The dependence of the point properties at the nucleus, electron density (Qe(0) )and spin density (Qs(0) ), on the nuclear cusp is examined for lithium atomic configuration interaction (CI) wave functions. Several series of CI wave functions with 18 and fewer terms, are studied. Importance of the triplet core spin function to Qs(0) is substantiated. Necessary, but not sufficient, spin and electron integral cusp conditions are applied as linear constraints. For the functions studied, Qs(0) improves on applying the spin cusp constraint if the free variational spin cusp is greater than -Z, but becomes worse otherwise. The electron cusp constraint invariably overcorrects Qe(0). The effect of necessary off-diagonal weighting constraints is also examined. No obvious trends could be found. It is concluded that forcing CI functions with a small number of terms to satisfy necessary diagonal or off-diagonal integral cusp conditions has very limited usefulness. A good Qs(0) can be obtained without constraining by (l) including triplet core spin terms. (2) optimizing orbital exponents. Sufficient nuclear cusp constraints are developed for CI wave functions. The generalized cusp-satisfying CI function has multiconfigurational SCF form with the correct cusp for each orbital. Sample calculations with a small basis set are presented. These simple functions give extremely good Qs(0) expectation values but convergence of Qs(0) with respect to basis set size is yet to be tested. The most interesting discovery is the appearance of Dirac [symbol omitted]-like correction basis orbitals from energy minimization of the orbital exponents. A scheme is depicted classifying previous and present work on cusp constraints in terms of necessity and/or sufficiency. / Science, Faculty of / Chemistry, Department of / Graduate

Wave energy conversion remains a promising technology with substantial renewable resources to be exploited in many parts of the world. However to be commercially attractive more effective conversion is desirable. There is scope for increasing power capture by use of several bodies responding with several modes, some or all of which may undergo resonance for frequencies within a wave climate. This theme is explored here with a floating moored line absorber system where the relative motion generates power by incorporation of a damper to represent the power take off. To be most effective the bodies should be responding in anti-phase requiring spacing between adjacent bodies of half a wavelength. First a converter design including two bodies is investigated experimentally and numerically responding solely in heave. The bodies have drafts to provide resonant frequencies within a wave spectrum, the stern diameter is as large as possible within the inertia regime and the bow diameter is optimised to provide maximum power. Experiments showed this system to be limited since the desirable anti phase heave modes were contaminated with other modes for off resonance response considerably reducing power generation. To stabilise motion in the desired modes another small float was introduced as the bow float rigidly connected by a beam to the mid float with the added benefit of adding forcing due to surge and pitch to some degree (following Prof Peter Stansby’s design). The sizes of the three floats increase from bow to stern, causing the line absorber to align with the wave direction. This system was optimised through experiments varying float spacing, diameter, draft and the hinge point above the mid float about which relative angular motion occurs. These experiments were undertaken at small scale in the wide Manchester University flume at about 1/40th scale. Regular and random (JONSWAP) waves were investigated including directionality and different spectral peakedness factor. Corresponding experiments were undertaken at five time larger scale (about 1/8th) in the wave basin at the COAST laboratory of Plymouth University. These tests were for a flat-based floats; the mechanical damping coefficient for larger scale was within the range for the smaller scale tests after appropriate (Froude) scaling. Tests at Manchester showed that the more rounded base floats (the mid float being hemi spherical) provided improved power capture. Device effectiveness is defined in terms of capture width ratio; that is the average power divided by the wave power per metre divided by the wavelength, defined by the energy period in the case of irregular waves. The experiments showed that capture width ratios were greater than 25% in regular waves and greater than 20% in irregular waves across a broad range of wave periods. With rounded base floats capture width ratios over 20% were achieved for a broad range of wave frequencies up to a maximum greater than 35%. Limited experiments at larger scale showed that increasing the damping coefficient could increase power capture by about 50%. Characterisation by capture width ratio is convenient for determining annual energy yield from scatter diagrams. This was undertaken for six sites of interest for wave energy conversion. It was assumed that the greatest power to weight ratio determines the most economic device; it was found that large devices could produce very large average power, for example average power of 2 MW, but the optimum power/weight ratio occurred at smaller scale, with average power typically 0.3 MW.

