Modeling of metal nanocluster growth on patterned substrates and surface pattern formation under ion bombardment

This thesis addresses the metal nanocluster growth process on prepatterned substrates, the development of atomistic simulation method with respect to an acceleration of the atomistic transition states, and the continuum model of the ion-beam inducing semiconductor surface pattern formation mechanism. Experimentally, highly ordered Ag nanocluster structures have been grown on pre-patterned amorphous SiO2 surfaces by oblique angle physical vapor deposition at room temperature. Despite the small undulation of the rippled surface, the stripe-like Ag nanoclusters are very pronounced, reproducible and well-separated. The first topic is the investigation of this growth process with a continuum theoretical approach to the surface gas condensation as well as an atomistic cluster growth model. The atomistic simulation model is a lattice-based kinetic Monte-Carlo (KMC) method using a combination of a simplified inter-atomic potential and experimental transition barriers taken from the literature. An effective transition event classification method is introduced which allows a boost factor of several thousand compared to a traditional KMC approach, thus allowing experimental time scales to be modeled. The simulation predicts a low sticking probability for the arriving atoms, millisecond order lifetimes for single Ag monomers and about 1 nm square surface migration ranges of Ag monomers. The simulations give excellent reproduction of the experimentally observed nanocluster growth patterns. The second topic specifies the acceleration scheme utilized in the metallic cluster growth model. Concerning the atomistic movements, a classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multi-dimensional Boolean valued functions in three dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. The third topic is the formation of ripple structures on ion bombarded semiconductor surfaces treated in the first topic as the prepatterned substrate of the metallic deposition. This intriguing phenomenon has been known since the 1960s and various theoretical approaches have been explored. These previous models are discussed and a new non-linear model is formulated, based on the local atomic flow and associated density change in the near surface region. Within this framework ripple structures are shown to form without the necessity to invoke surface diffusion or large sputtering as important mechanisms. The model can also be extended to the case where sputtering is important and it is shown that in this case, certain "magic" angles can occur at which the ripple patterns are most clearly defined. The results including some analytic solutions of the nonlinear equation of motions are in very good agreement with experimental observation.:1 Introduction: Atomistic Models 1 1.1 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Schroedinger equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Molecular Dynamics Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Lagrangian mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 MD algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Lattice Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.1 Thermodynamic variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.2 Metropolis Algorithm and limit theorem . . . . . . . . . . . . . . . . . . . . . 15 1.3.3 Kinetic Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3.4 Imaginary time reaction diffusion . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 Cluster Growth on Pre-patterned Surfaces 29 2.1 Nanocluster growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.1 Classical nucleation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.2 Cluster growth on substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.1.3 Experimental motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Local flux and surface ad-monomer diffusion . . . . . . . . . . . . . . . . . . . . . . 35 2.2.1 Surface topography and local flux . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2.2 Surface gas diffusion under inhomogeneous flux . . . . . . . . . . . . . . . . . 37 2.2.3 Surface migration of ad-monomers . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.4 Simulation vs. experimental gauge . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3 Nucleation models: Surface gas condensation . . . . . . . . . . . . . . . . . . . . . . 46 2.3.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.2 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.3 Evolution of sticking probability . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.4 Evolution of Ag cluster growth . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.3.5 Simulation time and system evolution . . . . . . . . . . . . . . . . . . . . . . 57 2.4 Extended cluster growth model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4.1 Modified setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.2 Simulation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.4.3 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3 A Markov chain model of transition states 63 3.1 Acceleration of thin film growth simulation . . . . . . . . . . . . . . . . . . . . . . . 63 3.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.3 Transition states of Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.1 Local transition events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.2 The Monte-Carlo method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.4 Effective transitions of objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.1 Convergence of the local fluctuation . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.2 The importance of individual local transitions . . . . . . . . . . . . . . . . . . 68 3.4.3 The modified algorithm for effective transition states . . . . . . . . . . . . . . 69 3.5 Cluster growth simulation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.1 The configuration energy and migration barriers . . . . . . . . . . . . . . . . 72 3.5.2 Transition events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.5.3 Comparison with Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5.4 Cluster growth stability evaluation . . . . . . . . . . . . . . . . . . . . . . . . 78 3.6 Stability of modified convergence limit . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.6.1 Acceleration of convergence to Gibbs field . . . . . . . . . . . . . . . . . . . . 80 3.6.2 Relative convergence speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.6.3 1D Ag models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.6.4 Stability theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4 Ion beam inducing surface pattern formation 89 4.1 Ion-inducing pattern formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1.1 Bradley-Harper equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1.2 Nonlinear continuum models . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.1.3 Other approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2 Simulation of surface defects induced by ion beams . . . . . . . . . . . . . . . . . . . 94 4.2.1 MD simulation of single ion impact . . . . . . . . . . . . . . . . . . . . . . . . 94 4.2.2 Monte-Carlo simulations of surface modification . . . . . . . . . . . . . . . . 96 4.2.3 Curvature dependent surface diffusion . . . . . . . . . . . . . . . . . . . . . . 102 4.3 Continuum model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.3.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.3.2 A travelling wave solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3.3 Lyapunov stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.3.4 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.5 Approximate solutions for other angles . . . . . . . . . . . . . . . . . . . . . . 110 4.4 Contribution of other effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.1 Surface diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.2 Surface Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5 Summary 119 Appendix 123 A The discrete reaction diffusion equation . . . . . . . . . . . . . . . . . . . . . . . . . 123 B The derivation of the solution (2.20) . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 C Contribution of overlapping migration area . . . . . . . . . . . . . . . . . . . . . . . 125 D The RGL potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 E Stability of the traveling wave solution . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Modeling of metal nanocluster growth on patterned substrates and surface pattern formation under ion bombardment

