This thesis descibes a theoretical study of nonlinear self-focusing as applied to the metrology of the nonlinear optical parameters of a medium. It also studies the phe- nomenon of optical power limiting which utilizes self-focusing e ects. As an analytical tool, a mode decomposition method which uses an orthogonal and complete set of Gaussian-Laguerre modes as a basis set is used to treat these problems. Nonlinear media both in the thin and thick limits are investigated. For thin media, a closed form expression is derived which describes the optical eld of an initally Gaussian beam that is perturbed by a thin nonlinear material which exhibits nonlinear absorption as well as nonlinear refraction. This result is valid for any regime of nonlinearity in the thin medium approximation. Thick media are treated using a numerical extension of the Gaussian-Laguerre Mode Decomposition technique. Spatial scanning techniques such as the Z-scan that rely on self-focusing e ects and that are used to measure the nonlinear optical parameters of a material are studied in detail. Optical limiting in both thick and thin media is also investigated.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / This paper proposes a new measure of core inflation called systematic core and makes a comparative evaluation with conventional cores used by the Central Bank of Brazil. To estimate the systematic core is proposed in this paper used the method of decomposition empirical methods, which is able to separate noise data by spectral decomposition and partial reconstruction of the series of inflation. The evaluation and comparison of the cores of inflation are performed by testing econometric predictions outside the sample. The empirical results show that conventional cores used by the Central Bank does not contribute to forecast inflation out of sample and not have all the desirable statistical properties for which a nucleus. Already the new measure of core obtained in this work contributed to predict inflation out of sample and answered the statistical properties of non-biased, attractor of inflation and weakly exogenous, having therefore the characteristics required for a measure to be useful to policy objectives monetary. / Este trabalho propÃe uma nova medida de nÃcleo da inflaÃÃo denominada nÃcleo sistemÃtico e faz uma avaliaÃÃo comparativa com os nÃcleos convencionais utilizados pelo Banco Central do Brasil. Para estimar o nÃcleo sistemÃtico proposto neste trabalho à utilizado o mÃtodo de decomposiÃÃo em modos empÃricos, que à capaz de separar ruÃdo dos dados atravÃs da decomposiÃÃo espectral e reconstruÃÃo parcial da sÃrie de inflaÃÃo. A avaliaÃÃo e comparaÃÃo dos nÃcleos da inflaÃÃo sÃo realizadas por meio de testes economÃtricos e previsÃes fora da amostra. Os resultados empÃricos apontam que os nÃcleos convencionais utilizados pelo Banco Central nÃo contribuem para prever a inflaÃÃo fora da amostra e nÃo possuem todas as propriedades estatÃsticas desejÃveis que para um nÃcleo. Jà a nova medida de nÃcleo obtida neste trabalho contribuiu para prever a inflaÃÃo fora da amostra e atendeu as propriedades estatÃsticas de ausÃncia de viÃs, atrator da inflaÃÃo e fracamente exÃgeno, possuindo, portanto, as caracterÃsticas exigidas para uma medida ser Ãtil aos objetivos da polÃtica monetÃria.

Detonation is a supersonic mode of combustion that is modeled by a system of conservation laws of compressible fluid mechanics coupled with the equations describing thermodynamic and chemical properties of the fluid. Mathematically, these governing equations admit steady-state travelling-wave solutions consisting of a leading shock wave followed by a reaction zone. However, such solutions are often unstable to perturbations and rarely observed in laboratory experiments. The goal of this work is to study the stability of travelling-wave solutions of detonation models by the following novel approach. We linearize the governing equations about a base travelling-wave solution and solve the resultant linearized problem using high-order numerical methods. The results of these computations are postprocessed using dynamic mode decomposition to extract growth rates and frequencies of the perturbations and predict stability of travelling-wave solutions to infinitesimal perturbations. We apply this approach to two models based on the reactive Euler equations for perfect gases. For the first model with a one-step reaction mechanism, we find agreement of our results with the results of normal-mode analysis. For the second model with a two-step mechanism, we find that both types of admissible travelling-wave solutions exhibit the same stability spectra. Then we investigate the Fickett’s detonation analogue coupled with a particular reaction-rate expression. In addition to the linear stability analysis of this model, we demonstrate that it exhibits rich nonlinear dynamics with multiple bifurcations and chaotic behavior.

