Diffusion is a phenomenon in which particles move from regions of higher density to regions of lower density. Many physical systems, in fields as diverse as plant biology and finance, are known to involve diffusion phenomena. Typically, diffusion systems are modeled by partial differential equations (PDEs), which include certain parameters. These parameters characterize a given diffusion system. Therefore, for both modeling and simulation of a diffusion system, one has to either know or determine these parameters. Moreover, as PDEs are infinite order dynamic systems, for computational purposes one has to approximate them by a finite order model. In this thesis, we investigate these two issues of model reduction and parameter estimation by considering certain specific cases of heat diffusion systems. We first address model reduction by considering two specific cases of heat diffusion systems. The first case is a one-dimensional heat diffusion across a homogeneous wall, and the second case is a two-dimensional heat diffusion across a homogeneous rectangular plate. In the one-dimensional case we construct finite order approximations by using some well known PDE solvers and evaluate their effectiveness in approximating the true system. We also construct certain other alternative approximations for the one-dimensional diffusion system by exploiting the different modal structures inherently present in it. For the two-dimensional heat diffusion system, we construct finite order approximations first using the standard finite difference approximation (FD) scheme, and then refine the FD approximation by using its asymptotic limit. As for parameter estimation, we consider the same one-dimensional heat diffusion system, as in model reduction. We estimate the parameters involved, first using the standard batch estimation technique. The convergence of the estimates are investigated both numerically and theoretically. We also estimate the parameters of the one-dimensional heat diffusion system recursively, initially by adopting the standard recursive prediction error method (RPEM), and later by using two different recursive algorithms devised in the frequency domain. The convergence of the frequency domain recursive estimates is also investigated.

This paper analyzes two main frameworks that challenge the “mainstream” finance theory and the random walk hypothesis. The first framework is based on investor irrationality and is called Behavioural Finance. The second framework views the financial market as a chaotic system and is called Fractal Theory of a financial market. Behavioural Finance attacks the assumption of investor rationality, thus challenging the conventional finance theories on the micro level. Fractal Theory challenges the EMH and the “macroeconomics” of finance. This paper presents a step towards unifying the frameworks of Behavioural Finance and Fractal Theory. After a review of the relevant literature, a model of the financial market is suggested that rests on the predictions of both Behavioural Finance and Fractal Theory. As a next step, a mathematical algorithm is described that allows to test the financial market for consistency with the presented model. The mathematical algorithm is applied to 10 years of daily S&P500 price quotes, and consistent statistical evidence shows that the predicted fractal pattern reveals itself in the S&P500 prices. The new model outperforms the random walk in out-of-sample forecasting.

Smart cards are widely used in different areas of modern life including identification, banking, and transportation cards. Some types of cards are able to store data and process information as well. A number of them can run cryptographic algorithms to enhance the security of their transactions and it is usually believed that the information and values stored in them are completely safe. However, this is generally not the case due to the threat of the side channel. Side channel analysis is the process of obtaining additional information from the internal activity of a physical device beyond that allowed by its specifications. There exist different techniques to attempt to obtain information from a cryptosystem using other ways than the normally permitted. This thesis presents a series of experiments intended to study the side channel from a particular type of smart card, known as Java Cards. This investigation uses the well known technique, Correlation Analysis, and a new type of side channel attack called fast correlation in the frequency domain to study the side channel of Java Cards. This research presents a giant magnetoresistor (GMR) probe and for the first time, this type of sensor is used to investigate the side channel. A novel setup designed for studying the side channel of smart cards is described and two metrics used to evaluate the analysis results are presented. After testing the GMR probe and methodology on electronic devices executing the Advanced Encryption Standard (AES), such as 8 bit microcontrollers and 128 bit AES implementations on FPGAs, these techniques were applied to analyse two different models of Java Cards working in the contactless mode. The results show that successful attacks on a software implementation of AES running on both models of Java Cards are possible.