This thesis addresses the metal nanocluster growth process on prepatterned substrates, the development of atomistic simulation method with respect to an acceleration of the atomistic transition states, and the continuum model of the ion-beam inducing semiconductor surface pattern formation mechanism. Experimentally, highly ordered Ag nanocluster structures have been grown on pre-patterned amorphous SiO^2 surfaces by oblique angle physical vapor deposition at room temperature. Despite the small undulation of the rippled surface, the stripe-like Ag nanoclusters are very pronounced, reproducible and well-separated. The first topic is the investigation of this growth process with a continuum theoretical approach to the surface gas condensation as well as an atomistic cluster growth model. The atomistic simulation model is a lattice-based kinetic Monte-Carlo (KMC) method using a combination of a simplified inter-atomic potential and experimental transition barriers taken from the literature. An effective transition event classification method is introduced which allows a boost factor of several thousand compared to a traditional KMC approach, thus allowing experimental time scales to be modeled. The simulation predicts a low sticking probability for the arriving atoms, millisecond order lifetimes for single Ag monomers and ≈1 nm square surface migration ranges of Ag monomers. The simulations give excellent reproduction of the experimentally observed nanocluster growth patterns. The second topic specifies the acceleration scheme utilized in the metallic cluster growth model. Concerning the atomistic movements, a classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multi-dimensional Boolean valued functions in three dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. The third topic is the formation of ripple structures on ion bombarded semiconductor surfaces treated in the first topic as the prepatterned substrate of the metallic deposition. This intriguing phenomenon has been known since the 1960\'s and various theoretical approaches have been explored. These previous models are discussed and a new non-linear model is formulated, based on the local atomic flow and associated density change in the near surface region. Within this framework ripple structures are shown to form without the necessity to invoke surface diffusion or large sputtering as important mechanisms. The model can also be extended to the case where sputtering is important and it is shown that in this case, certain \\lq magic\' angles can occur at which the ripple patterns are most clearly defined. The results including some analytic solutions of the nonlinear equation of motions are in very good agreement with experimental observation

Classification and modeling of power line noise using machine learning techniques

