First steps towards modeling a multi-scale Earth system

Recent advances in computational geodynamics are applied to explore the link between Earth’s heat, its chemistry and its mechanical behavior. Computational thermal-mechanical solutions are now allowing us to understand Earth patterns by solving the basic physics of heat transfer. This approach is currently used to solve basic convection patterns of terrestrial planets. Applying the same methodology to smaller scales delivers promising similarities between observed and predicted structures which are often the site of mineral deposits. The new approach involves a fully coupled solution to the energy, momentum and continuity equations of the system at all scales, allowing the prediction of fractures, shear zones and other typical geological patterns out of a randomly perturbed initial state. The results of this approach are linking a global geodynamic mechanical framework over regional-scale mineral deposits down to the underlying micro-scale processes. Ongoing work includes the challenge of incorporating chemistry into the formulation.

Desalination by a solar thermally driven distillation process

Desalination processes to remove dissolved salts from seawater or brackish water includes common industrial scale processes such as reverse osmosis, thermal processes (i.e. multi-stage flash, multiple-effect distillation) and mechanical vapour compression. These processes are very energy intensive. The Institute for Future Environments (IFE) has evaluated various alternative processes to accomplish desalination using renewable or sustainable energy sources. A new process - a solar, thermally driven distillation system . based on the principles of a solar still – has been examined. This work presents an initial evaluation of the process.

Desalination by a solar thermal membrane distillation process

A solar thermal membrane distillation pilot plant was operated for over 70 days in field conditions. The pilot plant incorporated a single spiral wound permeate gap membrane distillation style of module. All energy used to operate the unit was supplied by solar hot water collectors and photovoltaic panels. The process was able to produce a distillate stream of product water with a conductivity less than 10 µS/cm. Feed water concentration varied from 2,400 µS/cm to 106,000 µS/cm. The process is expected to find application in the production of drinking water for remote island and arid regions without the consumption of electrical energy.

Meal induced thermogenesis and appetite : methodological issues and responses to energy restriction

