This thesis models and analyzes an in-situ method for measuring the density of the thermosphere at low Earth orbit (LEO) altitudes in real time. As satellites orbit in the thermosphere, the sparse yet present air perturbs their orbits via the drag force. The drag force is poorly characterized and has a significant effect at LEO altitudes relative to other forces, making this perturbation force one of the greatest uncertainties in LEO orbit propagation. A steadily increasing number of satellites orbit at LEO altitudes, so for safety, it is critical to accurately track these satellites to avoid collisions. Therefore, better knowledge of the drag force is required. The drag force depends directly on the air mass density in the thermosphere, and current knowledge of the thermospheric density is limited. Models exist to describe the variations in density over time, but due to the many unpredictable factors which affect the thermosphere, the best of these models are only accurate to within 10%. Also, currently available techniques to measure the thermospheric density can only return time-averaged measurements, which causes inaccuracies in orbit propagation due to local density variations. Some planned in-situ density measurement missions rely on measuring acceleration caused by the drag force, but this requires a highly accurate accelerometer to be able to separate the drag force from other stronger forces acting on a satellite. The Satellite Producing Aerodynamic Torque to Understand LEO Atmosphere (SPATULA) concept was introduced as an alternative method, which infers density based on measurements of the drag torque. In the rotational regime, drag produces the strongest torque at LEO altitudes by far, making it possible to acquire accurate density measurements with inexpensive, commercially available sensors and actuators on a SPATULA spacecraft. This thesis expands upon a preliminary study of the SPATULA concept. A SPATULA spacecraft's dynamics are modeled in three dimensions, and a novel method is introduced for modeling the dependence of external torques on the geometry and attitude of the spacecraft. In addition to the dynamics model, discrete-time algorithms for guidance, system state filtering, attitude control, and density estimation are developed for the six degrees of freedom case. The MathWorks tools MATLAB and Simulink are used to simulate the physics and system models. The simulations are used to evaluate the performance of the SPATULA system's density measurements and compare them to conventional methods. It is found that the accuracy and bandwidth of the SPATULA system have a significant dependence on the assumed accuracy of the torque models in the system's filter. When the bandwidth is set to avoid significant phase shift errors, the SPATULA system can produce real-time measurements of density accurate over a minimum time scale of about 60 seconds, and the density error has a standard deviation of about 2 x 10^-14 kg/m^3. This accuracy is about 6 times better than the best thermospheric models, and it is also better than reported accuracies of most other density measurement methods. If bandwidth is sacrificed, the density error standard deviation can be decreased by a factor of 4. This introduces additional error due to phase shift delays, but these can be corrected with signal processing techniques. With the higher accuracy, the SPATULA system loses its real-time ability, but the data it produces would still provide excellent insight for improving thermospheric models. With high accuracy and low cost, the SPATULA concept is a promising path to pursue toward improving thermospheric density knowledge. / Master of Science / This thesis models and analyzes a method for measuring the density of the upper atmosphere in real time directly onboard a satellite. As low Earth orbit (LEO) satellites orbit at low altitudes, the sparse yet present atmosphere changes their orbits via the drag force. The drag force is poorly characterized and has a significant effect at LEO altitudes relative to other forces, making this perturbation force one of the greatest uncertainties in LEO orbit prediction. A steadily increasing number of satellites orbit at LEO altitudes, so for safety, it is critical to accurately track and predict the orbits of these satellites to avoid collisions. Therefore, better knowledge of the drag force is required. The drag force depends directly on air density, and current knowledge of the upper atmospheric density is limited. Models exist to describe the variations in density over time, but due to the many unpredictable factors which affect the atmosphere, the best of these models are only accurate to within 10%. Also, currently available techniques to measure the upper atmospheric density can only return time-averaged measurements, which causes inaccuracies in orbit prediction due to local density variations. Some planned density measurement missions rely on measuring acceleration caused by the drag force, but this requires a highly accurate accelerometer to be able to separate the drag force from other stronger forces acting on a satellite. The Satellite Producing Aerodynamic Torque to Understand LEO Atmosphere (SPATULA) concept was introduced as an alternative method, which infers density based on measurements of the drag torque. Drag produces the strongest torque at LEO altitudes by far, making it possible to acquire accurate density measurements with inexpensive, commercially available parts on a SPATULA spacecraft. This thesis expands upon a preliminary study of the SPATULA concept. A SPATULA spacecraft's motion and rotation is modeled in three dimensions, and a novel method is introduced for modeling the dependence of external torques on the geometry and orientation of the spacecraft. In addition to the dynamics model, algorithms that could be implemented on a satellite's computer are developed for determining the best orientation, estimating the state of the system, controlling the orientation, and estimating density. The MathWorks tools MATLAB and Simulink are used to simulate the physics and system models. The simulations are used to evaluate the performance of the SPATULA system's density measurements and compare them to conventional methods. It is found that the accuracy and bandwidth of the SPATULA system have a significant dependence on the assumed accuracy of the torque models used by the system. When a high bandwidth is used to avoid problems associated with low bandwidth, the SPATULA system can produce real-time measurements of density accurate over a minimum time scale of about 60 seconds, and the density error has a standard deviation of about 2 x 10^-14 kg/m^2. This accuracy is about 6 times better than the best upper atmospheric models, and it is also better than reported accuracies of most other density measurement methods. If bandwidth is sacrificed, the density error standard deviation can be decreased by a factor of 4. This introduces additional error due to delayed measurements of quickly varying components of the density, but these can be corrected with signal processing techniques. With the higher accuracy, the SPATULA system loses its real-time ability, but the data it produces would still provide excellent insight for improving atmospheric density models. With high accuracy and low cost, the SPATULA concept is a promising path to pursue toward improving density knowledge.

