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<p>Let $\Theta_n$ be the group of $h$-cobordism classes of homotopy spheres, i.e. closed smooth manifolds which are homotopy equivalent to $S^n$, under connected sum. A homotopy sphere $\Sigma^n$ which is not diffeomorphic to $S^n$ is called ``exotic.'' For an oriented smooth manifold $M^n$, the {\bf inertia group} $I(M)\subset\Theta_n$ is defined as the subgroup of homotopy spheres such that $M\#\Sigma$ is orientation-preserving diffeomorphic to $M$. This thesis collects together a number of results on $I(M)$ and provides a summary of some fundamental results in Geometric Topology. The focus is on dimension $7$, since it is the smallest known dimension with exotic spheres. The thesis also provides two new results: one specifically about $7$-manifolds with certain $S^1$ actions, and the other about the effect of surgery on the homotopy inertia group $I_h(M)$.</p> / Master of Science (MSc)

Traditional generators have been decommissioned or replaced by renewable energy generation due to utility long-standing goals. However, instead of flattening the entire plant, the rotating mass of generator can be utilized as a storage unit (inertia resource) to mitigate the frequency swings during transient caused by the renewables. The goal of this work is to design a control strategy utilizing the decommissioned generator interfaced with power grid via a back-to-back converter to provide inertia support. This is referred to as decoupled synchronous machine system (DSMS). On top of that, the grid-side converter is capable of providing reactive power as an auxiliary voltage controller. However, in a practical setting, for power utilities, the detailed state equations of such device as well as the complicated nonlinear power system are usually unobtainable making the controller design a challenging problem. Therefore, a model free, purely data-driven strategy for the nonlinear controller design using Koopman operator-based framework is proposed. Besides, the time delay embedding technique is adopted together with Koopman operator theory for the nonlinear system identification. Koopman operator provides a linear representation of the system and thereby the classical linear control algorithms can be applied. In this work, model predictive control is adopted to cope with the constraints of the control signals. The effectiveness and robustness of the proposed system are demonstrated in Kundur two-area system and IEEE 39-bus system. / Doctor of Philosophy / Power system is facing an energy transformation from the traditional fuel to sustainable renewable such as solar, wind and so on. Unlike the traditional fuel energized generators, the renewable has very little inertia to maintain frequency stability. Therefore, this work proposes a new system referred to as decoupled synchronous machine system (DSMS) to support the grid frequency. DSMS consists of the rotating mass of generator and a back-to-back converter which can be utilized as an inertia resource to mitigate the frequency oscillations. In addition, the grid-side converter can provide reactive power to improve voltage performance during faults. This work aims to design a control strategy utilizing DSMS to support grid frequency and voltage. However, an explicit mathematical model of such device is unobtainable in a practical setting making data-driven control the only option. A data-driven technique which is Koopman operator-based framework together with time delay embedding algorithm is proposed to obtain a linear representation of the system. The effectiveness and robustness of the proposed system are demonstrated in Kundur two-area system and IEEE 39-bus system.

This thesis is a product of the U.S. Army Corp of Engineer's desire to develop a more accurate procedure for estimating the load capacity of an in-service T-beam bridge. A bridge type that is a stumbling block for U.S. Army field engineers due to the unknown amount and placement of the flexural reinforcement in the T-beam girder cross-sections. Personnel from the U.S. Army Corp of Engineer's Waterways Experiment Station in cooperation with personnel from Virginia Tech conceived a procedure that is potentially more accurate, can be quickly executed in the field, and is relatively easy to use by field engineers. In general, the procedure provides a method for transition between the quantity of flexural reinforcement in a reinforced concrete T-beam and the member's actual moment of inertia. Specifically, the goal of this thesis is to evaluate the accuracy of selected, effective moment of inertia models as a component in the proposed analysis procedure. The accuracy of the selected models is evaluated with test data generated from a testing program detailed herein, which load tested full-scale reinforced concrete T-beams. The test specimens were subjected to a closely-spaced, tandem-axle load configuration, a load configuration typical of military equipment. / Master of Science

A vehicle has several rotating components such as a traction electric motor, the driveline, and the wheels and tires. The rotating inertia of these components is important in vehicle performance analyses. However, in many studies, the rotating inertias are typically lumped into an equivalent inertial mass to simplify the analysis, making it difficult to investigate the effect of those components and losses for vehicle energy use. In this study, a backward-tracking model from the wheels and tires to the power source (battery or fuel cell) is developed to estimate the effect of rotating inertias for each component during propulsion and regenerative braking of a vehicle. This paper presents the effect of rotating inertias on the power and energy for propulsion and regenerative braking for two-wheel drive (either front or rear) and all-wheel drive (AWD) cases. On-road driving and dynamometer tests are different since only one axle (two wheels) is rotating in the latter case, instead of two axles (four wheels). The differences between an on-road test and a dynamometer test are estimated using the developed model. The results show that the rotating inertias can contribute a significant fraction (8 -13 %) of the energy recovered during deceleration due to the relatively lower losses of rotating components compared to vehicle inertia, where a large fraction is dissipated in friction braking. In a dynamometer test, the amount of energy captured from available energy in wheel/tire assemblies is slightly less than that of the AWD case in on-road test. The total regenerative brake energy capture is significantly higher (> 70 %) for a FWD vehicle on a dynamometer compared to an on-road case. The rest of inertial energy is lost by inefficiencies in components, regenerative brake fraction, and friction braking on the un-driven axle. / Master of Science

Abstract The studies of the deformed nucleus for the Pb isotopes in the A~190 re- gion has been carried out by using the P.S.M. The comparison between the theoretical calculation of the transition energy, kinetic moment of ine- rtia, dynamic moment of inertia, paring gap, rotational energy, quadrupole moment, and B(M1)/B(E2) and the experiment observations are presented. We found that the kinetic moment of inertia is increased as the spin incre- ase for the even-even nuclei. This rise has been interpreted as being due to the combined alignment of the quasiparticles in the high-N intruder or- bit. And the kinetic moment of inertia is constant function of spin in the odd-even nuclei. It is interpreted as been due to the Pauli blocking of odd -quasineutron in the high-N intruder orbit.