Diet Induced Thermogenesis (DIT) is the energy expended consequent to meal consumption, and reflects the energy required for the processing and digestion of food consumed throughout each day. Although DIT is the total energy expended across a day in digestive processes to a number of meals, most studies measure thermogenesis in response to a single meal (Meal Induced Thermogenesis: MIT) as a representation of an individual’s thermogenic response to acute food ingestion. As a component of energy expenditure, DIT may have a contributing role in weight gain and weight loss. While the evidence is inconsistent, research has tended to reveal a suppressed MIT response in obese compared to lean individuals, which identifies individuals with an efficient storage of food energy, hence a greater tendency for weight gain. Appetite is another factor regulating body weight through its influence on energy intake. Preliminary research has shown a potential link between MIT and postprandial appetite as both are responses to food ingestion and have a similar response dependent upon the macronutrient content of food. There is a growing interest in understanding how both MIT and appetite are modified with changes in diet, activity levels and body size. However, the findings from MIT research have been highly inconsistent, potentially due to the vastly divergent protocols used for its measurement. Therefore, the main theme of this thesis was firstly, to address some of the methodological issues associated with measuring MIT. Additionally this thesis aimed to measure postprandial appetite simultaneously to MIT to test for any relationships between these meal-induced variables and to assess changes that occur in MIT and postprandial appetite during periods of energy restriction (ER) and following weight loss. Two separate studies were conducted to achieve these aims. Based on the increasing prevalence of obesity, it is important to develop accurate methodologies for measuring the components potentially contributing to its development and to understand the variability within these variables. Therefore, the aim of Study One was to establish a protocol for measuring the thermogenic response to a single test meal (MIT), as a representation of DIT across a day. This was done by determining the reproducibility of MIT with a continuous measurement protocol and determining the effect of measurement duration. The benefit of a fixed resting metabolic rate (RMR), which is a single measure of RMR used to calculate each subsequent measure of MIT, compared to separate baseline RMRs, which are separate measures of RMR measured immediately prior to each MIT test meal to calculate each measure of MIT, was also assessed to determine the method with greater reproducibility. Subsidiary aims were to measure postprandial appetite simultaneously to MIT, to determine its reproducibility between days and to assess potential relationships between these two variables. Ten healthy individuals (5 males, 5 females, age = 30.2 ± 7.6 years, BMI = 22.3 ± 1.9 kg/m2, %Fat Mass = 27.6 ± 5.9%) undertook three testing sessions within a 1-4 week time period. During the first visit, participants had their body composition measured using DXA for descriptive purposes, then had an initial 30-minute measure of RMR to familiarise them with the testing and to be used as a fixed baseline for calculating MIT. During the second and third testing sessions, MIT was measured. Measures of RMR and MIT were undertaken using a metabolic cart with a ventilated hood to measure energy expenditure via indirect calorimetry with participants in a semi-reclined position. The procedure on each MIT test day was: 1) a baseline RMR measured for 30 minutes, 2) a 15-minute break in the measure to consume a standard 576 kcal breakfast (54.3% CHO, 14.3% PRO, 31.4% FAT), comprising muesli, milk toast, butter, jam and juice, and 3) six hours of measuring MIT with two, ten-minute breaks at 3 and 4.5 hours for participants to visit the bathroom. On the MIT test days, pre and post breakfast then at 45-minute intervals, participants rated their subjective appetite, alertness and comfort on visual analogue scales (VAS). Prior to each test, participants were required to be fasted for 12 hours, and have undertaken no high intensity physical activity for the previous 48 hours. Despite no significant group changes in the MIT response between days, individual variability was high with an average between-day CV of 33%, which was not significantly improved by the use of a fixed RMR to 31%. The 95% limits of agreements which ranged from 9.9% of energy intake (%EI) to -10.7%EI with the baseline RMRs and between 9.6%EI to -12.4%EI with the fixed RMR, indicated very large changes relative to the size of the average MIT response (MIT 1: 8.4%EI, 13.3%EI; MIT 2: 8.8%EI, 14.7%EI; baseline and fixed RMRs respectively). After just three hours, the between-day CV with the baseline RMR was 26%, which may indicate an enhanced MIT reproducibility with shorter measurement durations. On average, 76, 89, and 96% of the six-hour MIT response was completed within three, four and five hours, respectively. Strong correlations were found between MIT at each of these time points and the total six-hour MIT (range for correlations r = 0.990 to 0.998; P < 0.01). The reproducibility of the proportion of the six-hour MIT completed at 3, 4 and 5 hours was reproducible (between-day CVs ≤ 8.5%). This indicated the suitability to use shorter durations on repeated occasions and a similar percent of the total response to be completed. There was a lack of strong evidence of any relationship between the magnitude of the MIT response and subjective postprandial appetite. Given a six-hour protocol places a considerable burden on participants, these results suggests that a post-meal measurement period of only three hours is sufficient to produce valid information on the metabolic response to a meal. However while there was no mean change in MIT between test days, individual variability was large. Further research is required to better understand which factors best explain the between-day variability in this physiological measure. With such a high prevalence of obesity, dieting has become a necessity to reduce body weight. However, during periods of ER, metabolic and appetite adaptations can occur which may impede weight loss. Understanding how metabolic and appetite factors change during ER and weight loss is important for designing optimal weight loss protocols. The purpose of Study Two was to measure the changes in the MIT response and subjective postprandial appetite during either continuous (CONT) or intermittent (INT) ER and following post diet energy balance (post-diet EB). Thirty-six obese male participants were randomly assigned to either the CONT (Age = 38.6 ± 7.0 years, weight = 109.8 ± 9.2 kg, % fat mass = 38.2 ± 5.2%) or INT diet groups (Age = 39.1 ± 9.1 years, weight = 107.1 ± 12.5 kg, % fat mass = 39.6 ± 6.8%). The study was divided into three phases: a four-week baseline (BL) phase where participants were provided with a diet to maintain body weight, an ER phase lasting either 16 (CONT) or 30 (INT) weeks, where participants were provided with a diet which supplied 67% of their energy balance requirements to induce weight loss and an eight-week post-diet EB phase, providing a diet to maintain body weight post weight loss. The INT ER phase was delivered as eight, two-week blocks of ER interspersed with two-week blocks designed to achieve weight maintenance. Energy requirements for each phase were predicted based on measured RMR, and adjusted throughout the study to account for changes in RMR. All participants completed MIT and appetite tests during BL and the ER phase. Nine CONT and 15 INT participants completed the post-diet EB MIT and 14 INT and 15 CONT participants completed the post-diet EB appetite tests. The MIT test day protocol was as follows: 1) a baseline RMR measured for 30 minutes, 2) a 15-minute break in the measure to consume a standard breakfast meal (874 kcal, 53.3% CHO, 14.5% PRO, 32.2% FAT), and 3) three hours of measuring MIT. MIT was calculated as the energy expenditure above the pre-meal RMR. Appetite test days were undertaken on a separate day using the same 576 kcal breakfast used in Study One. VAS were used to assess appetite pre and post breakfast, at one hour post breakfast then a further three times at 45-minute intervals. Appetite ratings were calculated for hunger and fullness as both the intra-meal change in appetite and the AUC. The three-hour MIT response at BL, ER and post-diet EB respectively were 5.4 ± 1.4%EI, 5.1 ± 1.3%EI and 5.0 ± 0.8%EI for the CONT group and 4.4 ± 1.0%EI, 4.7 ± 1.0%EI and 4.8 ± 0.8%EI for the INT group. Compared to BL, neither group had significant changes in their MIT response during ER or post-diet EB. There were no significant time by group interactions (p = 0.17) indicating a similar response to ER and post-diet EB in both groups. Contrary to what was hypothesised, there was a significant increase in postprandial AUC fullness in response to ER in both groups (p < 0.05). However, there were no significant changes in any of the other postprandial hunger or fullness variables. Despite no changes in MIT in both the CONT or INT group in response to ER or post-diet EB and only a minor increase in postprandial AUC fullness, the individual changes in MIT and postprandial appetite in response to ER were large. However those with the greatest MIT changes did not have the greatest changes in postprandial appetite. This study shows that postprandial appetite and MIT are unlikely to be altered during ER and are unlikely to hinder weight loss. Additionally, there were no changes in MIT in response to weight loss, indicating that body weight did not influence the magnitude of the MIT response. There were large individual changes in both variables, however further research is required to determine whether these changes were real compensatory changes to ER or simply between-day variation. Overall, the results of this thesis add to the current literature by showing the large variability of continuous MIT measurements, which make it difficult to compare MIT between groups and in response to diet interventions. This thesis was able to provide evidence to suggest that shorter measures may provide equally valid information about the total MIT response and can therefore be utilised in future research in order to reduce the burden of long measurements durations. This thesis indicates that MIT and postprandial subjective appetite are most likely independent of each other. This thesis also shows that, on average, energy restriction was not associated with compensatory changes in MIT and postprandial appetite that would have impeded weight loss. However, the large inter-individual variability supports the need to examine individual responses in more detail.

