Natural categories seem to be comprised of clustered stimuli that contain a myriad of correlated features; birds, for example, tend to fly, have wings, lay eggs, and make nests. Nonetheless, the evidence that people use these correlations during intentional category learning is overwhelmingly negative (Murphy, 2002). People do, however, show evidence of correlational sensitivity during other types of category learning tasks (e.g., feature prediction). The usual explanation is that intentional category learning tasks promote rule use, which discards the correlated feature information; whereas, other types of category learning tasks promote exemplar storage, which preserves correlated feature information. However, all of the intentional category learning tasks employed to examine correlational sensitivity to date have only used deterministic mappings of stimuli to categories (i.e., each stimulus belongs to only one category). The current thesis is concerned primarily with the effects introducing the probabilistic assignment of stimuli to categories on the acquisition of different types of correlational knowledge. If correlational knowledge depends on whether or not people selectively attend to the correlation then probabilistic reinforcement, which is predicted to increase attention shifting (Kruschke & Johansen, 1999), should lead to increased correlational sensitivity. The first paper of this thesis confirms that selective attention provides a way to explain the presence or absence of correlational knowledge in different tasks. However, selective attention models have been unable to account for tasks in which people use the correlation between a non-relevant cue and regions of the category space to switch between the application of multiple rules. This phenomenon, known as knowledge partitioning, is explored in the second paper of this thesis. This thesis also extends the empirical implications of the first two papers to existing research (see included paper 3) and also provides recommendations of how utilize this conceptualization of knowledge for practitioners in the applied setting (see included paper 4). Finally, in addition to increasing attention shifting, probabilistic feedback is also assumed to result in an attenuation of learning over time (Kruschke & Johansen, 1999); the fifth paper in this thesis provides empirical confirmation that people attenuate learning in response to unavoidable error.

It has been shown that neutrons emitted from the same 252Cf fission event are preferentially detected within small angles of each other and at angles around 180 degrees. The distribution of this angular anisotropy is dependent upon the nuclide emitting the neutrons. Coincident neutrons can be detected from a shielded source, so a study of the angular anisotropy between coincident neutrons is useful for this context. This could allow for the dynamic determination of the ratio of the rate of (alpha,n) neutron production to the spontaneous fission neutron production (designated alpha) used in neutron coincidence counting for safeguards. This could also be used to identify neutron emitting isotopes in a homeland security application. An angular frequency distribution for coincident neutrons was produced via experiments using an array of cylindrical liquid scintillators and a 252Cf source. It was found, in accordance with previous experiments, that the angular frequency distribution peaks at small angles and at angles around 180 degrees. A Monte Carlo, physics-based simulation program was created to simulate the distribution of angles between neutrons from the same fission event from 252Cf and 240Pu sources. The resulting distributions were clearly distinguishable from each other. The code was benchmarked to measured results from a 252Cf source at Lawrence Livermore National Laboratory. Knowledge of the unique angular distributions of coincident neutrons from various fissioning sources is useful for identification and verification purposes. Another practical application of angular anisotropy information for coincident neutrons from a given source is determining the ratio of the (alpha,n) to spontaneous fission rates for a source undergoing neutron coincidence counting. The utility of this was verified by using measurements made by faculty and students of the University of Michigan Nuclear Engineering Department for a MOX fuel pin at the Joint Research Center in Ispra, Italy. Good agreement between the predicted and declared values for alpha was found.

Thermal fluctuations and disorder strongly influence the behaviour of hightemperature superconductors. In particular the vortices play a key role in determining their properties. In this thesis the main focus lies on phase transitions, both in ultra-thin films and in three-dimensional systems, which are driven by vortex fluctuations. The last paper concerns the influence of antiferromagnetism on superconductivity in a simple model. A brief review of these topics is given in the introductory part. The main results are: The phase transition in ultra-thin superconducting/superfluid films is studied within the two-dimensional Coulomb gas model, which is known to have a Berezinskii-Kosterlitz-Thouless transition at low vortex densities. We construct the phase diagram from grand canonical Monte Carlo simulations on a continuum, without any restrictions on the vortex density. The dynamical universality classes for vortices in superconductors in zero magnetic field are studied by means of Monte Carlo simulations, with particular attention to the role of screening of the vortex interaction. We construct a formula for the k = 0 helicity modulus directly in terms of the vortex line fluctuations, which can serve as a useful way to detect superconducting coherence in model calculations. A method for simulating vortex lines on a continuum is developed, and used to study the melting of the Abrikosov vortex lattice. We study the critical dynamics for vortices in the presence of columnar defects. The linear resistivity and current-voltage characteristics are calculated in Monte Carlo simulations, and the critical behaviour extracted using finite size scaling. We reconsider the scaling properties as the magnetic field is tilted away from the direction of the columns. The influence of antiferromagnetic correlations on the superconducting properties is studied in a simplified lattice fermion model for superconductivity in the presence of an antiferromagnetic background. We find that the superconducting critical temperature is enhanced by antiferromagnetic order, and that a gap with dx2-y2-wave symmetry is the most stable. / QC 20100512

