APPLICATION OF THE KHOKHLOV-ZABOLOTSKAYA-KUZNETSOV EQUATION TO MODELING HIGH-INTENSITY FOCUSED ULTRASOUND BEAMS

High-intensity focused ultrasound is a form of therapeutic ultrasound which uses high amplitude acoustic waves to heat and ablate tissue. HIFU employs acoustic amplitudes that are high enough that nonlinear propagation effects are important in the evolution of the sound field. A common model for HIFU beams is the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation which accounts for nonlinearity, diffraction, and absorption. The KZK equation models diffraction using the parabolic or paraxial approximation. Many HIFU sources have an aperture diameter similar to the focal length and the paraxial approximation may not be appropriate. Here, results obtained using the “Texas code,” a time-domain numerical solution to the KZK equation, were used to assess when the KZK equation can be employed. In a linear water case comparison with the O’Neil solution, the KZK equation accurately predicts the pressure field in the focal region. The KZK equation was also compared to simulations of the exact fluid dynamics equations (no paraxial approximation). The exact equations were solved using the Fourier-Continuation (FC) method to approximate derivatives in the equations. Results have been obtained for a focused HIFU source in tissue. For a low focusing gain transducer (focal length 50λ and radius 10λ), the KZK and FC models showed excellent agreement, however, as the source radius was increased to 30λ, discrepancies started to appear. Modeling was extended to the case of tissue with the appropriate power law using a relaxation model. The relaxation model resulted in a higher peak pressure and a shift in the location of the peak pressure, highlighting the importance of employing the correct attenuation model. Simulations from the code that were compared to experimental data in water showed good agreement through the focal plane.

PROPAGATION OF SONIC BOOMS THROUGH A REAL, STRATIFIED ATMOSPHERE

Sonic boom propagation in a quiet) stratified) lossy atmosphere is the subject of this dissertation. Two questions are considered in detail: (1) Does waveform freezing occur? (2) Are sonic booms shocks in steady state? Both assumptions have been invoked in the past to predict sonic boom waveforms at the ground. A very general form of the Burgers equation is derived and used as the model for the problem. The derivation begins with the basic conservation equations. The effects of nonlinearity) attenuation and dispersion due to multiple relaxations) viscosity) and heat conduction) geometrical spreading) and stratification of the medium are included. When the absorption and dispersion terms are neglected) an analytical solution is available. The analytical solution is used to answer the first question. Geometrical spreading and stratification of the medium are found to slow down the nonlinear distortion of finite-amplitude waves. In certain cases the distortion reaches an absolute limit) a phenomenon called waveform freezing. Judging by the maturity of the distortion mechanism, sonic booms generated by aircraft at 18 km altitude are not frozen when they reach the ground. On the other hand, judging by the approach of the waveform to its asymptotic shape, N waves generated by aircraft at 18 km altitude are frozen when they reach the ground. To answer the second question we solve the full Burgers equation and for this purpose develop a new computer code, THOR. The code is based on an algorithm by Lee and Hamilton (J. Acoust. Soc. Am. 97, 906-917, 1995) and has the novel feature that all its calculations are done in the time domain, including absorption and dispersion. Results from the code compare very well with analytical solutions. In a NASA exercise to compare sonic boom computer programs, THOR gave results that agree well with those of other participants and ran faster. We show that sonic booms are not steady state waves because they travel through a varying medium, suffer spreading, and fail to approximate step shocks closely enough. Although developed to predict sonic boom propagation, THOR can solve other problems for which the extended Burgers equation is a good propagation model.

Bridge-vehicle interaction for structural health monitoring: potentials, applications, and limitations

Structural Health Monitoring (SHM) is an integral part of infrastructure maintenance and management systems due to socio-economic, safety and security reasons. The behaviour of a structure under vibration depends on structure characteristics. The change of structure characteristics may suggest the change in system behaviour due to the presence of damage(s) within. Therefore the consistent, output signal guided, and system dependable markers would be convenient tool for the online monitoring, the maintenance, rehabilitation strategies, and optimized decision making policies as required by the engineers, owners, managers, and the users from both safety and serviceability aspects. SHM has a very significant advantage over traditional investigations where tangible and intangible costs of a very high degree are often incurred due to the disruption of service. Additionally, SHM through bridge-vehicle interaction opens up opportunities for continuous tracking of the condition of the structure. Research in this area is still in initial stage and is extremely promising. This PhD focuses on using bridge-vehicle interaction response for SHM of damaged or deteriorating bridges to monitor or assess them under operating conditions. In the present study, a number of damage detection markers have been investigated and proposed in order to identify the existence, location, and the extent of an open crack in the structure. The theoretical and experimental investigation has been conducted on Single Degree of Freedom linear system, simply supported beams. The novel Delay Vector Variance (DVV) methodology has been employed for characterization of structural behaviour by time-domain response analysis. Also, the analysis of responses of actual bridges using DVV method has been for the first time employed for this kind of investigation.

