Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

Detonating the research plan: exploding the supervisory process

Bomb making is dangerous work. And not just because what you’re creating can blow up in your face. Even as you type in your search terms – how to make a bomb – you wonder who is watching, what algorithm might throw you up into the light of surveillance and trigger the knock at the door. (McKnight, 2014, p. 1)AbstractSo begins Lucinda’s PhD. In this dialogic paper of interwoven stories we employ a critical auto-ethnographic approach to explode moments of our lives and work together as we worked through the “research plan” at the heart of the supervision timeline. Lucinda’s thesis highlights the way curriculum emerges from the struggles of ideological becoming (Bakhtin 1981) as she and a group of teachers, sought to produce and perform both individual gendered identities (Butler 1997, 2007) and plans for the identities of student subjects, while negotiating subject positions made available to girls and women in broader social contexts. The link between the personal and political is created by a methodology combining narrative inquiry and discourse analysis as a heteroglossic (Bakhtin, 1981) text. In this paper we detonate the research plan developed in the first months of the PhD timeline as Jo responds to Lucinda’s narratives with her own, and we share jointly written narratives that try to capture some key moments of the process. We rework our own stories of the supervised and the supervisor through the competing discourses of our work and lives.

Talking it up! Project report : Aboriginal voices in the formulation of health policy that works : short report

Initially, there were three separate strands to the work of the project: a series of forums involving group interviews/discussions with community members; a policy analysis that reviewed policies relating to Aboriginal health at federal and state level; and a literature review. The results of these three separate strands of analysis were then brought together in a fourth strand to the work, a process involving community members to discuss and agree the overall recommendations contained in this report.

Through this structure, the project employed a participatory methodology as the basis for individual and collective empowerment in relation to health outcomes. As mentioned above, the need for the project was identified by Aboriginal people, through their own processes of healing. The need was presented by appropriate figures within their communities, namely community elders. They invited other Aboriginal people to take part through their own communication channels, thus ensuring that responsibility for engagement in the project, and in formulating action for improvement, remained with Aboriginal people and their families. However, the project design also recognised that Aboriginal people exist within broader structural and policy constraints which impact on their ability to manage their own lives successfully or otherwise. Thus the project sought to combine indigenous and non-indigenous knowledge through bringing together the three strands of work in the way described.

A Community Reference Group guided the work of the project at all stages, endorsed the findings and drafted the recommendations. The two elders who had identified the need for the project formed the core of the group, and worked on the project from start to finish. At different times during the project, other community members joined the group to assist in its work, including training Aboriginal researchers, letting others know about the forums, discussing findings and drafting recommendations.

Talking it up! Project report : Aboriginal voices in the formulation of health policy that works : full report

Initially, there were three separate strands to the work of the project: a series of forums involving group interviews/discussions with community members; a policy analysis that reviewed policies relating to Aboriginal health at federal and state level; and a literature review. The results of these three separate strands of analysis were then brought together in a fourth strand to the work, a process involving community members to discuss and agree the overall recommendations contained in this report.

Through this structure, the project employed a participatory methodology as the basis for individual and collective empowerment in relation to health outcomes. As mentioned above, the need for the project was identified by Aboriginal people, through their own processes of healing. The need was presented by appropriate figures within their communities, namely community elders. They invited other Aboriginal people to take part through their own communication channels, thus ensuring that responsibility for engagement in the project, and in formulating action for improvement, remained with Aboriginal people and their families. However, the project design also recognised that Aboriginal people exist within broader structural and policy constraints which impact on their ability to manage their own lives successfully or otherwise. Thus the project sought to combine indigenous and non-indigenous knowledge through bringing together the three strands of work in the way described.

A Community Reference Group guided the work of the project at all stages, endorsed the findings and drafted the recommendations. The two elders who had identified the need for the project formed the core of the group, and worked on the project from start to finish. At different times during the project, other community members joined the group to assist in its work, including training Aboriginal researchers, letting others know about the forums, discussing findings and drafting recommendations.
Initially, there were three separate strands to the work of the project: a series of forums involving group interviews/discussions with community members; a policy analysis that reviewed policies relating to Aboriginal health at federal and state level; and a literature review. The results of these three separate strands of analysis were then brought together in a fourth strand to the work, a process involving community members to discuss and agree the overall recommendations contained in this report.

Through this structure, the project employed a participatory methodology as the basis for individual and collective empowerment in relation to health outcomes. As mentioned above, the need for the project was identified by Aboriginal people, through their own processes of healing. The need was presented by appropriate figures within their communities, namely community elders. They invited other Aboriginal people to take part through their own communication channels, thus ensuring that responsibility for engagement in the project, and in formulating action for improvement, remained with Aboriginal people and their families. However, the project design also recognised that Aboriginal people exist within broader structural and policy constraints which impact on their ability to manage their own lives successfully or otherwise. Thus the project sought to combine indigenous and non-indigenous knowledge through bringing together the three strands of work in the way described.

A new method to warm up lubricating oil to improve the fuel efficiency during cold start

Cold start driving cycles exhibit an increase in friction losses due to the low temperatures of metal and media compared to normal operating engine conditions. These friction losses are responsible for up to 10% penalty in fuel economy over the official drive cycles like the New European Drive Cycle (NEDC), where the temperature of the oil even at the end of the 1180 s of the drive cycle is below the fully warmed up values of between 100°C and 120°C. At engine oil temperatures below 100°C the water from the blow by condensates and dilutes the engine oil in the oil pan which negatively affects engine wear. Therefore engine oil temperatures above 100°C are desirable to minimize engine wear through blow by condensate. The paper presents a new technique to warm up the engine oil that significantly reduces the friction losses and therefore also reduces the fuel economy penalty during a 22°C cold start NEDC. Chassis dynamometer experiments demonstrated fuel economy improvements of over 7% as well as significant emission reductions by rapidly increasing the oil temperature. Oil temperatures were increased by up to 60°C during certain parts of the NEDC. It is shown how a very simple sensitivity analysis can be used to assess the relative size or efficiency of different heat transfer passes and the resulting fuel economy improvement potential of different heat recovery systems system. Due to its simplicity the method is very fast to use and therefore also very cost effective. The method demonstrated a very good correlation for the fuel consumption within ±1% compared to measurements on a vehicle chassis roll.