The quest for obtaining higher Tc superconductivity led to the discovery of cuprates about 20 years ago. Since then, they continue to puzzle the scientific community with their bizarre properties like non-BCS superconductivity, pseudo gap, Fermi arcs, linear T resistivity etc. Since these materials show unusually high Tc, a novel mechanism is at play and strong correlations are believed to play an important role. The theme of this thesis work is to study physics of such strongly correlated systems in two dimensions at T = 0 along with development of new theoretical tools necessary for the study. The focus of the thesis is on the ground state studies of strongly correlated models like t-J and Hubbard models using variational Monte Carlo (VMC) and renormalized mean field theory (RMFT). The general method is to propose a variational wave function, motivated by the physics ideas, to be a candidate ground state of the system. Methods to efficiently evaluate the ground state energy and minimizing it with respect to the variational parameters are developed in this work. Antiferromagnetism-superconductivity competition and electron-hole asymmetry in the extended t-J model is investigated. The main result of this work is that increasing the magnitude of the next neighbor hopping (t') on hole doped side strengthen superconductivity while it stabilizes antiferromagnetism on the electron doped side. It is also shown that it is possible to characterize the T = 0 phase diagram with just one parameter called as Fermi Surface Convexity Parameter (FSCP). Next, the possibility of phase separation in the t-J model on a square lattice is investigated using local RMFT technique. It is found that for certain doping, the system phase separates into regions with antiferromagnetic and superconducting orders. Next, the role played by crystalline anisotropy of orthorhombic YBCO cuprates on their properties is examined using anisotropic tx-ty-J model and this ground state study suggests that the anisotropies seen in their properties are plausible solely due to the crystalline anisotropy. A new general method to study strongly correlated systems with singlet ground states is developed and tested in this thesis work. The last part of the thesis explores the possibility of high Tc superconductivity in graphene which is a intermediate coupling resonating valence bond (RVB) system. It is found that undoped graphene is not a superconductor, consistent with the experiments. On doping, the ground state of graphene is found to be a superconductor with “d+id” symmetry whose strength shows a dome as a function of doping which is reminiscent of RVB physics.

Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.

This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

Analog-to-digital converters are inevitable in the modern communication systems and there is always a need for the design of low-power converters. There are different A/D architectures to achieve medium resolution at medium speeds and among all those Cyclic/Algorithmic structure stands out due to its low hardware complexity and less die area costs. This thesis aims at discussing the ongoing trend in Cyclic/Algorithmic ADCs and their functionality. Some design techniques are studied on how to implement low power high resolution A/D converters. Also, non-ideal effects of SC implementation for Cyclic A/D converters are explored. Two kinds of Cyclic A/D architectures are compared. One is the conventional Cyclic ADC with RSD technique and the other is Cyclic ADC with Correlated Level Shift (CLS) technique. This ADC is a part of IMST Design + Systems International GmbH project work and was designed and simulated at IMST GmbH. This thesis presents the design of a 12-bit, 1 Msps, Cyclic/Algorithmic Analog-to-Digital Converter (ADC) using the “Redundant Signed Digit (RSD)” algorithm or 1.5-bit/stage architecture with switched-capacitor (SC) implementation. The design was carried out in 130nm CMOS process with a 1.5 V power supply. This ADC dissipates a power of 1.6  mW when run at full speed and works for full-scale input dynamic range. The op-amp used in the Cyclic ADC is a two-stage folded cascode structure with Class A output stage. This op-amp in typical corner dissipates 631 uW power at 1.5 V power supply and achieves a gain of 77 dB with a phase margin of 64° and a GBW of 54 MHz at 2 pF load.

