A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood 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 gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

Two-scale computational modelling of unsaturated flow in soils exhibiting small scale heterogeneities

Unsaturated water flow in soil is commonly modelled using Richards’ equation, which requires the hydraulic properties of the soil (e.g., porosity, hydraulic conductivity, etc.) to be characterised. Naturally occurring soils, however, are heterogeneous in nature, that is, they are composed of a number of interwoven homogeneous soils each with their own set of hydraulic properties. When the length scale of these soil heterogeneities is small, numerical solution of Richards’ equation is computationally impractical due to the immense effort and refinement required to mesh the actual heterogeneous geometry. A classic way forward is to use a macroscopic model, where the heterogeneous medium is replaced with a fictitious homogeneous medium, which attempts to give the average flow behaviour at the macroscopic scale (i.e., at a scale much larger than the scale of the heterogeneities). Using the homogenisation theory, a macroscopic equation can be derived that takes the form of Richards’ equation with effective parameters. A disadvantage of the macroscopic approach, however, is that it fails in cases when the assumption of local equilibrium does not hold. This limitation has seen the introduction of two-scale models that include at each point in the macroscopic domain an additional flow equation at the scale of the heterogeneities (microscopic scale). This report outlines a well-known two-scale model and contributes to the literature a number of important advances in its numerical implementation. These include the use of an unstructured control volume finite element method and image-based meshing techniques, that allow for irregular micro-scale geometries to be treated, and the use of an exponential time integration scheme that permits both scales to be resolved simultaneously in a completely coupled manner. Numerical comparisons against a classical macroscopic model confirm that only the two-scale model correctly captures the important features of the flow for a range of parameter values.

Primary alkaline battery cathodes a three-scale model

A mathematical model for the galvanostatic discharge and recovery of porous, electrolytic manganese dioxide cathodes, similar to those found within primary alkaline batteries is presented. The phenomena associated with discharge are modeled over three distinct size scales, a cathodic (or macroscopic) scale, a porous manganese oxide particle (or microscopic) scale, and a manganese oxide crystal (or submicroscopic) scale. The physical and chemical coupling between these size scales is included in the model. In addition, the model explicitly accounts for the graphite phase within the cathode. The effects that manganese oxide particle size and proton diffusion have on cathodic discharge and the effects of intraparticle voids and microporous electrode structure are predicted using the model.

Large-Eddy Simulation of physiological pulsatile non-newtonian flow in a channel with double constriction

Physiological pulsatile flow in a 3D model of arterial double stenosis, using the modified Power-law blood viscosity model, is investigated by applying Large Eddy Simulation (LES) technique. The computational domain has been chosen is a simple channel with biological type stenoses. The physiological pulsation is generated at the inlet of the model using the first four harmonics of the Fourier series of the physiological pressure pulse. In LES, a top-hat spatial grid-filter is applied to the Navier-Stokes equations of motion to separate the large scale flows from the subgrid scale (SGS). The large scale flows are then resolved fully while the unresolved SGS motions are modelled using the localized dynamic model. The flow Reynolds numbers which are typical of those found in human large artery are chosen in the present work. Transitions to turbulent of the pulsatile non-Newtonian along with Newtonian flow in the post stenosis are examined through the mean velocity, wall shear stress, mean streamlines as well as turbulent kinetic energy and explained physically along with the relevant medical concerns.

Epigenetic modelling

The field of epigenetics looks at changes in the chromosomal structure that affect gene expression without altering DNA sequence. A large-scale modelling project to better understand these mechanisms is gaining momentum. Early advances in genetics led to the all-genetic paradigm: phenotype (an organism's characteristics/behaviour) is determined by genotype (its genetic make-up). This was later amended and expressed by the well-known formula P = G + E, encompassing the notion that the visible characteristics of a living organism (the phenotype, P) is a combination of hereditary genetic factors (the genotype, G) and environmental factors (E). However, this method fails to explain why in diseases such as schizophrenia we still observe differences between identical twins. Furthermore, the identification of environmental factors (such as smoking and air quality for lung cancer) is relatively rare. The formula also fails to explain cell differentiation from a single fertilized cell. In the wake of early work by Waddington, more recent results have emphasized that the expression of the genotype can be altered without any change in the DNA sequence. This phenomenon has been tagged as epigenetics. To form the chromosome, DNA strands roll over nucleosomes, which are a cluster of nine proteins (histones), as detailed in Figure 1. Epigenetic mechanisms involve inherited alterations in these two structures, eg through attachment of a functional group to the amino acids (methyl, acetyl and phosphate). These 'stable alterations' arise during development and cell proliferation and persist through cell division. While information within the genetic material is not changed, instructions for its assembly and interpretation may be. Modelling this new paradigm, P = G + E + EpiG, is the object of our study.