A thesis submitted in ful lment of the requirements for the degree of Doctor of Philosophy in the School of Electrical and Information Engineering Faculty of Engineering and Built Environment June 2017The realization of robust, reliable and e cient data transmission have been the theme of recent research, most importantly in real channel such as the noisy, fading prone power line communication (PLC) channel. The focus is to exploit old techniques or create new techniques capable of improving the transmission reliability and also increasing the transmission capacity of the real communication channels. Multi-carrier modulation scheme such as Orthogonal Frequency Division Multiplexing (OFDM) utilizing conventional single-carrier modulation is developed to facilitate a robust data transmission, increasing transmission capacity (e cient bandwidth usage) and further reducing design complexity in PLC systems. On the contrary, the reliability of data transmission is subjected to several inhibiting factors as a result of the varying nature of the PLC channel. These inhibiting factors include noise, perturbation and disturbances. Contrary to the Additive White Gaussian noise (AWGN) model often assumed in several communication systems, this noise model fails to capture the attributes of noise encountered on the PLC channel. This is because periodic noise or random noise pulses injected by power electronic appliances on the network is a deviation from the AWGN. The nature of the noise is categorized as non-white non-Gaussian and unstable due to its impulsive attributes, thus, it is labeled as Non-additive White Gaussian Noise (NAWGN). These noise and disturbances results into long burst errors that corrupts signals being transmitted, thus, the PLC is labeled as a horrible or burst error channel. The e cient and optimal performance of a conventional linear receiver in the white Gaussian noise environment can therefore be made to drastically degrade in this NAWGN environment. Therefore, transmission reliability in such environment can be greatly enhanced if we know and exploit the knowledge of the channel's statistical attributes, thus, the need for developing statistical channel model based on empirical data. In this thesis, attention is focused on developing a recon gurable software de ned un-coded single-carrier and multicarrier PLC transceiver as a tool for realizing an optimized channel model for the narrowband PLC (NB-PLC) channel. First, a novel recon gurable software de ned un-coded single-carrier and multi-carrier PLC transceiver is developed for real-time NB-PLC transmission. The transceivers can be adapted to implement di erent waveforms for several real-time scenarios and performance evaluation. Due to the varying noise parameters obtained from country to country as a result of the dependence of noise impairment on mains voltages, topology of power line, place and time, the developed transceivers is capable of facilitating constant measurement campaigns to capture these varying noise parameters before statistical and mathematically inclined channel models are derived. Furthermore, the single-carrier (Binary Phase Shift Keying (BPSK), Di erential BPSK (DBPSK), Quadrature Phase Shift Keying (QPSK) and Di erential QPSK (DQPSK)) PLC transceiver system developed is used to facilitate a First-Order semi-hidden Fritchman Markov modeling (SHFMM) of the NB-PLC channel utilizing the e cient iterative Baum- Welch algorithm (BWA) for parameter estimation. The performance of each modulation scheme is evaluated in a mildly and heavily disturbed scenarios for both residential and laboratory site considered. The First-Order estimated error statistics of the realized First- Order SHFMM have been analytically validated in terms of performance metrics such as: log-likelihood ratio (LLR), error-free run distribution (EFRD), error probabilities, mean square error (MSE) and Chi-square ( 2) test. The reliability of the model results is also con rmed by an excellent match between the empirically obtained error sequence and the SHFMM regenerated error sequence as shown by the error-free run distribution plot. This thesis also reports a novel development of a low cost, low complexity Frequency-shift keying (FSK) - On-o keying (OOK) in-house hybrid PLC and VLC system. The functionality of this hybrid PLC-VLC transceiver system was ascertained at both residential and laboratory site at three di erent times of the day: morning, afternoon and evening. A First and Second-Order SHFMM of the hybrid system is realized. The error statistics of the realized First and Second-Order SHFMMs have been analytically validated in terms of LLR, EFRD, error probabilities, MSE and Chi-square ( 2). The Second-Order SHFMMs have also been analytically validated to be superior to the First-Order SHFMMs although at the expense of added computational complexity. The reliability of both First and Second-Order SHFMM results is con rmed by an excellent match between the empirical error sequences and SHFMM re-generated error sequences as shown by the EFRD plot. In addition, the multi-carrier (QPSK-OFDM, Di erential QPSK (DQPSK)-OFDM) and Di erential 8-PSK (D8PSK)-OFDM) PLC transceiver system developed is used to facilitate a First and Second-Order modeling of the NB-PLC system using the SHFMM and BWA for parameter estimation. The performance of each OFDM modulation scheme in evaluated and compared taking into consideration the mildly and heavily disturbed noise scenarios for the two measurement sites considered. The estimated error statistics of the realized SHFMMs have been analytically validated in terms of LLR, EFRD, error probabilities, MSE and Chi-square ( 2) test. The estimated Second-Order SHFMMs have been analytically validated to be outperform the First-Order SHFMMs although with added computational complexity. The reliability of the models is con rmed by an excellent match between the empirical data and SHFMM generated data as shown by the EFRD plot. The statistical models obtained using Baum-Welch to adjust the parameters of the adopted SHFMM are often locally maximized. To solve this problem, a novel Metropolis-Hastings algorithm, a Bayesian inference approach based on Markov Chain Monte Carlo (MCMC) is developed to optimize the parameters of the adopted SHFMM. The algorithm is used to optimize the model results obtained from the single-carrier and multi-carrier PLC systems as well as that of the hybrid PLC-VLC system. Consequently, as deduced from the results, the models obtained utilizing the novel Metropolis-Hastings algorithm are more precise, near optimal model with parameter sets that are closer to the global maxima. Generally, the model results obtained in this thesis are relevant in enhancing transmission reliability on the PLC channel through the use of the models to improve the adopted modulation schemes, create adaptive modulation techniques, develop and evaluate forward error correction (FEC) codes such as a concatenation of Reed-Solomon and Permutation codes and other robust codes suitable for exploiting and mitigating noise impairments encountered on the low voltage NB-PLC channel. Furthermore, the recon gurable software de ned NB-PLC transceiver test-bed developed can be utilized for future measurement campaign as well as adapted for multiple-input and multiple-output (MIMO) PLC applications.MT201

