This thesis is concerned with the solution of linear operator equations by projection methods known as minimal residual (MR) and orthogonal residual (OR) methods. We begin with a rather abstract framework of approximation by orthogonal and oblique projection in Hilbert space. When these approximation schemes are applied to sequences of nested spaces, with a simple requirement relating trial and test spaces in case of the OR method, one can derive at this rather general level the basic relations which have been proved for many specific Krylov subspace methods for solving linear systems of equations in the literature. The crucial quantities with which we describe the behavior of these methods are angles between subspaces. By replacing the given inner product with one that is basis-dependent, one can also incorporate methods based on non-orthogonal bases such as those based on the non-Hermitian Lanczos process for solving linear systems. In fact, one can show that any reasonable approximation method based on a nested sequence of approximation spaces can be interpreted as an MR or OR method in this way. When these abstract approximation techniques are applied to the solution of linear operator equations, there are three generic algorithmic formulations, which we identify with some algorithms in the literature. Specializing further to Krylov trial and test spaces, we recover the well known Krylov subspace methods. Moreover, we show that our general framework also covers in a natural way many recent generalizations of Krylov subspace methods, which employ techniques such as augmentation, deflation, restarts and truncation. We conclude with a chapter on error and residual bounds, deriving some old and new results based on the angles framework. This work provides a natural and consistent framework for the sometimes confusing plethora of methods of Krylov subspace type introduced in the last 50 years.

Surface acoustic wave (SAW) devices find uses in a plethora of applications including but not limited to chemical, biological sensing, and microfluidic actuation. The primary aim of this dissertation is to develop a SAW biosensor, capable of simultaneous detection of target biomarkers in fluid media at concentrations of picogram/ml to nanogram/ml levels and removal of non-specific proteins from sensor surface using the process of acoustic streaming, for potential chemical sensing, medical, and clinical diagnostic applications. The focus is on the development of three dimensional finite element structural and fluid-structure interaction models to study wave propagation and acoustic actuation of fluids in a SAW biosensor. This work represents a significant improvement in understanding fluid flow over SAW devices, over the currently available continuum model of Nyborg. The developed methodology includes use of a novel substrate, namely, Langasite coupled with various combinations of novel multidirectional interdigital transducer (IDT) configurations such as orthogonal, focused IDTs as well as sensor surface modifications, such as micro-cavities. The current approach exploits the capability of the anisotropic piezoelectric crystal to launch waves of different characteristics in different directions, which can be put to the multiple uses including but not limited to sensing via shear horizontal waves and biofouling elimination via Rayleigh wave induced acoustic streaming. Orthogonal IDTs gives rise to constructive interference, thereby enhancing the magnitudes of device displacements and fluid velocities. The net effect is an increase in device sensitivity and acoustic streaming intensity. The use of micro-cavities in the delay path provides a synergistic effect, thereby further enhancing the device sensitivity and streaming intensity. Focused IDTs are found to enhance the device displacements and fluid velocities, while focusing the device displacements and fluid motion at the device focal point, thereby enhancing the SAW device biosensing performance. The work presented in this dissertation has widespread and immediate use for enhancing sensor sensitivity and analyte discrimination capabilities as well as biofouling removal in medical diagnostic applications of SAW sensors. This work also has a broad relevance to the sensing of multiple biomarkers in medical applications as well as other technologies utilizing these devices such as microfluidic actuation.

Inhibiting protein-protein interactions to achieve a therapeutically desired effect has been a goal in the field of drug discovery for decades. Recently, advances in peptidomimetics have led researches to the use of cyclized peptides to achieve this goal. Cyclization of linear peptides restricts the number of conformations of the peptide, increasing the peptide's affinity to binding to the desired target. Cyclization also stabilizes the peptide, allowing the peptide to be resistant to proteases. This study explores the optimization of solution phase synthesis of an important integrin-mediated cell adhesion cyclic peptide for the therapeutic inhibition of multiple myeloma, cHYD1. cHYD1 was originally synthesized via solid phase peptide synthesis, and the need for a scaled up synthesis version was needed after positive bioactivity results were obtained. Chapter 3 includes the molecular modeling exploration of a possible new mechanism to which cyclized peptides could work, in which, rather than a recognition and non-recognition strand being implemented, a specific directional face is used for protein-protein interaction. This was done with the implementation of an antagonistic cyclic peptide to replace human growth hormone in its interaction with the human growth hormone receptor, and the subsequent di-cyclic peptide agonist.

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.

