This dissertation has two topics. The rst one is about rotating a supporting hyperplane on the convex hull of a nite point set to arrive at one of its facets. We present three procedures for these rotations in multiple dimensions. The rst two procedures rotate a supporting hyperplane for the polytope starting at a lower dimensional face until the support set is a facet. These two procedures keep current points in the support set and accumulate new points after the rotations. The rst procedure uses only algebraic operations. The second procedure uses LP. In the third procedure we rotate a hyperplane on a facet of the polytope to a dierent adjacent facet. Similarly to the rst procedure, this procedure uses only algebraic operations. Some applications to these procedures include data envelopment analysis (DEA) and integer programming. The second topic is in the eld of containment problems for polyhedral sets. We present three procedures to nd a circumscribing simplex that contains a point set in any dimension. The rst two procedures are based on the supporting hyperplane rotation ideas from the rst topic. The third circumscribing simplex procedure uses polar cones and other geometrical properties to nd facets of a circumscribing simplex. One application of the second topic discussed in this dissertation is in hyperspectral unmixing.

With environmental concern growing in both affluent and developing countries, roof top ventilators, a form of natural ventilation requiring only wind energy to ensure quality air circulation and comfort is becoming a considered choice of many households and industries. Unfortunately, however, many of these ventilators have evolved through trial and error and the flow physics associated with these ventilators is barely understood. The present experimental project was, therefore, undertaken as part of UNSW- Industry collaboration program funded under an Australian Research Council Grant to explore whether the aerodynamics forces acting on these ventilators during their operation could be obtained. A commercial roof top ventilator supplied by industry was, therefore, tested in an open jet wind tunnel of the University of New South Wales and the results are presented in this thesis. A novel feature of this project is the examination of the suitability of ???the three dimensional wake traverse??? technique to the wake of rotating ventilator. This technique has so far been applied with limited success to the wake of lifting bodies of fixed wing configuration only. In the absence of adequate data in the literature on rotating ventilator, the aerodynamics force components obtained by this technique have been compared against force balance measurements. The results show that the wake traverse technique is capable of determining lift and total drag forces associated with the ventilator flow during its operation from the pressure and velocity information gathered downstream of a ventilator in its wake. Generally, from these data, the technique also allows isolation of the profile and induced components of the drag force. However, from the induced drag value, while it is possible to determine the lift force, it is however, found that a more accurate value of lift force can be evaluated using axial vorticity formulation. The availability of the above technique which does not require measurements on the test specimen itself, will aid in providing a cost efficient investigation of the aerodynamic forces and consequently the performance of a roof top ventilator.

<p>This master's thesis develops an algorithm for tracking of cars robust enough to handle turning cars. It is implemented in the image processing environment Image Processing Application Programming Interface (IPAPI) for use with the WITAS project. </p><p>Firstly, algorithms, comparable with one currently used in the WITAS-project, are studied. The focus is on how rotation, that originates from the turning of the cars, affects tracking performance. The algorithms studied all perform an exhaustive search over a region, close to the last known position of the object being tracked, to find a match. After this, an iterative algorithm, based on the idea that a car can only rotate, translate and change scale, is introduced. The algorithm estimates the parameters describing this rotation, translation, and change of scale, iteratively. The iterative process needs a initial parameter estimate that is accurate enough for the algorithm to converge. The developed algorithm is based on an earlier publication on the subject, however the mathematical description, and deduction, of it is taken one step further than in this publication. </p><p>The iterative algorithm used performs well under the assumption that the data used fulfills some basic criteria. These demands comprises: placement of camera, template size as well as how the parameters may vary between two observations. The iterative algorithm is also potentially faster than exhaustive search methods, because few iterations are needed when the parameters change slowly. Better initial parameters should improve stability and speed of convergation. Other suggestions that could give better performance is discussed, e.g., methods to better extract the target from the surroundings.</p>

In chapter 3 of our paper we present equations of motion for continuous mass distribution subject to hydrodynamic forces in their most general form. We start with equations for discrete mass particles and then transform the equations so that it is appropriate for a continuous mass distribution. As we do that, new forms of interactions are generated and we successfully include these interactions, using the propagator theory, in the general form of our hydrodynamic equations for continuous mass distributions. We also took a deeper mathematical description of rotational flows. We were able to explain many physical phenomena successfully by our treatment of rotational flows in a more concrete and simple way, for example, the phenomenon of ripples that appear on ocean beaches and in desert sands. In chapter 4 we study the behavior of water surfaces. A liquid drop of water takes on a spherical shape because of the phenomenon of surface tension. A physical model based on the arrangement which the water molecules have on the surface is introduced to explain the above phenomenon. A mathematical model, as well as the physical model mentioned above, is introduced to describe the kind of forces involved on a wavy surface. The equations obtained describe the phenomenon of surface tension on a microscopic level very successfully. In chapter 5 we apply the results of chapters 3 and 4 to get an equation that gives a critical dynamical value which govern the interactions between the moving fluid and the dust particles residing on the ground. / Graduation date: 1996

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Meteorology and Physical Oceanography, 1982. / Supervised by Nelson Hogg. Includes bibliographical references (leaves 108-109).

