Yes / Based on the method of characteristics, an analytical solution for the one-dimensional shallow-water equations is developed to simulate the instantaneous dam-break flows propagating down a triangular wet bed channel in this study. The internal relationships between the hydraulic properties associated with the dam-break flow are investigated through the comparisons with the well-known analytical solutions for rectangular channels. Meanwhile, laboratory experiments are conducted in a prismatic, horizontal and smooth flume with a triangular cross-section. The non-intrusive digital image processing is applied for obtaining water surface profiles and stage hydrographs. Results show that the dam-break flow propagation depends on the dimensionless parameter defined as the ratio of initial tailwater depth over reservoir head. has significant effect on the dam-break wave in the downstream flooded area. For , the water surface profiles in the reservoir for different at a given time remains similar. For ≥ 0.5, extra negative waves occur in the reservoir, leading to the water surface undulations. Undular bores are generated at the dam site and propagate downstream. Time evolution of dam-break flows under three different reservoir heads is similar for the same . The inception of water surface profile change is earlier when the reservoir head is larger. The analytical model shows satisfactory agreement with the experimental results though some errors exist between the analytical solution and measurements due to the formation of extra negative waves, jet and undular bores. The similarities and discrepancies between the hydraulics in the triangular and rectangular channels are identified analytically in terms of the profiles of water depth, velocity, discharge, bore height and wave-front celerity with . The presented solution could be applied to predict the effect of wet bed condition on the dam-break wave in triangular channels, while laboratory measurement data could be used for validating analytical and numerical models. / National Natural Science Foundation of China (Grant No: 51879179), Sichuan Science and Technology Program (No. 2019JDTD0007) and Open Fund from the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (SKHL1809)

Systems of differential-algebraic equations (DAEs) arise in many areas including chemical engineering, electrical circuit simulation, and robotics. Such systems are routinely generated by simulation and modeling environments, like MapleSim, Matlab/Simulink, and those based on the Modelica language. Before a simulation starts and a numerical solution method is applied, some kind of structural analysis (SA) is performed to determine the structure and the index of a DAE system. Structural analysis methods serve as a necessary preprocessing stage, and among them, Pantelides's graph-theory-based algorithm is widely used in industry. Recently, Pryce's Σ-method is becoming increasingly popular, owing to its straightforward approach and capability of analyzing high-order systems. Both methods are equivalent in the sense that (a) when one succeeds, producing a nonsingular Jacobian, the other also succeeds, and that (b) the two give the same structural index in the case of either success or failure. When SA succeeds, the structural results can be used to perform an index reduction process, or to devise a stage-by-stage solution scheme for computing derivatives or Taylor coefficients up to some order. Although such a success occurs on fairly many problems of interest, SA can fail on some simple, solvable DAEs with an identically singular Jacobian, and give incorrect structural information that usually includes the index. In this thesis, we focus on the Σ-method and investigate its failures. Aiming at making this SA more reliable, we develop two conversion methods for fixing SA failures. These methods reformulate a DAE on which the Σ-method fails into an equivalent problem on which SA is more likely to succeed with a nonsingular Jacobian. The implementation of our methods requires symbolic computations. We also combine our conversion methods with block triangularization of a DAE. Using a block triangular form of a Jacobian sparsity pattern, we identify which diagonal block(s) of the Jacobian is identically singular, and then perform a conversion on each singular block. This approach can reduce the computational cost and improve the efficiency of finding a suitable conversion for fixing SA's failures. / Thesis / Doctor of Philosophy (PhD)

Biomechanics research investigating gait and balance of ultimate frisbee players is an unexplored topic. Ultimate requires a wide range of motions that could improve balance and is also a sport prone to frequent injury. This study explores the impact of playing ultimate on gait parameters associated with balance and knee angles associated with joint injury. Gait trials were conducted on 8 ultimate players and 8 control participants between the ages of 18 and 23 to obtain total double support time, stance phase time, single support time, load response time, abduction-adduction (AA) angles, internal-external (IE) rotation angles, and flexion angles of the dominant leg’s knee. Knee angles were obtained through the application of a Triangular Cosserat Point Element (TCPE) analysis for Soft-Tissue Artifact (STA) correction of knee kinematics. The gait parameters and knee angles were compared between ultimate players and control group participants using two-sample t tests. The results indicated that (1) playing ultimate may be used to improve balance, and (2) playing ultimate may reduce the range of IE rotation angles.