A research-scale solid-fuel ramjet test article has been developed to study the secondary combustion zone of solid fuel ramjets. Tests were performed at a constant core air mass flowrate of 0.77 kg/s with 0%, 15%, and 30% bypass ratios. The propulsive performance analysis results indicate that the 0% bypass case had the highest regression rate and fuel mass flowrate. The regression rate and fuel mass flowrate of fuel without carbon black was the lowest. The specific impulse with air mass flowrate included was highest for the 0% bypass case reaching 130 s and lowest for the 30% bypass case reaching 110 s. For specific impulse with air mass flowrate excluded, the 30% bypass case achieved 2,800 s while the 0% bypass case achieved 1,800 s. The characteristic velocity was greatest for 0% bypass reaching 1,025 m/s and lowest for 30% bypass reaching 900 m/s. The combustion efficiency was highest for the 15% bypass case with carbon black addition approaching 0.82. 50 kHz and 75 kHz CH* chemiluminescence imaging was performed. Analyzing thin slivers of the images over 40,001 frames with frequency-domain techniques showed that most of the high amplitude content occurred below 1-5kHz with small peaks near 20 kHz and 30 kHz. Dynamic mode decomposition (DMD) was performed on sets of 10,001 spatially-calibrated images and their corresponding uncalibrated, uncropped images. Most of the tests exhibited low-frequency axial pumping, transverse modes, and other mode shapes indicative of the secondary injection. The prominence of transverse and other jet-related modes over axial modes appeared to be related to increasing bypass ratio. High-frequency axial modes also appeared in a case thought to have high core-flow momentum that did not appear at these high frequencies for other cases. The DMD modes for 0% bypass were indiscernible due to high soot content. Most of the modes corresponding to the calibrated images also appeared in the uncalibrated images, however, with different mode amplitude rankings. PIV was performed at 5 kHz for one test at 15% bypass. The instantaneous vector fields for these tests displayed local velocities up to 600 m/s. The mean images showed velocities up to 250 m/s. The two-dimensional turbulent kinetic energies reached 200 m2/s2 in several regions throughout the flowfield. The turbulence intensity exceeded 0.20 near the bottom of the flowfield.

We examine the related nature of two identification algorithms, subspace identification (SID) and Dynamic Mode Decomposition (DMD), and their correctness properties over a broad range of problems. This investigation begins by noting the strong relationship between the two algorithms, both drawing significantly on the pseudoinverse calculation using singular value decomposition, and ultimately revealing that DMD can be viewed as a substep of SID. We then perform extensive computational studies, characterizing the performance of SID on problems of various model orders and noise levels. Specifically, we generate 10,000 random systems for each model order and noise level, calculating the average identification error for each case, and then repeat the entire experiment to ensure the results are, in fact, consistent. The results both quantify the intrinsic algorithmic error at zero-noise, monotonically increasing with model complexity, as well as demonstrate an asymptotically linear degradation to noise intensity, at least for the range under study. Finally, we close by demonstrating DMD's ability to recover system matrices, because its access to full state measurements makes them identifiable. SID, on the other hand, can't possibly hope to recover the original system matrices, due to their fundamental unidentifiability from input-output data. This is true even when SID delivers excellent performance identifying a correct set of equivalent system matrices.

High-cycle thermal fatigue arising from turbulent mixing of non-isothermal flows is a key issue associated with the life management and extension of nuclear power plants. The induced thermal loads and damage are not fully understood yet. With the aim of acquiring extensive data sets for the validation of codes modeling thermal mixing at reactor conditions, thermocouples recorded temperature time series at the inner surface of a vertical annular volume where turbulent mixing occurred. There, a stream at either 333 K or 423 K flowed upwards and mixed with two streams at 549 K. Pressure was set at 72E5 Pa. The annular volume was formed between two coaxial stainless-steel tubes. Since the thermocouples could only cover limited areas of the mixing region, the inner tube to which they were soldered was lifted, lowered, and rotated around its axis, to extend the measurement region both axially and azimuthally. Trends, which stemmed from the variation of the experimental boundary conditions over time, were subtracted from the inner-surface temperature time series collected. An estimator assessing intensity and inhomogeneity of the mixing process in the annulus was also computed. In addition, a frequency analysis of the detrended inner-surface temperature time series was performed. In the cases examined, frequencies between 0.03 Hz and 0.10 Hz were detected in the subregion where mixing inhomogeneity peaked. The uncertainty affecting such measurements was then estimated. Furthermore, a preliminary assessment of the radial heat flux at the inner surface was conducted. / <p>QC 20161116</p>

No description available.

Data-driven intelligent transportation systems (ITS) are increasingly playing a critical role in improving the efficiency of the existing transportation network and addressing traffic challenges in large cities, such as safety and road congestion. This dissertation employs data dimensionality reduction, reinforcement learning, and discrete outcome models to improve traffic flow and transportation safety. First, we propose a novel data-driven technique based on Koopman operator theory and dynamic mode decomposition (DMD) to address the complex nonlinear dynamics of signalized intersections. This approach not only provides a better understanding of intersection behavior but also offers faster computation times, making it a valuable tool for system identification and controller design. It represents a significant step towards more efficient and effective traffic management solutions. Second, we propose an innovative phase-switching approach for traffic light control using deep reinforcement learning, enhancing the efficiency of signalized intersections. The novel reward function, based on speed, waiting time, deceleration, and time to collision (TTC) for each vehicle, maximizes traffic flow and safety through real-time optimization. Finally, we introduce a mixed spline indicator pooled model, an approach for multivariate crash severity prediction, addressing the limitations of previous models by capturing temporal instability. It carefully incorporates additional independent variables to measure parameter slope changes over time, enhancing data fit and predictive accuracy. The developed models are estimated and validated using data from the Central Florida region.

