Properties of aggregates are affected by their morphological characteristics, including shape factors, angularity and texture. These morphological characteristics influence the aggregate's mutual interactions and strengths of bonds between the aggregates and the binder. The interactions between aggregates and bond strengths between the aggregate and the binder are vital to rheological properties, related to workability and friction resistance of mixtures. As a consequence, quantification of the aggregate's morphological characteristics is essential for better quality control and performance improvement of aggregates. With advancement of hardware and software, the computation capability has reached the stage to rapidly quantify morphological characteristics at multiple scales using digital imaging techniques. Various computational algorithms have been developed, including Hough transform, Fourier transform, and wavelet analysis, etc. Among the aforementioned computational algorithms, Fourier transform has been implemented in various areas by representing the original image/signal in the spatial domain as a summation of representing functions of varying magnitudes, frequencies and phases in the frequency domain. This dissertation is dedicated to developing the two-dimensional Fourier transform (FFT2) method using the Fourier Transform Interferometry (FTI) system that is capable to quantify aggregate morphological characteristics at different scales. In this dissertation, FFT2 method is adopted to quantify angularity and texture of aggregates based on surface coordinates acquired from digital images in the FTI system. This is followed by a comprehensive review on prevalent aggregate imaging techniques for the quantification of aggregate morphological characteristics, including the second generation of Aggregate Image Measurement System (AIMS II), University of Illinois Aggregate Image Analyzer (UIAIA), the FTI system, etc. Recommendations are made on the usage of aggregate imaging system in the measurements of morphological parameters that are interested. After that, the influence of parent rock, crushing, and abrasion/polishing on aggregate morphological characteristics are evaluated. Atomic-scale roughness is calculated for crystal structures of five representative minerals in four types of minerals (i.e., α-quartz for quartzite/granite/gravel/aplite, dolomite for dolomite, calcite for limestone, haematite and magnetite for iron ore); roughness ranking at atomic-scale is further compared with surface texture ranking at macroscale based on measurement results using the FTI system and AIMS II. Morphological characteristics of aggregates before and after crushing test and micro-deval test are measured to quantitatively evaluate the influences of the crushing process and the abrasion/polishing process on morphological characteristics of aggregates, respectively. / Ph. D.

Systems biology aims to understand cellular behavior in terms of the spatiotemporal interactions among cellular components, such as genes, proteins and metabolites. Comprehensive visualization tools for exploring multivariate data are needed to gain insight into the physiological processes reflected in these molecular profiles. Data fusion methods are required to integratively study high-throughput transcriptomics, metabolomics and proteomics data combined before systems biology can live up to its potential. In this work I explored mathematical and statistical methods and visualization tools to resolve the prominent issues in the nature of systems biology data fusion and to gain insight into these comprehensive data. In order to choose and apply multivariate methods, it is important to know the distribution of the experimental data. Chi square Q-Q plot and violin plot were applied to all M. truncatula data and V. vinifera data, and found most distributions are right-skewed (Chapter 2). The biplot display provides an effective tool for reducing the dimensionality of the systems biological data and displaying the molecules and time points jointly on the same plot. Biplot of M. truncatula data revealed the overall system behavior, including unidentified compounds of interest and the dynamics of the highly responsive molecules (Chapter 3). The phase spectrum computed from the Fast Fourier transform of the time course data has been found to play more important roles than amplitude in the signal reconstruction. Phase spectrum analyses on in silico data created with two artificial biochemical networks, the Claytor model and the AB2 model proved that phase spectrum is indeed an effective tool in system biological data fusion despite the data heterogeneity (Chapter 4). The difference between data integration and data fusion are further discussed. Biplot analysis of scaled data were applied to integrate transcriptome, metabolome and proteome data from the V. vinifera project. Phase spectrum combined with k-means clustering was used in integrative analyses of transcriptome and metabolome of the M. truncatula yeast elicitation data and of transcriptome, metabolome and proteome of V. vinifera salinity stress data. The phase spectrum analysis was compared with the biplot display as effective tools in data fusion (Chapter 5). The results suggest that phase spectrum may perform better than the biplot. This work was funded by the National Science Foundation Plant Genome Program, grant DBI-0109732, and by the Virginia Bioinformatics Institute. / Ph. D.