Neural transduction is the process by which neurons convert externally applied electrical energy into stable, propagating voltage pulses. Given some stimulus waveform with particular parameters such as duration, phase delay, etc., there is a minimum stimulus amplitude required in order for transduction of the waveform to result in an active neural response. The minimum amplitude for excitation, the threshold amplitude, is a strong function of many variables including stimulus waveshape, frequency and duration. This study reveals some details of the threshold characteristics of the Frankenhaeuser-Huxley (FH) model of myelinated nerve. These threshold transduction characteristics are studied with the aid of phase-space analysis, and are used to produce a model of neural excitation which is clinically applicable to human nerve. The full FH system of equations is used to predict threshold behaviour for in-vivo human nerve, and the predictions are shown to be in good agreement with clinically obtained threshold data. The study concludes by examining some of the additions to the FH model which would be necessary to model the accumulation of extra-nodal potassium ions. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis investigates water particle kinematics and the wave forces exerted on a slender rigid vertical cylinder in regular bidirectional wave fields. The instrumented portion of this cylinder is partitioned into nine independent segments enabling measurement of the vertical profile of hydrodynamic loading both in-line and transverse to the direction of wave propagation. Experiments conducted at the Hydraulics Laboratory of the National Research Council in Ottawa are described and some results are compared with the predictions of a wave force model based on the Morison equation and linear fluid kinematics. The influence of the crossing angle between the two wave components on the forces experienced by the column is determined. These experiments consider short-crested wave behavior in intermediate and deep water resulting from the interaction of two identical regular wave trains crossing at angles of 30, 60 and 90 degrees. The limit corresponding to unidirectional monochromatic waves is also investigated to provide a reference condition for comparison with the short-crested results. Conditions at the location of maximum short-crested wave height are of primary interest, however, forces at locations between the anti-node and node of the flow are also examined. In all, water surface elevations, flow velocities, and wave forces were measured in 24 short-crested and 8 different long-crested wave conditions spanning the range of Keulegan-Carpenter number between 4 and 24. The results of this study confirm the findings of previous researchers that short -crested waves with a certain period travel faster and rise higher before breaking than do their long-crested counterparts, but that in-line wave forces are not necessarily increased. Lift force maxima equal to half the maximum in-line force were measured; these forces can contribute significantly to the magnitude and direction of the total force resultant. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The waves produced by a flap-type wavemaker, hinged in the middle, are modelled using first-order linear wavemaker theory. A simplified closed-loop, discrete-time system is proposed. This includes a proportional plus integral plus derivative (PID) controller, and the wavemaker in order to compare the actual wave spectral density with the desired wave spectral density at a single frequency. Conventional discrete-time control theory is used with the major difference being the use of a relatively long timestep duration between changes in waveboard motion. The system response is calculated for many controller gain combinations by the computer simulation program CBGANES. System stability is analyzed for the gain combinations by using two different methods. One method is an extension of the Routh criterion to discrete-time and the other is a state-space eigenvalue approach. The computer simulation and the stability analysis provide a means for selecting possible controller gains for use at a specific frequency in an actual wave tank experiment. The computer simulation performance response and the two stability analyses predict the same results for varying controller gains. It is evident that integral control is essential in order to achieve a desired response for this long duration timestep application. The variation in discrete timestep duration and in desired spectral density (an indirect indication of frequency variation) provide variation in the constraints on controller gain selection. The controller gain combinations yielding the fastest stable response at a single frequency are for large proportional gain and small integral and derivative gains. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Electron momentum spectroscopy (EMS) provides experimental atomic and molecular electronic structure information in terms of the binding energy spectrum and the experimental momentum profile (XMP), which is a direct probe of the electron momentum distribution in specific molecular orbitals. The measured XMPs permit a detailed quantitative evaluation of theoretical ab initio wavefunctions in quantum chemistry and also provide a means to investigate traditional concepts in chemical reactivity at the fundamental electronic level. This thesis reports high momentum resolution EMS measurements of the valence orbitals of H₂0, D₂0, NH₃ and H₂CO obtained using an EMS spectrometer of the symmetric, non-coplanar type operated at an impact energy of 1200eV. The measured experimental momentum profiles for the valence orbitals of each molecule have been placed on a common intensity scale, which has allowed a stringent quantitative comparison between experiment and theory. These studies now confirm earlier preliminary investigations that suggested serious discrepancies between experimental and theoretical momentum distributions. Exhaustive consideration of possible rationalizations of these discrepancies indicate that double zeta quality and even near Hartree-Fock quality wavefunctions are insufficient in describing the outermost valence orbitals of H₂0 and NH₃. Preliminary results for H₂CO also indicate that near Hartree-Fock wavefunctions are incapable of describing the outermost 2b₂ orbital. Interactive and collaborative theoretical efforts have therefore led to the development of new Hartree-Fock limit and also highly correlated (CI) wavefunctions for H₂0, NH₃ and H₂CO. It is found that highly extended basis sets including diffuse functions and the adequate inclusion of correlation and relaxation effects are necessary in the accurate prediction of experimental momentum profiles as measured by electron momentum spectroscopy. New EMS measurements are also reported for the outermost valence orbitals of NF₃, NH₂CH₃, NH (CH₃)₂, N (CH₃)₃ and para-dichlorobenzene. These exploratory studies have illustrated useful chemical applications of EMS. In particular, EMS measurements of the outermost orbitals of the methylated amines have revealed chemical trends which are consistent with molecular orbital calculations. These calculations suggest extensive electron density derealization of the so-called nitrogen 'lone pair' in the methylated amines in comparison to the 'lone pair' in NH₃. EMS measurements of the non-degenerate π₃ and π₂ orbitals of para-dichlorobenzene show different experimental momentum profiles consistent with arguments based on inductive and resonance effects. These experimental trends, both in the case of the amines and para-dichlorobenzene, were qualitatively predicted by molecular orbital calculations using double zeta quality wavefunctions. However more accurate prediction of the experimental momentum profiles of these molecules will need more extended basis sets and the inclusion of correlation and relaxation effects as suggested by the studies based on the smaller molecules. An integrated computer package (HEMS) for momentum space calculations has also been developed based on improvements to existing programs. Development studies testing a new prototype multichannel (in the ɸ plane) EMS spectrometer are described. / Science, Faculty of / Chemistry, Department of / Graduate

