Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial systems. Extensive research has been carried out on FDI for one dimensional (1-D) systems, where variables vary only with time. The existing FDI strategies are mainly focussed on 1-D systems and can generally be classified as model based and process history data based methods. In many industrial systems, the state variables change with space and time (e.g., sheet forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems represent a great challenge in both theoretical development and applications and only limited research results are available. In this thesis, model based fault detection strategies for 2-D systems have been investigated based on the F-M and the Roesser models. A dead-beat observer based fault detection has been available for the F-M model. In this work, an observer based fault detection strategy is investigated for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique, a dead-beat observer is developed and the state estimate from the observer is then input to a residual generator to monitor occurrence of faults. An enhanced realization technique is combined to achieve efficient fault detection with reduced computations. Simulation results indicate that the proposed method is effective in detecting faults for systems without disturbances as well as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems but strict conditions are required in order for an observer and a residual generator to exist. These strict conditions may not be satisfied for some systems. The effect of process noises are also not considered in the observer based fault detection approaches for 2-D systems. To overcome the disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation error variances. Based on the state estimate from the Kalman filter, a residual is generated reflecting fault information. A model is formulated for the relation of the residual with faults over a moving evaluation window. Simulations are performed on two F-M models and results indicate that faults can be detected effectively and efficiently using the Kalman filter based fault detection. In the observer based and Kalman filter based fault detection approaches, the residual signals are used to determine whether a fault occurs. For systems with complicated fault information and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component analysis (DPCA). Based on historical data, the reference residuals are first generated using either the observer or the Kalman filter based approach. Based on the residual time-lagged data matrices for the reference data, the principal components are calculated and the threshold value obtained. In online applications, the T2 value of the residual signals are compared with the threshold value to determine fault occurrence. Simulation results show that applying DPCA to evaluation of 2-D residuals is effective.

Thesis advisor: Michael J. Naughton / In this dissertation I present studies of plasmonic interactions in different coupling regimes, from zero to strong coupling and approaching ultrastrong coupling. Different physics are manifest in each regime, with different possible applications. The first project uses finite element electromagnetic simulations to model plasmonic waveguides that couple near field light into the far-field for sub-diffraction limited microscopy. Wavelength/32 resolution is shown by minimizing coupling between adjacent waveguiding nanowires, with minimal attenuation over a few microns. The next two projects, by contrast, seek to maximize coupling between plasmons and excitons into the strong coupling regime where the optoelectronic properties are modified and quantum coherent phenomena may be observed. Strong exciton–plasmon coupling in MoS2 is shown experimentally at room temperature and found to be a general phenomenon in other semiconducting transition metal dichalcogenides using transfer matrix modeling. A semiclassical oscillator model is fit to the experimental data to discover coherent hybridization between the ground and first excited states of MoS2. Enhanced coupling is found at the third excitonic transition, approaching the ultrastrong coupling regime where exotic properties are predicted to emerge, such as ground state virtual photons. Our strong coupling studies motivate further studies of the TMDCs as a platform for coherent quantum physics with possible applications in quantum computing and cryptography. