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On the protection of compact DC power systems with high-power energy storage
Get PDFHigh-power energy storage systems (ESS) are being considered for future aerospace platforms and other compact DC power system applications to improve the overall transient performance of electrical power distribution systems. These sources are being integrated with advanced bidirectional power electronic converter interfaces with high bandwidth control systems and current limiting functionality. To date, the literature has primarily focused on the control and behaviour of high-power ESS during normal operating conditions with an emphasis on the systems level benefits they offer. Little consideration has been given to their response during network fault conditions.Through simulation and hardware experimentation, this thesis demonstrates that an ESS, by design, can contribute significant levels of current to a fault as it attempts to sustain the network voltage. This behaviour inadvertently reduces the fault current contribution from the primary source of power on the network, reducing the effectiveness of associated protection devices (protection blinding).The impact of several key DC power system design and operation parameters on the ESS fault response is quantified and a new critical fault impedance term, beyond which protection blinding can be expected to occur, is introduced. Building upon this new knowledge, enhancements to typical compact DC power system protection schemes which more effectively account for the presence of ESS are proposed and evaluated.Differential protection schemes are shown to eliminate protection blinding whilst offering the greatest flexibility in increasing protection speed and fault discrimination, and maximising ESS availability. Adaptive protection schemes are shown to be a reliable backup option where a consistent protection system response can be obtained despite the potentially intermittent nature of the ESS fault current contribution. A novel control strategy that actively modifies the fault response of the ESS to facilitate the use of conventional overcurrent schemes is also proposed and demonstrated for applications where communications-based protection is unfavourable. The thesis concludes by proposing a framework to guide protection engineers in the selection of appropriate protection and control strategies when considering the integration of high-power ESS within compact DC power systems.High-power energy storage systems (ESS) are being considered for future aerospace platforms and other compact DC power system applications to improve the overall transient performance of electrical power distribution systems. These sources are being integrated with advanced bidirectional power electronic converter interfaces with high bandwidth control systems and current limiting functionality. To date, the literature has primarily focused on the control and behaviour of high-power ESS during normal operating conditions with an emphasis on the systems level benefits they offer. Little consideration has been given to their response during network fault conditions.Through simulation and hardware experimentation, this thesis demonstrates that an ESS, by design, can contribute significant levels of current to a fault as it attempts to sustain the network voltage. This behaviour inadvertently reduces the fault current contribution from the primary source of power on the network, reducing the effectiveness of associated protection devices (protection blinding).The impact of several key DC power system design and operation parameters on the ESS fault response is quantified and a new critical fault impedance term, beyond which protection blinding can be expected to occur, is introduced. Building upon this new knowledge, enhancements to typical compact DC power system protection schemes which more effectively account for the presence of ESS are proposed and evaluated.Differential protection schemes are shown to eliminate protection blinding whilst offering the greatest flexibility in increasing protection speed and fault discrimination, and maximising ESS availability. Adaptive protection schemes are shown to be a reliable backup option where a consistent protection system response can be obtained despite the potentially intermittent nature of the ESS fault current contribution. A novel control strategy that actively modifies the fault response of the ESS to facilitate the use of conventional overcurrent schemes is also proposed and demonstrated for applications where communications-based protection is unfavourable. The thesis concludes by proposing a framework to guide protection engineers in the selection of appropriate protection and control strategies when considering the integration of high-power ESS within compact DC power systems
Tunable, continuous-wave semiconductor disk lasers with emission in the deep ultraviolet
