Experimental investigation of wheel/rail rolling contact at railhead edge

Wheel-rail rolling contact at railhead edge, such as a gap in an insulated rail joint, is a complex problem; there are only limited analytical, numerical and experimental studies available on this problem in the academic literature. This paper describes experimental and numerical investigations of railhead strains in the vicinity of the edge under the contact of a loaded wheel. A full-scale test rig was developed to cyclically apply wheel/rail rolling contact load to the edge zone of the railhead. An image analysis technique was employed to determine the railhead vertical, lateral and shear strain components. The vertical strains determined using the image analysis method have been validated with the strain gauge measurements and used for the calibration of a 3D nonlinear Finite Element Model (FEM) that simulates the wheel/rail contact at the railhead edge and use suitable boundary conditions commensurate to the experimental setup. The FEM was then used to determine other states of strains.

Adaption and use of a compressible flow code for turbomachinery design

The present paper presents and discusses the use of dierent codes regarding the numerical simulation of a radial-in ow turbine. A radial-in ow turbine test case was selected from published literature [1] and commercial codes (Fluent and CFX) were used to perform the steady-state numerical simulations. An in-house compressible- ow simulation code, Eilmer3 [2] was also adapted in order to make it suitable to perform turbomachinery simulations and preliminary results are presented and discussed. The code itself as well as its adaptation, comprising the addition of terms for the rotating frame of reference, programmable boundary conditions for periodic boundaries and a mixing plane interface between the rotating and non-rotating blocks are also discussed. Several cases with dierent orders of complexity in terms of geometry were considered and the results were compared across the dierent codes. The agreement between these results and published data is also discussed.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Analysis of heat transfer and fluid flow in a triangular enclosure in presence of an adiabatic fin

Natural convection thermal boundary layer adjacent to the heated inclined wall of a right angled triangle with an adiabatic fin attached to that surface is investigated by numerical simulations. The finite volume based unsteady numerical model is adopted for the simulation. It is revealed from the numerical results that the development of the boundary layer along the inclined surface is characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady stage. These three stages can be clearly identified from the numerical simulations. Moreover, in presence of adiabatic fin, the thermal boundary layer adjacent to the inclined wall breaks initially. However, it is reattached with the downstream boundary layer next to the fin. More attention has been given to the boundary layer development near the fin area.

Metastable carbon in two chondritic porous interplanetary dust particles

An understanding of carbonaceous matter in primitive extraterrestrial materials is an essential component of studies on dust evolution in the interstellar medium and the early history of the Solar System. We have suggested previously that a record of graphitization is preserved in chondritic porous (CP) aggregates and carbonaceous chondrites1,2 and that the detailed mineralogy of CP aggregates can place boundary conditions on the nature of both physical and chemical processes which occurred at the time of their formation2,3. Here, we report further analytical electron microscope (AEM) studies on carbonaceous material in two CP aggregates which suggest that a record of hydrocarbon carbonization may also be preserved in these materials. This suggestion is, based upon the presence of well-ordered carbon-2H (lonsdaleite) in CP aggregates W7029*A and W7010*A2. This carbon is a metastable phase resulting from hydrous pyrolysis below 300-350°C and may be a precursor to poorly graphitized carbons (PGCs) in primitive extraterrestrial materials2. © 1987 Nature Publishing Group.

Feasibility of agent-based modelling of articular cartilage including a conceptual representation of its structure