Proteins are diverse polymers of covalently linked amino acids. They play a role in almost every biological process that occurs within an organism. Twenty different amino acids are genetically encoded by mammalian cells to build proteins. The sequence of these amino acids determines the protein’s final shape, structure, and function. Modern molecular cloning techniques allow for the genetic encoding and expression of mutant proteins that have one or more amino acids replaced with one of the others. The roles of individual amino acids in a protein can therefore be studied. Proteins with novel functions have also been designed or evolved using this technology. However, the genetic code is limited to the twenty natural amino acids. Nonnatural amino acids have unique side groups that not found on any of the twenty natural amino acids. They can be site-specifically incorporated using a mutant orthogonal suppressor tRNA/aminoacyl-tRNA synthetase (aaRS) pair. Each pair only allows for one type of nonnatural amino acid to be genetically encoded. This technology has resulted in the incorporation of over fifty different types of nonnatural amino acids into proteins in prokaryotic and eukaryotic cells. Unfortunately, most of these pairs are not orthogonal outside of prokaryotic systems and only a few have been developed for mammalian cells. To create more mammalian pairs a nonnatural aaRS has to be evolved and screened in a cumbersome process. In this dissertation an approach is outlined that can be used to change the orthogonality of existing nonnatural suppressor tRNA/aaRS pairs. As a result of the orthogonality change many previously unavailable pairs can be shuttled into mammalian cells. The ability to genetically encode a 21st amino acid is a powerful tool in the study and engineering of proteins. / text

Recently, there has been an increasing demand for OFDM system operating in high mobility environment. In such situation, wireless channel is both frequency-selective and time-varying, a.k.a. doubly-selective, making it hard for the receiver to keep track of the channel state information (CSI). Moreover, the statistical information of channel, e.g., tap positions, channel length, Doppler shifts and noise power, is generally unknown to the receiver. In this thesis, two kinds of mobile OFDM systems are investigated for data detection and channel estimation. Different from previous works, which highly depend on the statistical information of the doubly selective channel to deliver accurate channel estimation and data detection results, we focus on more practical scenarios with unknown channel orders and Doppler frequencies. Firstly, point-to-point OFDM system with high mobility is considered. Due to the unknown channel characteristics, we formulate the channel using GCE-BEM with a large oversampling factor. The resulted GCE-BEM coefficients are sparse on delay-Doppler domain and contain only a few nonzero elements. To enable the identification of nonzero entries, sparsity enhancing Gaussian priors with Gamma hyperpriors are adopted. An iterative algorithm is developed under variational inference (VI) framework. The proposed algorithm iteratively estimate the channel, recover the unknown data using Viterbi algorithm and learn the channel and noise statistical information, using only limited number of pilot subcarrier in one OFDM symbol. Secondly, we investigate multihop amplify-and-forward (AF) OFDM system, where system structure is generally unknown to the receiver due to the variable number of hops and relaying paths in high mobility environment. We notice that in AF relaying systems, the composite source-relay-destination channel is sufficient for data detection. Then we integrate the multilink, multihop channel matrices into one composite channel matrix, which turns out to have the same structure as the point-to-point OFDM channel. The reformulated system model is more concise and a similar iterative algorithm to that of the point-to-point case can be derived to estimate the composite channel and detect data. This means that the proposed framework applies to OFDM system under high mobility regardless of the system structure. Simulation results show that the performance of the proposed algorithm is very close to that of the optimal channel estimation and data detection algorithm, which requires specific information of system structure, channel tap positions, channel lengths, Doppler shifts as well as noise powers. It is worth noting that, the close-to-ideal performance of the proposed algorithms is achieved with none of the above information. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

The stability and turbulence characteristics of a vortex filament emanating from a single-bladed rotor in hover are investigated using proper orthogonal decomposition. The rotor is operated at a tip chord Reynolds number and a tip Mach number of 218,000 and 0.22, respectively, and with a blade loading of CT /σ = 0.066. In-plane components of the velocity field (normal to the axis of the vortex filament) are captured by way of 2D particle image velocimetry with corrections for vortex wander being performed using the Γ1 method. Using the classical form of POD, the first POD mode alone is found to encompass nearly 75% of the energy for all vortex ages studied and is determined using a grid of sufficient resolution as to avoid numerical integration errors in the decomposition. The findings reveal an equal balance between the axisymmetric and helical modes during vortex roll-up which immediately transitions to helical mode dominance at all other vortex ages. This helical mode is one of the modes of the elliptic instability. While the snapshot POD is shown to reveal similar features of the first few energetic modes, the classical POD is employed here owing to the easier interpretation of the Fourier-azimuthal modes. The spatial eigenfunctions of the first few Fourier-azimuthal modes associated with the most energetic POD mode are shown to be sensitive to the choice of the wander correction technique used. Higher Fourier-azimuthal modes are observed in the outer portions of the vortex and appeared not to be affected by the choice of the wander correction technique used. / text

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