In this thesis, we consider three aspects of black holes. First, we examine a black hole boosted through a uniform magnetic field. We find that it can acquire an electric charge, just as a spinning black hole in an ambient magnetic field can, though the gravito-electrodynamics upstage naive arguments about screening electric fields in determining the value of the charge accrued. We study the chaotic behavior of the charged particles via their fractal basin boundaries. Second, we study the vanishing of Love numbers for black holes from a geometric perspective and connect it to the existence of quasinormal modes in de Sitter space. Behind each phenomenon is a ladder structure with a geometric/representation-theoretic origin which makes it possible to connect the asymptotic behavior of solutions at different boundaries. Third, we model the formation of a black hole in dRGT massive gravity in a de Sitter background with a collapsing homogeneous and pressureless ball of dust or ``star''. We focus on several choices of parameters corresponding to models of interest. We compute the position of the apparent horizon where it crosses the surface of the star, the Ricci curvature at the boundary, and the finite correction to the curvature of the apparent horizon due to the graviton mass. We argue that our collapsing solutions cannot be matched to a static, spherically symmetric vacuum solution at the star's surface, providing further evidence that physical black hole solutions in massive gravity are likely time-dependent.

Quantum communication protocols require maximally entangled state of pair of qubits (spin-1/2 states in this context) to be shared between sender and the receiver. The entangled qubits lose entanglement because of random magnetic field disturbances. The dynamics in the form of joint density matrix of random pure entangled state provide the steady (joint) state and the associated timescales (time taken by the pair to reach the steady state) providing a scope in future to quantify the effective utilization of quantum communication protocols. / The dynamics of an identical pair of entangled spin-1/2 particles, both subjected to the identical, independent, correlated random magnetic fields is studied. The dynamics of the pure joint state of the pair is derived using stochastic calculus. In case of identical fields, an ensemble of such pure states are combined using the modified spin joint density matrix and the joint relaxation time is obtained for the pair of spin-1/2 particles. These dynamics can be interpreted as special kind of correlations involving the spatial components of the Bloch polarization vectors of the constituent entangled spin-1/2 particles. In case of independent random magnetic fields, the dynamics are obtained by considering a pure joint state of entangled spin-1/2 particles. The disentanglement time defined as the time taken for the particles to become disentangled, is obtained. In case of correlated random magnetic fields, the dynamics of a maximally entangled pair of spin-1/2 particles are derived in terms of the joint density matrix of the entangled pair from which the steady state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix in this case represents a state of (partial) disentanglement. In other words, there is a persistent entanglement in case of correlated field disturbances. / Thesis / Doctor of Philosophy (PhD) / Maximally entangled pair of quantum bits (in the form of spin-1/2 states) lose entanglement either partially or completely depending upon the nature of random magnetic field disturbances around them (correlated/independent/identical fields). The dynamics of entangled states (in the form of density matrix of a random pure state) in the presence of random magnetic fields are obtained using the ideas of stochastic calculus to understand the steady state of the pair and the associated timescales to be reached.

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Thesis. 1977. M.S.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Microfiche copy available in Archives and Science. / Bibliography : leaves 72-73. / M.S.

Yes / Novel machine-learning and feature-selection algorithms have been developed to study: (i) the flare prediction capability of magnetic feature (MF) properties generated by the recently developed Solar Monitor Active Region Tracker (SMART); (ii) SMART's MF properties that are most significantly related to flare occurrence. Spatio-temporal association algorithms are developed to associate MFs with flares from April 1996 to December 2010 in order to differentiate flaring and non-flaring MFs and enable the application of machine learning and feature selection algorithms. A machine-learning algorithm is applied to the associated datasets to determine the flare prediction capability of all 21 SMART MF properties. The prediction performance is assessed using standard forecast verification measures and compared with the prediction measures of one of the industry's standard technologies for flare prediction that is also based on machine learning - Automated Solar Activity Prediction (ASAP). The comparison shows that the combination of SMART MFs with machine learning has the potential to achieve more accurate flare prediction than ASAP. Feature selection algorithms are then applied to determine the MF properties that are most related to flare occurrence. It is found that a reduced set of 6 MF properties can achieve a similar degree of prediction accuracy as the full set of 21 SMART MF properties.