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With the rapid development of mobile devices technology, they are becoming very popular and a part of our everyday lives. These devices, which are equipped with wireless radios, such as cellular and WiFi radios, affect almost every aspect of our lives. People use smartphone and tablets to access the Internet, watch videos, chat with their friends, and etc. The wireless connections that these devices provide is more convenient than the wired connections. However, there are two main challenges in wireless networks: error-prone wireless links and network resources limitation. Network coding is widely used to provide reliable data transmission and to use the network resources efficiently. Network coding is a technique in which the original packets are mixed together using algebraic operations. In this dissertation, we study the applications of network coding in making the wireless transmissions robust against transmission errors and in efficient resource management. In many types of data, the importance of different parts of the data are different. For instance, in the case of numeric data, the importance of the data decreases from the most significant to the least significant bit. Also, in multi-layer videos, the importance of the packets in different layers of the videos are not the same. We propose novel data transmission methods in wireless networks that considers the unequal importance of the different parts of the data. In order to provide robust data transmissions and use the limited resources efficiently, we use random linear network coding technique, which is a type of network coding. In the first part of this dissertation, we study the application of network coding in resource management. In order to use the the limited storage of cache nodes efficiently, we propose to use triangular network coding for content distribution. We also design a scalable video-on-demand system, which uses helper nodes and network coding to provide users with their desired video quality. In the second part, we investigate the application of network coding in providing robust wireless transmissions. We propose symbol-level network coding, in which each packet is partitioned to symbols with different importance. We also propose a method that uses network coding to make multi-layer videos robust against transmission errors. / Computer and Information Science

A Numerical Solution is presented for the problem of flow past a highly swept, slender wing with sharp leading edges. The lifting surface is modelled as a bound vortex sheet, while the wake is modelled as a force-free vortex sheet. The solution is obtained by the use of a unsteady Vortex-Lattice Method which includes the effect of leading edge separation. Numerical predictions for the aerodynamic loads and pressure distributions are compared with experimental data. A 75° Delta wing and a 60° Delta wing with Leading Edge Vortex flaps in uniform, symmetric and steady flow are studied. Uniform and cosine distributions are used to determine the effect of lattice shape on the solution. The results show that good aerodynamic load predictions are obtained by this Vortex-lattice method. The results also indicated that fewer cosine distribution control points predict pressures as well as the use of a larger number of uniform distribution control points. The numerical results for wings with LEVFs show good agreement with experimental data away from the trailing edge. This may be due to the viscous effects in the experiment not modelled in this method. It is also apparent that the size of the wake, trailing and leading edge wakes, is the important factor effecting computation times. / M.S.

Sandwich Panels with cellular cores are widely used in the aerospace industry for their higher stiffness to mass, strength to mass ratio, and excellent energy absorption capability. Even though, sandwich panels are considered state of the art for lightweight aerospace structures, the requirement to further reduce the mass exists due to the direct impact of mass on mission costs. Traditional manufacturing techniques have limited the shape of the cores to be either hexagonal or rectangular, but, with rapid advancements in additive manufacturing, other core shapes can now be explored. This research aims to identify and evaluate the mechanical performance of two-dimensional cores having standard wall geometry, which provide higher specific stiffness than honeycomb cores. Triangular cores were identified to have higher specific in-plane moduli and equivalent specific out-of-plane and transverse shear moduli. To consider practical use of the triangular cores, elastic and elastic-plastic structural analysis was performed to evaluate the stiffness, strength, failure, and energy absorption characteristics of both the core and sandwich panels. The comparison made between triangular cores and hexagonal cores having the same cell size and relative density showed that triangular cores outperform hexagonal cores in elastic range and for applications where in-plane loading is dominant. Triangular cores also have excellent in-plane energy absorption capabilities at higher densities. / Master of Science / Sandwich panels with cellular cores are widely used in aerospace structures to reduce weight, which helps increase payload and improve fuel efficiency. They also have the ability to absorb energy during accidental impacts. Sandwich construction typically consists of two thin facesheets separated by a lightweight core and, is analogous to I-beams used in civil structures. Most commonly used core is the hexagonal honeycomb core inspired by beehives. While sandwich panels constructed using honeycomb cores are considered the state-of-the-art for lightweight aerospace structures, there is a need to further reduce the mass due to the direct impact on mission costs. This research aims to explore other core shapes that provide better stiffness to mass ratio than the hexagonal core. Among the two-dimensional cores explored, the triangular shaped core was identified to have higher stiffness than the hexagonal core of the same size and weight. To consider practical use of triangular cores, mechanical performance and failure behavior of sandwich panels constructed using triangular core sandwich panels was compared to hexagonal core sandwich panels. It was concluded that the triangular panels provided higher stiffness for the same mass and was more resistant to failure when axially loaded. Triangular cores also have excellent in-plane energy absorption capabilities at higher densities.