Thesis (Ph. D.)--Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1982. / Bibliography: p. 139-140.

Even though fluid mechanics is well developed as a science, there are many physical phenomena that we do not yet fully understand. One of these is the deformation rates and fluid stresses generated in a boundary layer for a non-Newtonian fluid. One such non-Newtonian fluid would be a waxy crude oil flowing in a centrifugal pump. This type of flow can be numerically modeled by a rotating disk system, in combination with an appropriate constitutive equation, such as the relation for a Bingham fluid. A Bingham fluid does not begin to flow until the stress magnitude exceeds the yield stress. However, experimental measurements are also required to serve as a database against which the results of the numerical simulation can be interpreted and validated. The purpose of the present research is to gain a better understanding of the behavior of a Bingham fluid in the laminar boundary layer on a rotating disk. For this project, two different techniques were employed: numerical simulation, and laboratory investigations using Particle Image Velocimetry (PIV) and flow visualization. Both methods were applied to the flow of a Bingham fluid over a rotating disk. In the numerical investigations, the flow was characterized by the dimensionless yield stress Bingham number, By, which is the ratio of the yield and viscous stresses. Using von Kármáns similarity transformation, and introducing the rheological behavior of the fluid into the conservation equations, the corresponding nonlinear two-point boundary value problem was formulated. A solution to the problem under investigation was obtained by numerical integration of the set of Ordinary Differential Equations (ODEs) using a multiple shooting method. The influence of the Bingham number on the flow behavior was identified. It decreases the magnitude of the radial and axial velocity components, and increases the magnitude of the tangential velocity component, which has a pronounced effect on the moment coefficient, CM, and the volume flow rate, Q. In the laboratory investigations, since the waxy crude oils are naturally opaque, an ambitious experimental plan to create a transparent oil that was rheologically similar to the Amna waxy crude oil from Libya was developed. The simulant was used for flow visualization experiments, where a transparent fluid was required. To fulfill the demand of the PIV system for a higher degree of visibility, a second Bingham fluid was created and rheologically investigated. The PIV measurements were carried out for both filtered tap water and the Bingham fluid in the same rotating disk apparatus that was used for the flow visualization experiments. Both the axial and radial velocity components in the (r-z) plane were measured for various rotational speeds. Comparison between the numerical and experimental results for the axial and radial velocity profiles for water was found to be satisfactory. Significant discrepancies were found between numerical results and measured values for the Bingham fluid, especially at low rotational speeds, mostly relating to the formation of a yield surface within the tank. Even though the flow in a pump is in some ways different from that of a disk rotating in a tank, some insight about the behavior of the pump flow can be drawn. One conclusion is that the key difference between the flow of a Bingham fluid in rotating equipment from that of a Newtonian fluid such as water relates to the yield surface introduced by the yield stress of the material, which causes an adverse effect on the performance and efficiency of such equipment.

TerraPower LLC is designing a fast breed and burn reactor intended to operate for up to 40 years without refueling, designated as the Travelling Wave Reactor (TWR). Various U-Zr alloy fuel designs have been proposed for the TWR that may require a powder feed for fabrication. A simple and economic option for laboratory scale powder production is the Rotating Electrode Process (REP), which produces microsphere shaped powder by melting the tip of a rotating bar with an electric arc. In order to fully characterize this process for various U-Zr alloys and provide the feed material for testing fabrication techniques, a Rotating Electrode System (RES) was designed and built. The RES is largely based on a combination of two designs; an early REP system developed by Starmet Corporation in the 19xxa and a later design optimized for U-Mo powder production by Idaho National Laboratory (INL). The RES designed for this work was improved based on input from vendors specializing in their respective areas of expertise and is capable of atomizing up to a 1.26 cm diameter metal alloy rod at 40,000 RPM. Every component of the machine can be disassembled and transferred through a 35.56 cm (14 in) diameter air lock of a glovebox so that it can operate in a controlled environment. The RES was tested by atomizing various diameter copper rods to prove system functionality. The tests were carried out in air using an argon cover gas in the powder collection chamber, known as the catch pan to limit oxidation rates of the newly generated microspheres. The powder produced showed strong sphericity ranging from 50 µm to 500 µm in diameter. Problems and areas of concern that were encountered during operation have been addressed so that the RES can be further optimized to better atomize U-Zr alloys once transferred into the glovebox.