IMO mandatory energy efficiency measures for international shipping : the first mandatory global greenhouse gas reduction instrument for an international industry

Bunker fuels used in the aviation and maritime sectors are responsible for nearly 10% of global greenhouse gas emissions.1 According to a scientific survey: ‘[s]hipping is estimated to have emitted 1,046 million tonnes of CO2 in 2007, which corresponds to 3.3% of the global emissions during 2007. International shipping is estimated to have emitted 870 million tonnes, or about 2.7% of the global emissions of CO2 in 2007’. The study also predicted that ‘by 2050, in the absence of policies, ship emissions may grow by 150% to 250% (compared to the emissions in 2007) as a result of the growth in shipping.’

Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

Achieving high reliability for ambiguity resolutions with multiple GNSS constellations

Global Navigation Satellite Systems (GNSS)-based observation systems can provide high precision positioning and navigation solutions in real time, in the order of subcentimetre if we make use of carrier phase measurements in the differential mode and deal with all the bias and noise terms well. However, these carrier phase measurements are ambiguous due to unknown, integer numbers of cycles. One key challenge in the differential carrier phase mode is to fix the integer ambiguities correctly. On the other hand, in the safety of life or liability-critical applications, such as for vehicle safety positioning and aviation, not only is high accuracy required, but also the reliability requirement is important. This PhD research studies to achieve high reliability for ambiguity resolution (AR) in a multi-GNSS environment. GNSS ambiguity estimation and validation problems are the focus of the research effort. Particularly, we study the case of multiple constellations that include initial to full operations of foreseeable Galileo, GLONASS and Compass and QZSS navigation systems from next few years to the end of the decade. Since real observation data is only available from GPS and GLONASS systems, the simulation method named Virtual Galileo Constellation (VGC) is applied to generate observational data from another constellation in the data analysis. In addition, both full ambiguity resolution (FAR) and partial ambiguity resolution (PAR) algorithms are used in processing single and dual constellation data. Firstly, a brief overview of related work on AR methods and reliability theory is given. Next, a modified inverse integer Cholesky decorrelation method and its performance on AR are presented. Subsequently, a new measure of decorrelation performance called orthogonality defect is introduced and compared with other measures. Furthermore, a new AR scheme considering the ambiguity validation requirement in the control of the search space size is proposed to improve the search efficiency. With respect to the reliability of AR, we also discuss the computation of the ambiguity success rate (ASR) and confirm that the success rate computed with the integer bootstrapping method is quite a sharp approximation to the actual integer least-squares (ILS) method success rate. The advantages of multi-GNSS constellations are examined in terms of the PAR technique involving the predefined ASR. Finally, a novel satellite selection algorithm for reliable ambiguity resolution called SARA is developed. In summary, the study demonstrats that when the ASR is close to one, the reliability of AR can be guaranteed and the ambiguity validation is effective. The work then focuses on new strategies to improve the ASR, including a partial ambiguity resolution procedure with a predefined success rate and a novel satellite selection strategy with a high success rate. The proposed strategies bring significant benefits of multi-GNSS signals to real-time high precision and high reliability positioning services.