Classification and modeling of power line noise using machine learning techniques

A thesis submitted in ful lment of the requirements for the degree of Doctor of Philosophy in the School of Electrical and Information Engineering Faculty of Engineering and Built Environment June 2017The realization of robust, reliable and e cient data transmission have been the theme of recent research, most importantly in real channel such as the noisy, fading prone power line communication (PLC) channel. The focus is to exploit old techniques or create new techniques capable of improving the transmission reliability and also increasing the transmission capacity of the real communication channels. Multi-carrier modulation scheme such as Orthogonal Frequency Division Multiplexing (OFDM) utilizing conventional single-carrier modulation is developed to facilitate a robust data transmission, increasing transmission capacity (e cient bandwidth usage) and further reducing design complexity in PLC systems. On the contrary, the reliability of data transmission is subjected to several inhibiting factors as a result of the varying nature of the PLC channel. These inhibiting factors include noise, perturbation and disturbances. Contrary to the Additive White Gaussian noise (AWGN) model often assumed in several communication systems, this noise model fails to capture the attributes of noise encountered on the PLC channel. This is because periodic noise or random noise pulses injected by power electronic appliances on the network is a deviation from the AWGN. The nature of the noise is categorized as non-white non-Gaussian and unstable due to its impulsive attributes, thus, it is labeled as Non-additive White Gaussian Noise (NAWGN). These noise and disturbances results into long burst errors that corrupts signals being transmitted, thus, the PLC is labeled as a horrible or burst error channel. The e cient and optimal performance of a conventional linear receiver in the white Gaussian noise environment can therefore be made to drastically degrade in this NAWGN environment. Therefore, transmission reliability in such environment can be greatly enhanced if we know and exploit the knowledge of the channel's statistical attributes, thus, the need for developing statistical channel model based on empirical data. In this thesis, attention is focused on developing a recon gurable software de ned un-coded single-carrier and multicarrier PLC transceiver as a tool for realizing an optimized channel model for the narrowband PLC (NB-PLC) channel. First, a novel recon gurable software de ned un-coded single-carrier and multi-carrier PLC transceiver is developed for real-time NB-PLC transmission. The transceivers can be adapted to implement di erent waveforms for several real-time scenarios and performance evaluation. Due to the varying noise parameters obtained from country to country as a result of the dependence of noise impairment on mains voltages, topology of power line, place and time, the developed transceivers is capable of facilitating constant measurement campaigns to capture these varying noise parameters before statistical and mathematically inclined channel models are derived. Furthermore, the single-carrier (Binary Phase Shift Keying (BPSK), Di erential BPSK (DBPSK), Quadrature Phase Shift Keying (QPSK) and Di erential QPSK (DQPSK)) PLC transceiver system developed is used to facilitate a First-Order semi-hidden Fritchman Markov modeling (SHFMM) of the NB-PLC channel utilizing the e cient iterative Baum- Welch algorithm (BWA) for parameter estimation. The performance of each modulation scheme is evaluated in a mildly and heavily disturbed scenarios for both residential and laboratory site considered. The First-Order estimated error statistics of the realized First- Order SHFMM have been analytically validated in terms of performance metrics such as: log-likelihood ratio (LLR), error-free run distribution (EFRD), error probabilities, mean square error (MSE) and Chi-square ( 2) test. The reliability of the model results is also con rmed by an excellent match between the empirically obtained error sequence and the SHFMM regenerated error