Student Number: 0008522F Master of Science Faculty of Engineering & The Built Environment School of Mechanical, Industrial & Aeronautical Engineering / An aircraft travelling at supersonic speeds close to the ground generates a bow wave, which is reflected off the ground surface. When the aircraft enters a valley, the three-dimensional bow wave is reflected off the valley walls, such that it could focus behind the aircraft. Complex threedimensional wave surfaces will result. The real situation of an aircraft entering a valley can be modelled and tested experimentally in a shock tube. To simulate the process a planar shock wave, generated in a shock tube, is moved over several notched wedge configurations. Schlieren photographs were produced to identify the resulting complex three-dimensional wave structures and then verified by three-dimensional CFD. The valley geometries investigated are rectangular, triangular, parabolic and conical. Three hill geometries were also investigated. The three-dimensional reflected surfaces from the rectangular valleys were found to vary only slightly as the valley floor inclination is increased. As the incident wave interacts with both the wedge and valley floor surfaces two prominent reflections occur. A primary reflected wave surface is generated from regular reflection off the wedge. This surface flows over into the valley contacting the incident wave at a second contact point. A secondary reflected wave is found underneath the primary reflected wave, generated due to Mach reflection occurring over the full width off the valley floor. The area of the incident wave between the second contact point and the triple point is seen to bow out into the downstream flow. The Mach stem of the reflection off the valley floor tends to become less pronounced for the larger valley floor inclination angles. In all the rectangular valleys, a shear layer is present, cascading down the valley wall and then along the valley entrance. The shear layer tends to decrease in size as the valley floor inclination increases. Both prominent reflected shock surfaces are almost conical in nature at close proximity to the valley wall. The triangular valleys show similar reflection patterns as the rectangular valleys. As the incident shock wave initially interacts with the wedge surface only regular reflection occurs. The resulting reflected wave forms the primary reflected surface which flows over into the valley. The reflection changes to Mach reflection as the incident wave interacts with the valley floor. The Mach stem of the reflection off the valley floor increases in characteristic height as one moves from the valley entrance wall to the plane of symmetry. The Mach stem is much smaller for the higher valley floor inclinations. A secondary reflected wave is found underneath the primary reflected surface. The secondary wave is Mach reflection near the plane of symmetry which turns iii to regular reflection closer to the valley wall. The primary and secondary reflected surfaces merge near the plane of symmetry and again along the wedge surface. A shear layer is found to cascade down the valley entrance wall for all geometries, decreasing in strength as the valley inclination angle increases. The parabolic valleys show similar reflection patterns as the triangular valleys. As the incident wave interacts with both the wedge and valley surfaces two reflections occur. The reflection off the wedge surface is regular. As the incident wave flows over into the valley the initial reflection off the valley floor is regular. This regular reflection then turns into Mach reflection the closer one moves to the symmetry plane. The Mach reflection off the valley floor forms a secondary reflected wave underneath the primary reflected wave that is found to flow over into the valley. The primary reflected wave contacts the incident wave at a second contract point found above the triple point. This contact point moves closer to the triple point and eventually along the secondary reflected wave as the incident wave advances downstream. The second contact point at a single time instant is also seen to move closer to the triple point as one moves closer to the plane of symmetry. A shear layer is found cascading down the valley entrance wall. The secondary reflected wave of the Mach reflection off valley floor forms a semi-circular surface which contacts the floor just after the shear layer. The Mach reflection off the valley floor changes to regular reflection as the surface begins to climb up along the valley entrance wall. The conical valleys once again show similar reflection patterns as those found in the other valley geometries. As the incident wave interacts with both the wedge and valley surfaces two reflections occur. Regular reflection occurs off the wedge surface with the resulting primary reflected wave flowing over into the valley. This primary reflected wave contacts the incident shock at a second contact point in the valley. The reflection off the valley floor is regular close to the valley entrance wall changing to Mach reflection nearer the symmetry plane. The reflected wave from the Mach reflection forms the secondary reflected surface found beneath the primary reflected wave. The secondary reflected Mach wave changes to regular reflection as the surface nears the valley wall, with the reflection point travelling along the valley floor until coincident with the valley entrance wall, where it then travels along the entrance wall. The second contact point found on the incident wave is found above the triple point and moves down the incident shock to eventually coincide with the triple point. A weak shear layer is found to cascade down the valley entrance wall. A weak separation also occurs at the entry point of the valley. iv The three hill geometries, triangular, parabolic and conical, all display similar reflection patterns. As the incident wave advances downstream regular reflection occurs off both the wedge and hill surfaces. The reflected waves come together at a point off the surface. At this point a double triple point occurs with two resulting Mach stems. One Mach stem contacts the wedge surface while the other contacts the hill surface. The resulting double Mach stem surface wraps around the base of the hill getting progressively tighter the closer it gets to the incident wave. The only major differences between all three geometries is the shape of the resulting reflected wave off the hill surface (which tends to follow the same geometric shape as the hill) and the distance between the two triple points for the conical and parabolic hills tends to be larger than that found for the triangular hill.

