abstract: The dynamics of a fluid flow inside 2D square and 3D cubic cavities under various configurations were simulated and analyzed using a spectral code I developed. This code was validated against known studies in the 3D lid-driven cavity. It was then used to explore the various dynamical behaviors close to the onset of instability of the steady-state flow, and explain in the process the mechanism underlying an intermittent bursting previously observed. A fairly complete bifurcation picture emerged, using a combination of computational tools such as selective frequency damping, edge-state tracking and subspace restriction. The code was then used to investigate the flow in a 2D square cavity under stable temperature stratification, an idealized version of a lake with warmer water at the surface compared to the bottom. The governing equations are the Navier-Stokes equations under the Boussinesq approximation. Simulations were done over a wide range of parameters of the problem quantifying the driving velocity at the top (e.g. wind) and the strength of the stratification. Particular attention was paid to the mechanisms associated with the onset of instability of the base steady state, and the complex nontrivial dynamics occurring beyond onset, where the presence of multiple states leads to a rich spectrum of states, including homoclinic and heteroclinic chaos. A third configuration investigates the flow dynamics of a fluid in a rapidly rotating cube subjected to small amplitude modulations. The responses were quantified by the global helicity and energy measures, and various peak responses associated to resonances with intrinsic eigenmodes of the cavity and/or internal retracing beams were clearly identified for the first time. A novel approach to compute the eigenmodes is also described, making accessible a whole catalog of these with various properties and dynamics. When the small amplitude modulation does not align with the rotation axis (precession) we show that a new set of eigenmodes are primarily excited as the angular velocity increases, while triadic resonances may occur once the nonlinear regime kicks in. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019

Multi-helix rotating shield brachytherapy (RSBT) applicator and multi-source RSBT apparatus are two novel intensity-modulated brachytherapy techniques for the treatment of cervical and prostate cancer, respectively. The use of imaging techniques such as magnetic resonance imaging guided brachytherapy has enabled the precise identification and contouring of tumor volumes for treatment planning, as well as demonstrated the challenges associated with using conventional high dose rate brachytherapy (HDR-BT) approaches to conform the radiation dose to the target and avoid surrounding sensitive healthy tissues. The target conformity of conventional HDR-BT dose distributions is restricted based on the geometrical constraints imposed by the position and shape of the tube-shaped applicators, as well as the radially-symmetric radiation dose distributions produced by the radiation sources. Dose distribution conformity for cervical and prostate cancer can be significantly improved relative to conventional HDR-BT through the use of multi-helix and multi-source RSBT techniques, respectively. In this study, two novel RSBT concepts for treating cervical and prostate cancer were introduced and the dosimetric impact was evaluated. A Henschke-type cervical cancer applicator, designed for an electronic brachytherapy (eBx) source (Xoft AxxentTM) and a 0.5 mm thick tungsten partial shield with 180° or 45° azimuthal emission angles, is proposed. The interior wall of the applicator contains six evenly-spaced helical keyways that rigidly define the emission direction of the partial radiation shield as a function of depth in the applicator. The shield contains three uniformly-distributed protruding keys on its exterior wall and is attached to the source such that it rotates freely, thus longitudinal translational motion of the source is transferred to rotational motion of the shield. RSBT treatment plans were generated for five cervical cancer patients with a diverse range of high-risk target volume (HR-CTV) shapes and applicator positions. Treatment delivery time and tumor coverage (D90 of HR-CTV) were the two metrics used as the basis for evaluation and comparison. With multi-source RSBT apparatus, precise angular and linear positioning of partially-shielded 153Gd brachytherapy sources in interstitial needles for the treatment of locally-advanced prostate cancer is carried out. Following needle implantation through the patient template, an angular drive mechanism is docked to the patient template. Each needle is coupled to a multisource afterloader catheter by a connector passing through a shaft. The shafts are rotated about their axes by translating a moving template between two stationary templates. Shafts’ surfaces and moving template holes are helically threaded with the same pattern such that translation of the moving template causes simultaneous rotation of the shafts. The catheter angles are simultaneously incremented throughout treatment. For each rotation angle, source depth in each needle is controlled by a multisource afterloader, which is proposed as an array of belt-driven linear actuators, each of which drives a wire that controls catheter depth in a needle. In conclusion, the helical RSBT approach for treating cervical cancer and the multi-catheter RSBT approach for treating prostate cancer, powered with novel radiation sources amenable to shielding, are clinically- and mechanically-feasible techniques that dosimetrically outperform conventional brachytherapy methods while minimizing damage to healthy tissues inside and/or adjacent to the target.