<p>Approximating the exchange-correlation energy in density functional theory (DFT) is a crucial task. As the only missing element in the Kohn-Sham DFT, the search for better exchange-correlation functionals has been an active field of research for fifty years. Many models and approximations are known and they can be summarized in what is known as the Jacob’s ladder. All the functionals in that ladder are local in the sense that they rely on the information of only one electronic coordinate. That is, even though the exchange-correlation hole, the cornerstone in density functional theory, is a two-electron coordinate quantity, one of the coordinates is averaged over in “Jacob’s ladder functionals.” This makes the calculations considerably more efficient. On the other hand, some of the important constraints on the form of the exchange-correlation functional become inaccessible in the one-point forms. The violation of these constraints leads to functionals plagued by systematic errors, leading to qualitatively incorrect descriptions of some chemical and physical processes.</p> <p>In this thesis the idea of a weighted density approximation (WDA) is explored. More specifically, a symmetric and normalized two-point functional is proposed for the exchange-correlation energy functional. The functional is based entirely on the hole for the uniform electron gas. By construction, these functionals fulfill two of the most important constraints: the normalization of the exchange-correlation hole and the uniform electron gas limit. The findings suggest that we should pursue a whole new generation of “new Jacob’s ladder” functionals.</p> <p>A further step was considered. Given the relevance of the long-range behavior of the exchange-correlation hole, a study of the electronic direct correlation function was performed. The idea was to build up the long-range character of the hole as convoluted pieces of the simple and short-ranged direct correlation function. This direct correlation function provides better results, at least for the correlation energy in the spin-polarized uniform electron gas.</p> <p>The advantage of one-point functionals is their computational efficiency. We therefore attempted to develop new methods that mitigate the relative computational inefficiency of two-point functionals. This led to new methods for evaluating the six-dimensional integrals that are inherent to the exchange-correlation energy.</p> / Doctor of Philosophy (PhD)

Yes / This note presents a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing st

A commonly used process for the formation of ceramic wall tile bodies is powder compaction. Variations in density in wall tile bodies introduced by the compaction process can cause rejection at later stages of production. Quality control equipment currently employed does not identify reject bodies in the unfired state. Scope exists to reduce production costs by the timely removal of reject bodies in the unfired state. In this thesis an ultrasonic non-destructive technique is presented which allows the mapping of the density variations found in wall tile bodies in the unfired and fired states to an accuracy of ± 0.5%. An effective medium theory for the propagation of ultrasound in porous media is developed. The significance of the dependence of Young's modulus on density in determining the relationship between compression wave propagation velocity and density is explored. Using a vibrational resonance technique, it is shown that the evolution of Young's modulus and Poisson's ratio in the wall tile body material are very sensitive to the conditions used for the firing operation. The Biot two-phase theory of acoustic propagation in fluid saturated porous media which considers dissipation due to friction between the fluid and porous frame is reviewed, and the applicability to the wall tile body material assessed. It is shown that this dissipation mechanism is insignificant for this particular material. A modification is made to the model in an attempt to include dissipation due to the inelasticity and scattering of the porous frame. The results show that the two-phase theory reduces to an effective medium theory in the limit of the saturating fluid being air. The thesis concludes that density variations in wall tile bodies can be measured using and ultrasonic technique and that an effective medium theory can be used to describe the propagation of ultrasound in porous media.

The emerging need for smart and wearable electronic systems are driving new electronics technology paradigms in miniaturization, functionality and cost.The operating voltages and power levels for devices in these systems are becoming increasingly varied with increased diversity of devices to serve these heterogeneous functions. Power convertor technologies are incorporated into various parts of these systems to step-up or step-down battery voltages and currents to address these diverse needs. Hence, multiple power converters, each requiring several passive components, are used to create stable power-supplies. This is placing significant challenges in ultra-miniaturized and ultra-efficient power management technologies. A typical power convertor consists of magnetic components such as inductors perform the basic energy storage and delivery functions from the source to the load. These power components are still at microscale in lithography and milliscale in component size. They occupy a large volume fraction of the power circuitry. Power convertors therefore, are a major bottleneck to system miniaturization. There is, thus, a need for ultra-miniaturized and high-performance power inductors for scaling down such power convertors. The critical parameters governing the size and performance of power inductors are its inductance density and power handling capability. These parameters are limited by the magnetic properties of the present inductor core materials. A new approach to inductor cores that achieves the best magnetic properties and yet allows integration of power inductors into ultra-thin substrates to meet the emerging needs for performance and size is therefore required. The objective of this research is to model, design and synthesize a novel multilayered ferromagnetic-polymer composite structure for inductor cores with high permeability and saturation magnetization.The multilayered composite structure consists of thin magnetic layers interspersed with ultra-thin polymers. A fabrication approach to integrate the composite structure in inductor devices is also demonstrated.

published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

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