This master's thesis develops an algorithm for tracking of cars robust enough to handle turning cars. It is implemented in the image processing environment Image Processing Application Programming Interface (IPAPI) for use with the WITAS project. Firstly, algorithms, comparable with one currently used in the WITAS-project, are studied. The focus is on how rotation, that originates from the turning of the cars, affects tracking performance. The algorithms studied all perform an exhaustive search over a region, close to the last known position of the object being tracked, to find a match. After this, an iterative algorithm, based on the idea that a car can only rotate, translate and change scale, is introduced. The algorithm estimates the parameters describing this rotation, translation, and change of scale, iteratively. The iterative process needs a initial parameter estimate that is accurate enough for the algorithm to converge. The developed algorithm is based on an earlier publication on the subject, however the mathematical description, and deduction, of it is taken one step further than in this publication. The iterative algorithm used performs well under the assumption that the data used fulfills some basic criteria. These demands comprises: placement of camera, template size as well as how the parameters may vary between two observations. The iterative algorithm is also potentially faster than exhaustive search methods, because few iterations are needed when the parameters change slowly. Better initial parameters should improve stability and speed of convergation. Other suggestions that could give better performance is discussed, e.g., methods to better extract the target from the surroundings.

Even though fluid mechanics is well developed as a science, there are many physical phenomena that we do not yet fully understand. One of these is the deformation rates and fluid stresses generated in a boundary layer for a non-Newtonian fluid. One such non-Newtonian fluid would be a waxy crude oil flowing in a centrifugal pump. This type of flow can be numerically modeled by a rotating disk system, in combination with an appropriate constitutive equation, such as the relation for a Bingham fluid. A Bingham fluid does not begin to flow until the stress magnitude exceeds the yield stress. However, experimental measurements are also required to serve as a database against which the results of the numerical simulation can be interpreted and validated. The purpose of the present research is to gain a better understanding of the behavior of a Bingham fluid in the laminar boundary layer on a rotating disk. For this project, two different techniques were employed: numerical simulation, and laboratory investigations using Particle Image Velocimetry (PIV) and flow visualization. Both methods were applied to the flow of a Bingham fluid over a rotating disk. In the numerical investigations, the flow was characterized by the dimensionless yield stress Bingham number, By, which is the ratio of the yield and viscous stresses. Using von Kármáns similarity transformation, and introducing the rheological behavior of the fluid into the conservation equations, the corresponding nonlinear two-point boundary value problem was formulated. A solution to the problem under investigation was obtained by numerical integration of the set of Ordinary Differential Equations (ODEs) using a multiple shooting method. The influence of the Bingham number on the flow behavior was identified. It decreases the magnitude of the radial and axial velocity components, and increases the magnitude of the tangential velocity component, which has a pronounced effect on the moment coefficient, CM, and the volume flow rate, Q. In the laboratory investigations, since the waxy crude oils are naturally opaque, an ambitious experimental plan to create a transparent oil that was rheologically similar to the Amna waxy crude oil from Libya was developed. The simulant was used for flow visualization experiments, where a transparent fluid was required. To fulfill the demand of the PIV system for a higher degree of visibility, a second Bingham fluid was created and rheologically investigated. The PIV measurements were carried out for both filtered tap water and the Bingham fluid in the same rotating disk apparatus that was used for the flow visualization experiments. Both the axial and radial velocity components in the (r-z) plane were measured for various rotational speeds. Comparison between the numerical and experimental results for the axial and radial velocity profiles for water was found to be satisfactory. Significant discrepancies were found between numerical results and measured values for the Bingham fluid, especially at low rotational speeds, mostly relating to the formation of a yield surface within the tank. Even though the flow in a pump is in some ways different from that of a disk rotating in a tank, some insight about the behavior of the pump flow can be drawn. One conclusion is that the key difference between the flow of a Bingham fluid in rotating equipment from that of a Newtonian fluid such as water relates to the yield surface introduced by the yield stress of the material, which causes an adverse effect on the performance and efficiency of such equipment.