Articular cartilage is a complex structure with an architecture in which fluid-swollen proteoglycans constrained within a 3D network of collagen fibrils. Because of the complexity of the cartilage structure, the relationship between its mechanical behaviours at the macroscale level and its components at the micro-scale level are not completely understood. The research objective in this thesis is to create a new model of articular cartilage that can be used to simulate and obtain insight into the micro-macro-interaction and mechanisms underlying its mechanical responses during physiological function. The new model of articular cartilage has two characteristics, namely: i) not use fibre-reinforced composite material idealization ii) Provide a framework for that it does probing the micro mechanism of the fluid-solid interaction underlying the deformation of articular cartilage using simple rules of repartition instead of constitutive / physical laws and intuitive curve-fitting. Even though there are various microstructural and mechanical behaviours that can be studied, the scope of this thesis is limited to osmotic pressure formation and distribution and their influence on cartilage fluid diffusion and percolation, which in turn governs the deformation of the compression-loaded tissue. The study can be divided into two stages. In the first stage, the distributions and concentrations of proteoglycans, collagen and water were investigated using histological protocols. Based on this, the structure of cartilage was conceptualised as microscopic osmotic units that consist of these constituents that were distributed according to histological results. These units were repeated three-dimensionally to form the structural model of articular cartilage. In the second stage, cellular automata were incorporated into the resulting matrix (lattice) to simulate the osmotic pressure of the fluid and the movement of water within and out of the matrix; following the osmotic pressure gradient in accordance with the chosen rule of repartition of the pressure. The outcome of this study is the new model of articular cartilage that can be used to simulate and study the micromechanical behaviours of cartilage under different conditions of health and loading. These behaviours are illuminated at the microscale level using the socalled neighbourhood rules developed in the thesis in accordance with the typical requirements of cellular automata modelling. Using these rules and relevant Boundary Conditions to simulate pressure distribution and related fluid motion produced significant results that provided the following insight into the relationships between osmotic pressure gradient and associated fluid micromovement, and the deformation of the matrix. For example, it could be concluded that: 1. It is possible to model articular cartilage with the agent-based model of cellular automata and the Margolus neighbourhood rule. 2. The concept of 3D inter connected osmotic units is a viable structural model for the extracellular matrix of articular cartilage. 3. Different rules of osmotic pressure advection lead to different patterns of deformation in the cartilage matrix, enabling an insight into how this micromechanism influences macromechanical deformation. 4. When features such as transition coefficient were changed, permeability (representing change) is altered due to the change in concentrations of collagen, proteoglycans (i.e. degenerative conditions), the deformation process is impacted. 5. The boundary conditions also influence the relationship between osmotic pressure gradient and fluid movement at the micro-scale level. The outcomes are important to cartilage research since we can use these to study the microscale damage in the cartilage matrix. From this, we are able to monitor related diseases and their progression leading to potential insight into drug-cartilage interaction for treatment. This innovative model is an incremental progress on attempts at creating further computational modelling approaches to cartilage research and other fluid-saturated tissues and material systems.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Compaction control of topography and fault network structure along strike-slip faults in sedimentary basins

Strike-slip faults commonly display structurally complex areas of positive or negative topography. Understanding the development of such areas has important implications for earthquake studies and hydrocarbon exploration. Previous workers identified the key factors controlling the occurrence of both topographic modes and the related structural styles. Kinematic and stress boundary conditions are of first-order relevance. Surface mass transport and material properties affect fault network structure. Experiments demonstrate that dilatancy can generate positive topography even under simple-shear boundary conditions. Here, we use physical models with sand to show that the degree of compaction of the deformed rocks alone can determine the type of topography and related surface fault network structure in simple-shear settings. In our experiments, volume changes of ∼5% are sufficient to generate localized uplift or subsidence. We discuss scalability of model volume changes and fault network structure and show that our model fault zones satisfy geometrical similarity with natural flower structures. Our results imply that compaction may be an important factor in the development of topography and fault network structure along strike-slip faults in sedimentary basins.

Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

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.

Mechanical testing and modelling of a bone-implant construct

Finite Element modelling of bone fracture fixation systems allows computational investigation of the deformation response of the bone to load. Once validated, these models can be easily adapted to explore changes in design or configuration of a fixator. The deformation of the tissue within the fracture gap determines its healing and is often summarised as the stiffness of the construct. FE models capable of reproducing this behaviour would provide valuable insight into the healing potential of different fixation systems. Current model validation techniques lack depth in 6D load and deformation measurements. Other aspects of the FE model creation such as the definition of interfaces between components have also not been explored. This project investigated the mechanical testing and FE modelling of a bone– plate construct for the determination of stiffness. In depth 6D measurement and analysis of the generated forces, moments and movements showed large out of plane behaviours which had not previously been characterised. Stiffness calculated from the interfragmentary movement was found to be an unsuitable summary parameter as the error propagation is too large. Current FE modelling techniques were applied in compression and torsion mimicking the experimental setup. Compressive stiffness was well replicated, though torsional stiffness was not. The out of plane behaviours prevalent in the experimental work were not replicated in the model. The interfaces between the components were investigated experimentally and through modification to the FE model. Incorporation of the interface modelling techniques into the full construct models had no effect in compression but did act to reduce torsional stiffness bringing it closer to that of the experiment. The interface definitions had no effect on out of plane behaviours, which were still not replicated. Neither current nor novel FE modelling techniques were able to replicate the out of plane behaviours evident in the experimental work. New techniques for modelling loads and boundary conditions need to be developed to mimic the effects of the entire experimental system.