Get PDFThe work here presented is focused around the design, characterization and ultimately first demonstration of a deep ultraviolet, frequency tripled semiconductor disk laser (SDL). The construction of such a laser is described, together with a review of the relevant theory and investigation of the underlying processes in order to improve the system.;SDLs based on gallium indium phosphide have attracted intense investigation over the last ten years for their fundamental emission in the 660 nm - 690 nm (visible red emission), a region previously only available to SDLs by means of nonlinear frequency conversion. Such frequency conversion applied to red SDLs provides access to the highly energetic ultraviolet region of the electromagnetic spectum but, although its conversion to the near ultraviolet has been rather successful, further extension into the deep UV presents a new set of challenges that must be addressed in order to achieve efficient laser emission.;78 μW of deep ultraviolet emission at 225nm have been achieved in continuous-wave operation. The output wavelength is tunable for 350 cm−1. This is the shortest wavelength emitted from an SDL to date and is the first implementation of intracavity frequency tripling in a visible SDL.The work here presented is focused around the design, characterization and ultimately first demonstration of a deep ultraviolet, frequency tripled semiconductor disk laser (SDL). The construction of such a laser is described, together with a review of the relevant theory and investigation of the underlying processes in order to improve the system.;SDLs based on gallium indium phosphide have attracted intense investigation over the last ten years for their fundamental emission in the 660 nm - 690 nm (visible red emission), a region previously only available to SDLs by means of nonlinear frequency conversion. Such frequency conversion applied to red SDLs provides access to the highly energetic ultraviolet region of the electromagnetic spectum but, although its conversion to the near ultraviolet has been rather successful, further extension into the deep UV presents a new set of challenges that must be addressed in order to achieve efficient laser emission.;78 μW of deep ultraviolet emission at 225nm have been achieved in continuous-wave operation. The output wavelength is tunable for 350 cm−1. This is the shortest wavelength emitted from an SDL to date and is the first implementation of intracavity frequency tripling in a visible SDL
Multiplexed nanosensic of metal pollutants from the urban environment
Get PDFSurface enhanced Raman scattering (SERS) is a useful tool for the detection of metal ions due to the characteristic vibrational spectra that can be produced. Complexing different metal ions to a single ligand in solution can uniquely alter the SERS spectrum of that ligand, with the changes being specific to each individual metal ion. This approach has been used to research a nanoparticle-based sensor that can detect a number of metalions using SERS for environmental monitoring purposes. Research commenced by studying the small Raman reporter molecules, 4-mercaptobenzoic acid (4-MBA) and 4-mercaptopyridine (4-MPY), which were functionalised onto the surface of AgNPs. Upon addition of different metal ions, the AgNPs would aggregate resulting in an increased SERS response and characteristic frequency shifts in certain bands, which allowed discrimination of different species. The potential of 2,2'-bipyridyl (bipy) as a chelating ligand for the SERS detection of multiple metal ions has also been investigated. It has been shown that coordination of six different metal ions to this ligand produces characteristic changes throughout the entire spectral region, and therefore the presence of a metal ion can be identified with greater confidence. Not only that, the sensitivity is also greatly improved, with both Zn(II)and Cu(II) capable of being detected below the World Health Organisation (WHO) recommended limits of 0.22 and 0.6 ppm, respectively. Finally, the characteristic changes produced in the SERS spectrum of salen by Ni(II), Cu(II), Co(II) and Mn(II) is discussed. Although a smaller range of species can be detected compared to bipy, detection limits are significantly improved and changes produced by the different metal ions are arguably more pronounced. This approach has also been applied to real environmental freshwater samples in order to determine whether it is suitable for environmental sampling. A contaminated water sample known to contain elevated levels of Mn(II) was tested and it has been demonstrated that this method is indeed capable of detecting high levels of metal ions in natural freshwater samples.Surface enhanced Raman scattering (SERS) is a useful tool for the detection of metal ions due to the characteristic vibrational spectra that can be produced. Complexing different metal ions to a single ligand in solution can uniquely alter the SERS spectrum of that ligand, with the changes being specific to each individual metal ion. This approach has been used to research a nanoparticle-based sensor that can detect a number of metalions using SERS for environmental monitoring purposes. Research commenced by studying the