Design of digital differentiators

A digital differentiator simply involves the derivation of an input signal. This work includes the presentation of first-degree and second-degree differentiators, which are designed as both infinite-impulse-response (IIR) filters and finite-impulse-response (FIR) filters. The proposed differentiators have low-pass magnitude response characteristics, thereby rejecting noise frequencies higher than the cut-off frequency. Both steady-state frequency-domain characteristics and Time-domain analyses are given for the proposed differentiators. It is shown that the proposed differentiators perform well when compared to previously proposed filters. When considering the time-domain characteristics of the differentiators, the processing of quantized signals proved especially enlightening, in terms of the filtering effects of the proposed differentiators. The coefficients of the proposed differentiators are obtained using an optimization algorithm, while the optimization objectives include magnitude and phase response. The low-pass characteristic of the proposed differentiators is achieved by minimizing the filter variance. The low-pass differentiators designed show the steep roll-off, as well as having highly accurate magnitude response in the pass-band. While having a history of over three hundred years, the design of fractional differentiator has become a ‘hot topic’ in recent decades. One challenging problem in this area is that there are many different definitions to describe the fractional model, such as the Riemann-Liouville and Caputo definitions. Through use of a feedback structure, based on the Riemann-Liouville definition. It is shown that the performance of the fractional differentiator can be improved in both the frequency-domain and time-domain. Two applications based on the proposed differentiators are described in the thesis. Specifically, the first of these involves the application of second degree differentiators in the estimation of the frequency components of a power system. The second example concerns for an image processing, edge detection application.

Feasibility of combined wind-wave energy platforms

The European Union has set out an ambitious 20% target for renewable energy use by 2020. It is expected that this will be met mainly by wind energy. Looking towards 2050, reductions in greenhouse gas emissions of 80-95% are to be sought. Given the issues securing this target in the transport and agriculture sectors, it may only be possible to achieve this target if the power sector is carbon neutral well in advance of 2050. This has permitted the vast expansion of offshore renewables, wind, wave and tidal energy. Offshore wind has undergone rapid development in recent years however faces significant challenges up to 2020 to ensure commercial viability without the need for government subsidies. Wave energy is still in the very early stages of development so as yet there has been no commercial roll out. As both of these technologies are to face similar challenges in ensuring they are a viable alternative power generation method to fossil fuels, capitalising on the synergies is potentially a significant cost saving initiative. The advent of hybrid solutions in a variety of configurations is the subject of this thesis. A singular wind-wave energy platform embodies all the attributes of a hybrid system, including sharing space, transmission infrastructure, O&M activities and a platform/foundation. This configuration is the subject of this thesis, and it is found that an OWC Array platform with multi-MegaWatt wind turbines is a technically feasible, and potentially an economically feasible solution in the long term. Methods of design and analysis adopted in this thesis include numerical and physical modelling of power performance, structural analysis, fabrication cost modelling, simplified project economic modelling and time domain reliability modelling of a 210MW hybrid farm. The application of these design and analysis methods has resulted in a hybrid solution capable of producing energy at a cost between €0.22/kWh and €0.31/kWh depending on the source of funding for the project. Further optimisation through detailed design is expected to lower this further. This thesis develops new and existing methods of design and analysis of wind and wave energy devices. This streamlines the process of early stage development, while adhering to the widely adopted Concept Development Protocol, to develop a technically and economically feasible, combined wind-wave energy hybrid solution.

Time-dependent transport through molecular junctions.

We investigate transport properties of molecular junctions under two types of bias--a short time pulse or an ac bias--by combining a solution for Green's functions in the time domain with electronic structure information coming from ab initio density functional calculations. We find that the short time response depends on lead structure, bias voltage, and barrier heights both at the molecule-lead contacts and within molecules. Under a low frequency ac bias, the electron flow either tracks or leads the bias signal (resistive or capacitive response) depending on whether the junction is perfectly conducting or not. For high frequency, the current lags the bias signal due to the kinetic inductance. The transition frequency is an intrinsic property of the junctions.

Flow stabilization with active hydrodynamic cloaks

We demonstrate that fluid flow cloaking solutions, based on active hydrodynamic metamaterials, exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers (Re's), up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for Re's in the range of 5-119. The first highly efficient method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120 or five times greater than for a bare uncloaked cylinder. © 2012 American Physical Society.

Multigrid for American option pricing with stochastic volatility

The paper describes an implicit finite difference approach to the pricing of American options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices and adaptive time-stepping.

Multiscale modelling of dendrite growth during vacuum arc remelting

Vacuum Arc Remelting (VAR) is the accepted method for producing homogeneous, fine microstructures that are free of inclusions required for rotating grade applications. However, as ingot sizes are increasing INCONEL 718 becomes increasingly susceptible to defects such as freckles, tree rings, and white spots increases for large diameter billets. Therefore, predictive models of these defects are required to allow optimization of process parameters. In this paper, a multiscale and multi-physics model is presented to predict the development of microstructures in the VAR ingot during solidification. At the microscale, a combined stochastic nucleation approach and finite difference solution of the solute diffusion is applied in the semi-solid zone of the VAR ingot. The micromodel is coupled with a solution of the macroscale heat transfer, fluid flow and electromagnetism in the VAR process through the temperature, pressure and fluid flow fields. The main objective of this study is to achieve a better understanding of the formation of the defects in VAR by quantifying the influence of VAR processing parameters on grain nucleation and dendrite growth. In particular, the effect of different ingot growth velocities on the microstructure formation was investigated. It was found that reducing the velocity produces significantly more coarse grains.