The cyclic prefix (CP) is usually adopted in single carrier frequency domain equalization (SC-FDE) system to avoid inter-block interference (IBI) and inter-symbol interference (ISI) in multipath fading channels. In addition, the use of CP also converts the linear convolution between the transmitted signal and the channel into a circular convolution, leading to significant decrease in receiver equalization. However, the use of CP reduces the bandwidth efficiency. Therefore the SC-FDE system without CP is investigated in this thesis. A number of schemes have been proposed to improve the performance of systems without CP, where both IBI and ICI are dramatically increased. Unfortunately, most of the existing schemes have extremely high computational complexity and are difficult to realize. In this thesis, a novel low-complexity CP reconstruction (CPR) scheme is proposed for interference cancellation, where the successive interference cancellation (SIC) and QR decomposition (QRD) are adopted. In addition, the system performance is further improved by using the fact that the interferences of different symbols are not the same. Simulation experiments are conducted to verify the system performance of the proposed scheme. It is shown that the proposed scheme can effectively reduce the interference, while maintain a low computational complexity.

Frequency domain photon migration (FDPM) measurements are used to study the properties of dense colloidal dispersions with hard sphere and electrostatic interactions, which are otherwise difficult to analyze due to multiple scattering effects. Hard sphere interactions were studied using a theoretical model based upon a polydisperse mixture of particles using the hard sphere Percus Yevick theory. The particle size distribution and volume fraction were recovered by solving a non linear inverse problem using genetic algorithms. The mean sizes of the particles of 144 and 223 nm diameter were recovered within an error range of 0-15.53% of the mean diameters determined from dynamic light scattering measurements. The volume fraction was recovered within an error range of 0-24% of the experimentally determined volume fractions. At ionic strengths varying between 0.5 and 4 mM, multiple wavelength (660, 685, 785 and 828 nm) FDPM measurements of isotropic scattering coefficients were made of 144 and 223 nm diameter, monodisperse dispersions varying between 15% - 22% volume fraction, as well as of bidisperse mixtures of 144 and 223 nm diameter latex particles in 1:3, 1:1 and 3:1 mixtures varying between volume fractions of 15% - 24%. Structure factor models with Yukawa potential were computed by Monte Carlo (MC) simulations and numerical solution of the coupled Ornstein Zernike equations. In monodisperse dispersions of particle diameter 144 nm the isotropic scattering coefficient versus ionic strength show an increase with increasing ionic strength consistent with model predictions, whereas there was a reversal of trends and fluctuations for the particle diameter of 223 nm. In bidisperse mixtures for the case of maximum number of smaller particles, the isotropic scattering coefficient increased with increasing ionic strength and the trends were in conformity with MC simulations of binary Yukawa potential models. As the number of larger diameter particles increased in the dispersions, the isotropic scattering coefficients depicted fluctuations, and no match was found between the models and measurements for a number ratio of 1:3. The research lays the foundation for the determination of particle size distribution, volume fractions and an estimate of effective charge for high density of particles.

In this thesis, the conventional low voltage power line communication methods is investigated in the axis of automated meter reading applications and the classification and experimental verification of common noise types for low voltage power line communication network. The investigated system provides the real time transmission of electricity consumption data recorded by electricity meters, initially to a local computer via a low voltage line through a low speed PLC (Power Line Carrier) environment and subsequently to a corporate network through a high speed data transmission medium. The automated meter system provides a more effective tracking and data acquisition, a more detailed and vigorous knowledge about consumer behavior for subscriber assessment in electricity distribution in association with a brand new management and system supervision concept in electricity distribution control and management technology. The theoretical studies are experimentally verified for the Turkish low voltage power infrastructure through laboratory experiments performed in METU Electrical and Electronics Engineering Department, Electrical Machines and Drives Laboratory and R&amp / D Laboratories of MAKEL facilities in Hadimk&ouml / y. The single phase voltage of the mains line between the phase and neutral is monitored to exhibit the disturbing effects of various noise sources. The resulting voltage spectrum is logged by using digital data acquisition devices in time and frequency domain. The waveforms are converted to frequency domain using the Fast Fourier Transform (FFT) functions of the MATLAB. The experimental results are compared to the theoretical findings obtained through literature survey.