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Cette thèse porte sur le développement et l'application en physique statistique d'un nouveau paradigme pour les méthodes sans rejet de Monte-Carlo par chaînes de Markov irréversibles, grâce à la mise en œuvre du filtre factorisé de Metropolis et du concept de lifting. Les deux premiers chapitres présentent la méthode de Monte-Carlo et ses différentes applications à des problèmes de physique statistique. Une des principales limites de ces méthodes se rencontre dans le voisinage des transitions de phase, où des phénomènes de ralentissement dynamique entravent fortement la thermalisation des systèmes. Le troisième chapitre présente la nouvelle classe des algorithmes de Metropolis factorisés et irréversibles. Se fondant sur le concept de lifting des chaînes de Markov, le filtre factorisé de Metropolis permet de décomposer un potentiel multidimensionnel en plusieurs autres unidimensionnels. De là, il est possible de définir un algorithme sans rejet de Monte-Carlo par chaînes de Markov irréversibles. Le quatrième chapitre examine les performances de ce nouvel algorithme dans une grande variété de systèmes. Des accélérations du temps de thermalisation sont observées dans des systèmes bidimensionnels de particules molles, des systèmes bidimensionnels de spins XY ferromagnétiques et des systèmes tridimensionnels de verres de spins XY. Finalement, une réduction importante du ralentissement critique est exposée pour un système tridimensionnel de spins Heisenberg ferromagnétiques. / This thesis deals with the development and application in statistical physics of a general framework for irreversible and rejection-free Markov-chain Monte Carlo methods, through the implementation of the factorized Metropolis filter and the lifting concept. The first two chapters present the Markov-chain Monte Carlo method and its different implementations in statistical physics. One of the main limitations of Markov-chain Monte Carlo methods arises around phase transitions, where phenomena of dynamical slowing down greatly impede the thermalization of the system. The third chapter introduces the new class of irreversible factorized Metropolis algorithms. Building on the concept of lifting of Markov chains, the factorized Metropolis filter allows to decompose a multidimensional potential into several unidimensional ones. From there, it is possible to define a rejection-free and completely irreversible Markov-chain Monte Carlo algorithm. The fourth chapter reviews the performance of the irreversible factorized algorithm in a wide variety of systems. Clear accelerations of the thermalization time are observed in bidimensional soft-particle systems, bidimensional ferromagnetic XY spin systems and three-dimensional XY spin glasses. Finally, an important reduction of the critical slowing down is exhibited in three-dimensional ferromagnetic Heisenberg spin systems.

It is well known from Mermin-Wagner theorem that a two dimensional(2D) system with continuous symmetry can have no long-range order at finite temperature. However such systems can undergo a transition from a low temperature phase with quasi-long range order to a disordered phase at high temperatures. This is known as Berezinskii Kosterlitz Thouless (BKT) transition. The BKT transition is characterized by the presence of bound vortex pairs at low temperature which dissociate into free vortices above the critical temperature and has been observed in thin superconducting films, 2D superfluids, 2D liquid crystals etc. In this thesis work, we have used resistance/current fluctuations (low frequency/shotnoise) as a probe to investigate the BKT transition in different 2D systems. This work can be divided into three parts: In the first part, we probe the ground state of interacting electrons in 2D in the presence of disorder. We show that at low enough temperatures (~ 270mK),the conductivity tends to zero at a nonzero carrier density with a BKT-like transition. Our experiments with many two dimensional electron systems in GaAs/AlGaAs heterostructures suggest that the charge transport at low carrier densities is due to the melting of an underlying ordered ground state through proliferation of topological defects. Independent measurement of low-frequency conductivity noise supports this scenario. In the second part, we probe the presence of long-range correlations in phase fluctuations by analyzing the higher-order spectrum of resistance fluctuations in ultrathin NbN superconducting films. The non-Gaussian component of resistance fluctuations is found to be sensitive to film thickness close to the transition, which allows us to distinguish between mean field and BKT type superconducting transitions. The extent of non-Gaussianity was found to be bounded by the BKT and mean field transition temperatures and depends strongly on the roughness and structural inhomogeneity of the superconducting films. In the final part of the thesis, we explore the transport mechanism in disordered 2D superconductors using shot noise. The resistivity shows an activated transport in the patterned ultrathin films of NbN at low temperatures signifying the presence of large scale inhomogeneities in the sample. The measurement of current fluctuations yield a giant excess noise at low temperatures which eventually decreases below the measurement background at a temperature corresponding to the normal state of the original sample(before patterning). We attribute the enhancement in the shot noise to a possible occurrence of multiple Andreev reflections occurring in a network of SNS(superconductor-normal-superconductor) junctions formed due to the interplay of disorder and superconducting fluctuations.