Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

Chemical variability of groundwater samples collected from a Coal Seam Gas exploration well, Maramarua, New Zealand

A pilot study has produced 31 groundwater samples from a coal seam gas (CSG) exploration well located in Maramarua, New Zealand. This paper describes sources of CSG water chemistry variations, and makes sampling and analytical recommendations to minimize these variations. The hydrochemical character of these samples is studied using factor analysis, geochemical modelling, and a sparging experiment. Factor analysis unveils carbon dioxide (CO2) degassing as the principal cause of sample variation (about 33%). Geochemical modelling corroborates these results and identifies minor precipitation of carbonate minerals with degassing. The sparging experiment confirms the effect of CO2 degassing by showing a steady rise in pH while maintaining constant alkalinity. Factor analysis correlates variations in the major ion composition (about 17%) to changes in the pumping regime and to aquifer chemistry variations due to cation exchange reactions with argillaceous minerals. An effective CSG water sampling program can be put into practice by measuring pH at the well head and alkalinity at the laboratory; these data can later be used to calculate the carbonate speciation at the time the sample was collected. In addition, TDS variations can be reduced considerably if a correct drying temperature of 180°C is consistently implemented.

Regulation of land access for resource development: A coal seam gas case study from Queensland

A number of regulatory statutes provide for agreements with landowners which are given extended effect, that is, are binding upon the landowner’s successors (‘statutory agreements’). Several Queensland statutes require a project proponent to enter into a statutory agreement with a landowner before a resource development activity can be carried out on private land or by accessing private land. Provisions of Queensland’s Petroleum and Gas (Production and Safety) Act 2004 make certain types of statutory agreements binding upon successors and assigns of the landowner, but do not clearly prescribe the nature and contents of an agreement, nor require that the agreement be recorded on the land title or petroleum register. If statutory agreements are to be used for such purposes, their purpose and content should be more clearly defined by statute and they should be recorded on a searchable register.

Coal seam gas waters - their geochemical signature and potential environmental implications

Coal Seam Gas (CSG) is a form of natural gas (mainly methane) sorbed in underground coal beds. To mine this gas, wells are drilled directly into an underground coal seam and groundwater (CSG water) is pumped out to the surface. This lowers the downhole piezometric pressure and enables gas desporption from the coal matrix. In the United States, this gas has been extracted commercially since the 1980s. The economic success of US CSG projects has inspired exploration and development in Australia and New Zealand. In Australia, Queensland’s Bowen and Surat basins have been the subject of increased CSG development over the last decade. CSG growth in other Australian basins has not matured to the same level but exploration and development are taking place at an accelerated pace in the Sydney Basin (Illawarra and the Hunter Valley, NSW) and in the Gunnedah Basin. Similarly, CSG exploration in New Zealand has focused in the Waikato region (Maramarua and Huntly), in the West Coast region (Buller, Reefton, and Greymouth), and in Southland (Kaitangata, Mataura, and Ohai). Figure 1 shows a Shcoeller diagram with CSG samples from selected basins in Australia, New Zealand, and the USA. CSG water from all of these basins exhibit the same geochemical signature – low calcium, low magnesium, high bicarbonate, low sulphate and, sometimes, high chloride. This water quality is a direct result of specific biological and geological processes that have taken part in the formation of CSG. In general, these processes include the weathering of rocks (carbonates, dolomite, and halite), cation exchange with clays (responsible for enhanced sodium and depleted calcium and magnesium), and biogenic processes (accounting for the presence of high bicarbonate concentrations). The salinity of CSG waters tends to be brackish (TDS < 30000 mg/l) with a fairly neutral pH. These particular characteristics need to be taken into consideration when assessing water management and disposal alternatives. Environmental issues associated with CSG water disposal have been prominent in developed basins such as the Powder River Basin (PRB) in the United States. When disposed on the land or used for irrigation, water having a high dissolved salts content may reduce water availability to crops thus affecting crop yield. In addition, the high sodium, low calcium and low magnesium concentrations increase the potential to disperse soils and significantly reduce the water infiltration rate. Therefore, CSG waters need to be properly characterised, treated, and disposed to safeguard the environment without compromising other natural resources.