small Raman reporter molecules, 4-mercaptobenzoic acid (4-MBA) and 4-mercaptopyridine (4-MPY), which were functionalised onto the surface of AgNPs. Upon addition of different metal ions, the AgNPs would aggregate resulting in an increased SERS response and characteristic frequency shifts in certain bands, which allowed discrimination of different species. The potential of 2,2'-bipyridyl (bipy) as a chelating ligand for the SERS detection of multiple metal ions has also been investigated. It has been shown that coordination of six different metal ions to this ligand produces characteristic changes throughout the entire spectral region, and therefore the presence of a metal ion can be identified with greater confidence. Not only that, the sensitivity is also greatly improved, with both Zn(II)and Cu(II) capable of being detected below the World Health Organisation (WHO) recommended limits of 0.22 and 0.6 ppm, respectively. Finally, the characteristic changes produced in the SERS spectrum of salen by Ni(II), Cu(II), Co(II) and Mn(II) is discussed. Although a smaller range of species can be detected compared to bipy, detection limits are significantly improved and changes produced by the different metal ions are arguably more pronounced. This approach has also been applied to real environmental freshwater samples in order to determine whether it is suitable for environmental sampling. A contaminated water sample known to contain elevated levels of Mn(II) was tested and it has been demonstrated that this method is indeed capable of detecting high levels of metal ions in natural freshwater samples
Impact of end groups of PLGA on polymer properties and ocular implant performance
Get PDFThe unique anatomy of the eye and its efficient barrier mechanisms challenge the development of ophthalmic dosage forms. Conventionally, most ophthalmic drugs are delivered topically in the form of eye drops. However, the short pre-corneal residence time requires frequent instillation which results in fluctuations in therapeutic concentration, and low patient compliance coupled with high health care cost. Glaucoma is the second leading cause of vision loss after cataract in the world. Approximately 10% of people with glaucoma who receive proper treatment still experience loss of vision. This makes the long-term effectiveness and efficacy of current therapies questionable. Biodegradable polymeric implants offer potential for exact drug delivery at the intraocular target site. The FDA‑approved PLGA has been investigated for implantable ocular dosage forms. From a manufacturing stand point, the copolymer provides several merits. However, the risk of distortion on hydration causing endothelial contact, the biological fate of the polymeric system and the physico-chemical properties of the active compound are all issues that need to be integrated into the design. The effect of the copolymer composition and molecular weight has been addressed. However the effect of endcapping of PLGA polymers on hydrophilicity and drug-polymer interaction in attempts to tune drug delivery is scarce in the literature. The current study investigates the utilization of end capping in achieving desired drug release kinetics and implant mechanical profiles upon intraocular exposure.The unique anatomy of the eye and its efficient barrier mechanisms challenge the development of ophthalmic dosage forms. Conventionally, most ophthalmic drugs are delivered topically in the form of eye drops. However, the short pre-corneal residence time requires frequent instillation which results in fluctuations in therapeutic concentration, and low patient compliance coupled with high health care cost. Glaucoma is the second leading cause of vision loss after cataract in the world. Approximately 10% of people with glaucoma who receive proper treatment still experience loss of vision. This makes the long-term effectiveness and efficacy of current therapies questionable. Biodegradable polymeric implants offer potential for exact drug delivery at the intraocular target site. The FDA‑approved PLGA has been investigated for implantable ocular dosage forms. From a manufacturing stand point, the copolymer provides several merits. However, the risk of distortion on hydration causing endothelial contact, the biological fate of the polymeric system and the physico-chemical properties of the active compound are all issues that need to be integrated into the design. The effect of the copolymer composition and molecular weight has been addressed. However the effect of endcapping of PLGA polymers on hydrophilicity and drug-polymer interaction in attempts to tune drug delivery is scarce in the literature. The current study investigates the utilization of end capping in achieving desired drug release kinetics and implant mechanical profiles upon intraocular exposure
Towards quantifying the intracellular trafficking of silk nanoparticles in cancer cells : establishing biomarkers in the laboratory setting for the characterisation of subcellular fractions