Active vibration control is a widely implemented method for the helicopter vibration control. Due to the significant progress in microelectronics, this technique outperforms the traditional passive control technique due to weight penalty and lack of adaptability for the changing flight conditions. In this thesis, an optimal controller is designed to attenuate the rotor blade vibration. The mathematical model of the triply coupled vibration of the rotating cantilever beam is used to develop the state-space model of an isolated rotor blade. The required natural frequencies are determined by the modified Galerkin method and only the principal aerodynamic forces acting on the structure are considered to obtain the elements of the input matrix. A linear quadratic regulator is designed to achieve the vibration reduction at the optimum level and the controller is tuned for the hovering and forward flight with different advance ratios.

<p>Microrobots have a promising prospect to be used in healthcare and bioengineering applications due to their capability to gently access small and delicate body sites. Unfortunately, traditional materials used for the fabrication of microrobots are rigid, hindering safe operation due to the transfer of high stresses to the surrounding tissue. Additionally, traditional microrobots are often not biocompatible, which threatens the health of the patient if not properly retrieved. This dissertation describes the fabrication and actuation of small-scale (several micrometers in all dimensions) magnetic robots that are soft, biocompatible, and capable of moving over smooth and corrugated surface. <u>S</u>oft <u>M</u>agnetic <u>M</u>icro <u>R</u>obots (SMµRs) can carry payloads in their porous interior and release them using external magnetic inputs. SMµRs has therefore the potential to be used in a wide range of applications—including targeted drug release and remote biosensing and bio sampling—and access a number of difficult-to-reach sites in the human body, such as intestines or blood vessels. The structure of SMµRs consist of three thin layers: Two layers of polymer with embedded magnetic particles aligned along a preferential direction. One porous layer, in between the magnetic layers, where the SMµRs can accumulate and release payloads. SMµRs are small, light in weight, and fast and inexpensive to fabricate. Moreover, the manufacturing of SMµRs is compatible with large-scale production processes, facilitating their future commercial exploitation. Using external rotating magnetic fields, the position of the SMµRs can be controlled wirelessly <i>via</i> tumbling locomotion. We demonstrate two types of tumbling locomotion (length-wise and side-wise) as well as the possibility to release the internal payload of the SMµRs in a discrete or continuous manner using only changes in the intensity of the external magnetic field. We studied the performance of SMµRs under a variety of environmental conditions as well as their capability of overcoming obstacles.</p>

Harvesting of algal biomass presents a large barrier to the success of biofuels made from algae feedstock. Small cell sizes coupled with dilute concentrations of biomass in lagoon systems make separation an expensive and energy intense-process. The rotating algal biofilm reactor (RABR) has been developed at USU to provide a sustainable technology solution to this issue. Algae cells grown as a biofilm are concentrated in one location for ease of harvesting of high density biomass. A mathematical model of this biofilm system was developed based on data generated from three pilot scale reactors at the City of Logan, Utah wastewater reclamation plant. The data were fit using nonlinear regression to a modified logistic growth equation. The logistic growth equation was used to estimate nitrogen and phosphorus removal from the system, and to find the best harvesting time for the reactors. These values were extrapolated to determine yields of methane and biodiesel from algae biomass that could be used to provide energy to the City of Logan if these reactors were implemented at full scale. For transesterification into biodiesel, algae need to have high lipid content. Algae biofilms have been relatively unexplored in terms of cell lipid composition accumulation and changes with regard to environmental stressors. Results indicated that biofilm biomass was largely unaffected by nutrient stresses. Neither nitrogen limitation nor excess inorganic carbon triggered a significant change in lipid content. Biofilm algae grown with indoor lighting produced an average of 4.2% lipid content by dry weight. Biofilm algae gown outdoors yielded an average of 6.2% lipid content by dry weight.