In the single carrier systems with cyclic-prefix (CP), the use of CP does not only eliminate the inter-block interference (IBI), but also convert linear convolution of the transmitted signal with the channel into circular convolution, which leads to the computation complexity of the frequency domain equalization (FDE) at the receiver is reduced. Unfortunately, the use of CP considerably decreases the bandwidth utilization. In order to increase the bandwidth utilization, the single carrier systems with frequency domain equalization (SC-FDE) is investigated. When FDE is used in a single carrier system without CP, the IBI is induced by the modulated symbols and then the bit-error rate (BER) is increased. To reduce the interference and then improve the system performance, a novel interference cancellation scheme is proposed in this thesis. After FDE, it is shown that interference is induced from the right end of a time domain signal block and most of the interference is located at both ends of an equalized time domain signal block. Based on this observation, the modulated symbols which induce the interference are detected according to the maximum-likelihood (ML) principle and then the interference is regenerated and eliminated. For simplifying the computation complexity, we further propose a successive interference cancellation scheme, which is implemented by using the Viterbi algorithm. The simulation results demonstrate that the proposed scheme improves BER performance significantly in SC-FDE systems. In addition, the proposed architecture has comparable BER performance with the SC-CP systems when the multi-path channel is exponentially decayed.

Accurate single-shot visualization of laser wakefield structures can improve our fundamental understanding of plasma-based accelerators. Previously, frequency domain holography (FDH) was used to visualize weakly nonlinear sinusoidal wakes in plasmas of density n[subscript e] < 0.6 × 10¹⁹/cm³ that produced few or no relativistic electrons. Here, I address the more challenging task of visualizing highly nonlinear wakes in plasmas of density n[subscript e] ~ 1 to 3× 10¹⁹/cm³ that can produce high-quality relativistic electron beams. Nonlinear wakes were driven by 30 TW, 30 fs, 800 nm pump pulses. When bubbles formed, part of a 400 nm, co-propagating, overlapping probe pulse became trapped inside them, creating a light packet of plasma wavelength dimensions--that is, an optical "bullet"--that I reconstruct by FDH methods. As ne increased, the bullets first appeared at 0.8 × 10¹⁹/cm³, the first observation of bubble formation below the electron capture threshold. WAKE simulations confirmed bubble formation without electron capture and the trapping of optical bullets at this density. At n[subscript] >1× 10¹⁹/cm³, bullets appeared with high shot-to-shot stability together with quasi-monoenergetic relativistic electrons. I also directly observed the temporal walk-off of the optical bullet from the beam-loaded plasma bubble revealed by FDH phase shift data, providing unprecedented visualization of the electron injection and beam loading processes. There are five chapters in this thesis. Chapter 1 introduces general laser plasma- based accelerators (LPA). Chapter 2 discusses the FDH imaging technique, including the setup and reconstruction process. In 2006, Dr. N. H. Matlis used FDH to image a linear plasma wakefield. His work is also presented in Chapter 2 but with new analyses. Chapter 3, the main part of the thesis, discusses the visualization of LPAs in the bubble regime. Chapter 4 presents the concept of frequency domain tomography. Chapter 5 suggests future directions for research in FDH. / text