This work is directed towards linear and nonlinear three dimensional magnetostatic field analysis and computation in electrical devices. Question regarding the validity and uniqueness of numerical field solutions, obtained on the basis of the curl curl approach, has been resolved through analytical proofs, numerical demonstrations, as well as experimental verifications. A nonlinear three dimensional magnetostatic field formulation is developed using the Newton-Raphson approach in conjunction with the three dimensional finite element method for inclusion of nonlinearities in laminated iron cores under saturated conditions. The developed, formulation was successfully implemented and applied to a practical example with considerable magnetic saturation. A method, for the calculation of saturated device winding inductance, is presented. This method is based on an energy perturbation technique and was successfully applied numerically and verified experimentally. Two methods for the calculation of forces on conductor segments as well as magnetized ferrous parts are developed in conjunction with the three dimensional finite element vector potential method. The proximity effect, resulting from considering small or large solution volumes on the field distribution, and the calculated values of force, is examined. It is demonstrated that a large solution volume, with Dirichlet boundary conditions imposed on the outermost surfaces of the volume considered, yield practically the same result, as when the Neumman boundary conditions were imposed on such surfaces. This result is of a considerable significance, from a practical standpoint, since the imposition of Dirichlet type boundary conditions on the outermost boundaries of the volume considered, results in a fewer number of equations to be solved. This, in turn, results in savings of the total execution time and memory costs required for the solution of large problems of two dimensional, and three dimensional fields by finite elements. It is demonstrated that three dimensional field solutions reduce to the corresponding two dimensional field solutions for problems which are inherently two dimensional in nature due to axial symmetry. This result provides a further verification of the validity of the three dimensional finite element formulation presented in this work. / Ph. D.

Recent developments in smart grid technology have spawned interest in the use of phasor measurement units to help create a reliable power system transmission and distribution infrastructure. Wide-area monitoring systems (WAMSs) utilizing synchrophasor measurements can help with understanding, forecasting, or even controlling the status of power grid stability in real-time. A power system Frequency Monitoring Network (FNET) was first proposed in 2001 and was established in 2004. As a pioneering WAMS, it serves the entire North American power grid through advanced situational awareness techniques, such as real-time event alerts, accurate event location estimation, animated event visualization, and post event analysis. Traditionally, Phasor Measurement Units (PMUs) have utilized signals obtained from current transformers (CTs) to compute current phasors. Unfortunately, this requires that CTs must be directly connected with buses, transformers or power lines. Chapters 2, 3 will introduce an innovative phasor measurement instrument, the Non-contact Frequency Disturbance Recorder (NFDR), which uses the magnetic and electric fields generated by power transmission lines to obtain current phasor measurements. The NFDR is developed on the same hardware platform as the Frequency Disturbance Recorder (FDR), which is actually a single phase PMU. Prototype testing of the NFDR in both the laboratory and the field environments were performed. Testing results show that measurement accuracy of the NFDR satisfies the requirements for power system dynamics observation. Researchers have been developing various techniques in power system phasor measurement and frequency estimation, due to their importance in reflecting system health. Each method has its own pros and cons regarding accuracy and speed. The DFT (Discrete Fourier Transform) based algorithm that is adopted by the FDR device is particularly suitable for tracking system dynamic changes and is immune to harmonic distortions, but it has not proven to be very robust when the input signal is polluted by random noise. Chapter 4 will discuss the Least Mean Squares-based methods for power system frequency tracking, compared with a DFT-based algorithm. Wide-area monitoring systems based on real time PMU measurements can provide great visibility to the angle instability conditions. Chapter 5 focuses on developing an early warning algorithm on the FNET platform. / Ph. D.

I develop the first magnetospheric accretion model to take account of the observed complexity of T Tauri magnetic fields, and the influence of stellar coronae. It is now accepted that accretion onto classical T Tauri stars is controlled by the stellar magnetosphere, yet to date the majority of accretion models have assumed that the stellar magnetic field is dipolar. By considering a simple steady state accretion model with both dipolar and complex magnetic fields I find a correlation between mass accretion rate and stellar mass of the form M[dot above] proportional to M[asterisk subscript, alpha superscript], with my results consistent within observed scatter. For any particular stellar mass there can be several orders of magnitude difference in the mass accretion rate, with accretion filling factors of a few percent. I demonstrate that the field geometry has a significant effect in controlling the location and distribution of hot spots, formed on the stellar surface from the high velocity impact of accreting material. I find that hot spots are often at mid to low latitudes, in contrast to what is expected for accretion to dipolar fields, and that particularly for higher mass stars, accreting material is predominantly carried by open field lines. Material accreting onto stars with fields that have a realistic degree of complexity does so with a distribution of in-fall speeds. I have also modelled the rotational modulation of X-ray emission from T Tauri stars assuming that they have isothermal, magnetically confined coronae. By extrapolating from surface magnetograms I find that T Tauri coronae are compact and clumpy, such that rotational modulation arises from X-ray emitting regions being eclipsed as the star rotates. Emitting regions are close to the stellar surface and inhomogeneously distributed about the star. However some regions of the stellar surface, which contain wind bearing open field lines, are dark in X-rays. From simulated X-ray light curves, obtained using stellar parameters from the Chandra Orion Ultradeep Project, I calculate X-ray periods and make comparisons with optically determined rotation periods. I find that X-ray periods are typically equal to, or are half of, the optical periods. Further, I find that X-ray periods are dependent upon the stellar inclination, but that the ratio of X-ray to optical period is independent of stellar mass and radius. I also present some results that show that the largest flares detected on T Tauri stars may occur inside extended magnetic structures arising from the reconnection of open field lines within the disc. I am currently working to establish whether such large field line loops can remain closed for a long enough time to fill with plasma before being torn open by the differential rotation between the star and the disc. Finally I discuss the current limitations of the model and suggest future developments and new avenues of research.