Recent developments in smart grid technology have spawned interest in the use of phasor measurement units to help create a reliable power system transmission and distribution infrastructure. Wide-area monitoring systems (WAMSs) utilizing synchrophasor measurements can help with understanding, forecasting, or even controlling the status of power grid stability in real-time. A power system Frequency Monitoring Network (FNET) was first proposed in 2001 and was established in 2004. As a pioneering WAMS, it serves the entire North American power grid through advanced situational awareness techniques, such as real-time event alerts, accurate event location estimation, animated event visualization, and post event analysis. Traditionally, Phasor Measurement Units (PMUs) have utilized signals obtained from current transformers (CTs) to compute current phasors. Unfortunately, this requires that CTs must be directly connected with buses, transformers or power lines. Chapters 2, 3 will introduce an innovative phasor measurement instrument, the Non-contact Frequency Disturbance Recorder (NFDR), which uses the magnetic and electric fields generated by power transmission lines to obtain current phasor measurements. The NFDR is developed on the same hardware platform as the Frequency Disturbance Recorder (FDR), which is actually a single phase PMU. Prototype testing of the NFDR in both the laboratory and the field environments were performed. Testing results show that measurement accuracy of the NFDR satisfies the requirements for power system dynamics observation. Researchers have been developing various techniques in power system phasor measurement and frequency estimation, due to their importance in reflecting system health. Each method has its own pros and cons regarding accuracy and speed. The DFT (Discrete Fourier Transform) based algorithm that is adopted by the FDR device is particularly suitable for tracking system dynamic changes and is immune to harmonic distortions, but it has not proven to be very robust when the input signal is polluted by random noise. Chapter 4 will discuss the Least Mean Squares-based methods for power system frequency tracking, compared with a DFT-based algorithm. Wide-area monitoring systems based on real time PMU measurements can provide great visibility to the angle instability conditions. Chapter 5 focuses on developing an early warning algorithm on the FNET platform. / Ph. D.

No / We analyze the possibility and efficiency of nonholonomic control over quantum devices with exponentially large number of Hilbert space dimensions. We show that completely controllable devices of this type can be assembled from elementary units of arbitrary physical nature, and can be employed efficiently for universal quantum computations and simulation of quantum-field dynamics. As an example we describe a toy device that can perform Toffoli-gate transformations and discrete Fourier transform on 9 qubits.

Jump-diffusion models can under certain assumptions be expressed as partial integro-differential equations (PIDE). Such a PIDE typically involves a convection term and a nonlocal integral like for the here considered models of Merton and Kou. We transform the PIDE to eliminate the convection term, discretize it implicitly using finite differences and the second order backward difference formula (BDF2) on a uniform grid. The arising dense linear system is solved by an iterative method, either a splitting technique or a circulant preconditioned conjugate gradient method. Exploiting the Fast Fourier Transform (FFT) yields the solution in only $O(n\log n)$ operations and just some vectors need to be stored. Second order accuracy is obtained on the whole computational domain for Merton's model whereas for Kou's model first order is obtained on the whole computational domain and second order locally around the strike price. The solution for the PIDE with convection term can oscillate in a neighborhood of the strike price depending on the choice of parameters, whereas the solution obtained from the transformed problem is stabilized. / Master of Science

The Fourier Transform Infrared spectrometer (FTIR) has been used increasingly as a detector for various forms of chromatography. Clearly the most established marriage has been that of the Gas Chromatograph (GC) with the FTIR. GC-FTIR has been developed well beyond other forms. The main objective of this thesis, however, is to extend the FTIR as a detector to previously untested forms of chromatography using a flow cell interface. These forms of chromatography include High Performance Liquid Chromatography (HPLC), both normal-phase and reversed-phase, and packed-column Supercritical Fluid Chromatography (SFC). Normal phase HPLC-FTIR was demonstrated on not only analytical scale columns, but semi-preparative and microbore scales as well. Significant advantages, particularly with respect to the low solvent consumption, were found in the microbore HPLC-FTIR experiment. This led to the development of a chromatographically improved flow cell, the Zero Dead Volume (ZDV) HPLC-FTIR interface. The ZDV cell shows superior chromatographic characteristics and has unique spectrometric characteristics because of its unusual cross-section. Detection limits as low as 40 ng were observed. Extension to reversed-phase HPLC-FTIR required incorporation of the Flow Injection Analysis (FIA) technique of low-dispersion flowing extraction. The compounds separated by HPLC are extracted into an infrared-transparent solvent, and the extracted compounds are detected by similar means to normal-phase HPLC-FTIR. Investigation of SFC-FTIR incorporated a high-pressure, gold-lined lightpipe flow cell to detect the components separated by the supercritical C0₂/packed-column chromatograph. Several unusual spectrometric characteristics were noted. Detection limits as low as 50 ng were observed with SFC-FTIR. / Ph. D.

