The speed and simplicity of the metal-semiconductor-metal (MSM) detector has made it a prime candidate for use in integrated optoelectronic circuits. While in most applications the optical input is coupled in through the top surface of the device, it is also possible to distribute the optical signal by means of transparent waveguides that are located below the absorbing detector layer. By controlling the degree of coupling between the waveguide and detector layers the detectors can be made to act as optical taps. The optical signal can thus be shared among a series of detectors as required in optoelectronic switching applications. We have made a series of simple ridge waveguides, each with a number of MSM structures designed for the characterization of absorption, responsivity and frequency response. A 4x4 optoelectronic switch was also fabricated and analyzed. We show that balancing the switch is accomplished by tailoring the absorption coefficient in the detector region so that all detectors absorb equal amounts of optical power. / Thesis / Master of Engineering (ME)

The objective of this research is to explore the feasibility of a chipless RFID tag that stores a data signature in the form of complex frequency plane singularities. To this end an existing chipless RFID tag, the notched elliptical dipole tag, was analyzed first with simulations and then measurements. A pole signature was extracted from simulations, and individual poles were determined via experimentation to be attributable to specific controllable features of the tag. The poles were shown to be independent of both excitation and observation. A prototype tag was measured, and the pole signature was retrieved from the scattered fields. The tag was successfully read for different orientations showing that embedded singularities can be used as a means for encoding and retrieving data. / Master of Science

In recent decades science has become an increasingly multidisciplinary field in which the lines that used to divide starkly different fields have blurred or disappeared completely. This work is a compendium of different angles focused at exploring disease progression of cancer biology through the perspective of mechanical engineering. We explore cancer through a holistic approach considering mechanistic, physical, genetic biology, biochemical, and immune cells to explore how the interplay with fiber networks can expand our understanding. We explored the physical interplay with biological processes of fibroblastic cells and show how these are critically regulated by forces that alter their ability to coil depends on fiber curvature and adhesion strength; thus, showing how cellular processes are driven by the balances of mechanical forces. Conversely, not all cell types are driven by the same factors, where we report that the structural features of migratory DCs enable them to be less influenced by the differences in fiber diameters, contrasting drastically what we previously reported on the other cell lines. Finally developing a novel composite nanofiber platform, we reported how some cancer cells are mechanistically influenced by the architecture of a substrate and thus resulting in completely different migratory responses that we have associated with key regulatory genes and responding completely differently when in the presence of clinically relevant molecular therapies. Overall, we investigated cancer biology through stiffness gradients, geometric influence through biophysics on myoblasts, and immune cell migration forces as a strong indicator of cell behavior. / Master of Science / Biology has historically been studied through chemistry and genetics, an approach that has produced incredible scientific discoveries such as vaccines and various therapies. Similarly, mechanical engineering has taken us to corners of the world that we never thought possible through the creation of machines, vehicles and the creation of new metal alloys. This research work is part of an emergent field of collaborative science which is paving the way to new ideas and the development of compound fields such as mechanobiology. Here we investigate how cells migrate through small rope-like environments that imitate the same fibers our cells can encounter in the body. We control the thickness, the arrangement, the orientation and the strength of these ropes to investigate how cells react to these environments, thus reporting on the new behaviors cells adopts in these conditions as well as their potential medical implications. Overall, we have developed new methods of studying cancer and other types of cells by tackling new questions using a mechanical perspective.

Self-organizing maps (SOMs) are self-organized projections of high dimensional data onto a low, typically two dimensional (2D), map wherein vector similarity is implicitly translated into topological closeness in the 2D projection. They are thus used for clustering and visualization of high dimensional data. However it is often challenging to interpret the results due to drawbacks of currently used methods for identifying and visualizing cluster boundaries in the resulting feature maps. In this thesis we introduce a new phase to the SOM that we refer to as the Cluster Reinforcement (CR) phase. The CR phase amplifies within-cluster similarity with the consequence that cluster boundaries become much more evident. We also define a new Boundary (B) matrix that makes cluster boundaries easy to visualize, can be thresholded at various levels to make cluster hierarchies apparent, and can be overlain directly onto maps of component planes (something that was not possible with previous methods). The combination of the SOM, CR phase and B-matrix comprise an automated method for improved identification and informative visualization of clusters in high dimensional data. We demonstrate these methods on three data sets: the classic 13- dimensional binary-valued “animal” benchmark test, actual 60-dimensional binaryvalued phonetic word clustering problem, and 3-dimensional real-valued geographic data clustering related to fuel efficiency of vehicle choice.

A new method is presented for the numerical computation of the generalized eigen- values of real Hamiltonian or symplectic pencils and matrices. The method is strongly backward stable, i.e., it is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order sqrt(epsilon), where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.

This report is both a users guide and a programmers manual for running and modifying the program SHAMAT, an interactive matrix calculator. The program is written in Turbo Pascal version 3.0 for MS-DOS computers. This software enables the user to type in matrix equations for solving statistical problems such as multiple regression, analysis of variance, etc. All matrix operations necessary for linear models analysis are included in this program. Since each operation uses a separate subroutine, program enhancement, modification and updating is demonstrated to be easy.

