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Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N(^2). The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement Random sampling is a technique which overcomes the alias problem in regular sampling. The randomization, however, destroys the symmetry property of the transform kernel of the discrete Fourier transform. Hence, when transforming a randomly sampled sequence to its frequency spectrum, the Fast Fourier transform cannot be applied and the computational complexity is N"^. The objectives of this research project are (1) To devise sampling methods for random sampling such that computation may be reduced while the anti-alias property of random sampling is maintained : Two methods of inserting limited regularities into the randomized sampling grids are proposed. They are parallel additive random sampling and hybrid additive random sampling, both of which can save at least 75% , of the multiplications required. The algorithms also lend themselves to the implementation by a multiprocessor system, which will further enhance the speed of the evaluation. (2) To study the auto-correlation sequence of a randomly sampled sequence as an alternative means to confirm its anti-alias property : The anti-alias property of the two proposed methods can be confirmed by using convolution in the frequency domain. However, the same conclusion is also reached by analysing in the spatial domain the auto-correlation of such sample sequences. A technique to evaluate the auto-correlation sequence of a randomly sampled sequence with a regular step size is proposed. The technique may also serve as an algorithm to convert a randomly sampled sequence to a regularly spaced sequence having a desired Nyquist frequency. (3) To provide a rapid spectral estimation using a coarse kernel : The approximate method proposed by Mason in 1980, which trades the accuracy for the speed of the computation, is introduced for making random sampling more attractive. (4) To suggest possible applications for random and pseudo-random sampling : To fully exploit its advantages, random sampling has been adopted in measurement instruments where computing a spectrum is either minimal or not required. Such applications in instrumentation are easily found in the literature. In this thesis, two applications in digital signal processing are introduced. (5) To suggest an inverse transformation for random sampling so as to complete a two-way process and to broaden its scope of application. Apart from the above, a case study of realizing in a transputer network the prime factor algorithm with regular sampling is given in Chapter 2 and a rough estimation of the signal-to-noise ratio for a spectrum obtained from random sampling is found in Chapter 3. Although random sampling is alias-free, problems in computational complexity and noise prevent it from being adopted widely in engineering applications. In the conclusions, the criteria for adopting random sampling are put forward and the directions for its development are discussed.

Assembly lines are no longer systems designed to produce as much as possible at the lower cost. Nowadays several factors such as mass customization and variation in demand have led the manufacturers to consider the flexibility of the assembly systems as one of the most important facts to take into account when designing an assembly line. In this context, this study attempts to test a new paradigm of the workload balance, which is based on a dynamic allocation of the assembly operations. In order to test the hypothesis, a real assembly system of engines has been used as a base model to implement the new approach. The work developed, uses the simulation as a means to carry out the study, which has required the development of several simulation scenarios. The hypothesis has been studied from two different approaches; on one hand a total dynamic allocation of assembly operations, which was expected to cause a wide operational range of the stations. On the other hand, the second approach implements a flow control which aims to reduce the operational range and workload fluctuations. The results obtained show a significant improvement of the system performance in comparison with the current assembly line. It has been found that any improvement implemented in the system is directly reflected in the total performance of the line, regardless if the improvement is made in a system constraint. Moreover, the results have proven a better response of the system to changes in the frequency of models production.  Finally, based on the results, this study suggests several paths of future work in order to acquire the needed information to implement the hypothesis in the real world context. / Flexa project

This thesis will address several problems in discrete optimization. These problems are considered hard to solve. However, good approximation algorithms for these problems may be helpful in approximating problems in computational biology and computer science. Given an undirected graph G=(V,E) and a family of subsets of vertices S, the minimum crossing spanning tree is a spanning tree where the maximum number of edges crossing any single set in S is minimized, where an edge crosses a set if it has exactly one endpoint in the set. This thesis will present two algorithms for special cases of minimum crossing spanning trees. The first algorithm is for the case where the sets of S are pairwise disjoint. It gives a spanning tree with the maximum crossing of a set being 2OPT+2, where OPT is the maximum crossing for a minimum crossing spanning tree. The second algorithm is for the case where the sets of S form a laminar family. Let b_i be a bound for each S_i in S. If there exists a spanning tree where each set S_i is crossed at most b_i times, the algorithm finds a spanning tree where each set S_i is crossed O(b_i log n) times. From this algorithm, one can get a spanning tree with maximum crossing O(OPT log n). Given an undirected graph G=(V,E), and a family of subsets of vertices S, the minimum crossing perfect matching is a perfect matching where the maximum number of edges crossing any set in S is minimized. A proof will be presented showing that finding a minimum crossing perfect matching is NP-hard, even when the graph is bipartite and the sets of S are pairwise disjoint.