This thesis considers various strongly correlated quantum phases in solid state and cold atom spin systems. In the first part we focus on phases emerging in multi-orbital materials. We study even-parity spin-triplet superconductivity originating from Hund's coupling between t2g orbitals and investigate the effect of spin-orbit interaction on spin-triplet and spin-singlet pairing. Various aspects of the pairing state are discussed against the backdrop of the spin-triplet superconductor Sr2RuO4. Motivated by the remarkable phenomena observed in the bilayer compound Sr3Ru2O7, which point to the formation of an electronic nematic phase in the presence of critical fluctuations, we investigate how such a broken symmetry state emerges from electronic interactions. Since the broken x-y symmetry is revealed experimentally by applying a small in-plane magnetic field component, we examine nematic phases in a bilayer system and the role of the in-plane magnetic field using a phenomenological approach. In addition, we propose a microscopic mechanism for nematic phase formation specific to Sr3Ru2O7. The model is based on a realistic multi-orbital band structure and local and nearest neighbour interactions. Considering all t2g-orbital derived bands on an equal footing, we find a nematic quantum critical point and a nearby meta-nematic transition in the phase diagram. This finding harbours important implications for the phenomena observed in Sr3Ru2O7. The second part is devoted to the study of the anisotropic bilinear biquadratic spin-1 Heisenberg model, where the existence of an unusual direct phase transition between a spin-nematic phase and a dimerized valence bond solid phase in the quasi-1D limit was conjectured based on Quantum Monte Carlo simulations. We establish the quasi-1D phase diagram using a large-N Schwinger boson approach and show that the phase transition is largely conventional except possibly at two particular points. We further discuss how to realize and to detect such phases in an optical lattice.

Modern societies increasingly depend on the reliable functioning of urban infrastructure systems in the aftermath of natural disasters such as hurricane and earthquake events. Apart from a sizable capital for maintenance and expansion, the reliable performance of infrastructure systems under extreme hazards also requires strategic planning and effective resource assignment. Hence, efficient system reliability and risk assessment methods are needed to provide insights to system stakeholders to understand infrastructure performance under different hazard scenarios and accordingly make informed decisions in response to them. Moreover, efficient assignment of limited financial and human resources for maintenance and retrofit actions requires new methods to identify critical system components under extreme events. Infrastructure systems such as highway bridge networks are spatially distributed systems with many linked components. Therefore, network models describing them as mathematical graphs with nodes and links naturally apply to study their performance. Owing to their complex topology, general system reliability methods are ineffective to evaluate the reliability of large infrastructure systems. This research develops computationally efficient methods such as a modified Markov Chain Monte Carlo simulations algorithm for network reliability, and proposes a network reliability framework (BRAN: Bridge Reliability Assessment in Networks) that is applicable to large and complex highway bridge systems. Since the response of system components to hazard scenario events are often correlated, the BRAN framework enables accounting for correlated component failure probabilities stemming from different correlation sources. Failure correlations from non-hazard sources are particularly emphasized, as they potentially have a significant impact on network reliability estimates, and yet they have often been ignored or only partially considered in the literature of infrastructure system reliability. The developed network reliability framework is also used for probabilistic risk assessment, where network reliability is assigned as the network performance metric. Risk analysis studies may require prohibitively large number of simulations for large and complex infrastructure systems, as they involve evaluating the network reliability for multiple hazard scenarios. This thesis addresses this challenge by developing network surrogate models by statistical learning tools such as random forests. The surrogate models can replace network reliability simulations in a risk analysis framework, and significantly reduce computation times. Therefore, the proposed approach provides an alternative to the established methods to enhance the computational efficiency of risk assessments, by developing a surrogate model of the complex system at hand rather than reducing the number of analyzed hazard scenarios by either hazard consistent scenario generation or importance sampling. Nevertheless, the application of surrogate models can be combined with scenario reduction methods to improve even further the analysis efficiency. To address the problem of prioritizing system components for maintenance and retrofit actions, two advanced metrics are developed in this research to rank the criticality of system components. Both developed metrics combine system component fragilities with the topological characteristics of the network, and provide rankings which are either conditioned on specific hazard scenarios or probabilistic, based on the preference of infrastructure system stakeholders. Nevertheless, they both offer enhanced efficiency and practical applicability compared to the existing methods. The developed frameworks for network reliability evaluation, risk assessment, and component prioritization are intended to address important gaps in the state-of-the-art management and planning for infrastructure systems under natural hazards. Their application can enhance public safety by informing the decision making process for expansion, maintenance, and retrofit actions for infrastructure systems.

Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.