Although a tropical cyclone may conceptually be regarded as an axisymmetric vortex, there is substantial evidence that asymmetric dynamics play an important role. In this thesis, dynamical impacts of rotating convective asymmetries are examined in this thesis. Two types of rotating convective asymmetries are considered: rotating eyewall convective maximum which is located in the core region of the storm and spiral bands which are located outside the core. Both of them can be characterized as rotating asymmetric convective heat sources, and they are superimposed on a balanced, axisymmetric vortex to approximate the effect of rotating eyewall convective maximum and spiral bands on tropical cyclone by using a simple nonhydrostatic three-dimensional, but linear model that is based on vortex anelastic equations. The evolution of rotating convective asymmetric heat sources on a balanced, axisymmetric vortex, which is modeled after tropical cyclones, is investigated to examine angular momentum transport by gravity waves that radiate away from the core region. Results show that gravity waves can transport angular momentum away from a tropical cyclone, but a very small amount, which is several orders of magnitude smaller than the estimate by recent studies. The significantly large difference may largely be due to the difference between two-dimensional and three-dimensional adjustment processes. Assuming that the effects of spiral bands on tropical cyclone wind field are caused by the response to diabatic heating in their convection, rotating asymmetric heat sources are constructed to reflect observations of spiral bands. These heat sources are rotated around a realistic but idealized balanced axisymmetric vortex. Simulation results show that the response of tropical cyclone wind field to idealized spiral band heat sources can successfully capture a number of observed well-known features of spiral band circulation, such as overturning secondary circulation, descending mid-level inflow, and cyclonic tangential acceleration. Comparison to full-physics numerical simulations confirms the validity of this method which provides a simple dynamical framework to better understand the impact of spiral bands in tropical cyclone.

Today, emission legislations for engine exhaust particles are mass based. The engines of today are low-emitting with respect to particle mass, with the emissions approaching the detection limit of the current measurement method. This calls for new and improved measurement methods. Both from the point of view of the engine developers and regarding human health effects, particle number seem to be the particle property of greatest interest to legislate upon. Recently, a proposal for a new particle number based measurement methodology has been put forward by the United Nations Economic Commission for Europe (UN ECE). The gas and particle mixture (the aerosol) of engine exhaust is not a stable system. The size and the number of the particles change over time as the temperature and pressure change. Particle number measurements call for dilution which changes the gas-phase concentrations of the condensing gases. The dilution process alters the conditions in the aerosol and thereby influences the measurements. Within the current project it was desired to better understand the outcome of particle number measurements and the complexities of particle sampling, dilution and conditioning prior to measurements. Two experimental set-ups have been developed within the project. The first system includes a rotating disc diluter followed by a volatility Tandem Differential Mobility Analyser (v-TDMA). The second set-up, called the EMIR-system, includes ejector diluters in series followed by a stand-alone Condensation Particle Counter (CPC). After the development of these experimental set-ups, the v-TDMA has been used to study the volatility and the size distributed number concentration of exhaust particles. The EMIR-system was used for total number concentration measurements including only the solid fraction of the aerosol. The experimental work has given practical experience that can be used to estimate the benefits and disadvantages of upcoming measuring methodology. For the engine developers, in order to produce engines that meet future legislation limits, it is essential to know how the measurement procedure influences the aerosol. In summary, the experimental studies have shown that the number of nucleation mode particles is strongly affected by varied dilution. No upper threshold value of the dilution has been found where the dilution effect diminishes. The volatility studies have shown that it is mainly the nucleation mode particles that are affected by heat. The v-TDMA instrument have shown to be a sensitive analytical tool which, if desired to use for further engine exhaust particle characterization, needs some development work. Experimental work with the EMIR-system, which in principle is similar to the instruments proposed for a future standard, shows that these types of measurement systems are sensitive to small changes in the detector cut-off. The major outcome of the project lies in the new detailed knowledge about particle number measurements from engines. / QC 20100628