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The aim of this work is to look into the applicability of Discrete Element Modelling (DEM) coupled to Computational Fluid Dynamics (CFD) to simulate micro-scale colloidal particles immersed in fluid. Numerical methods were implemented through the commercial framework of EDEM2.3. As opposed to dissolved matter, which behaves as a continuum within the fluid medium, particulate matter is made of discrete entities that interact amongst themselves, and with the fluid and any physical boundaries. Particulate matter is ubiquitous in many purification processes that would beneficiate from having an easy way to model particle dynamics immersed in water. In an effort to understand better the dynamics of particle deposition under surface forces and hydraulic forces, a micro-scale numerical model was built adopting both a mechanistic and a statistical approach to represent the forces involved in colloidal suspension. The primary aim of the model was to simulate particle aggregation, deposition and cluster re-suspension in real world micro-systems. Case studies include colloidal flocculation in a constricted tube, and colloidal fouling around membrane filtration feed spacers. This work used a DEM-CFD coupling method that combined the DEM particle flow simulation with hydrodynamics forces from a velocity field computed through CFD. It also implemented boundary-particle and particle-particle interactions by enabling the modelling of surface and interfacial forces. Two kinds of coupling method were considered: two-way and one-way coupling. Two-way coupling is suitable for high particle concentration flow where particle loading affects the hydrodynamics. One-way coupling is suitable for dispersed particle configuration where the flow field is assumed to be undisturbed by the particles. The advantages and drawbacks of both techniques for micron-size particles were investigated. EDEM 2.3 was customised with plug-ins to implement Van der Waals forces and Brownian forces and its post-processing features offered the ability to investigate easily the microparticles behaviour under the influence of fluid forces. In this context, DEM-CFD modelling using EDEM 2.3 represents an improvement on previously published works as it enables higher visibility and reproducibility along with increasing the number of potential users of such modelling. Emphasis was given in presenting original findings and validation results that illustrate DEMCFD applicability, with respect to modelling of hydraulically mediated colloidal surface interaction; while highlighting factors that limit the ability of the technique. For instance, the effect of particle disturbance on the surrounding medium currently proves difficult to model.

The Faraday rotation spectrum of composites containing magnetite nanoparticles is found to be dependent on the interparticle spacing of the constituent nanoparticles. The composite materials are prepared by combining chemicallysynthesized Fe3O4 (magnetite) nanoparticles (8 nm diameter) and poly(methylmethacrylate) (PMMA). Composites are made containing a range of nanoparticle concentrations. The peak of the main spectral feature depends on nanoparticle concentration; this peak is observed to shift from approximately 470 nm for (dilute composites) to 560 nm (concentrated). A theory is presented based on the dipole approximation which accounts for optical coupling between magnetite particles. Qualitative correlations between theoretical calculations and experimental data suggest the shifts in spectral peak position depend on both interparticle distance and geometrical configuration.

Image completion is the process of filling missing regions of an image based on the known sections of the image. This technique is useful for repairing damaged images or removing unwanted objects from images. Research on this technique is plentiful. This thesis compares three different approaches to image completion. In addition, a new method is proposed which combines features from two of these algorithms to improve efficiency.

This thesis concerns the relationship of submanifold geometry, in both the smooth and discrete sense, to representation theory and the theory of integrable systems. We obtain Lie theoretic generalisations of the transformation theory of projectively and Lie applicable surfaces, and M�obius-flat submanifolds of the conformal n-sphere. In the former case, we propose a discretisation. We develop a projective approach to centro-ane hypersurfaces, analogous to the conformal approach to submanifolds in spaceforms. This yields a characterisation of centro-ane hypersurfaces amongst M�obius-flat projective hypersurfaces using polynomial conserved quantities. We also propose a discretisation of curved flats in symmetric spaces. After developing the transformation theory for this, we see how Darboux pairs of discrete isothermicnets arise as discrete curved flats in the symmetric space of opposite point pairs. We show how discrete curves in the 2-sphere fit into this framework.