891 resultados para 2ND ORDER PERIODIC PROBLEMS


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The importance of sustainable development has been internationally recognized and the principles have been widely used as an impetus for promoting housing sustainability. In the situation of mixed-use urban development in close proximity to heavy industrial areas in Malaysia, rising incomes are developing hand in hand with higher expectations for better and more sustainable housing designs. Negative environmental impacts due current deficiency in Malaysia’s approach to the implementation of sustainable development principles can be seen in this case study of the Pasir Gudang Industrial Area in Malaysia. This study aimed to highlight the level of residents’ satisfaction with living near the industrial area, and to relate their awareness of the relevance of sustainable principles with indoor environmental conditions, which found that the residents’ has limited understanding of the environmental problems in their indoor living conditions and in their neighborhoods. This study has suggested that proactive and integrated involvement by housing authorities from all levels of government in Malaysia should be encouraged in order to rationalise the approaches to develop better planning solutions for such mixed-used urban developments. This initiative should then encourage housing vendors to provide innovative ‘smart’ technological changes to their projects and so, to achieve a new direction in sustainable housing development.

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Presbyopia affects individuals from the age of 45 years onwards, resulting in difficulty in accurately focusing on near objects. There are many optical corrections available including spectacles or contact lenses that are designed to enable presbyopes to see clearly at both far and near distances. However, presbyopic vision corrections also disturb aspects of visual function under certain circumstances. The impact of these changes on activities of daily living such as driving are, however, poorly understood. Therefore, the aim of this study was to determine which aspects of driving performance might be affected by wearing different types of presbyopic vision corrections. In order to achieve this aim, three experiments were undertaken. The first experiment involved administration of a questionnaire to compare the subjective driving difficulties experienced when wearing a range of common presbyopic contact lens and spectacle corrections. The questionnaire was developed and piloted, and included a series of items regarding difficulties experienced while driving under day and night-time conditions. Two hundred and fifty five presbyopic patients responded to the questionnaire and were categorised into five groups, including those wearing no vision correction for driving (n = 50), bifocal spectacles (BIF, n = 54), progressive addition lenses spectacles (PAL, n = 50), monovision (MV, n = 53) and multifocal contact lenses (MTF CL, n = 48). Overall, ratings of satisfaction during daytime driving were relatively high for all correction types. However, MV and MTF CL wearers were significantly less satisfied with aspects of their vision during night-time than daytime driving, particularly with regard to disturbances from glare and haloes. Progressive addition lens wearers noticed more distortion of peripheral vision, while BIF wearers reported more difficulties with tasks requiring changes in focus and those who wore no vision correction for driving reported problems with intermediate and near tasks. Overall, the mean level of satisfaction for daytime driving was quite high for all of the groups (over 80%), with the BIF wearers being the least satisfied with their vision for driving. Conversely, at night, MTF CL wearers expressed the least satisfaction. Research into eye and head movements has become increasingly of interest in driving research as it provides a means of understanding how the driver responds to visual stimuli in traffic. Previous studies have found that wearing PAL can affect eye and head movement performance resulting in slower eye movement velocities and longer times to stabilize the gaze for fixation. These changes in eye and head movement patterns may have implications for driving safety, given that the visual tasks for driving include a range of dynamic search tasks. Therefore, the second study was designed to investigate the influence of different presbyopic corrections on driving-related eye and head movements under standardized laboratory-based conditions. Twenty presbyopes (mean age: 56.1 ± 5.7 years) who had no experience of wearing presbyopic vision corrections, apart from single vision reading spectacles, were recruited. Each participant wore five different types of vision correction: single vision distance lenses (SV), PAL, BIF, MV and MTF CL. For each visual condition, participants were required to view videotape recordings of traffic scenes, track a reference vehicle and identify a series of peripherally presented targets while their eye and head movements were recorded using the faceLAB® eye and head tracking system. Digital numerical display panels were also included as near visual stimuli (simulating the visual displays of a vehicle speedometer and radio). The results demonstrated that the path length of eye movements while viewing and responding to driving-related traffic scenes was significantly longer when wearing BIF and PAL than MV and MTF CL. The path length of head movements was greater with SV, BIF and PAL than MV and MTF CL. Target recognition was less accurate when the near stimulus was located at eccentricities inferiorly and to the left, rather than directly below the primary position of gaze, regardless of vision correction type. The third experiment aimed to investigate the real world driving performance of presbyopes while wearing different vision corrections measured on a closed-road circuit at night-time. Eye movements were recorded using the ASL Mobile Eye, eye tracking system (as the faceLAB® system proved to be impractical for use outside of the laboratory). Eleven participants (mean age: 57.25 ± 5.78 years) were fitted with four types of prescribed vision corrections (SV, PAL, MV and MTF CL). The measures of driving performance on the closed-road circuit included distance to sign recognition, near target recognition, peripheral light-emitting-diode (LED) recognition, low contrast road hazards recognition and avoidance, recognition of all the road signs, time to complete the course, and driving behaviours such as braking, accelerating, and cornering. The results demonstrated that driving performance at night was most affected by MTF CL compared to PAL, resulting in shorter distances to read signs, slower driving speeds, and longer times spent fixating road signs. Monovision resulted in worse performance in the task of distance to read a signs compared to SV and PAL. The SV condition resulted in significantly more errors made in interpreting information from in-vehicle devices, despite spending longer time fixating on these devices. Progressive addition lenses were ranked as the most preferred vision correction, while MTF CL were the least preferred vision correction for night-time driving. This thesis addressed the research question of how presbyopic vision corrections affect driving performance and the results of the three experiments demonstrated that the different types of presbyopic vision corrections (e.g. BIF, PAL, MV and MTF CL) can affect driving performance in different ways. Distance-related driving tasks showed reduced performance with MV and MTF CL, while tasks which involved viewing in-vehicle devices were significantly hampered by wearing SV corrections. Wearing spectacles such as SV, BIF and PAL induced greater eye and head movements in the simulated driving condition, however this did not directly translate to impaired performance on the closed- road circuit tasks. These findings are important for understanding the influence of presbyopic vision corrections on vision under real world driving conditions. They will also assist the eye care practitioner to understand and convey to patients the potential driving difficulties associated with wearing certain types of presbyopic vision corrections and accordingly to support them in the process of matching patients to optical corrections which meet their visual needs.