The rise of machine learning has seen an increase in digital methods for use within health care. Arrythmia detection is one of the areas where this increase is obvious. However, many machine learning methods for arrythmia detection utilise models that are computationally expensive, such as convolutional neural networks, CNNs. This thesis examines whether it is viable to use the Fast Fourier Transform to transform an Electrocardiogram, ECG, signal into its frequency components before training a neural network, NN, on the data. This could allow for a lower computational cost and wider availability of arrythmia detection technology. The results from the model were compared to that of a CNN trained on time domain data. The results show that the CCN model outperforms the NN trained on FFT transformed data but the performance of the model still indicates that valuable information about heart arrythmias does exist within the frequency space. This suggests a potential for future work on the subject.

Formaldehyde-based adhesives have been reported to be detrimental to health. Petrochemical-based adhesives are non-renewable, limited and costly. Therefore, the improvement of environmental-friendly adhesive from natural agricultural products has awakened noteworthy attention. A novel adhesive for wood application was successfully prepared with enhanced shear strength and water resistance. The Fourier transmform infrared spectra showed the surface functionalities of the functionalized carbon nanotubes (FCNTs) and soy protein isolate nanocomposite adhesive. The attachment of carboxylic functional group on the surface of the carbon nanotubes (CNTs) after purification contributed to the effective dispersion of the CNTs in the nanocomposite adhesive. Hence, enhanced properties of FCNTs were successfully transferred into the SPI/CNTs nanocomposite adhesive. These unique functionalities on FCNTs however, improved the mechanical properties of the adhesive. The shear strength and water resistance of SPI/FCNTs was higher than that of the SPI/CNTs. SEM images showed the homogenous dispersion of CNTs in the SPI/CNTs nanocomposite adhesive. The carbon nanotubes were distributed uniformly in the soy protein adhesive with no noticeable clusters at relatively reduced fractions of CNTs as shown in the SEM images, which resulted into better adhesion on wood surface. Mechanical (shear) mixing and ultrasonication with 30 minutes of shear mixing both showed an improved dispersion of CNTs in the soy protein matrix. However, ultrasonication method of dispersion showed higher tensile shear strength and water resistance than in mechanical (shear) mixing method. Thermogravimetric analysis of the samples also showed that the CNTs incorporated increases the thermal stability of the nanocomposite adhesive at higher loading fraction. Incorporation of CNTs into soy protein isolate adhesive improved both the shear strength and water resistance of the adhesive prepared at a relatively reduced concentration of 0.3%.The result showed that tensile shear strength of SPI/FCNTs adhesive was 0.8 MPa and 7.25MPa at dry and wet state respectively, while SPI/CNTs adhesive had 6.91 MPa and 5.48MPa at dry and wet state respectively. There was over 100% increase in shear strength both at dry and wet state compared to the pure SPI adhesive. The 19% decrease in value of the new adhesive developed compared to the minimum value of ≥10MPa of European standard for interior wood application may be attributed to the presence of metallic particles remaining after purification of CNTs. The presence of metallic particles will prevent the proper penetration of the adhesive into the wood substrate. The type of wood used in this study as well as the processing parameters could also result into lower value compared to the value of European standard. Therefore, optimization of the processing parameter as well as the conversion of carboxylic acid group on the surface of the CNTs into acyl chloride group may be employed in future investigation. However, the preparation of new nanocomposite adhesive from soy protein isolate will replace the formaldehyde and petrochemical adhesive in the market and be of useful application in the wood industry. / Civil and Chemical Engineering / M. Tech. (Chemical Engineering)

Thesis submitted in fulfilment of the requirements for the degree Master of Technology Chemistry in the Faculty of (Science) Supervisor: Professor T.N. van der Walt Bellville campus Date submitted: October 2011 / It is important to quantify polymeric components in a coating because they greatly influence the performance of a coating. The difficulty associated with analysis of polymers by Fourier transform infrared (FTIR) analysis’s is that colinearities arise from similar or overlapping spectral features. A quantitative FTIR method with attenuated total reflectance coupled to multivariate/ chemometric analysis is presented. It allows for simultaneous quantification of 3 polymeric components; a rheology modifier, organic opacifier and styrene acrylic binder, with no prior extraction or separation from the paint. The factor based methods partial least squares (PLS) and principle component regression (PCR) permit colinearities by decomposing the spectral data into smaller matrices with principle scores and loading vectors. For model building spectral information from calibrators and validation samples at different analysis regions were incorporated. PCR and PLS were used to inspect the variation within the sample set. The PLS algorithms were found to predict the polymeric components the best. The concentrations of the polymeric components in a coating were predicted with the calibration model. Three PLS models each with different analysis regions yielded a coefficient of correlation R2 close to 1 for each of the components. The root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) was less than 5%. The best out-put was obtained where spectral features of water was included (Trial 3). The prediction residual values for the three models ranged from 2 to -2 and 10 to -10. The method allows paint samples to be analysed in pure form and opens many opportunities for other coating components to be analysed in the same way.

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