Get PDFSilk has emerged as a promising contender for drug delivery applications, including the use of silk nanoparticles for anticancer drug delivery. Nanoparticles are internalised into cells via endocytosis; thus, silk nanoparticles have been proposed for lysosomotropic drug delivery. However, the intracellular fate of these nanoparticles has not been documented.;One approach for quantifying the intracellular fate of silk nanoparticles is subcellular fractionation. Adequate, but gentle, homogenisation of cells, followed by characterisation of the subcellular fractions using biochemical markers, are key requirements for quantitative trafficking studies. Therefore, the aim of this thesis was to develop wet-lab tested biochemical marker assays for B16F10 cell subcellular fractions.;The following biochemical marker assays were first scaled and refined: alkaline phosphatase to assay for the plasma membrane, succinate dehydrogenase for mitochondria, lactate dehydrogenase for the cytosol, N-acetyl-ß-glucosaminidase for lysosomes and DNA for the nucleus. A homogenisation scheme was then developed, using a cell cracker with 7 μm clearance. At four passes, this device provided over 80% ± 15 cell breakage, while retaining high lysosomal latency (82% ± 1 3.6), thereby providing a sample representative of the whole cell population.;Trafficking studies require the use of non-toxic nanoparticle concentrations; therefore, silk nanoparticles were assessed for cytotoxicity in B16F10 cells using an MTT assay. The IC50 of silk nanoparticles was 17.58 μg/ml, using dextran (IC50 >200 μg/ml) and PEI (IC50 8.8 μg/ml) as negative and positive controls, respectively. These silk nanoparticles had a 131 nm diameter, with a polydispersity of 0.2, and a zeta potential in distilled water of -34.6 mV, as characterised by dynamic light scattering and zeta potential measurements, respectively.;In conclusion, this thesis lays the groundwork for subsequent performance of wet-lab biomarker assays on subcellular fractions to quantify the intracellular trafficking of silk nanoparticles.Silk has emerged as a promising contender for drug delivery applications, including the use of silk nanoparticles for anticancer drug delivery. Nanoparticles are internalised into cells via endocytosis; thus, silk nanoparticles have been proposed for lysosomotropic drug delivery. However, the intracellular fate of these nanoparticles has not been documented.;One approach for quantifying the intracellular fate of silk nanoparticles is subcellular fractionation. Adequate, but gentle, homogenisation of cells, followed by characterisation of the subcellular fractions using biochemical markers, are key requirements for quantitative trafficking studies. Therefore, the aim of this thesis was to develop wet-lab tested biochemical marker assays for B16F10 cell subcellular fractions.;The following biochemical marker assays were first scaled and refined: alkaline phosphatase to assay for the plasma membrane, succinate dehydrogenase for mitochondria, lactate dehydrogenase for the cytosol, N-acetyl-ß-glucosaminidase for lysosomes and DNA for the nucleus. A homogenisation scheme was then developed, using a cell cracker with 7 μm clearance. At four passes, this device provided over 80% ± 15 cell breakage, while retaining high lysosomal latency (82% ± 1 3.6), thereby providing a sample representative of the whole cell population.;Trafficking studies require the use of non-toxic nanoparticle concentrations; therefore, silk nanoparticles were assessed for cytotoxicity in B16F10 cells using an MTT assay. The IC50 of silk nanoparticles was 17.58 μg/ml, using dextran (IC50 >200 μg/ml) and PEI (IC50 8.8 μg/ml) as negative and positive controls, respectively. These silk nanoparticles had a 131 nm diameter, with a polydispersity of 0.2, and a zeta potential in distilled water of -34.6 mV, as characterised by dynamic light scattering and zeta potential measurements, respectively.;In conclusion, this thesis lays the groundwork for subsequent performance of wet-lab biomarker assays on subcellular fractions to quantify the intracellular trafficking of silk nanoparticles
The assessment of juvenile offenders : learning lessons for Saudi Arabia from a contextual comparison with Scotland
Get PDFThe diversity in systems and procedures for treating juvenile offenders who commit similar offences under similar circumstances around the world raises a number of questions. These questions concern the organisational and procedural structures, the value orientation, and the historical, political and legal factors, that determine the works and outcome of a juvenile justice system. While both claiming to uphold a 'welfare' approach, with the best interests of the child at their core, Saudi Arabia and Scotland apply dissimilar procedures when dealing with juvenile offenders.;Employing comparative study techniques, this research aims to unravel the similarities and differences between the juvenile justice systems in both countries, discover strengthens and weaknesses, and learn from the experience of both systems as to how to ultimately strengthen and make more effective a