Three-dimensional simulation of the influence of convection on dendritic solidification

Bulk and interdendritic flow during solidification alters the microstructure development, potentially leading to the formation of defects. In this paper, a 3D numerical model is presented for the simulation of dendritic growth in the presence of fluid flow in both liquid and semi-solid zones during solidification. The dendritic growth was solved by the combination of a stochastic nucleation approach with a finite difference solution of the solute diffusion equation and. a projection method solution of the Navier-Stokes equations. The technique was applied first to simulate the growth of a single dendrite in 2D and 3D in an isothermal environment with forced fluid flow. Significant differences were found in the evolution of dendritic morphology when comparing the 2D and 3D results. In 3D the upstream arm has a faster growth velocity due to easier flow around the perpendicular arms. This also promotes secondary arm formation on the upstream arm. The effect of fluid flow on columnar dendritic growth and micro-segregation in constrained solidification conditions is then simulated. For constrained growth, 2D simulations lead to even greater inaccuracies as compared to 3D.

Dissociative ionization of molecules in intense laser fields

Accurate and efficient grid based techniques for the solution of the time-dependent Schrodinger equation for few-electron diatomic molecules irradiated by intense, ultrashort laser pulses are described. These are based on hybrid finite-difference, Lagrange mesh techniques. The methods are applied in three scenarios, namely H-2(+) with fixed internuclear separation, H-2(+) with vibrating nuclei and H-2 with fixed internuclear separation and illustrative results presented.

Efficient grid treatment of the ionization dynamics of laser-driven H-2(+)

We implement a parallel, time-dependent hybrid finite-difference Lagrange mesh code to model the electron dynamics of the fixed-nuclei hydrogen molecular ion subjected to intense ultrashort laser Pulses, Ionization rates are calculated and compared with results from a previous finite-difference approach and also with published Floquet results. The sensitivity of the results to the gauge describing the electron-field interaction is studied. Visualizations of the evolving wave packets are also presented in which the formation of a stable bound-state resonance is observed.

Extrinsic parameter extraction and RF modelling of CMOS

An analytical approach for CMOS parameter extraction which includes the effect of parasitic resistance is presented. The method is based on small-signal equivalent circuit valid in all region of operation to uniquely extract extrinsic resistances, which can be used to extend the industry standard BSIM3v3 MOSFET model for radio frequency applications. The verification of the model was carried out through frequency domain measurements of S-parameters and direct time domain measurement at 2.4 GHz in a large signal non-linear mode of operation. (C) 2003 Elsevier Ltd. All rights reserved.

Modulating the selectivity for CO and butane oxidation over heterogeneous catalysis through amorphous catalyst coatings

The preparation of porous films directly deposited onto the surface of catalyst particles is attracting increasing attention. We report here for the first time a method that can be carried out at ambient pressure for the preparation of porous films deposited over 3 mm diameter catalyst particles of silica-supported Pt-Fe. Characterization of the sample prepared at ambient pressure (i.e., open air, OA) and its main structural differences as compared with a Na-A (LTA) coated catalyst made using an autoclave-based method are presented. The OA-coated material predominantly exhibited an amorphous film over the catalyst surface with between 4 and 13% of crystallinity as compared with fully crystallized LTA zeolite crystals. This coated sample was highly selective for CO oxidation in the presence of butane with no butane oxidation observed up to 350 degrees C. This indicates, for the first time, that the presence of a crystalline membrane is not necessary for the difference in light off temperature between CO and butane to be achieved and that amorphous films may also produce this effect. An examination of the space velocity dependence and adsorption of Na+ on the catalysts indicates that the variation in CO and butane oxidation activity is not caused by site blocking predominantly, although the Pt activity was lowered by contact with this alkali.

Time-dependent R -matrix theory for ultrafast atomic processes

We describe an ab initio nonperturbative time-dependent R-matrix theory for ultrafast atomic processes. This theory enables investigations of the interaction of few-femtosecond and -attosecond pulse lasers with complex multielectron atoms and atomic ions. A derivation and analysis of the basic equations are given, which propagate the atomic wave function in the presence of the laser field forward in time in the internal and external R-matrix regions. To verify the accuracy of the approach, we investigate two-photon ionization of Ne irradiated by an intense laser pulse and compare current results with those obtained using the R-matrix Floquet method and an alternative time-dependent method. We also verify the capability of the current approach by applying it to the study of two-dimensional momentum distributions of electrons ejected from Ne due to irradiation by a sequence of 2 as light pulses in the presence of a 780 nm laser field.