Numerical Solution of Linear Ordinary Differential Equations and Differential-Algebraic Equations by Spectral Methods

This thesis involves the implementation of spectral methods, for numerical solution of linear Ordinary Differential Equations (ODEs) and linear Differential-Algebraic Equations (DAEs). First we consider ODEs with some ordinary problems, and then, focus on those problems in which the solution function or some coefficient functions have singularities. Then, by expressing weak and strong aspects of spectral methods to solve these kinds of problems, a modified pseudo-spectral method which is more efficient than other spectral methods is suggested and tested on some examples. We extend the pseudo-spectral method to solve a system of linear ODEs and linear DAEs and compare this method with other methods such as Backward Difference Formulae (BDF), and implicit Runge-Kutta (RK) methods using some numerical examples. Furthermore, by using appropriate choice of Gauss-Chebyshev-Radau points, we will show that this method can be used to solve a linear DAE whenever some of coefficient functions have singularities by providing some examples. We also used some problems that have already been considered by some authors by finite difference methods, and compare their results with ours. Finally, we present a short survey of properties and numerical methods for solving DAE problems and then we extend the pseudo-spectral method to solve DAE problems with variable coefficient functions. Our numerical experience shows that spectral and pseudo-spectral methods and their modified versions are very promising for linear ODE and linear DAE problems with solution or coefficient functions having singularities. In section 3.2, a modified method for solving an ODE is introduced which is new work. Furthermore, an extension of this method for solving a DAE or system of ODEs which has been explained in section 4.6 of chapter four is also a new idea and has not been done by anyone previously. In all chapters, wherever we talk about ODE or DAE we mean linear

Design of serrate-semi-circular riblets with application to skin friction reduction on engineering surface

Drag reduction in wall-bounded flows can be achieved by the passive flow control technique through the application of bio-inspired riblet surfaces. This paper presents the innovative design of Serrate-Semi-Circular riblet surfaces particularly focusing on the intrinsic relationship between the riblet features and the turbulent boundary layer structure resulting from these surfaces in engineering applications. The available experimental facilities, instrumentation (i.e. hotwire) and measurement techniques (i.e. velocity spectra) have been employed to investigate the boundary layer velocity profiles and skin friction for flat plate and Serrate-Semi-Circular riblet surfaces. Both the simulation and experimental wind tunnel testing results show that the Serrate-Semi-Circular riblet surface can provide 7% drag reduction, which is better than other riblet configurations, such as V and U shaped ones

An investigation on design and analysis of micro-structured surfaces with application to friction reduction

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel UniversityDrag reduction in wall-bounded flows can be achieved by the passive flow control technique using riblets and surface grooves aligned in the mean direction of an overlying turbulent flow. They were inspired by the skin of fast sharks covered with small longitudinal ribs on their skin surfaces. Although it was found that the drag reduction depends on the riblets’ geometrical characteristics, their physical mechanisms have not yet been fully understood in the scientific terms. Regarding riblets sizing, it has been critically explained in the literature how riblets with vanishing size interact with the turbulent flow and produce a change in the drag proportional to their size. Their shapes are focused upon because these are most significant from a technological perspective, and also less well understood. Different riblet shapes have been designed, some with complicated geometries, but except for the simple ones, such as U and V grooves, there has not been enough study regarding shape features. Therefore, special effort is undertaken to the design of an innovative type of ribleted surface, e.g. the Serrate-Semi-Circular shape, and its effect on the skin friction and drag reduction. In this work, the possible physical mechanisms of riblets for turbulent drag reduction have been explored. The modelling and experiments concerning the relationship between the riblets features and the turbulent boundary layer structure have also been reviewed. Moreover, numerical simulations on riblets with different shapes and sizes are presented and studied in detail. An accurate treatment based on k-ε turbulence model was adopted to investigate the flow alteration and the consequent drag reduction on ribleted surfaces. The interaction of the overlying turbulent flow with riblets and its impact on their drag reduction properties are further investigated. In addition, the experimental facilities, instrumentation (e.g. hotwires) and measurement techniques (e.g. time-averaged turbulence structure) have been employed to experimentally investigate the boundary layer velocity profiles and skin friction for smooth and micro-structured surfaces (the proposed riblet shape, respectively and the presented new design of riblets with serration inside provides 7% drag reduction. The results do not show significant reduction in momentum transfer near the surface by riblets, in particular, around the outer region of the turbulent boundary layer. Conclusions with respect to the holistic investigation on the drag reduction with Serrate-Semi-Circular riblets have been drawn based on the research objectives as achieved. Recommendations for future work have been put forward particularly for further future research in the research area.Brunel University and KIMM (Korea Institute of Machinery and Materials