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The middle years of schooling are increasingly recognised as a crucial stage in students' lives, one that has significant consequences for ongoing educational success. International research indicates that young adolescents benefit from programs designed especially for their needs. Teaching Middle Years offers a systematic overview of the philosophy, principles and issues in middle schooling. It includes contributions from academics and school-based practitioners on intellectual and emotional development in early adolescence, pedagogy, curriculum and assessment of middle years students. This second edition is fully revised to reflect the latest research findings. It includes new chapters on students with diverse needs, school partnerships with families and community, and effective team teaching. Also new to this edition is a chapter that brings middle schooling concepts to life by providing real examples of reform in action.

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Using a feminist reflexive approach this paper reports on interviews with single mother’s in the Brisbane area about their experiences with food shopping and household food security. Preliminary findings suggest that most experience significant stress around the amount of money they have available for food. As the price of food and other costs of living increase, the only budget item that is flexible – groceries - is squeezed tighter. All women expressed a reluctance to ask for help from strangers at agencies instead relying on the support of family and friends to keep them food secure. Sometimes family and friends had no spare resources to help or were not aware of the extent their friend or relative might be struggling. The increased risks of poverty and food insecurity mean many go without as feeding the children takes precedence. The quality of their diets is variable with many reporting on aiming for quantity rather than being concerned with nutritional balance. Exhaustion and stress from being over-committed doing three roles, mother, father and housekeeper was self-identified as a key factor leading to mental health conditions such as depression, burnout and break down. Female single parent households are vulnerable to reducing welfare benefits as children grow or child support changes. Current policy forces single parents out to work but many can only manage part-time work for lower wages and are barely able to cope with this extra burden often resenting the reduction in benefits it brings. Public perceptions, derision and the notions of choice surrounding single parenting leave the cohort divided and silent for fear of reprisals. In my investigation issues arise about welfare policy that keep benefits low and workplace patriarchal power that can contribute to systemic poverty and the widening of the gender gap in poverty. So far analysis suggests a better support system around community food security including some hands on home help services, nutritional information, cooking classes, community gardening and other social capital building activities are needed for these women in order to avoid long-term health problems and help them better care for the next generation.