juvenile justice system.;The research question posed is: How does the Saudi juvenile justice system assess young offenders once the juvenile offender is referred to the system, and how does this affect the decisions regarding the response, compared with the Scottish system? This issue was examined and addressed by implementing a qualitative approach which focuses on the meanings and interpretations given to the practice and purpose of assessment. It applies empirical study techniques in the form of in-depth semi-structured interviews with social workers, judges and children's panel members.;The research findings explored the considerations taken into account by juvenile judges and the children's hearing panel when making a decision regarding juveniles who commit offences, and also illustrated how the social worker's report influences the decision made, and its relative importance in each country. It also illustrated the assessment methods applied, to display the strengths and weaknesses in practice in both countries.The diversity in systems and procedures for treating juvenile offenders who commit similar offences under similar circumstances around the world raises a number of questions. These questions concern the organisational and procedural structures, the value orientation, and the historical, political and legal factors, that determine the works and outcome of a juvenile justice system. While both claiming to uphold a 'welfare' approach, with the best interests of the child at their core, Saudi Arabia and Scotland apply dissimilar procedures when dealing with juvenile offenders.;Employing comparative study techniques, this research aims to unravel the similarities and differences between the juvenile justice systems in both countries, discover strengthens and weaknesses, and learn from the experience of both systems as to how to ultimately strengthen and make more effective a juvenile justice system.;The research question posed is: How does the Saudi juvenile justice system assess young offenders once the juvenile offender is referred to the system, and how does this affect the decisions regarding the response, compared with the Scottish system? This issue was examined and addressed by implementing a qualitative approach which focuses on the meanings and interpretations given to the practice and purpose of assessment. It applies empirical study techniques in the form of in-depth semi-structured interviews with social workers, judges and children's panel members.;The research findings explored the considerations taken into account by juvenile judges and the children's hearing panel when making a decision regarding juveniles who commit offences, and also illustrated how the social worker's report influences the decision made, and its relative importance in each country. It also illustrated the assessment methods applied, to display the strengths and weaknesses in practice in both countries
Self-organized magnetization patterns in cold atoms
Get PDFThis Thesis reports on a realization of self-organized magnetization patterns in a cloud of cold atoms driven far from equilibrium by a pump laser beam. The experiments are performed in the single mirror feedback configuration, where transverse ordering occurs due to amplification of fluctuations in the atomic medium at critical lengthscales via the optical non-linearity and the Talbot effect. For a linearly polarized pump beam a generation of modulated light with orthogonal polarization is seen to occur, signaling the presence of a polarization instability. Imaging of the refractive index modulations at the end of the cloud reveals complementary regions of the two orthogonal circularly polarized components of the imaged light, which is related to the ordering of atomic spins. A detailed investigation of dependence of pattern properties on the direction and strength of the applied B-fields is presented. In addition to this, a theoretical model describing the dynamics and coupling of atomic magnetic moments and the laser light in the relevant parameter regime is developed and shown to provide good agreement with results of the experiment. Non-equilibrium self-organization of atomic degrees of freedom in cold gases can in some cases be mapped onto phase transitions in condensed matter systems. In this respect, the single mirror feedback configuration is particularly interesting as it provides a simple arrangement where ordering breaks the continuous translational and rotational symmetries of the initial system.This Thesis reports on a realization of self-organized magnetization patterns in a cloud of cold atoms driven far from equilibrium by a pump laser beam. The experiments are performed in the single mirror feedback configuration, where transverse ordering occurs due to amplification of fluctuations in the atomic medium at critical lengthscales via the optical non-linearity and the Talbot effect. For a linearly polarized pump beam a generation of modulated light with orthogonal polarization is seen to occur, signaling the presence of a polarization instability. Imaging