The use of a periodic rectangular groove profile to eliminate specular reflection from a conducting surface is studied. The concentration of all scattered power in the principal backscatter mode, i.e., in a direction opposite to the incident wave, is possible under plane wave illumination if the period d = λ/(2sinθ₁): where θ₁. is the angle of incidence from the surface normal and A is the wavelength; and the width and depth of the grooves are properly chosen. An analytical and numerical study of the scattering is carried.out for arbitrary polarization to determine these groove dimensions and the effect of systematic errors in them. Experiments were performed at 35 GHz using brass plates of finite size under non-plane wave illumination. The experimental results show that the plates behave essentially as predicted. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The performance of a flexible structure as a breakwater is investigated numerically. The structure is a hemicylinder and is filled with water of uniform pressure. It is anchored along the sides. Only flexural modes are present. The structure is modeled as an elastic shell using the finite element program ABAQUS. The fluid is assumed to be inviscid and incompressible. The fluid flow is analyzed using a boundary integral method and the integral equation is solved numerically by a panel method. The vibration characteristics of the structure are analyzed both in the absence and presence of water. The hydrodynamic coefficients, forces, and the dynamic response of the structure in waves are obtained as a function of the wave number. Two different water depths of 5 m and 6 m are considered. For each water depth, normal and oblique incident waves are considered. The free surface elevation in front of and behind the structure is evaluated for different wave frequencies and directions. The results indicate that the flexible structure is effective in reducing the incident wave intensity over a wide range of frequencies. / Master of Science

Indiana University-Purdue University Indianapolis (IUPUI) / Pressure wave supercharger is an application of wave rotor technology that utilizes compression waves produced by high-pressure engine exhaust gas to compress the fresh intake air within the channels. The phenomena within the wave rotor channels are governed by compression and expansion waves initiated when the channel ends are periodically exposed to differing pressure ports. Two incoming fluids are brought into contact for a very short amount of time to facilitate efficient energy and momentum transfer, thereby exchanging pressure dynamically between the fluids by means of unsteady pressure waves. Since the energy transfer is based on unsteady pressure waves, correct matching of waves and ports is essential for optimum results. Mistiming of the waves in the channels is detrimental to the efficient exchange of pressure and low-pressure exhaust scavenging, which ensures minimum exhaust gas recirculation. Due to varying speed and load conditions of the unit to be supercharged, it is not always possible to maintain the rotor speed constant at the design point. To mitigate the effects of wave mistiming due to varying speed, a well-designed combination of wall-pockets was used in Comprex® pressure wave supercharger. The wall-pockets are the recesses provided in the endplates of pressure wave superchargers to create necessary pressure zones at desired locations. This thesis details an extensive qualitative and computational investigation of the performance of pressure wave superchargers with pockets. Numerical simulations of pressure wave superchargers have been performed using the wave rotor analysis codes employed at the Combustion and Propulsion Research Laboratory at IUPUI. This work also pays close attention to inspecting the numerical schemes and modeling of different physical phenomena used in each code. A comparative verification of the wave rotor analysis codes has been conducted to ensure that the same fundamental numerical scheme is correctly implemented in each code. The issue of low-pressure scavenging has been demonstrated by simulating the four-port (pocketless) pressure wave supercharger operating at lower speeds. The wall-pockets have been modeled using a simple lumped volume technique. The gas state in the lumped volume of pockets is estimated using the continuity and energy equations such that the net mass and energy fluxes between each pocket and the wave rotor channels are close to zero. The lumped volume models of pockets have been implemented in the four-port wave rotor configurations to simulate the pressure wave superchargers with pockets. The simulation results show that the pockets assist to maintain sufficient pressure in the desired zones to facilitate proper low-pressure scavenging during lower rotor speed operations. The Comprex simulation results have been observed to be in good agreement with experimental data and qualitative analysis. Specific observations on the performance of each code and comprehensive simulation results have been presented.

The simulation of solitary wave run up on a slope is evaluated using a volume of fluid method in OpenFOAM. The simulated results are compared to experimental and nonlinear potential flow results for a 1 to 15 run up slope. The breaking region profile is shown to agree well with previous results except a larger jet tip calculated by OpenFOAM. Elevation through the run up of the wave is compared to the same data set. OpenFOAM shows a decreased peak amplitude when compared. A grid study is completed. The dissipation is investigated and a correction is applied to the OpenFOAM results. Corrected data shows a more accurate profile in the breaking region. Results shown indicate that more work is needed to improve two phase modeling within OpenFOAM for application to the case of solitary wave run up on a slope. Simulations are also completed for a vehicle fording case.