Multicomponent charge transport in electrolyte solutions

The work presented in this thesis investigates the mathematical modelling of charge transport in electrolyte solutions, within the nanoporous structures of electrochemical devices. We compare two approaches found in the literature, by developing onedimensional transport models based on the Nernst-Planck and Maxwell-Stefan equations. The development of the Nernst-Planck equations relies on the assumption that the solution is infinitely dilute. However, this is typically not the case for the electrolyte solutions found within electrochemical devices. Furthermore, ionic concentrations much higher than those of the bulk concentrations can be obtained near the electrode/electrolyte interfaces due to the development of an electric double layer. Hence, multicomponent interactions which are neglected by the Nernst-Planck equations may become important. The Maxwell-Stefan equations account for these multicomponent interactions, and thus they should provide a more accurate representation of transport in electrolyte solutions. To allow for the effects of the electric double layer in both the Nernst-Planck and Maxwell-Stefan equations, we do not assume local electroneutrality in the solution. Instead, we model the electrostatic potential as a continuously varying function, by way of Poisson’s equation. Importantly, we show that for a ternary electrolyte solution at high interfacial concentrations, the Maxwell-Stefan equations predict behaviour that is not recovered from the Nernst-Planck equations. The main difficulty in the application of the Maxwell-Stefan equations to charge transport in electrolyte solutions is knowledge of the transport parameters. In this work, we apply molecular dynamics simulations to obtain the required diffusivities, and thus we are able to incorporate microscopic behaviour into a continuum scale model. This is important due to the small size scales we are concerned with, as we are still able to retain the computational efficiency of continuum modelling. This approach provides an avenue by which the microscopic behaviour may ultimately be incorporated into a full device-scale model. The one-dimensional Maxwell-Stefan model is extended to two dimensions, representing an important first step for developing a fully-coupled interfacial charge transport model for electrochemical devices. It allows us to begin investigation into ambipolar diffusion effects, where the motion of the ions in the electrolyte is affected by the transport of electrons in the electrode. As we do not consider modelling in the solid phase in this work, this is simulated by applying a time-varying potential to one interface of our two-dimensional computational domain, thus allowing a flow field to develop in the electrolyte. Our model facilitates the observation of the transport of ions near the electrode/electrolyte interface. For the simulations considered in this work, we show that while there is some motion in the direction parallel to the interface, the interfacial coupling is not sufficient for the ions in solution to be "dragged" along the interface for long distances.

Investigation of energy efficient approaches for the energy performance improvement of commercial buildings

Energy efficiency of buildings is attracting significant attention from the research community as the world is moving towards sustainable buildings design. Energy efficient approaches are measures or ways to improve the energy performance and energy efficiency of buildings. This study surveyed various energy-efficient approaches for commercial building and identifies Envelope Thermal Transfer Value (ETTV) and Green applications (Living wall, Green facade and Green roof) as most important and effective methods. An in-depth investigation was carried out on these energy-efficient approaches. It has been found that no ETTV model has been developed for sub-tropical climate of Australia. Moreover, existing ETTV equations developed for other countries do not take roof heat gain into consideration. Furthermore, the relationship of ETTV and different Green applications have not been investigated extensively in any literature, and the energy performance of commercial buildings in the presence of Living wall, Green facade and Green roof has not been investigated in the sub-tropical climate of Australia. The study has been conducted in two phases. First, the study develops the new formulation, coefficient and bench mark value of ETTV in the presence of external shading devices. In the new formulation, roof heat gain has been included in the integrated heat gain model made of ETTV. In the 2nd stage, the study presents the relationship of thermal and energy performance of (a) Living wall and ETTV (b) Green facade and ETTV (c) Combination of Living wall, Green facade and ETTV (d) Combination of Living wall, Green Roof and ETTV in new formulations. Finally, the study demonstrates the amount of energy that can be saved annually from different combinations of Green applications, i.e., Living wall, Green facade; combination of Living wall and Green facade; combination of Living wall and Green roof. The estimations are supported by experimental values obtained from extensive experiments of Living walls and Green roofs.