On gauge invariant regularization of fermion currents

We compare Schwinger and complex powers methods to construct regularized fermion currents. We show that although both of them are gauge invariant they not always yield the same result.Comment: 10 pages, 1 figur

Use of Coherent Point Drift in computer vision applications

This thesis presents the novel use of Coherent Point Drift in improving the robustness of a number of computer vision applications. CPD approach includes two methods for registering two images - rigid and non-rigid point set approaches which are based on the transformation model used. The key characteristic of a rigid transformation is that the distance between points is preserved, which means it can be used in the presence of translation, rotation, and scaling. Non-rigid transformations - or affine transforms - provide the opportunity of registering under non-uniform scaling and skew. The idea is to move one point set coherently to align with the second point set. The CPD method finds both the non-rigid transformation and the correspondence distance between two point sets at the same time without having to use a-priori declaration of the transformation model used. The first part of this thesis is focused on speaker identification in video conferencing. A real-time, audio-coupled video based approach is presented, which focuses more on the video analysis side, rather than the audio analysis that is known to be prone to errors. CPD is effectively utilised for lip movement detection and a temporal face detection approach is used to minimise false positives if face detection algorithm fails to perform. The second part of the thesis is focused on multi-exposure and multi-focus image fusion with compensation for camera shake. Scale Invariant Feature Transforms (SIFT) are first used to detect keypoints in images being fused. Subsequently this point set is reduced to remove outliers, using RANSAC (RANdom Sample Consensus) and finally the point sets are registered using CPD with non-rigid transformations. The registered images are then fused with a Contourlet based image fusion algorithm that makes use of a novel alpha blending and filtering technique to minimise artefacts. The thesis evaluates the performance of the algorithm in comparison to a number of state-of-the-art approaches, including the key commercial products available in the market at present, showing significantly improved subjective quality in the fused images. The final part of the thesis presents a novel approach to Vehicle Make & Model Recognition in CCTV video footage. CPD is used to effectively remove skew of vehicles detected as CCTV cameras are not specifically configured for the VMMR task and may capture vehicles at different approaching angles. A LESH (Local Energy Shape Histogram) feature based approach is used for vehicle make and model recognition with the novelty that temporal processing is used to improve reliability. A number of further algorithms are used to maximise the reliability of the final outcome. Experimental results are provided to prove that the proposed system demonstrates an accuracy in excess of 95% when tested on real CCTV footage with no prior camera calibration

The quantitative changes of silicon and diatoms in southern part of Caspian Sea

The purpose or this study was to evaluate the changes of dissolved silicon concentration and biomass of diatoms in southern part of Caspian Sea, 1270 plankton and water samples were collected seasonally from 77 stations for further quantitative and qualitative analysis.The results showed that the minimum and maximum density of dissolved silicon and biomass of diatoms were varied from 0.195 to 0308 ppm and 33 to 179 mg/m3 respectively. As well as the fluctuation of dissolved silicon concentration in different depths of photic zone. It was indicated that the maximum and minimum concentration of this element were found in the eastern area with 0.269 ppm and western area with 0.180 ppm. The most and the least biomass of diatoms were observed in the western and central areas with 180 and 89 mg/m3, respectively. The concentration or silicon in offshore waters was more than coastal waters and on the contrary, the biomass of diatoms from coastal to offshore waters indicated decreasing trend. In a conclusion, the concentration of dissolved silicon and biomass of diatoms could be affected by different physical parameters such as: water circulation, river currents, exchange of biogenic sediments in photic and aphotic zones. Also, there was a significant relationship between the biomass of diatoms and silicon concentration