Arterial pulse pressure is critically important to a number of diseases such as isolated systolic hypertension, coronary artery disease and heart failure. Determining the cause of increased pulse pressure has been hampered for two reasons. First, pulse pressure results from contraction of the heart and the load formed by the complex arterial tree. Pressure pulses travel from the heart to the peripheral arteries. As they reach a bifurcation or change in arterial wall properties, some of the pulses get reflected and propagate retrograde towards the heart. Second, two different modeling approaches (0-D and 1-D) describe the arterial system. The Windkessel model ascribed changes in pulse pressure to changes in total arterial compliance (Ctot) and total arterial resistance, whereas the transmission model ascribed them to changes in the magnitude, timing and sites of reflection. Our investigation has addressed both these limitations by finding that a complex arterial system degenerates into a simple 2-element Windkessel model when wavelength of the propagated pulse increases. This theoretical development has yielded three practical results. First, isolated systolic hypertension can be viewed as a manifestation of a system that has degenerated into a Windkessel, and thus increased pulse pressure is due to decreased Ctot. Second, the well-discussed Augmentation Index does not truly describe augmentation of pulse pressure by pulse reflection. Third, the simple 2-element Windkessel can be used to characterize the interaction among heart, arterial system and axial-flow left ventricular assist device analytically. The fact that arterial systems degenerate into Windkessels explains why it becomes much easier to estimate total arterial compliance in hypertension?total arterial compliance is the dominant determinant of pulsatile pressure.

Arterial pulse pressure is critically important to a number of diseases such as isolated systolic hypertension, coronary artery disease and heart failure. Determining the cause of increased pulse pressure has been hampered for two reasons. First, pulse pressure results from contraction of the heart and the load formed by the complex arterial tree. Pressure pulses travel from the heart to the peripheral arteries. As they reach a bifurcation or change in arterial wall properties, some of the pulses get reflected and propagate retrograde towards the heart. Second, two different modeling approaches (0-D and 1-D) describe the arterial system. The Windkessel model ascribed changes in pulse pressure to changes in total arterial compliance (Ctot) and total arterial resistance, whereas the transmission model ascribed them to changes in the magnitude, timing and sites of reflection. Our investigation has addressed both these limitations by finding that a complex arterial system degenerates into a simple 2-element Windkessel model when wavelength of the propagated pulse increases. This theoretical development has yielded three practical results. First, isolated systolic hypertension can be viewed as a manifestation of a system that has degenerated into a Windkessel, and thus increased pulse pressure is due to decreased Ctot. Second, the well-discussed Augmentation Index does not truly describe augmentation of pulse pressure by pulse reflection. Third, the simple 2-element Windkessel can be used to characterize the interaction among heart, arterial system and axial-flow left ventricular assist device analytically. The fact that arterial systems degenerate into Windkessels explains why it becomes much easier to estimate total arterial compliance in hypertension?total arterial compliance is the dominant determinant of pulsatile pressure.

Different types of breakwaters have been developed in the past for the protection of valuable coastal property, commercial activity and beach morphology. Among these, gravity-type breakwaters are the most common and provide good surface wave attenuation. However, these breakwaters are not always suitable due to their adverse impact on the coastal environment. To alleviate the problem, free surface breakwaters with a variety of caisson designs have been proposed and developed. The main advantages of such breakwaters are low capital cost, freedom from silting and scouring, short construction period, circulation of water beneath the breakwater and exertion of relatively low hydrodynamic forces on the structure as compared to conventional breakwaters. However, complete tranquillity on the lee side is not likely to occur due to wave energy transfer through the permeable parts of the breakwater. The degree of wave attenuation primarily depends on the configuration of the breakwater, the water depth and the incident wave conditions. The hydrodynamic performance of such free surface breakwaters is the subject of this thesis. Semicircular breakwaters mounted on a low-crested rubble mound structure were successfully built for harbour protection in Japan and China. However, the concept of having semicircular structures as free surface breakwaters has not yet been explored by the research community. As a result, this research is initiated with the aim of developing a free surface semicircular breakwater (SCB) that would serve as an anti-reflection barrier and provide reasonably good wave protection to coastal and marine infrastructures. To meet this research goal, a free surface SCB models were constructed and tested in a wave flume under various wave conditions. The experiments were conducted in three stages. For the first stage, the SCB model was initially tested without any perforations on the curved surface (i.e. a solid SCB) for different depths of immersion from the still water level in the wave flume. For the second stage, the front curved wall of the model was subsequently perforated with rectangular openings of different dimensions, producing front wall porosity of 9, 18 and 27%. Following this, two rows of rectangular openings near the crest of the rear curved wall were provided so as to facilitate water infiltration and escape of the run-up waves. For the third stage, additional effort was made to extend the draft of the breakwater by adding a wave screen at the front or/and rear. The screen porosity was 25, 40 and 50%. The hydrodynamic characteristics of the SCB models were investigated in both regular and irregular seas through a series of systematic experimental programme. The water surface elevations were measured at different locations upstream and downstream of the models to determine the coefficients of wave transmission (CT), reflection (CR) and energy dissipation (CL) as well as the wave climate coefficients in front and inside the breakwater chamber. The horizontal wave forces exerted on the SCB models and the wave screen(s) were also measured and subsequently normalised to yield the force coefficients in the analysis. These hydrodynamic coefficients for the respective test cases are presented and discussed in this thesis. The experimental results revealed that even though the solid SCB was a better wave attenuator than the perforated ones, it produced a considerable amount of wave reflection. The perforated SCB with 9% porosity of the front wall (denoted as SCB9) outperformed the other perforated breakwater models; however, it produced high wave transmission when the draft was limited and subjected to longer period waves. Hence, wave screens were added to further enhance the performance of the SCB9. The SCB9 with double screens of 25% porosity was found to provide the highest hydraulic performance. Empirical equations were developed using a multiple regression technique to provide design formulae for wave transmission, wave reflection and horizontal wave forces. The proposed empirical equations showed good agreement with the experimental data. These equations are intended to be of direct use to engineers in predicting the hydrodynamic performance of free surface SCBs. However, sensible engineering judgement must be taken while using these equations as they are based on small scale laboratory tests.

