studies.

This paper is devoted to asymptotic estimates for the condition numbers $\kappa(T_n(a))=||T_n(a)|| ||T_n^(-1)(a)||$ of large $n\cross n$ Toeplitz matrices $T_N(a)$ in the case where $\alpha \element L^\infinity$ and $Re \alpha \ge 0$ . We describe several classes of symbols $\alpha$ for which $\kappa(T_n(a))$ increases like $(log n)^\alpha, n^\alpha$ , or even $e^(\alpha n)$ . The consequences of the results for singular values, eigenvalues, and the finite section method are discussed. We also consider Wiener-Hopf integral operators and multidimensional Toeplitz operators.

Thesis (Ph. D.)--Mississippi State University. Department of Electrical and Computer Engineering. / Title from title screen. Includes bibliographical references.

The heavily developed Long Key is located in Pinellas County in west-central Florida. The structured Blind Pass at the north end of the barrier island interrupts the southward longshore sediment transport, resulting in severe and chronic beach erosion along the northern portion of the island. Frequent beach nourishments were conducted to mitigate the erosion. In this study, the performance of the most recent beach nourishment in 2010 is quantified through time-series beach profile surveys. Over the 34-month period, the nourished northern portion of the island, Upham Beach, lost up to 330 m3/m of sand, with a landward shoreline retreat of up to 100 m. The middle portion of the island gained up to 25 m3/m of sand, benefiting from the sand lost from Upham Beach. The southern portion of Long Key lost a modest amount of sediment, largely due to Tropical Storm Debby, which approached from the south in June 2012. The severe erosion along Upham Beach is induced by a large negative longshore transport gradient. The beach here has no sand bar and retreated landward persistently over the 34-month study period. In contrast the profiles in the central section of the island generally have a sand bar which moved landward and seaward in response to seasonal and storm-induced wave-energy changes. The sand volume across the entire profile in the central portion of the island is mostly conserved. Two typical example beach profiles, LK3A and R157, were selected to examine the ability of the commonly used principal component analysis (PCA), also commonly known as empirical orthogonal function analysis (EOF), to identify beach profile ix changes induced by longshore and cross-shore sediment transport gradients. For the longshore-transport driven changes at the non-barred profile LK3A, the principal eigenvector accounted for over 91% of the total variance, with a dominant broad peak in the cross-shore distribution. At the barred R157, the profile changes were caused mainly by cross-shore transport gradients with modest contribution from longshore transport gradient; eigenvalue one only accounted for less than 51% of the total variance, and eigenvalues two and three still contributed considerably to the overall variance. In order to verify the uniqueness of the PCA results from LK3A and R157, five numerical experiments were conducted, simulating changes at a barred and non-barred beach driven by longshore, cross-shore, and combined sediment transport gradients. Results from LK3A and R157 compare well with simulated beach erosion (or accretion) due to variable longshore sediment transport gradients and due to both cross-shore and longshore sediment transport gradients, respectively. Different PCA results were obtained from different profile change patterns.

High-throughput methods systematically measure the internal state of the entire cell, but powerful computational tools are needed to infer dynamics from their raw data. Therefore, we have developed a new computational method, Eigen-genomic System Dynamic-pattern Analysis (ESDA), which uses systems theory to infer dynamic parameters from a time series of gene expression measurements. As many genes are measured at a modest number of time points, estimation of the system matrix is underdetermined and traditional approaches for estimating dynamic parameters are ineffective; thus, ESDA uses the principle of dimensionality reduction to overcome the data imbalance. We identify degradation dynamic patterns of a genomic system using ESDA. We also combine ESDA and Principal-oscillation-pattern (POP) analysis, which has been widely used in geosciences, to identify oscillation patterns. We demonstrate the first application of POP analysis to genome-wide time-series gene-expression data. Both simulation data and real-world data are used in this study to demonstrate the applicability of ESDA to genomic data. The biological interpretations of dynamic patterns are provided. We also show that ESDA not only compares favorably with previous experimental methods and existing computational methods, but that it also provides complementary information relative to other approaches. / text

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Le problème d’oscillation de fluides dans un conteneur est un problème classique d’hydrodynamique qui est etudié par des mathématiciens et ingénieurs depuis plus de 150 ans. Le présent travail est lié à l’étude de l’alternance des fonctions propres paires et impaires du problème de Steklov-Neumann pour les domaines à deux dimensions ayant une forme symétrique. On obtient des résultats sur la parité de deuxième et troisième fonctions propres d’un tel problème pour les trois premiers modes, dans le cas de domaines symétriques arbitraires. On étudie aussi la simplicité de deux premières valeurs propres non nulles d’un tel problème. Il existe nombre d’hypothèses voulant que pour le cas des domaines symétriques, toutes les valeurs propres sont simples. Il y a des résultats de Kozlov, Kuznetsov et Motygin [1] sur la simplicité de la première valeur propre non nulle obtenue pour les domaines satisfaisants la condition de John. Dans ce travail, il est montré que pour les domaines symétriques, la deuxième valeur propre non-nulle du problème de Steklov-Neumann est aussi simple. / The study of liquid sloshing in a container is a classical problem of hydrodynamics that has been actively investigated by mathematicians and engineers over the past 150 years. The present thesis is concerned with the properties of eigenfunctions of the two-dimensional sloshing problem on axially symmetric planar domains. Here the axis of symmetry is assumed to be orthogonal to the free surface of the fluid. In particular, we show that the second and the third eigenfunctions of such a problem are, respectively, odd and even with respect to the axial symmetry. There is a well-known conjecture that all eigenvalues of the two-dimensional sloshing problem are simple. Kozlov, Kuznetsov and Motygin [1] proved the simplicity of the first non-zero eigenvalue for domains satisfying the John's condition. In the thesis we show that for axially symmetric planar domains, the first two non-zero eigenvalues of the sloshing problem are simple.

A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive(respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrix A, the sign pattern class of A, denoted Q(A), is defined as {B: sgn(B) = A}. An n by n sign pattern matrix A requires all distinct eigenvalues if every real matrix whose sign pattern is represented by A has n distinct eigenvalues. In this thesis, a number of sufficient and/or necessary conditions for a sign pattern to reuiqre all distinct eigenvalues are reviewed. In addition, for n=2 and 3, the n by n sign patterns that require all distinct eigenvalues are surveyed. We determine most of the 4 by 4 irreducible sign patterns that require four distinct eigenvalues.