One of the greatest technological challenges of the world today is reducing the size and weight of the existing products to make them portable. Specifically, in electric vehicles such as electric cars, UAVs and aero planes, the size of battery chargers and inverters needs to be reduced so as to make space for more parts in these vehicles. Electromagnetic Interference (EMI) filters take up a more than 80 % of these power converters, the size of these filters can be reduced by pushing the switching frequency higher. High frequency operation (> 300 kHz) leads to a size in reduction of EMI filters though it also leads to an increase in switching losses thus compromising on efficiency. Thus, soft switching becomes necessary to reduce the losses, adding more electrical components to the converter to achieve soft switching is a common method. However, it increases the physical complexity of the system. Hence, advanced control methods are adopted for today's power converters that enable soft switching for devices specifically ZVS turn-on as the turn-off losses of next generation WBG devices are negligible. Thus, the goal of this research is to discover novel switching algorithms for soft turn-on. The state-of the-art control methods namely CRM and TCM achieve soft turn-on by enabling bi-directional current such that the anti-parallel body diode starts conducting before the device is turned on. CRM and TCM result in variable switching frequency which leads to asynchronous operation in multi-phase and multi-converter systems. Hence, TCM is modified in this dissertation to achieve constant switching frequency, as the goal of this research is to be able to achieve ZVS turn-on for a three-phase converter. Further, Triangular Current Mode (TCM) to achieve soft switching and phase synchronization for three-phase two-level converters is proposed. It is shown how soft switching and sinusoidal currents can be achieved by operating the phases in a combination of discontinuous conduction mode (DCM), TCM and clamped mode. The proposed scheme can achieve soft switching ZVS turn-on for all the three phases. The algorithm is tested and validated on a GaN converter, 99% efficiency is achieved at 0.7 kW with a density of 110 W/in3. The discussion of TCM in current literature is limited to unity power factor assumption, however this limits the algorithm's adoption in real world applications. It is shown how proposed TCM algorithm can be extended to accommodate phase shift with all the three phases operating in a combination of DCM+TCM+Clamped modes of operation. The algorithm is tested and validated on a GaN converter, 99% efficiency is achieved at 0.7 kVA with a density of 110 W/in3. TCM operation results in 33 % higher rms current which leads to higher conduction losses, as WBG devices have lower on-resistance, these devices are the ideal candidates for TCM operation, hence to accurately obtain the device parameters, a detailed device characterization is performed. Further, proposed TCM+DCM+Clamped control algorithm is extended to three-level topologies, the control is modified to extract the advantage of reduced Common Mode Voltage (CMV) switching states of the three-level topology, the switching frequency can thus be pushed to 3 times higher as compared to state-of-the-art SVPWM control while maintaining close to 99 % efficiency. Two switching schemes are presented and both of them have a very small switching frequency variation (6%) as compared to state-of-the-art methods with >200% switching frequency variation. / Doctor of Philosophy / Power supplies are at the heart of today's advanced technological systems like aero planes, UAVs, electrical cars, uninterruptible power supplies (UPS), smart grids etc. These performance driven systems have high requirements for the power conversion stage in terms of efficiency, density and reliability. With the growing demand of reduction in size for electromechanical and electronic systems, it is highly desirable to reduce the size of the power supplies and power converters while maintaining high efficiency. High density is achieved by pushing the switching frequency higher to reduce the size of the magnetics. High switching frequency leads to higher losses if conventional hard switching methods are used, this drives the need for soft switching methods without adding to the physical complexity of the system. This dissertation proposes novel soft switching techniques to improve the performance and density of AC/DC and DC/AC converters at high switching frequency without increasing the component count. The concept and the features of this new proposed control scheme, along with the comparison of its benefits as compared to conventional control methodologies, have been presented in detail in different chapters of this dissertation.