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Purpose: Poor image quality in the peripheral field may lead to myopia. Most studies measuring the higher order aberrations in the periphery have been restricted to the horizontal visual field. The purpose of this study was to measure higher order monochromatic aberrations across the central 42º horizontal x 32º vertical visual fields in myopes and emmetropes. ---------- Methods: We recruited 5 young emmetropes with spherical equivalent refractions +0.17 ± 0.45D and 5 young myopes with spherical equivalent refractions -3.9 ± 2.09D. Measurements were taken with a modified COAS-HD Hartmann-Shack aberrometer (Wavefront Sciences Inc). Measurements were taken while the subjects looked at 38 points arranged in a 7 x 6 matrix (excluding four corner points) through a beam splitter held between the instrument and the eye. A combination of the instrument’s software and our own software was used to estimate OSA Zernike coefficients for 5mm pupil diameter at 555nm for each point. The software took into account the elliptical shape of the off-axis pupil. Nasal and superior fields were taken to have positive x and y signs, respectively. ---------- Results: The total higher order RMS (HORMS) was similar on-axis for emmetropes (0.16 ± 0.02 μm) and myopes (0.17 ± 0.02 μm). There was no common pattern for HORMS for emmetropes across the visual field where as 4 out of 5 myopes showed a linear increase in HORMS in all directions away from the minimum. For all subjects, vertical and horizontal comas showed linear changes across the visual field. The mean rate of change of vertical coma across the vertical meridian was significantly lower (p = 0.008) for emmetropes (-0.005 ± 0.002 μm/deg) than for myopes (-0.013 ± 0.004 μm/deg). The mean rate of change of horizontal coma across the horizontal meridian was lower (p = 0.07) for emmetropes (-0.006 ± 0.003 μm/deg) than myopes (-0.011 ± 0.004 μm/deg). ---------- Conclusion: We have found differences in patterns of higher order aberrations across the visual fields of emmetropes and myopes, with myopes showing the greater rates of change of horizontal and vertical coma.

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The play Tango Femme places the lesbian centre stage by creating characters, narrative and drama in the world of same-sex dancing. The accompanying exegesis examines the problems and issues associated with creating lesbian characters in theatre, using a synthesized, practice led methodology. During the process of imagining, constructing and writing my case study play, I have investigated lesbian theatre productions and companies in order to make sense of my personal experiences in the theatre world. I have also reflected on the lesbian as represented in mainstream theatre and popular culture. Through journal writing and contemplation, I have sought to identify difficulties inherent in writing this type of play, using my own journey as a focus. My study illuminates the historical and sociological circumstances in the eighties and nineties in Australia and concludes that as a lesbian playwright I was caught between a rock and a hard place: the rock being lesbian theatre on a community level, as defined and attended primarily by separatist lesbians, and the hard place being mainstream theatre, located within the dominant, heteronormative discourse. The play Tango Femme has developed in conversation with my reflective practice and research and is written in the space outside the master narrative as "an instance of lesbian discourse" (Davy 1996, p.153).

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Criminology has tended to treat crime as predominantly an urban phenomenon. A review of the available, albeit rather limited, empirical evidence regarding crime and law and order in rural New South Wales (NSW) raises some doubts about the urban-centric focus of criminology and opens up a range of other interesting questions concerning the differential social construction of crime problems in some rural localities, in particular the tendency to racialise questions of crime and law and order. Rather than simply developing an empirical and theoretical account of urban/rural differences, however, the paper suggests a conceptual framework for local and regional studies drawing on the work of Norbert Elias and Robert Putnam.

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This approach to sustainable design explores the possibility of creating an architectural design process which can iteratively produce optimised and sustainable design solutions. Driven by an evolution process based on genetic algorithms, the system allows the designer to “design the building design generator” rather than to “designs the building”. The design concept is abstracted into a digital design schema, which allows transfer of the human creative vision into the rational language of a computer. The schema is then elaborated into the use of genetic algorithms to evolve innovative, performative and sustainable design solutions. The prioritisation of the project’s constraints and the subsequent design solutions synthesised during design generation are expected to resolve most of the major conflicts in the evaluation and optimisation phases. Mosques are used as the example building typology to ground the research activity. The spatial organisations of various mosque typologies are graphically represented by adjacency constraints between spaces. Each configuration is represented by a planar graph which is then translated into a non-orthogonal dual graph and fed into the genetic algorithm system with fixed constraints and expected performance criteria set to govern evolution. The resultant Hierarchical Evolutionary Algorithmic Design System is developed by linking the evaluation process with environmental assessment tools to rank the candidate designs. The proposed system generates the concept, the seed, and the schema, and has environmental performance as one of the main criteria in driving optimisation.