The thesis is devoted to the frequency-resolved investigation of the relaxation processes in optoelectronic materials and devices. Conventional fluorescence decay time measurement technique in the frequency domain was adapted for the use with light-emitting diode (LED) excitation and signal registration by a lock-in amplifier. Inorganic phosphors synthesized by aqueous sol-gel combustion method for using as wavelength converters in white LEDs as well as advanced organic semiconducting materials were investigated by photoluminescence decay time and quantum yield measurement techniques. The photoluminescence decay time measurement technique with extremely low quasi-continuous UV LED excitation was applied for the carrier dynamics research in GaN epitaxial layers. The investigation under such a low excitation conditions revealed the contribution of donor-acceptor recombination in the yellow luminescence of GaN. The techniques for in-situ thermal characterization of encapsulated LEDs, including the measurements of phosphors converter temperature and heat relaxation time constants inside a LED, were developed and demonstrated for the investigation of commercial low- and high- power LEDs. / Disertacija yra skirta relaksacijos procesų, vykstančių optoelektronikos medžiagose ir prietaisuose, tyrimui dažninės skyros metodu. Įprastas fluorescencijos gesimo trukmės tyrimo metodas, veikiantis harmoniškai moduliuoto žadinimo režimu, buvo adaptuotas žadinimui puslaidininkiniais šviestukais ir signalų registravimui radijo dažnių faziniu detektoriumi. Neorganiniai vandeniniu zolių-gelių metodu susintetinti fosforai, skirti baltų puslaidininkinių šviestukų gamybai, ir modernios organinės optoelektronikos medžiagos buvo ištirtos fotoliuminescencijos gesimo dėsnio ir kvantinės išeigos matavimo metodikomis, siekiant nustatyti krūvininkų rekombinacijos savybes ir optimizuoti sintezės parametrus. Realizuotas GaN epitaksinių sluoksnių liuminescencijos kinetikos tyrimas labai žemo kvazitolydinio sužadinimo atveju patvirtino rekombinacijos per priemaišas svarbą šio tipo medžiagose. Buvo sukurtos naujos prekinių šviestukų šiluminių savybių in-situ tyrimo metodikos, veikiančios dažninės skyros režimu. Bangos ilgio keitiklių temperatūra baltuose šviestukuose ir šilumos relaksacijos konstantos įvairaus tipo šviestukų konstrukciniuose elementuose buvo išmatuotos esant vardiniam šviestukų veikimo režimui.

Disertacija yra skirta relaksacijos procesų, vykstančių optoelektronikos medžiagose ir prietaisuose, tyrimui dažninės skyros metodu. Įprastas fluorescencijos gesimo trukmės tyrimo metodas, veikiantis harmoniškai moduliuoto žadinimo režimu, buvo adaptuotas žadinimui puslaidininkiniais šviestukais ir signalų registravimui radijo dažnių faziniu detektoriumi. Neorganiniai vandeniniu zolių-gelių metodu susintetinti fosforai, skirti baltų puslaidininkinių šviestukų gamybai, ir modernios organinės optoelektronikos medžiagos buvo ištirtos fotoliuminescencijos gesimo dėsnio ir kvantinės išeigos matavimo metodikomis, siekiant nustatyti krūvininkų rekombinacijos savybes ir optimizuoti sintezės parametrus. Realizuotas GaN epitaksinių sluoksnių liuminescencijos kinetikos tyrimas labai žemo kvazitolydinio sužadinimo atveju patvirtino rekombinacijos per priemaišas svarbą šio tipo medžiagose. Buvo sukurtos naujos prekinių šviestukų šiluminių savybių in-situ tyrimo metodikos, veikiančios dažninės skyros režimu. Bangos ilgio keitiklių temperatūra baltuose šviestukuose ir šilumos relaksacijos konstantos įvairaus tipo šviestukų konstrukciniuose elementuose buvo išmatuotos esant vardiniam šviestukų veikimo režimui. / The thesis is devoted to the frequency-resolved investigation of the relaxation processes in optoelectronic materials and devices. Conventional fluorescence decay time measurement technique in the frequency domain was adapted for the use with light-emitting diode (LED) excitation and signal registration by a lock-in amplifier. Inorganic phosphors synthesized by aqueous sol-gel combustion method for using as wavelength converters in white LEDs as well as advanced organic semiconducting materials were investigated by photoluminescence decay time and quantum yield measurement techniques. The photoluminescence decay time measurement technique with extremely low quasi-continuous UV LED excitation was applied for the carrier dynamics research in GaN epitaxial layers. The investigation under such a low excitation conditions revealed the contribution of donor-acceptor recombination in the yellow luminescence of GaN. The techniques for in-situ thermal characterization of encapsulated LEDs, including the measurements of phosphors converter temperature and heat relaxation time constants inside a LED, were developed and demonstrated for the investigation of commercial low- and high- power LEDs.