Climate variability over the last 35,000 years recorded in marine and terrestrial archives in the Australian region : an OZ-INTIMATE compilation

The Australian region spans some 60° of latitude and 50° of longitude and displays considerable regional climate variability both today and during the Late Quaternary. A synthesis of marine and terrestrial climate records, combining findings from the Southern Ocean, temperate, tropical and arid zones, identifies a complex response of climate proxies to a background of changing boundary conditions over the last 35,000 years. Climate drivers include the seasonal timing of insolation, greenhouse gas content of the atmosphere, sea level rise and ocean and atmospheric circulation changes. Our compilation finds few climatic events that could be used to construct a climate event stratigraphy for the entire region, limiting the usefulness of this approach. Instead we have taken a spatial approach, looking to discern the patterns of change across the continent. The data identify the clearest and most synchronous climatic response at the time of the Last Glacial Maximum (LGM) (21 ± 3 ka), with unambiguous cooling recorded in the ocean, and evidence of glaciation in the highlands of tropical New Guinea, southeast Australia and Tasmania. Many terrestrial records suggest drier conditions, but with the timing of inferred snowmelt, and changes to the rainfall/runoff relationships, driving higher river discharge at the LGM. In contrast, the deglaciation is a time of considerable south-east to north-west variation across the region. Warming was underway in all regions by 17 ka. Post-glacial sea level rise and its associated regional impacts have played an important role in determining the magnitude and timing of climate response in the north-west of the continent in contrast to the southern latitudes. No evidence for cooling during the Younger Dryas chronozone is evident in the region, but the Antarctic cold reversal clearly occurs south of Australia. The Holocene period is a time of considerable climate variability associated with an intense monsoon in the tropics early in the Holocene, giving way to a weakened monsoon and an increasingly El Niño-dominated ENSO to the present. The influence of ENSO is evident throughout the southeast of Australia, but not the southwest. This climate history provides a template from which to assess the regionality of climate events across Australia and make comparisons beyond our region. The data identify the clearest and most synchronous climatic response at the time of the Last Glacial Maximum (LGM) (21 ± 3 ka), with unambiguous cooling recorded in the ocean, and evidence of glaciation in the highlands of tropical New Guinea, southeast Australia and Tasmania. Many terrestrial records suggest drier conditions, but with the timing of inferred snowmelt, and changes to the rainfall/runoff relationships, driving higher river discharge at the LGM. In contrast, the deglaciation is a time of considerable south-east to north-west variation across the region. Warming was underway in all regions by 17 ka. Post-glacial sea level rise and its associated regional impacts have played an important role in determining the magnitude and timing of climate response in the north-west of the continent in contrast to the southern latitudes. No evidence for cooling during the Younger Dryas chronozone is evident in the region, but the Antarctic cold reversal clearly occurs south of Australia. The Holocene period is a time of considerable climate variability associated with an intense monsoon in the tropics early in the Holocene, giving way to a weakened monsoon and an increasingly El Niño-dominated ENSO to the present. The influence of ENSO is evident throughout the southeast of Australia, but not the southwest. This climate history provides a template from which to assess the regionality of climate events across Australia and make comparisons beyond our region.

Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method

The details of an application of the finite strip method to the elastic buckling analysis of thin-walled structures with various boundary conditions and subjected to single or combined loadings of longitudinal compression, transverse compression, bending and shear are presented. The presence of shear loading is accounted for by modifying the displacement functions which are commonly used in cases when shear is absent. A program based on the finite strip method was used to obtain the elastic buckling stress, buckling plot and buckling mode of thin-walled structures and some of these results are presented.