954 resultados para Eigenfunctions and fundamental solution


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The internationally accepted Wolfson Heat Treatment Centre Engineering Group test was used to evaluate the cooling characteristics of the most popular commercial polymer quenchants: polyalkylene glycols, polyvinylpyrrolidones and polyacrylates. Prototype solutions containing poly(ethyloxazoline) were also examined. Each class of polymer was capable of providing a wide range of cooling rates depending on the product formulation, concentration, temperature, agitation, ageing and contamination. Cooling rates for synthetic quenchants were generally intermediate between those of water and oil. Control techniques, drag-out losses and response to quenching in terms of hardness and residual stress for a plain carbon steel, were also considered. A laboratory scale method for providing a controllable level of forced convection was developed. Test reproducibility was improved by positioning the preheated Wolfson probe 25mm above the geometric centre of a 25mm diameter orifice through which the quenchant was pumped at a velocity of 0.5m/s. On examination, all polymer quenchants were found to operate by the same fundamental mechanism associated with their viscosity and ability to form an insulating polymer-rich-film. The nature of this film, which formed at the vapour/liquid interface during boiling, was dependent on the polymer's solubility characteristics. High molecular weight polymers and high concentration solutions produced thicker, more stable insulating films. Agitation produced thinner more uniform films. Higher molecular weight polymers were more susceptible to degradation, and increased cooling rates, with usage. Polyvinylpyrrolidones can be cross-linked resulting in erratic performance, whilst the anionic character of polyacrylates can lead to control problems. Volatile contaminants tend to decrease the rate of cooling and salts to increase it. Drag-out increases upon raising the molecular weight of the polymer and its solution viscosity. Kinematic viscosity measurements are more effective than refractometer readings for concentration control, although a quench test is the most satisfactory process control method.

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Computerised production control developments have concentrated on Manufacturing Resources Planning (MRP II) systems. The literature suggests however, that despite the massive investment in hardware, software and management education, successful implementation of such systems in manufacturing industries has proved difficult. This thesis reviews the development of production planning and control systems, in particular, investigates the causes of failures in implementing MRP/MRP II systems in industrial environments and argues that the centralised and top-down planning structure, as well as the routine operational methodology of such systems, is inherently prone to failure. The thesis reviews the control benefits of cellular manufacturing systems but concludes that in more dynamic manufacturing environments, techniques such as Kanban are inappropriate. The basic shortcomings of MRP II systems are highlighted and a new enhanced operational methodology based on distributed planning and control principles is introduced. Distributed Manufacturing Resources Planning (DMRP), was developed as a capacity sensitive production planning and control solution for cellular manufacturing environments. The system utilises cell based, independently operated MRP II systems, integrated into a plant-wide control system through a Local Area Network. The potential benefits of adopting the system in industrial environments is discussed and the results of computer simulation experiments to compare the performance of the DMRP system against the conventional MRP II systems presented. DMRP methodology is shown to offer significant potential advantages which include ease of implementation, cost effectiveness, capacity sensitivity, shorter manufacturing lead times, lower working in progress levels and improved customer service.

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The work described in this thesis is an attempt to elucidate the relationships between the pore system and a number of engineering properties of hardened cement paste, particularly tensile strength and resistances to carbonation and ionic penetration. By examining aspects such as the rate of carbonisation, the pore size distribution, the concentration of ions in the pore solution and the phase composition of cement pastes, relationships between the pore system (pores and pore solution) and the resistance to carbonation were investigated. The study was carried out in two parts. First, cement pastes with different pore systems were compared, whilst secondly comparisons were made between the pore systems of cement pastes with different degrees of carbonation. Relationships between the pore structure and ionic penetration were studied by comparing kinetic data relating to the diffusion of various ions in cement pastes with different pore systems. Diffusion coefficients and activation energies for the diffusion process of Cl- and Na+ ions in carbonated and non-carbonated cement pastes were determined by a quasi-steady state technique. The effect of the geometry of pores on ionic diffusion was studied by comparing the mechanisms of ionic diffusion for ions with different radii. In order to investigate the possible relationship between tensile strength and macroporosity, cement paste specimens with cross sectional areas less than 1mm2 were produced so that the chance of a macropore existing within them was low. The tensile strengths of such specimens were then compared with those of larger specimens.

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With the competitive challenge facing business today, the need to keep cost down and quality up is a matter of survival. One way in which wire manufacturers can meet this challenge is to possess a thorough understanding of deformation, friction and lubrication during the wire drawing process, and therefore to make good decisions regarding the selection and application of lubricants as well as the die design. Friction, lubrication and die design during wire drawing thus become the subject of this study. Although theoretical and experimental investigations have been being carried out ever since the establishment of wire drawing technology, many problems remain unsolved. It is therefore necessary to conduct further research on traditional and fundamental subjects such as the mechanics of deformation, friction, lubrication and die design in wire drawing. Drawing experiments were carried out on an existing bull-block under different cross-sectional area reductions, different speeds and different lubricants. The instrumentation to measure drawing load and drawing speed was set up and connected to the wire drawing machine, together with a data acquisition system. A die box connected to the existing die holder for using dry soap lubricant was designed and tested. The experimental results in terms of drawing stress vs percentage area reduction curves under different drawing conditions were analysed and compared. The effects on drawing stress of friction, lubrication, drawing speed and pressure die nozzle are discussed. In order to determine the flow stress of the material during deformation, tensile tests were performed on an Instron universal test machine, using the wires drawn under different area reductions. A polynomial function is used to correlate the flow stress of the material with the plastic strain, on which a general computer program has been written to find out the coefficients of the stress-strain function. The residual lubricant film on the steel wire after drawing was examined both radially and longitudinally using an SEM and optical microscope. The lubricant film on the drawn wire was clearly observed. Therefore, the micro-analysis by SEM provides a way of friction and lubrication assessment in wire drawing.