sequence as shown by the error-free run distribution plot. This thesis also reports a novel development of a low cost, low complexity Frequency-shift keying (FSK) - On-o keying (OOK) in-house hybrid PLC and VLC system. The functionality of this hybrid PLC-VLC transceiver system was ascertained at both residential and laboratory site at three di erent times of the day: morning, afternoon and evening. A First and Second-Order SHFMM of the hybrid system is realized. The error statistics of the realized First and Second-Order SHFMMs have been analytically validated in terms of LLR, EFRD, error probabilities, MSE and Chi-square ( 2). The Second-Order SHFMMs have also been analytically validated to be superior to the First-Order SHFMMs although at the expense of added computational complexity. The reliability of both First and Second-Order SHFMM results is con rmed by an excellent match between the empirical error sequences and SHFMM re-generated error sequences as shown by the EFRD plot. In addition, the multi-carrier (QPSK-OFDM, Di erential QPSK (DQPSK)-OFDM) and Di erential 8-PSK (D8PSK)-OFDM) PLC transceiver system developed is used to facilitate a First and Second-Order modeling of the NB-PLC system using the SHFMM and BWA for parameter estimation. The performance of each OFDM modulation scheme in evaluated and compared taking into consideration the mildly and heavily disturbed noise scenarios for the two measurement sites considered. The estimated error statistics of the realized SHFMMs have been analytically validated in terms of LLR, EFRD, error probabilities, MSE and Chi-square ( 2) test. The estimated Second-Order SHFMMs have been analytically validated to be outperform the First-Order SHFMMs although with added computational complexity. The reliability of the models is con rmed by an excellent match between the empirical data and SHFMM generated data as shown by the EFRD plot. The statistical models obtained using Baum-Welch to adjust the parameters of the adopted SHFMM are often locally maximized. To solve this problem, a novel Metropolis-Hastings algorithm, a Bayesian inference approach based on Markov Chain Monte Carlo (MCMC) is developed to optimize the parameters of the adopted SHFMM. The algorithm is used to optimize the model results obtained from the single-carrier and multi-carrier PLC systems as well as that of the hybrid PLC-VLC system. Consequently, as deduced from the results, the models obtained utilizing the novel Metropolis-Hastings algorithm are more precise, near optimal model with parameter sets that are closer to the global maxima. Generally, the model results obtained in this thesis are relevant in enhancing transmission reliability on the PLC channel through the use of the models to improve the adopted modulation schemes, create adaptive modulation techniques, develop and evaluate forward error correction (FEC) codes such as a concatenation of Reed-Solomon and Permutation codes and other robust codes suitable for exploiting and mitigating noise impairments encountered on the low voltage NB-PLC channel. Furthermore, the recon gurable software de ned NB-PLC transceiver test-bed developed can be utilized for future measurement campaign as well as adapted for multiple-input and multiple-output (MIMO) PLC applications.MT201

Adaptive Radiation in Mediterranean Cistus (Cistaceae)

lineage consists of 12 species primarily distributed in Mediterranean habitats and is herein subject to analysis. lineages), which display asymmetric characteristics: number of species (2 vs. 10), leaf morphologies (linear vs. linear to ovate), floral characteristics (small, three-sepalled vs. small to large, three- or five-sepalled flowers) and ecological attributes (low-land vs. low-land to mountain environments). A positive phenotype-environment correlation has been detected by historical reconstructions of morphological traits (leaf shape, leaf labdanum content and leaf pubescence). Ecological evidence indicates that modifications of leaf shape and size, coupled with differences in labdanum secretion and pubescence density, appear to be related to success of new species in different Mediterranean habitats.

