Left-invariant optimal control problems on the Heisenberg group and the associated Hamilton-Poisson systems: classification, stability and integration
- Authors: Bartlett, Catherine Eve
- Date: 2015-04-10
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/480312 , vital:78428
- Description: This thesis examines the left-invariant control affine systems of full rank, evolving on the three-dimensional Heisenberg group H3. Such systems are classified under state space equivalence, detached feedback equivalence and strongly detached feedback equivalence; a complete list of equivalence representatives is obtained. The equivalence of cost-extended control systems corresponding to left-invariant optimal control problems on H3 with fixed terminal time, affine dynamics, and affine quadratic cost is also considered. To left-invariant optimal control problems on H3 with quadratic cost, one may, via the Pontryagin Maximum Principle, associate a quadratic Hamilton-Poisson system on the (minus) Lie-Poisson space h3. Homogeneous and inhomogeneous quadratic Hamilton-Poisson systems are investigated. These systems are classified up to an affine isomorphism. Furthermore, the stability nature of the equilibria of the systems are analysed and explicit expressions for all integral curves are determined. , Thesis (MSc) -- Faculty of Science, Mathematics (Pure and Applied), 2015
- Full Text:
- Date Issued: 2015-04-10
- Authors: Bartlett, Catherine Eve
- Date: 2015-04-10
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/480312 , vital:78428
- Description: This thesis examines the left-invariant control affine systems of full rank, evolving on the three-dimensional Heisenberg group H3. Such systems are classified under state space equivalence, detached feedback equivalence and strongly detached feedback equivalence; a complete list of equivalence representatives is obtained. The equivalence of cost-extended control systems corresponding to left-invariant optimal control problems on H3 with fixed terminal time, affine dynamics, and affine quadratic cost is also considered. To left-invariant optimal control problems on H3 with quadratic cost, one may, via the Pontryagin Maximum Principle, associate a quadratic Hamilton-Poisson system on the (minus) Lie-Poisson space h3. Homogeneous and inhomogeneous quadratic Hamilton-Poisson systems are investigated. These systems are classified up to an affine isomorphism. Furthermore, the stability nature of the equilibria of the systems are analysed and explicit expressions for all integral curves are determined. , Thesis (MSc) -- Faculty of Science, Mathematics (Pure and Applied), 2015
- Full Text:
- Date Issued: 2015-04-10
Use of microbial fuel cells in the beneficiation of algal biomass for bioelectricity production
- Mtambanengwe, Kudzai Tapiwanashe Esau
- Authors: Mtambanengwe, Kudzai Tapiwanashe Esau
- Date: 2015-04-10
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/480334 , vital:78432
- Description: Microbial fuel cells (MFCs) offer an alternative technology that is able to convert organic matter into electrical energy by making use of bacterial biomass as the biocatalysts. Performance of the MFCs is dependent on many factors such as substrate, biocatalyst, electrode material and optimum operational conditions including temperature and pH. Significant research has been conducted on the use of different substrates to fuel the MFC. The possibility of harvesting energy from organic waste sources in the MFC makes the technology attractive. In this study, we have investigated the use of Chlorella, Arthrospira and a mixed algal consortium obtained from the local wastewater treatment facility in Grahamstown, courtesy of the Institute for Environmental Biotechnology, Rhodes University (EBRU) as feedstock in an MFC with Enterobacter cloacae as the biocatalyst. Pre-treatment of the algae-based feedstock was studied as well as the influence of treatment on nutrient release and biocatalyst performance during growth studies and MFC operations. Sonication, autoclaving and a combination of the two were used as the pre-treatment methods. Pre-treatment resulted in the release of nutrients from algal cells to the media. Peak nutrient realease was observed when a combination of sonicating and autoclaving was employed. Sonicating and autoclaving the mixed consortium from EBRU resulted in an MFC peak power density of 101.2 (± 4.58) mW.m-2. This represented more than 80% of the peak power density obtained in RCM medium. Operational conditions during MFC studies such as pH, temperature, nutrient utilisation by the biocatalyst and performance of the proton exchange membrane were measured during the course of the study. Growth kinetics and MFC operations were shown to be optimal when the substrate feedstock was acidic. However, for longer MFC operations (120 hours), total power output was greater by 3 to 5 fold when the feedstock was at acidic pH (4-6) than when the pH of the substrate feedstock was alkaline (8 and 9). Further MFC studies were performed on the effect of electrode materials including activated carbon fibre and carbon paper. The study examined also the use of live Chlorella and Arthrospira cultures as biocathodes in an MFC. We also showed that activated carbon fibre performs well as an electrode catalyst for both anode and cathode without any need of modification. Biocathode studies showed that the main limiting factor to biocathodes performance was light irradiance. , Thesis (MSc) -- Faculty of Science, Biotechnology Innovation Centre, 2015
- Full Text:
- Date Issued: 2015-04-10
- Authors: Mtambanengwe, Kudzai Tapiwanashe Esau
- Date: 2015-04-10
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/480334 , vital:78432
- Description: Microbial fuel cells (MFCs) offer an alternative technology that is able to convert organic matter into electrical energy by making use of bacterial biomass as the biocatalysts. Performance of the MFCs is dependent on many factors such as substrate, biocatalyst, electrode material and optimum operational conditions including temperature and pH. Significant research has been conducted on the use of different substrates to fuel the MFC. The possibility of harvesting energy from organic waste sources in the MFC makes the technology attractive. In this study, we have investigated the use of Chlorella, Arthrospira and a mixed algal consortium obtained from the local wastewater treatment facility in Grahamstown, courtesy of the Institute for Environmental Biotechnology, Rhodes University (EBRU) as feedstock in an MFC with Enterobacter cloacae as the biocatalyst. Pre-treatment of the algae-based feedstock was studied as well as the influence of treatment on nutrient release and biocatalyst performance during growth studies and MFC operations. Sonication, autoclaving and a combination of the two were used as the pre-treatment methods. Pre-treatment resulted in the release of nutrients from algal cells to the media. Peak nutrient realease was observed when a combination of sonicating and autoclaving was employed. Sonicating and autoclaving the mixed consortium from EBRU resulted in an MFC peak power density of 101.2 (± 4.58) mW.m-2. This represented more than 80% of the peak power density obtained in RCM medium. Operational conditions during MFC studies such as pH, temperature, nutrient utilisation by the biocatalyst and performance of the proton exchange membrane were measured during the course of the study. Growth kinetics and MFC operations were shown to be optimal when the substrate feedstock was acidic. However, for longer MFC operations (120 hours), total power output was greater by 3 to 5 fold when the feedstock was at acidic pH (4-6) than when the pH of the substrate feedstock was alkaline (8 and 9). Further MFC studies were performed on the effect of electrode materials including activated carbon fibre and carbon paper. The study examined also the use of live Chlorella and Arthrospira cultures as biocathodes in an MFC. We also showed that activated carbon fibre performs well as an electrode catalyst for both anode and cathode without any need of modification. Biocathode studies showed that the main limiting factor to biocathodes performance was light irradiance. , Thesis (MSc) -- Faculty of Science, Biotechnology Innovation Centre, 2015
- Full Text:
- Date Issued: 2015-04-10
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