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The aim of the study is to identify the opportunities and challenges a local government public asset manager is most likely to deal with when adopting the appropriate Public Asset Management Framework especially in developing countries. In order to achieve its aim, this study employs a Case Study in Indonesia for collecting all data i.e. interviews, document analysis and observations at South Sulawesi Province, Indonesia. The study concludes that there are significant opportunities and challenges that local governments in developing countries, especially Indonesia, might be required to manage if apply public asset management framework appropriately. The opportunities are more effective and efficient local government, accountable and auditable local government organization, increase local government portfolio, reflect up to date information for decision makers in local government, and improve the quality of public services. On the other hand, there are also challenges. Those challenges are local governments has no clear legal and institutional framework to support the asset management application, non-profit principle of public assets, cross jurisdictions and applications in public asset management, the complexity of public organization objectives, and data availability required for managing public property. The study only covers the condition of developing countries where Indonesia as an example, which could not represent exactly the whole local governments’ condition in the world. Further study to develop an asset management system applicable for all local governments in developing countries is urgently needed. Findings from this study will provide useful input for the policy maker, scholars and asset management practitioners to develop an asset management framework for more efficient and effective local governments.

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Differential axial shortening in vertical members of reinforced concrete high-rise buildings occurs due to shrinkage, creep and elastic shortening, which are time dependent effects of concrete. This has to be quantified in order to make adequate provisions and mitigate its adverse effects. This paper presents a novel procedure for quantifying the axial shortening of vertical members using the variations in vibration characteristics of the structure, in lieu of using gauges which can pose problems in use during and after the construction. This procedure is based on the changes in the modal flexiblity matrix which is expressed as a function of the mode shapes and the reciprocal of the natural frequencies. This paper will present the development of this novel procedure.

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This paper details a systematic literature review identifying problems in extant research relating to teachers’ attitudes towards reporting child sexual abuse, and offers a model for new attitude scale development and testing. Scale development comprised a five-phase process grounded in contemporary attitude theories including: a) developing the initial item pool; b) conducting a panel review; c) refining the scale via an expert focus group; d) building content validity through cognitive interviews; e) assessing internal consistency via field testing. The resulting 21-item scale displayed construct validity in preliminary testing. The scale may prove useful as a research tool, given the theoretical supposition that attitudes may be changed with time, context, experience, and education. Further investigation with a larger sample is warranted.

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In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