Impact energy dependence of Al13 cluster deposition on Ni(001) surface

In this paper, the influence of the impact energy on the initial fabrication of thin films formed by low energy cluster deposition was investigated by molecular dynamics simulation of All 3 clusters depositing on Ni(0 0 1) substrate. In the case of soft-landing, (0.01 eV/atom), clusters are rearranged from I-h symmetry into fcc-like clusters on the surface. Then they aggregate each other, which result in thin film growing in 3D island mode. While, growth will be in layer-by-layer mode at the impact energy of a few electron volt due to the transient lateral spread of cluster atoms induced by dense collision cascade. This effect has been traced to collision cascade inside the cluster. which is enhanced by collision with a hard Ni substrate. (C) 2002 Elsevier Science B.V. All rights reserved.

Energy dependence of methyl-radical adsorption on diamond (001)-(2×1) surface

The deposition of hyperthermal CH3 on diamond (001)-(2×1) surface at room temperature has been studied by means of molecular dynamics simulation using the many-body hydrocarbon potential. The energy threshold effect has been observed. That is, with fixed collision geometry, chemisorption can occur only when the incident energy of CH3 is above a critical value (Eth). Increasing the incident energy, dissociation of hydrogen atoms from the incident molecule was observed. The chemisorption probability of CH3 as a function of its incident energy was calculated and compared with that of C2H2. We found that below 10 eV, the chemisorption probability of C2H2 is much lower than that of CH3 on the same surface. The interesting thing is that it is even lower than that of CH3 on a hydrogen covered surface at the same impact energy. It indicates that the reactive CH3 molecule is the more important species than C2H2 in diamond synthesis at low energy, which is in good agreement with the experimental observation.

Energy window effect in chemisorption of C36 on diamond (001)-(/2×1) surface

In this paper, the collision of a C36, with D6h symmetry, on diamond (001)-(/2×1) surface was investigated using molecular dynamics (MD) simulation based on the semi-empirical Brenner potential. The incident kinetic energy of the C36 ranges from 20 to 150 eV per cluster. The collision dynamics was investigated as a function of impact energy Ein. The C36 cluster was first impacted towards the center of two dimers with a fixed orientation. It was found that when Ein was lower than 30 eV, C36 bounces off the surface without breaking up. Increasing Ein to 30-45 eV, bonds were formed between C36 and surface dimer atoms, and the adsorbed C36 retained its original free-cluster structure. Around 50-60 eV, the C36 rebounded from the surface with cage defects. Above 70 eV, fragmentation both in the cluster and on the surface was observed. Our simulation supported the experimental findings that during low-energy cluster beam deposition small fullerenes could keep their original structure after adsorption (i.e. the memory effect), if Ein is within a certain range. Furthermore, we found that the energy threshold for chemisorption is sensitive to the orientation of the incident C36 and its impact position on the asymmetric surface.

From solving puzzles to designing solutions : integrating design thinking into evidence based practice

Evidence based practice (EBP) focuses on solving ‘tame’ problems, where literature supports question construction toward determining a solution. What happens when there is no existing evidence, or when the need for agility precludes a full EBP implementation? How might we build a more agile and innovative practice that facilitates the design of solutions to complex and wicked problems, particularly in cases where there is no existing literature? As problem solving and innovation methods, EBP and design thinking overlap considerably. The literature indicates the potential benefits to be gained for evidence based practice from adopting a human-centred rather than literature-focused foundation. The design thinking process is social and collaborative by nature, which enables it to be more agile and produce more innovative results than evidence based practice. This paper recommends a hybrid approach to maximise the strengths and benefits of the two methods for designing solutions to wicked problems. Incorporating design thinking principles and tools into EBP has the potential to move its applicability beyond tame problems and continuous improvement, and toward wicked problem solving and innovation. The potential of this hybrid approach in practice is yet to be explored.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Analytical benchmark solutions for steel frame structures subject to local buckling effects

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. This paper contains a comprehensive set of analytical benchmark solutions for steel frames comprising non-compact sections, which can be used to verify the accuracy of simplified concentrated plasticity methods of advanced analysis. The analytical benchmark solutions were obtained using a distributed plasticity shell finite element model that explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. A brief description and verification of the shell finite element model is provided in this paper.