3D Organization of Eukaryotic and Prokaryotic Genomes

There is a complex mutual interplay between three-dimensional (3D) genome organization and cellular activities in bacteria and eukaryotes. The aim of this thesis is to investigate such structure-function relationships. A main part of this thesis deals with the study of the three-dimensional genome organization using novel techniques for detecting genome-wide contacts using next-generation sequencing. These so called chromatin conformation capture-based methods, such as 5C and Hi-C, give deep insights into the architecture of the genome inside the nucleus, even on a small scale. We shed light on the question how the vastly increasing Hi-C data can generate new insights about the way the genome is organized in 3D. To this end, we first present the typical Hi-C data processing workflow to obtain Hi-C contact maps and show potential pitfalls in the interpretation of such contact maps using our own data pipeline and publicly available Hi-C data sets. Subsequently, we focus on approaches to modeling 3D genome organization based on contact maps. In this context, a computational tool was developed which interactively visualizes contact maps alongside complementary genomic data tracks. Inspired by machine learning with the help of probabilistic graphical models, we developed a tool that detects the compartmentalization structure within contact maps on multiple scales. In a further project, we propose and test one possible mechanism for the observed compartmentalization within contact maps of genomes across multiple species: Dynamic formation of loops within domains. In the context of 3D organization of bacterial chromosomes, we present the first direct evidence for global restructuring by long-range interactions of a DNA binding protein. Using Hi-C and live cell imaging of DNA loci, we show that the DNA binding protein Rok forms insulator-like complexes looping the B. subtilis genome over large distances. This biological mechanism agrees with our model based on dynamic formation of loops affecting domain formation in eukaryotic genomes. We further investigate the spatial segregation of the E. coli chromosome during cell division. In particular, we are interested in the positioning of the chromosomal replication origin region based on its interaction with the protein complex MukBEF. We tackle the problem using a combined approach of stochastic and polymer simulations. Last but not least, we develop a completely new methodology to analyze single molecule localization microscopy images based on topological data analysis. By using this new approach in the analysis of irradiated cells, we are able to show that the topology of repair foci can be categorized depending the distance to heterochromatin

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Bayesian Spatial Modeling of Complex and High Dimensional Data

The main objective of this dissertation is to apply Bayesian modeling to different complex and high-dimensional spatial data sets. I develop Bayesian hierarchical spatial models for both the observed location and the observation variable. Throughout this dissertation I execute the inference of the posterior distributions using Markov chain Monte Carlo by developing computational strategies that can reduce the computational cost. I start with a "high level" image analysis by modeling the pixels with a Gaussian process and the objects with a marked-point process. The proposed method is an automatic image segmentation and classification procedure which simultaneously detects the boundaries and classifies the objects in the image into one of the predetermined shape families. Next, I move my attention to the piecewise non-stationary Gaussian process models and their computational challenges for very large data sets. I simultaneously model the non-stationarity and reduce the computational cost by using the innovative technique of full-scale approximation. I successfully demonstrate the proposed reduction technique to the Total Ozone Matrix Spectrometer (TOMS) data. Furthermore, I extend the reduction method for the non-stationary Gaussian process models to a dynamic partition of the space by using a modified Treed Gaussian Model. This modification is based on the use of a non-stationary function and the full-scale approximation. The proposed model can deal with piecewise non-stationary geostatistical data with unknown partitions. Finally, I apply the method to the TOMS data to explore the non-stationary nature of the data