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The Queensland University of Technology (QUT) allows the presentation of theses for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of ten published /submitted papers and book chapters of which nine have been published and one is under review. This project is financially supported by an Australian Research Council (ARC) Discovery Grant with the aim of investigating multilevel topologies for high quality and high power applications, with specific emphasis on renewable energy systems. The rapid evolution of renewable energy within the last several years has resulted in the design of efficient power converters suitable for medium and high-power applications such as wind turbine and photovoltaic (PV) systems. Today, the industrial trend is moving away from heavy and bulky passive components to power converter systems that use more and more semiconductor elements controlled by powerful processor systems. However, it is hard to connect the traditional converters to the high and medium voltage grids, as a single power switch cannot stand at high voltage. For these reasons, a new family of multilevel inverters has appeared as a solution for working with higher voltage levels. Besides this important feature, multilevel converters have the capability to generate stepped waveforms. Consequently, in comparison with conventional two-level inverters, they present lower switching losses, lower voltage stress across loads, lower electromagnetic interference (EMI) and higher quality output waveforms. These properties enable the connection of renewable energy sources directly to the grid without using expensive, bulky, heavy line transformers. Additionally, they minimize the size of the passive filter and increase the durability of electrical devices. However, multilevel converters have only been utilised in very particular applications, mainly due to the structural limitations, high cost and complexity of the multilevel converter system and control. New developments in the fields of power semiconductor switches and processors will favor the multilevel converters for many other fields of application. The main application for the multilevel converter presented in this work is the front-end power converter in renewable energy systems. Diode-clamped and cascade converters are the most common type of multilevel converters widely used in different renewable energy system applications. However, some drawbacks – such as capacitor voltage imbalance, number of components, and complexity of the control system – still exist, and these are investigated in the framework of this thesis. Various simulations using software simulation tools are undertaken and are used to study different cases. The feasibility of the developments is underlined with a series of experimental results. This thesis is divided into two main sections. The first section focuses on solving the capacitor voltage imbalance for a wide range of applications, and on decreasing the complexity of the control strategy on the inverter side. The idea of using sharing switches at the output structure of the DC-DC front-end converters is proposed to balance the series DC link capacitors. A new family of multioutput DC-DC converters is proposed for renewable energy systems connected to the DC link voltage of diode-clamped converters. The main objective of this type of converter is the sharing of the total output voltage into several series voltage levels using sharing switches. This solves the problems associated with capacitor voltage imbalance in diode-clamped multilevel converters. These converters adjust the variable and unregulated DC voltage generated by renewable energy systems (such as PV) to the desirable series multiple voltage levels at the inverter DC side. A multi-output boost (MOB) converter, with one inductor and series output voltage, is presented. This converter is suitable for renewable energy systems based on diode-clamped converters because it boosts the low output voltage and provides the series capacitor at the output side. A simple control strategy using cross voltage control with internal current loop is presented to obtain the desired voltage levels at the output voltage. The proposed topology and control strategy are validated by simulation and hardware results. Using the idea of voltage sharing switches, the circuit structure of different topologies of multi-output DC-DC converters – or multi-output voltage sharing (MOVS) converters – have been proposed. In order to verify the feasibility of this topology and its application, steady state and dynamic analyses have been carried out. Simulation and experiments using the proposed control strategy have verified the mathematical analysis. The second part of this thesis addresses the second problem of multilevel converters: the need to improve their quality with minimum cost and complexity. This is related to utilising asymmetrical multilevel topologies instead of conventional multilevel converters; this can increase the quality of output waveforms with a minimum number of components. It also allows for a reduction in the cost and complexity of systems while maintaining the same output quality, or for an increase in the quality while maintaining the same cost and complexity. Therefore, the asymmetrical configuration for two common types of multilevel converters – diode-clamped and cascade converters – is investigated. Also, as well as addressing the maximisation of the output voltage resolution, some technical issues – such as adjacent switching vectors – should be taken into account in asymmetrical multilevel configurations to keep the total harmonic distortion (THD) and switching losses to a minimum. Thus, the asymmetrical diode-clamped converter is proposed. An appropriate asymmetrical DC link arrangement is presented for four-level diode-clamped converters by keeping adjacent switching vectors. In this way, five-level inverter performance is achieved for the same level of complexity of the four-level inverter. Dealing with the capacitor voltage imbalance problem in asymmetrical diodeclamped converters has inspired the proposal for two different DC-DC topologies with a suitable control strategy. A Triple-Output Boost (TOB) converter and a Boost 3-Output Voltage Sharing (Boost-3OVS) converter connected to the four-level diode-clamped converter are proposed to arrange the proposed asymmetrical DC link for the high modulation indices and unity power factor. Cascade converters have shown their abilities and strengths in medium and high power applications. Using asymmetrical H-bridge inverters, more voltage levels can be generated in output voltage with the same number of components as the symmetrical converters. The concept of cascading multilevel H-bridge cells is used to propose a fifteen-level cascade inverter using a four-level H-bridge symmetrical diode-clamped converter, cascaded with classical two-level Hbridge inverters. A DC voltage ratio of cells is presented to obtain maximum voltage levels on output voltage, with adjacent switching vectors between all possible voltage levels; this can minimize the switching losses. This structure can save five isolated DC sources and twelve switches in comparison to conventional cascade converters with series two-level H bridge inverters. To increase the quality in presented hybrid topology with minimum number of components, a new cascade inverter is verified by cascading an asymmetrical four-level H-bridge diode-clamped inverter. An inverter with nineteen-level performance was achieved. This synthesizes more voltage levels with lower voltage and current THD, rather than using a symmetrical diode-clamped inverter with the same configuration and equivalent number of power components. Two different predictive current control methods for the switching states selection are proposed to minimise either losses or THD of voltage in hybrid converters. High voltage spikes at switching time in experimental results and investigation of a diode-clamped inverter structure raised another problem associated with high-level high voltage multilevel converters. Power switching components with fast switching, combined with hard switched-converters, produce high di/dt during turn off time. Thus, stray inductance of interconnections becomes an important issue and raises overvoltage and EMI issues correlated to the number of components. Planar busbar is a good candidate to reduce interconnection inductance in high power inverters compared with cables. The effect of different transient current loops on busbar physical structure of the high-voltage highlevel diode-clamped converters is highlighted. Design considerations of proper planar busbar are also presented to optimise the overall design of diode-clamped converters.