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We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.

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Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

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A new bridge technique for the measurement of the dielectric absorption of liquids and solutions at microwave frequencies has been described and its accuracy assessed. 'l'he dielectric data of the systems studied is discussed in terms of the relaxation processes contributing to the dielectric absorption and the apparent dipole moments. Pyridine, thiophen and furan in solution have a distribution of relaxation times which may be attributed to the small size of the solute molecules relative to the solvent. Larger rigid molecules in solution were characterized by a single relaxation time as would be anticipated from theory. The dielectric data of toluene, ethyl-, isopropyl- and t-butylbenzene as pure liquids and in solution were described by two relaxation times, one identified with molecular re-orientation and a shorter relaxation time.· The subsequent work was investigation of the possible explanations of this short relaxation process. Comparable short relaxation times were obtained from the analysis of the dielectric data of solutions of p-chloro- and p-bromotoluene below 40°C, o- and m-xylene at 25°C and 1-methyl- and 2 methylnaphthalene at 50 C. Rigid molecules of similar shapes and sizes were characterized by a single relaxation time identified with molecular re-orientation. Contributions from a long relaxation process attributed to dipolar origins were reported for solutions of nitrobenzene, benzonitrile and p-nitrotoluene. A short relaxation process of possible dipolar origins contributed to the dielectric absorption of 4-methyl- and 4-t-butylpyridine in cyclohexane at 25°C. It was concluded that the most plausible explanation of the short relaxation process of the alkyl-aryl hydrocarbons studied appears to be intramolecular relaxation about the alkyl-aryl bond. Finally the mean relaxation times of some phenylsubstituted compounds were investigated to evaluate any shortening due to contributions from the process of relaxation about the phenyl-central atom bond. The relaxation times of triphenylsilane and phenyltrimethylsilane were significantly short.

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We report results of an experimental study, complemented by detailed statistical analysis of the experimental data, on the development of a more effective control method of drug delivery using a pH sensitive acrylic polymer. New copolymers based on acrylic acid and fatty acid are constructed from dodecyl castor oil and a tercopolymer based on methyl methacrylate, acrylic acid and acryl amide were prepared using this new approach. Water swelling characteristics of fatty acid, acrylic acid copolymer and tercopolymer respectively in acid and alkali solutions have been studied by a step-change method. The antibiotic drug cephalosporin and paracetamol have also been incorporated into the polymer blend through dissolution with the release of the antibiotic drug being evaluated in bacterial stain media and buffer solution. Our results show that the rate of release of paracetamol getss affected by the pH factor and also by the nature of polymer blend. Our experimental data have later been statistically analyzed to quantify the precise nature of polymer decay rates on the pH density of the relevant polymer solvents. The time evolution of the polymer decay rates indicate a marked transition from a linear to a strictly non-linear regime depending on the whether the chosen sample is a general copolymer (linear) or a tercopolymer (non-linear). Non-linear data extrapolation techniques have been used to make probabilistic predictions about the variation in weight percentages of retained polymers at all future times, thereby quantifying the degree of efficacy of the new method of drug delivery.

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A hybrid passive-active damping solution with improved system stability margin and enhanced dynamic performance is proposed for high power grid interactive converters. In grid connected active rectifier/inverter application, line side LCL filter improves the high frequency attenuation and makes the converter compatible with the stringent grid power quality regulations. Passive damping though offers a simple and reliable solution but it reduces overall converter efficiency. Active damping solutions do not increase the system losses but can guarantee the stable operation up to a certain speed of dynamic response which is limited by the maximum bandwidth of the current controller. This paper examines this limit and introduces a concept of hybrid passive-active damping solution with improved stability margin and high dynamic performance for line side LCL filter based active rectifier/inverter applications. A detailed design, analysis of the hybrid approach and trade-off between system losses and dynamic performance in grid connected applications are reported. Simulation and experimental results from a 10 kVA prototype demonstrate the effectiveness of the proposed solution. An analytical study on system stability and dynamic response with the variations of various controller and passive filter parameters is presented.

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Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.