of the refractive index modulations at the end of the cloud reveals complementary regions of the two orthogonal circularly polarized components of the imaged light, which is related to the ordering of atomic spins. A detailed investigation of dependence of pattern properties on the direction and strength of the applied B-fields is presented. In addition to this, a theoretical model describing the dynamics and coupling of atomic magnetic moments and the laser light in the relevant parameter regime is developed and shown to provide good agreement with results of the experiment. Non-equilibrium self-organization of atomic degrees of freedom in cold gases can in some cases be mapped onto phase transitions in condensed matter systems. In this respect, the single mirror feedback configuration is particularly interesting as it provides a simple arrangement where ordering breaks the continuous translational and rotational symmetries of the initial system
Open dialogues for business model innovation
Get PDFThis thesis was previously held under moratorium from until 20th June 2018 until 30th July 2021.A growing body of research is highlighting how open innovative business models support the growth and economic success of new ideas and technologies. In this Ph.D., building on an action research study in SMEs, I develop the Open Business Model Innovation Framework that accounts for the interactions between value creation and active participation in the development of unmet needs to new business formations. I begin to unpack the process of open business model innovation development supporting the ability of SMEs to build and re-build their businesses.A growing body of research is highlighting how open innovative business models support the growth and economic success of new ideas and technologies. In this Ph.D., building on an action research study in SMEs, I develop the Open Business Model Innovation Framework that accounts for the interactions between value creation and active participation in the development of unmet needs to new business formations. I begin to unpack the process of open business model innovation development supporting the ability of SMEs to build and re-build their businesses
Advanced signal processing solutions for ATR and spectrum sharing in distributed radar systems
Get PDFPreviously held under moratorium from 11 September 2017 until 16 February 2022This Thesis presents advanced signal processing solutions for AutomaticTarget Recognition (ATR) operations and for spectrum sharing in distributed radar systems.Two Synthetic Aperture Radar (SAR) ATR algorithms are described forfull- and single-polarimetric images, and tested on the GOTCHA and theMSTAR datasets. The first one exploits the Krogager polarimetric decomposition in order to enhance peculiar scattering mechanisms from manmade targets, used in combination with the pseudo-Zernike image moments. The second algorithm employs the Krawtchouk image moments,that, being discrete defined, provide better representations of targets’ details. The proposed image moments based framework can be extended tothe availability of several images from multiple sensors through the implementation of a simple fusion rule.A model-based micro-Doppler algorithm is developed for the identification of helicopters. The approach relies on the proposed sparse representation of the signal scattered from the helicopter’s rotor and received bythe radar. Such a sparse representation is obtained through the application of a greedy sparse recovery framework, with the goal of estimatingthe number, the length and the rotation speed of the blades, parametersthat are peculiar for each helicopter’s model. The algorithm is extended todeal with the identification of multiple helicopters flying in formation thatcannot be resolved in another domain. Moreover, a fusion rule is presentedto integrate the results of the identification performed from several sensorsin a distributed radar system. Tests performed both on simulated signalsand on real signals acquired from a scale model of a helicopter, confirmthe validity of the algorithm.Finally, a waveform design framework for joint radar-communication systems is presented. The waveform is composed by quasi-orthogonal chirpsub-carriers generated through the Fractional Fourier Transform (FrFT),with the aim of preserving the radar performance of a typical Linear Frequency Modulated (LFM) pulse while embedding data to be sent to acooperative system. Techniques aimed at optimise the design parameters and mitigate the Inter-Carrier Interference (ICI) caused by the quasiorthogonality of the chirp sub-carriers are also described. The FrFT basedwaveform is extensively tested and compared with Orthogonal FrequencyDivision Multiplexing (OFDM) and LFM waveforms, in order to assessboth its radar and communication performance.This Thesis presents advanced signal processing solutions for AutomaticTarget Recognition (ATR) operations and for spectrum sharing in distributed radar systems.Two Synthetic Aperture Radar (SAR) ATR algorithms are described forfull- and