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In Markov chain models in finance and healthcare a transition matrix over a certain time interval is needed but only a transition matrix over a longer time interval may be available. The problem arises of determining a stochastic $p$th root of astochastic matrix (the given transition matrix). By exploiting the theory of functions of matrices, we develop results on the existence and characterization of stochastic $p$th roots. Our contributions include characterization of when a real matrix hasa real $p$th root, a classification of $p$th roots of a possibly singular matrix,a sufficient condition for a $p$th root of a stochastic matrix to have unit row sums,and the identification of two classes of stochastic matrices that have stochastic $p$th roots for all $p$. We also delineate a wide variety of possible configurationsas regards existence, nature (primary or nonprimary), and number of stochastic roots,and develop a necessary condition for existence of a stochastic root in terms of the spectrum of the given matrix. On the computational side, we emphasize finding an approximate stochastic root: perturb the principal root $A^{1/p}$ or the principal logarithm $\log(A)$ to the nearest stochastic matrix or the nearest intensity matrix, respectively, if they are not valid ones;minimize the residual $\normF{X^p-A}$ over all stochastic matrices $X$ and also over stochastic matrices that are primary functions of $A$. For the first two nearness problems, the global minimizers are found in the Frobenius norm. For the last two nonlinear programming problems, we derive explicit formulae for the gradient and Hessian of the objective function $\normF{X^p-A}^2$ and investigate Newton's method, a spectral projected gradient method (SPGM) and the sequential quadratic programming method to solve the problem as well as various matrices to start the iteration. Numerical experiments show that SPGM starting with the perturbed $A^{1/p}$to minimize $\normF{X^p-A}$ over all stochastic matrices is method of choice.Finally, a new algorithm is developed for computing arbitrary real powers $A^\a$ of a matrix $A\in\mathbb{C}^{n\times n}$. The algorithm starts with a Schur decomposition,takes $k$ square roots of the triangular factor $T$, evaluates an $[m/m]$ Pad\'e approximant of $(1-x)^\a$ at $I - T^$, and squares the result $k$ times. The parameters $k$ and $m$ are chosen to minimize the cost subject to achieving double precision accuracy in the evaluation of the Pad\'e approximant, making use of a result that bounds the error in the matrix Pad\'e approximant by the error in the scalar Pad\'e approximant with argument the norm of the matrix. The Pad\'e approximant is evaluated from the continued fraction representation in bottom-up fashion, which is shown to be numerically stable. In the squaring phase the diagonal and first superdiagonal are computed from explicit formulae for $T^$, yielding increased accuracy. Since the basic algorithm is designed for $\a\in(-1,1)$, a criterion for reducing an arbitrary real $\a$ to this range is developed, making use of bounds for the condition number of the $A^\a$ problem. How best to compute $A^k$ for a negative integer $k$ is also investigated. In numerical experiments the new algorithm is found to be superior in accuracy and stability to several alternatives,including the use of an eigendecomposition, a method based on the Schur--Parlett\alg\ with our new algorithm applied to the diagonal blocks and approaches based on the formula $A^\a = \exp(\a\log(A))$.

Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.

Al-Mg alloys were infiltrated into porous alumina preforms at temperatures greater than 950°C where significant amount of nitride forms in the matrix. The present work aims to obtain a process window for growing A1N rich composites over uniform thicknesses so that bulk fabrication of these composites could be carried out. Initial experiments were carried out in a thermo-gravimetric analyser (TGA) to establish suitable conditions for growing useful thicknesses. Al- 2wt% Mg alloy, alumina preforms of particle size 53-63μm and N2 - 2% H2 (5ppm O2) were used for the present study based on previous work carried out in the fabrication of MMCs at low temperatures. Experiments carried out in the TGA indicate that oxygen in the system has to be gettered for the growth of nitride rich composites. Infiltration heights of about 8mm were obtained using an external getter (Al - 5wt%Mg) alloy in addition to the base alloy used for infiltration. The above process conditions were subsequently employed in a tube furnace to fabricate bulk composites and to study the effect of temperature on the volume fraction of aluminium nitride in the matrix. The volume fraction of nitride in the composite varied between 30 and 95 vol % with increase in process temperature from 950°C to 1075°C. Microstructures of these composites indicate that A1N starts to form on the particle surface and tends to grow outwards. The metal supplied through channels adjacent to the particle surface nitride until a point is reached when the composite growing from the adjacent particles meet each other and isolate the melt underneath from nitrogen thereby leading to a metal rich region underneath. Increase in temperature results in an increased nitridation rate resulting in reduced metal pocket size. Composites fabricated at 975°C had a minor leak at the O-rings, which seal the tube. This led to infiltration under conditions of varying oxygen partial pressure leading to different nitride fractions in the composite. The above fact was confirmed by conducting an experiment with commercial purity nitrogen, which has an oxygen content of about 5000ppm. The composite had an A1N content of about 30% whereas the composite fabricated with N2 -2%H2 (5ppm oxygen) showed a nitride content of 64%. This suggests that one can vary the nitride content in the composite by varying the oxygen content in the system at a particular process temperature. The hardness of the matrix increases with increase in process temperature from 3.5 ± 0.7 GPa at 975°C to about 9.8 ± 0.9 GPa at 1075°C. Porosity was observed in the composite processed at 1075°C. This increased porosity leads to decreased hardness though the nitride content in the composite has increased by 11%. The scatter in the data is attributed to variations in the microstructure as well as due to interference from underlying metal pockets or particles as well as due to porosity introduced in the composite at high processing temperatures.