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Cold-formed steel members are extensively used in the building construction industry, especially in residential, commercial and industrial buildings. In recent times, fire safety has become important in structural design due to increased fire damage to properties and loss of lives. However, past research into the fire performance of cold-formed steel members has been limited, and was confined to compression members. Therefore a research project was undertaken to investigate the structural behaviour of compact cold-formed steel lipped channel beams subject to inelastic local buckling and yielding, and lateral-torsional buckling effects under simulated fire conditions and associated section and member moment capacities. In the first phase of this research, an experimental study based on tensile coupon tests was undertaken to obtain the mechanical properties of elastic modulus and yield strength and the stress-strain relationship of cold-formed steels at uniform ambient and elevated temperatures up to 700oC. The mechanical properties deteriorated with increasing temperature and are likely to reduce the strength of cold-formed beams under fire conditions. Predictive equations were developed for yield strength and elastic modulus reduction factors while a modification was proposed for the stressstrain model at elevated temperatures. These results were used in the numerical modelling phases investigating the section and member moment capacities. The second phase of this research involved the development and validation of two finite element models to simulate the behaviour of compact cold-formed steel lipped channel beams subject to local buckling and yielding, and lateral-torsional buckling effects. Both models were first validated for elastic buckling. Lateral-torsional buckling tests of compact lipped channel beams were conducted at ambient temperature in order to validate the finite element model in predicting the non-linear ultimate strength behaviour. The results from this experimental study did not agree well with those from the developed experimental finite element model due to some unavoidable problems with testing. However, it highlighted the importance of magnitude and direction of initial geometric imperfection as well as the failure direction, and thus led to further enhancement of the finite element model. The finite element model for lateral-torsional buckling was then validated using the available experimental and numerical ultimate moment capacity results from past research. The third phase based on the validated finite element models included detailed parametric studies of section and member moment capacities of compact lipped channel beams at ambient temperature, and provided the basis for similar studies at elevated temperatures. The results showed the existence of inelastic reserve capacity for compact cold-formed steel beams at ambient temperature. However, full plastic capacity was not achieved by the mono-symmetric cold-formed steel beams. Suitable recommendations were made in relation to the accuracy and suitability of current design rules for section moment capacity. Comparison of member capacity results from finite element analyses with current design rules showed that they do not give accurate predictions of lateral-torsional buckling capacities at ambient temperature and hence new design rules were developed. The fourth phase of this research investigated the section and member moment capacities of compact lipped channel beams at uniform elevated temperatures based on detailed parametric studies using the validated finite element models. The results showed the existence of inelastic reserve capacity at elevated temperatures. Suitable recommendations were made in relation to the accuracy and suitability of current design rules for section moment capacity in fire design codes, ambient temperature design codes as well as those proposed by other researchers. The results showed that lateral-torsional buckling capacities are dependent on the ratio of yield strength and elasticity modulus reduction factors and the level of non-linearity in the stress-strain curves at elevated temperatures in addition to the temperature. Current design rules do not include the effects of non-linear stress-strain relationship and therefore their predictions were found to be inaccurate. Therefore a new design rule that uses a nonlinearity factor, which is defined as the ratio of the limit of proportionality to the yield stress at a given temperature, was developed for cold-formed steel beams subject to lateral-torsional buckling at elevated temperatures. This thesis presents the details and results of the experimental and numerical studies conducted in this research including a comparison of results with predictions using available design rules. It also presents the recommendations made regarding the accuracy of current design rules as well as the new developed design rules for coldformed steel beams both at ambient and elevated temperatures.

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When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.