single-polarimetric images, and tested on the GOTCHA and theMSTAR datasets. The first one exploits the Krogager polarimetric decomposition in order to enhance peculiar scattering mechanisms from manmade targets, used in combination with the pseudo-Zernike image moments. The second algorithm employs the Krawtchouk image moments,that, being discrete defined, provide better representations of targets’ details. The proposed image moments based framework can be extended tothe availability of several images from multiple sensors through the implementation of a simple fusion rule.A model-based micro-Doppler algorithm is developed for the identification of helicopters. The approach relies on the proposed sparse representation of the signal scattered from the helicopter’s rotor and received bythe radar. Such a sparse representation is obtained through the application of a greedy sparse recovery framework, with the goal of estimatingthe number, the length and the rotation speed of the blades, parametersthat are peculiar for each helicopter’s model. The algorithm is extended todeal with the identification of multiple helicopters flying in formation thatcannot be resolved in another domain. Moreover, a fusion rule is presentedto integrate the results of the identification performed from several sensorsin a distributed radar system. Tests performed both on simulated signalsand on real signals acquired from a scale model of a helicopter, confirmthe validity of the algorithm.Finally, a waveform design framework for joint radar-communication systems is presented. The waveform is composed by quasi-orthogonal chirpsub-carriers generated through the Fractional Fourier Transform (FrFT),with the aim of preserving the radar performance of a typical Linear Frequency Modulated (LFM) pulse while embedding data to be sent to acooperative system. Techniques aimed at optimise the design parameters and mitigate the Inter-Carrier Interference (ICI) caused by the quasiorthogonality of the chirp sub-carriers are also described. The FrFT basedwaveform is extensively tested and compared with Orthogonal FrequencyDivision Multiplexing (OFDM) and LFM waveforms, in order to assessboth its radar and communication performance
Stabilised fine element methods for fictitious domain problems
Get PDFPreviously held under moratorium from 11 September 2017 until 17 February 2022This thesis deals with the solution of the Laplace and heat equations on complicateddomains. The approach follows the idea of the fictitious domain method, in which alarger (simpler) domain is introduced with the idea of avoiding the use of meshes thatresolve the geometry.The first part of the thesis is dedicated to propose and analyse a new stabilised finiteelement method for the heat equation. The analysis, not available to date, is basedon the introduction of a new projected initial condition that satisfies the boundaryconditions of the original problem weakly. This allows us to prove inconditional stabilityand optimal convergence of the solution, thus avoiding the restriction linking the timediscretisation and mesh width parameters present in previous references.In the second part of this thesis the methodology has been adapted and extended tocover the case in which the problem at hand is posed in a domain containing severalinclusions of small size. For this case, the usual fictitious domain approach is no longerapplicable, and then a new method that compensates for the lack of stability of theoriginal one is proposed, analysed and tested numerically. The numerical analysis hasbeen carried out for the steady state case, but its applicability to time dependentproblems is sketched and shown by means of numerical experiments.This thesis deals with the solution of the Laplace and heat equations on complicateddomains. The approach follows the idea of the fictitious domain method, in which alarger (simpler) domain is introduced with the idea of avoiding the use of meshes thatresolve the geometry.The first part of the thesis is dedicated to propose and analyse a new stabilised finiteelement method for the heat equation. The analysis, not available to date, is basedon the introduction of a new projected initial condition that satisfies the boundaryconditions of the original problem weakly. This allows us to prove inconditional stabilityand optimal convergence of the solution, thus avoiding the restriction linking the timediscretisation and mesh width parameters present in previous references.In the second part of this thesis the methodology has been adapted and extended tocover the case in which the problem at hand is posed in a domain containing severalinclusions of small size. For this case, the usual fictitious domain approach is no longerapplicable, and then a new method that compensates for the lack of stability of theoriginal one is proposed, analysed and tested numerically. The numerical analysis hasbeen carried out for the steady state case, but its applicability to time dependentproblems is sketched and shown by means of numerical experiments
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