Unsteady flowfields are integral to high-speed applications, demanding precise modelling to characterize their unsteady features accurately. The simulation of unsteady supersonic and hypersonic flows is inherently computationally expensive, requiring a highly refined mesh to capture these unsteady effects. While anisotropic metric-based adaptive mesh refinement has proven effective in achieving accuracy with much less complexity, current algorithms are primarily tailored for steady flow fields. This thesis presents a novel approach to address the challenges of anisotropic grid adaptation of unsteady flows by leveraging a data-driven technique called Dynamic Mode Decomposition (DMD). DMD has proven to be a powerful tool to model complex nonlinear flows, given its links to the Koopman operator, and also its easy mathematical implementation. This research proposes the integration of DMD into the process of anisotropic grid adaptation to dynamically adjust the mesh in response to evolving flow features. The effectiveness of the proposed approach is demonstrated through numerical experiments on representative unsteady flow configurations, such as a cylinder in a subsonic flow and a cylinder in a supersonic channel flow. Results indicate that the incorporation of DMD enables an accurate representation of unsteady flow dynamics. Overall, this thesis contributes to making advances in the adaptation of unsteady flows. The novel framework proposed makes it computationally tractable to track the evolution of the main coherent features of the flowfield without losing out on accuracy by using a data-driven method. / Master of Science / Simulating unsteady, high-speed fluid flows around objects like aircraft and rockets poses a significant computational challenge. These flows exhibit rapidly evolving, intricate pattern structures that demand highly refined computational meshes to capture accurately. However, using a statically refined mesh for the entire simulation is computationally prohibitive. This research proposes a novel data-driven approach to enable efficient anisotropic mesh adaptation for such unsteady flow simulations. It leverages a technique called Dynamic Mode Decomposition (DMD) to model the dominant coherent structures and their evolution from snapshot flow field data. DMD has shown powerful capabilities in identifying the most energetic flow features and their time dynamics from numerical or experimental data. By integrating DMD into the anisotropic mesh adaptation process, the computational mesh can be dynamically refined anisotropically just in regions containing critical time-varying flow structures. The efficacy of this DMD-driven anisotropic adaptation framework is demonstrated in representative test cases - an unsteady subsonic flow over a circular cylinder and a supersonic channel flow over a cylinder. Results indicate that it enables accurate tracking and resolution of the key unsteady flow phenomena like vortex shedding using far fewer computational cells compared to static mesh simulations. In summary, this work makes anisotropic mesh adaptation computationally tractable for unsteady flow simulations by leveraging data-driven DMD modelling of the evolving coherent structures. The developed techniques pave the way for more accurate yet efficient unsteady CFD simulations.

Power networks are sophisticated dynamical systems whose stable operation is essential to modern society. We study the swing equation for networks and its linearization (LSEN) as a tool for modeling power systems. Nowadays, phasor measurement units (PMUs) are used across power networks to measure the magnitude and phase angle of electric signals. Given the abundant data that PMUs can produce, we study applications of the dynamic mode decomposition (DMD) and Loewner framework to power systems. The matrices that define the LSEN model have a particular structure that is not recovered by DMD. We thus propose a novel variant of DMD, called structure-preserving DMD (SPDMD), that imposes the LSEN structure upon the recovered system. Since the solution of the LSEN can potentially exhibit interesting transient dynamics, we study the transient growth for the exponential matrix related to the LSEN. We follow Godunov's approach to get upper bounds for the transient growth and also analyze the relationship of such bounds with classical bounds based on the spectrum, numerical range, and pseudospectra. We show how Godunov's bounds can be optimized to bound the solution operator at a given time. The Loewner framework provides a tool for identifying a dynamical system from tangential measurements. The singular values of Loewner matrices guide the discovery of the true order of the underlying system. However, these singular values can exhibit rapid decay when the interpolation points are far from the poles of the system. We establish a range of bounds for this decay of singular values and apply this analysis to power systems. / Doctor of Philosophy / Power networks are sophisticated dynamical systems whose stable operation is essential to modern society. We study a mathematical model called the LSEN to understand and recover the dynamics of power networks. The LSEN model defines some matrices that have special structures dictated by the application. We propose a novel method to recover matrices with this desired structure from data. We also study some properties of the solution of the LSEN model related to the exponential of a matrix, connecting classical results with the particular approach that we follow. In the system identification context, we also study bounds on the singular values of Loewner matrices to understand the interplay between the data (measurements of the system) and mathematical artifacts (poles of the system).