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2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

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Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

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Mediation techniques provide interoperability and support integrated query processing among heterogeneous databases. While such techniques help data sharing among different sources, they increase the risk for data security, such as violating access control rules. Successful protection of information by an effective access control mechanism is a basic requirement for interoperation among heterogeneous data sources. ^ This dissertation first identified the challenges in the mediation system in order to achieve both interoperability and security in the interconnected and collaborative computing environment, which includes: (1) context-awareness, (2) semantic heterogeneity, and (3) multiple security policy specification. Currently few existing approaches address all three security challenges in mediation system. This dissertation provides a modeling and architectural solution to the problem of mediation security that addresses the aforementioned security challenges. A context-aware flexible authorization framework was developed in the dissertation to deal with security challenges faced by mediation system. The authorization framework consists of two major tasks, specifying security policies and enforcing security policies. Firstly, the security policy specification provides a generic and extensible method to model the security policies with respect to the challenges posed by the mediation system. The security policies in this study are specified by 5-tuples followed by a series of authorization constraints, which are identified based on the relationship of the different security components in the mediation system. Two essential features of mediation systems, i. e., relationship among authorization components and interoperability among heterogeneous data sources, are the focus of this investigation. Secondly, this dissertation supports effective access control on mediation systems while providing uniform access for heterogeneous data sources. The dynamic security constraints are handled in the authorization phase instead of the authentication phase, thus the maintenance cost of security specification can be reduced compared with related solutions. ^

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This research presents several components encompassing the scope of the objective of Data Partitioning and Replication Management in Distributed GIS Database. Modern Geographic Information Systems (GIS) databases are often large and complicated. Therefore data partitioning and replication management problems need to be addresses in development of an efficient and scalable solution. ^ Part of the research is to study the patterns of geographical raster data processing and to propose the algorithms to improve availability of such data. These algorithms and approaches are targeting granularity of geographic data objects as well as data partitioning in geographic databases to achieve high data availability and Quality of Service(QoS) considering distributed data delivery and processing. To achieve this goal a dynamic, real-time approach for mosaicking digital images of different temporal and spatial characteristics into tiles is proposed. This dynamic approach reuses digital images upon demand and generates mosaicked tiles only for the required region according to user's requirements such as resolution, temporal range, and target bands to reduce redundancy in storage and to utilize available computing and storage resources more efficiently. ^ Another part of the research pursued methods for efficient acquiring of GIS data from external heterogeneous databases and Web services as well as end-user GIS data delivery enhancements, automation and 3D virtual reality presentation. ^ There are vast numbers of computing, network, and storage resources idling or not fully utilized available on the Internet. Proposed "Crawling Distributed Operating System "(CDOS) approach employs such resources and creates benefits for the hosts that lend their CPU, network, and storage resources to be used in GIS database context. ^ The results of this dissertation demonstrate effective ways to develop a highly scalable GIS database. The approach developed in this dissertation has resulted in creation of TerraFly GIS database that is used by US government, researchers, and general public to facilitate Web access to remotely-sensed imagery and GIS vector information. ^

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Chromium (Cr) is a metal of particular environmental concern, owing to its toxicity and widespread occurrence in groundwater, soil, and soil solution. A combination of hydrological, geochemical, and microbiological processes governs the subsurface migration of Cr. Little effort has been devoted to examining how these biogeochemical reactions combine with hydrologic processes influence Cr migration. This study has focused on the complex problem of predicting the Cr transport in laboratory column experiments. A 1-D reactive transport model was developed and evaluated against data obtained from laboratory column experiments. ^ A series of dynamic laboratory column experiments were conducted under abiotic and biotic conditions. Cr(III) was injected into columns packed with β-MnO 2-coated sand at different initial concentrations, variable flow rates, and at two different pore water pH (3.0 and 4.0). In biotic anaerobic column experiments Cr(VI) along with lactate was injected into columns packed with quartz sand or β-MnO2-coated sand and bacteria, Shewanella alga Simidu (BrY-MT). A mathematical model was developed which included advection-dispersion equations for the movement of Cr(III), Cr(VI), dissolved oxygen, lactate, and biomass. The model included first-order rate laws governing the adsorption of each Cr species and lactate. The equations for transport and adsorption were coupled with nonlinear equations for rate-limited oxidation-reduction reactions along with dual-monod kinetic equations. Kinetic batch experiments were conducted to determine the reduction of Cr(VI) by BrY-MT in three different substrates. Results of the column experiments with Cr(III)-containing influent solutions demonstrate that β-MnO2 effectively catalyzes the oxidation of Cr(III) to Cr(VI). For a given influent concentration and pore water velocity, oxidation rates are higher, and hence effluent concentrations of Cr(VI) are greater, at pH 4 relative to pH 3. Reduction of Cr(VI) by BrY-MT was rapid (within one hour) in columns packed with quartz sand, whereas Cr(VI) reduction by BrY-MT was delayed (57 hours) in presence of β-MnO 2-coated sand. BrY-MT grown in BHIB (brain heart infusion broth) reduced maximum amount of Cr(VI) to Cr(III) followed by TSB (tryptic soy broth) and M9 (minimum media). The comparisons of data and model results from the column experiments show that the depths associated with Cr(III) oxidation and transport within sediments of shallow aquatic systems can strongly influence trends in surface water quality. The results of this study suggests that carefully performed, laboratory column experiments is a useful tool in determining the biotransformation of redox-sensitive metals even in the presence of strong oxidant, like β-MnO2. ^