Measurement constructs to explore innovation diffusion in construction

Although the drivers of innovation have been studied extensively in construction, greater attention is required on how innovation diffusion can be effectively assessed within this complex and interdependent project-based industry. The authors draw on a highly cited innovation diffusion model by Rogers (2006) and develop a tailored conceptual framework to guide future empirical work aimed at assessing innovation diffusion in construction. The conceptual framework developed and discussed in this paper supports a five-stage process model of innovation diffusion namely: 1) knowledge and idea generation, 2) persuasion and evaluation; 3) decision to adopt, 4) integration and implementation, and 5) confirmation. As its theoretical contribution, this paper proposes three critical measurements constructs which can be used to assess the effectiveness of the diffusion process. These measurement constructs comprise: 1) nature and introduction of an innovative idea, 2) organizational capacity to acquire, assimilate, transform and exploit an innovation, and 3) rates of innovation facilitation and adoption. The constructs are interpreted in the project-based context of the construction industry, extending the contribution of general management theorists. Research planned by the authors will test the validity and reliability of the constructs developed in this paper.

Conductometric gas sensors based on nanostructured WO3 thin films

Nanostructured WO3 thin films have been prepared by thermal evaporation to detect hydrogen at low temperatures. The influence of heat treatment on the physical, chemical and electronic properties of these films has been investigated. The films were annealed at 400oC for 2 hours in air. AFM and TEM analysis revealed that the as-deposited WO3 film is high amorphous and made up of cluster of particles. Annealing at 400oC for 2 hours in air resulted in very fine grain size of the order of 5 nm and porous structure. GIXRD and Raman analysis revealed that annealing improved the crystallinity of WO3 film. Gas sensors based on annealed WO3 films have shown a high response towards various concentrations (10-10000 ppm) H2 at an operating temperature of 150oC. The improved sensing performance at low operating temperature is due to the optimum physical, chemical and electronic properties achieved in the WO3 film through annealing.

Planar radial spots in a three-component FitzHugh-Nagumo system

Localized planar patterns arise in many reaction-diffusion models. Most of the paradigm equations that have been studied so far are two-component models. While stationary localized structures are often found to be stable in such systems, travelling patterns either do not exist or are found to be unstable. In contrast, numerical simulations indicate that localized travelling structures can be stable in three-component systems. As a first step towards explaining this phenomenon, a planar singularly perturbed three-component reaction-diffusion system that arises in the context of gas-discharge systems is analysed in this paper. Using geometric singular perturbation theory, the existence and stability regions of radially symmetric stationary spot solutions are delineated and, in particular, stable spots are shown to exist in appropriate parameter regimes. This result opens up the possibility of identifying and analysing drift and Hopf bifurcations, and their criticality, from the stationary spots described here.

Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

Coexistence of stable spots and fronts in a three-component FitzHugh-Nagumo system

We investigate regions of bistability between different travelling and stationary structures in a planar singularly-perturbed three-component reaction-diffusion system that arises in the context of gas discharge systems. In previous work, we delineated the existence and stabil-ity regions of stationary localized spots in this system. Here, we complement this analysis by establishing the stability regions of planar travelling fronts and stationary stripes. Taken together, these results imply that stable fronts and spots can coexist in three-component systems. Numerical simulations indicate that the stable fronts never move towards stable spots but instead move away from them.

A note on a reaction-diffusion model describing the bone morphogen protein gradient in Drosophila embryonic patterning

In this article, we consider the Eldar model [3] from embryology in which a bone morphogenic protein, a short gastrulation protein, and their compound react and diffuse. We carry out a perturbation analysis in the limit of small diffusivity of the bone morphogenic protein. This analysis establishes conditions under which some elementary results of [3] are valid.

Near-Wall Turbulent Pressure Diffusion Modeling and Influence in Three-Dimensional Secondary Flows

The purpose of this paper is to develop a second-moment closure with a near-wall turbulent pressure diffusion model for three-dimensional complex flows, and to evaluate the influence of the turbulent diffusion term on the prediction of detached and secondary flows. A complete turbulent diffusion model including a near-wall turbulent pressure diffusion closure for the slow part was developed based on the tensorial form of Lumley and included in a re-calibrated wall-normal-free Reynolds-stress model developed by Gerolymos and Vallet. The proposed model was validated against several one-, two, and three-dimensional complex flows.