Slow speed rotating machines are the mainstay of several industrial applications worldwide. They can be found in paper and steel mills, rotating biological contractors, wind turbines etc. Operational experience of such machinery has not only revealed the early design problems but has also presented opportunities for further significant improvements in the technology and economics of the machines. Slow speed rotating machinery maintenance, mostly related to bearings, shafts and gearbox problems, represents the cause of extended outages. Rotating machinery components such as gearboxes, shafts and bearings degrade slowly with operating time. Such a slow degradation process can be identified if a robust on-line monitoring and predictive maintenance technology is used to detect impending problems and allow repairs to be scheduled. To keep machines functioning at optimal levels, failure detection of such vital components is important as any mechanical degradation or wear, if is not impeded in time, will often progress to more serious damage affecting the operational performance of the machine. This requires far more costly repairs than simply replacing a part. Over the last few years there have been many developments in the use of Acoustic Emission (AE) technology and its analysis for monitoring the condition of rotating machinery whilst in operation, particularly on slow speed rotating machinery. Unlike conventional technologies such as thermography, oil analysis, strain measurements and vibration, AE has been introduced due to its increased sensitivity in detecting the earliest stages of loss of mechanical integrity. This programme of research involves laboratory tests for monitoring slow speed rotating machinery components (shafts and bearings) using AE technology. To implement this objective, two test rigs have been designed to assess the capability of AE as an effective tool for detection of incipient defects within low speed machine components (e.g. shafts and bearings). The focus of the experimental work will be on the initiation and growth of natural defects. Further, this research work investigates the source characterizations of AE signals associated with such bearings whilst in operation. It is also hoped that at the end of this research program, a reliable on-line monitoring scheme used for slow speed rotating machinery components can be developed.

No description available.

In confined bulk crystal growth techniques such as the traveling heater method, base materials in an ampoule are melted and resolidified as a single crystal. During this process, flow control is desired so that the resulting alloy semiconductors are uniform in composition and have minimal defects. Such control allows for tuned lattice parameters and bandgap energy, properties necessary to produce custom materials for specific electro-optical applications. For ternary alloys, bulk crystal growth methods suffer from slow diffusion rates between elements, severely limiting growth rates and reducing uniformity. Exposing the electrically conducting melt to an external alternating magnetic field can accelerate the mixing. A rotating magnetic field (RMF) can be used to stir the melt in the azimuthal direction, which reduces temperature variations and controls the shape at the solidification front. A traveling magnetic field (TMF) imposes large body forces in the radial and axial directions, which helps reduce the settling of denser components and return them to the growth front. In either case, mixing is desired, but turbulence is not. At large magnetic Taylor numbers the flow becomes unstable to first laminar and then turbulent transitions. It is imperative that crystal growers know when these transitions will occur and how the flow physics is affected. Here, the melt driven by electromagnetic forces is analyzed through the use of 3D numerical simulations of the flow field up to and beyond the point of laminar instability. The analysis aims to emulate laboratory conditions for generating electromagnetic forces for both types of alternating magnetic fields and highlights the differences between laboratory forces and the analytical approximations that are often assumed. Comparisons are made between the resulting forces, flow fields, and points of instability as the frequency of the alternating field varies. Critical Taylor numbers and the resulting unstable flow fields are compared to the results from linear stability theory.