Modeling biomolecules: interactions, forces and free energies

La biología ha sido tradicionalmente una ciencia cualitativa. El principal problema que presenta es que trata con sistemas muy complejos, mucho más que las moléculas de las que se ocupa la química, o que muchos sistemas físicos. Sin embargo, en los últimos años, hemos sido testigos de un desarrollo enorme hacia planteamientos cuantitativos para resolver problemas biológicos, impulsado principalmente por el desarrollo de diversas técnicas avanzadas en biofísica, o por la emergencia de las herramientas computacionales. En particular, en biofísica computacional, dado un determinado problema a estudiar, la estrategia es proponer un modelo que describa el comportamiento de nuestro sistema y realizar simulaciones numéricas sobre este modelo. Este planteamiento presenta una dificultad principal que es la elección de la escala a la cual realizamos nuestro modelo. Es necesario llegar a un compromiso entre el nivel de detalle y la capacidad computacional de que disponemos. Así, modelos muy detallados son capaces de proporcionar información de gran resolución, sin embargo sólo para sistemas moleculares de tamaño limitado, con propiedades que se manifiesten a escalas temporales cortas. Si necesitamos tratar con sistemas de mayor tamaño, o nos interesan propiedades que se manifiestan en escalas temporales mayores, es necesario identificar cuáles son los grados de libertad relevantes para nuestro sistema y despreciar el resto. Aparte de este problema, el siguiente reto que se nos plantea es transformar todos los datos numéricos producidos en información relevante que pueda responder de manera objetiva a las preguntas que nos planteamos. Para ello, debemos disponer de métodos de análisis lo bastante robustos como para transformar la información en bruto producida en nuestras simulaciones, en conocimiento directo de una manera no sesgada. La presente Tesis Doctoral se enmarca en este ámbito, ya que estudiaremos tres problemas biológicos diferentes haciendo énfasis en la fase de modelización de nuestro sistema, así como en el empleo de técnicas de análisis avanzadas para comprenderlo. En la primera parte, nos centramos en el análisis de la dinámica de proteínas, enfatizando las distintas descripciones que pueden usarse para comprender su paisaje de energía libre. Para ello escogemos un sistema relativamente simple, una proteína modelo coarse-grained a la cual aplicamos una fuerza constante para promover su desplegamiento. Realizaremos simulaciones numéricas en este sistema y nos plantearemos cuál es la mejor manera de obtener una descripción fiel de su espacio configuracional así como de su mecanismo de desplegamiento. Para ello emplearemos dos métodos distintos. Primero, proyectaremos su paisaje de energía libre –de gran dimensión- sobre distintos parámetros de orden, obteniendo representaciones unidimensionales. Éstas proporcionarán una visión globalmente correcta del sistema, sin embargo fallarán en la descripción adecuada de su mecanismo de desnaturalización. Por otra parte, emplearemos modelos de Markov para representar el paisaje de energía libre. Estos revelarán un espacio configuracional más complejo que el previsto anteriormente, con varios intermediarios que tendrán un papel relevante, especialmente para comprender el mecanismo de desplegamiento. En la segunda parte de la Tesis Doctoral, mostramos el estudio de un modelo de DNA al nivel del par de bases, el modelo de Peyrard-Bishop-Dauxois. En particular, extenderemos este modelo para introducir la interacción proteína-DNA. Proponiendo un método de análisis adecuado basado en modelos de Markov, podremos emplear este modelo para analizar secuencias de promotores, relacionando los estados que encontramos en la dinámica del sistema con sitios de unión proteína-DNA. Este modelo lo emplearemos para el análisis de nueve secuencias de promotores de una cianobacteria en particular. Nos centraremos en la identificación del sitio de inicio de la transcripción (TSS), región donde se une la RNA polimerasa para iniciar este proceso. En cada uno de los promotores, gracias al modelo somos capaces de identificar esta región como un estado de relevancia en la dinámica, con tendencia a que la partícula se una, formando una burbuja. Asimismo, gracias al método de análisis, cuantificamos estos estados, proporcionando magnitudes estadísticas que podemos relacionar con el conocimiento biológica acerca de estos promotores. La tercera parte está dedicada a los experimentos de molécula individual. Presentamos una colaboración experimental en la cual analizamos experimentos de disociación mecánica de dos complejos proteína:proteína. Nuestro objetivo es proporcionar una visión adecuada del paisaje de energía libre que gobierna este proceso. Para ello proponemos un método que permite recuperar la barrera de energía libre así como la energía libre de disociación para complejos biológicos. En particular, emplearemos este método para analizar experimentos de espetroscopía de fuerza, permitiendo obtener estas magnitudes y discutirlas en el contexto de la biología del sistema. Asimismo, proponemos un modelo físico para este tipo de experimentos, sobre el cual realizamos simulaciones numéricas que analizamos con el mismo método, con objeto de validarlo y respaldar su empleo