Daylighting design in the architectural design studio

This paper discusses two different approaches to teaching design and their modes of delivery and reflects upon their successes and failures. Two small groups of third year design students have been given projects focussing on incorporation of daylighting to architectural design in studios having different design themes. In association with the curriculum, the themes were Digital Tools and Sustainability. Although both studios had the topic of daylighting, the aim and methodology used were different. Digital Tool studio’s aim was to teach how to design daylighting by using a digital tool, where as, Sustainability studio aimed at using scale modelling as a tool to learn about daylighting and integrating it into design. Positive results for providing student learning success within the University context were the students’ chance to learn and practice some new skills –using a new tool for designing; integration of the tutors’ extensive research expertise to their teaching practice; and the students’ construction of their own understanding of knowledge in a student-centred educational environment. This environment created a very positive attitude in the form of exchanging ideas and collaboration among the students of Digital Tools students at the discussion forum. Sustainability group students were enthusiastic about designing and testing various proposals. Problems that both studios experienced were mainly related to timing. Synchronizing with other groups of their studios and learning of a new skill on top of an already complicated process of design learning were the setbacks.

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.

Visualisation modelling in 3D of an alluvial aquifer system at a valley-wide scale to understand groundwater status : Lockyer, QLD

Visualisation provides a method to efficiently convey and understand the complex nature and processes of groundwater systems. This technique has been applied to the Lockyer Valley to aid in comprehending the current condition of the system. The Lockyer Valley in southeast Queensland hosts intensive irrigated agriculture sourcing groundwater from alluvial aquifers. The valley is around 3000 km2 in area and the alluvial deposits are typically 1-3 km wide and to 20-35 m deep in the main channels, reducing in size in subcatchments. The configuration of the alluvium is of a series of elongate “fingers”. In this roughly circular valley recharge to the alluvial aquifers is largely from seasonal storm events, on the surrounding ranges. The ranges are overlain by basaltic aquifers of Tertiary age, which overall are quite transmissive. Both runoff from these ranges and infiltration into the basalts provided ephemeral flow to the streams of the valley. Throughout the valley there are over 5,000 bores extracting alluvial groundwater, plus lesser numbers extracting from underlying sandstone bedrock. Although there are approximately 2500 monitoring bores, the only regularly monitored area is the formally declared management zone in the lower one third. This zone has a calibrated Modflow model (Durick and Bleakly, 2000); a broader valley Modflow model was developed in 2002 (KBR), but did not have extensive extraction data for detailed calibration. Another Modflow model focused on a central area river confluence (Wilson, 2005) with some local production data and pumping test results. A recent subcatchment simulation model incorporates a network of bores with short-period automated hydrographic measurements (Dvoracek and Cox, 2008). The above simulation models were all based on conceptual hydrogeological models of differing scale and detail.

Numerical modelling and full scale testing of load bearing steel walls under real fires

Fire safety has become an important part in structural design due to the ever increasing loss of properties and lives during fires. Fire rating of load bearing wall systems made of Light gauge Steel Frames (LSF) is determined using fire tests based on the standard time-temperature curve given in ISO 834. However, modern residential buildings make use of thermoplastic materials, which mean considerably high fuel loads. Hence a detailed fire research study into the performance of load bearing LSF walls was undertaken using a series of realistic design fire curves developed based on Eurocode parametric curves and Barnett’s BFD curves. It included both full scale fire tests and numerical studies of LSF walls without any insulation, and the recently developed externally insulated composite panels. This paper presents the details of fire tests first, and then the numerical models of tested LSF wall studs. It shows that suitable finite element models can be developed to predict the fire rating of load bearing walls under real fire conditions. The paper also describes the structural and fire performances of externally insulated LSF walls in comparison to the non-insulated walls under real fires, and highlights the effects of standard and real fire curves on fire performance of LSF walls.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.