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This thesis presents Bayesian geoacoustic inversion of seabed reflection-coefficient data as part of the U.S. Office of Naval Research Seabed Characterization Experiment 2017 at the New England Mud Patch. First, a linearized, ray-based Bayesian inversion of acoustic arrival times is carried out for high-precision estimation of experiment geometry and uncertainties, representing an important first step to inferring seabed properties using geoacoustic inversion methods such as reflection inversion. The high-precision estimates for source-receiver ranges, source depths, receiver depths, and water depths at reflection points along the survey track are used to calculate grazing angles, with angle uncertainties computed using Monte Carlo methods. The experiment geometry uncertainties are obtained using analytic linearized estimates, and verified with nonlinear analysis. Second, a trans-dimensional (trans-D) Bayesian inversion of reflection-coefficient data is carried out for geoacoustic parameters and uncertainties of fine-grained/cohesive sediments. The trans-D inversion samples probabilistically over an unknown number of seabed interfaces and the parameters of a zeroth- or first-order autoregressive error model. The numerical method of parallel tempering reversible jump Markov-chain Monte Carlo sampling is employed. Spherical-wave reflection coefficient modelling is applied using plane-wave decomposition in the Sommerfeld integral. The inversion provides marginal posterior probability profiles for Buckingham's viscous grain-shearing parameters: porosity, grain-to-grain compressional modulus, material exponent, and compressional viscoelastic time constant as a function of depth in the sediment. These parameters are used to compute dispersion relationships for each layer in the model, providing marginal posterior probability profiles for compressional-wave velocity and attenuation at different frequencies, as well as density. The geoacoustic inversion results are compared to independent measurements of sediment properties. / Graduate

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Coronary stents have become a very popular treatment for cardiovascular disease, historically the leading cause of death in the United States. Stents, while successful in the short term, are subject to high failure rates (up to 24% in the first six months) due to wall regrowth and clotting, probably due to a combination of abnormal mechanical stresses and disruption of the arterial blood flow. The goal of this research was to develop recommendations concerning ways in which stent design might be improved, focusing on the problem of pressure wave reflections. A one-dimensional finite-difference model was developed to predict these reflections, and effects of variations in stent and vessel properties were examined, including stent stiffness, length, and compliance transition region, as well as vessel radius and wall thickness. The model was solved using a combination of Weighted Essentially Non-Oscillatory (WENO) and Runge-Kutta methods. Over 100 cases were tested. Results showed that reasonable variations in these parameters could induce changes in reflection magnitude of up to ±50%. It was also discovered that the relationship between each of these properties and the resulting wave reflection could be described simply, and the effect of all of them together could in fact be encompassed by a single non-dimensional parameter. This parameter was titled"Stent Authority," and several variations were proposed. It is believed this parameter is a novel way of relating the energy imposed upon the arterial wall by the stent, to the fraction of the incident pressure energy which is reflected from the stented region. / Master of Science

No / The bandwidth of a microstrip patch antenna is expressed in terms of minimum achievable reflection coefficient using an equivalent circuit and the Bode-Fano theory. The bandwidth-reflection coefficient product is found to be proportional to antenna height and largely independent of feed probe position, for small bandwidths. The product can be computed directly from a numerical evaluation of the first-order Bode-Fano integral. Curves are presented showing how the product becomes limited by the feed probe inductance at very large bandwidths. It is concluded that this effect is unlikely to be a limit on the potential bandwidth of a practical patch antenna. If as a minimal correction the feed inductance is tuned out, the realized bandwidth with low order matching or optimal over-coupling shows the expected relationship to the theoretical limit.