Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Hydrofluoroalkanes as carrier solvents for timber preservation

Hydrofluoroalkanes are a specific category of hydrofluorocarbon (HFC) commonly used in refrigeration applications. Some HFCs hold potential for use as carrier fluids for preservatives used to protect timber above ground. They do not share the most significant disadvantages of currently used carriers for these applications. At ‘conventional’ operating pressures, they are capable of rapid, full penetration of some timbers generally considered refractory, such as spruce and the heartwood of radiata pine. But they are comparatively expensive and, while they are not detrimental to the ozone layer, they would contribute significantly to the greenhouse effect if released. Impregnation process conditions can be optimised to maximise biocide solubility and impregnation speed and depth.

Modulation of arginine decarboxylase activity in cucumber (Cucumis sativus) cotyledons in short-term organ culture

Among the various amines administered to excisedCucumis sativus cotyledons in short-term organ culture, agmatine (AGM) inhibited arginine decarboxylase (ADC) activity to around 50%, and putrescine was the most potent entity in this regard. Homoarginine (HARG) dramatically stimulated (3- to 4-fold) the enzyme activity. Both AGM inhibition and HARG stimulation of ADC were transient, the maximum response being elicited at 12 h of culture. Mixing experiments ruled out involvement of a macromolecular effector in the observed modulation of ADC. HARG-stimulated ADC activity was completely abolished by cycloheximide, whereas AGM-mediated inhibition was unaffected. Half-life of the enzyme did not alter on treatment with either HARG or AGM. The observed alterations in ADC activity are accompanied by change in Km of the enzyme. HARG-stimulated ADC activity is additive to that induced by benzyladenine (BA) whereas in presence of KCl, HARG failed to enhance ADC activity, thus demonstrating the overriding influence of K+ on amine metabolism.

Natural Preservation Technologies for Tropical Fruits

The project intends to establish a cross DEEDI industry-leveraged project for tropical fruit convenience products.

Solutions for archiving data in long-term studies: A reply to Whitlock et al.

In our recent paper [1], we discussed some potential undesirable consequences of public data archiving (PDA) with specific reference to long-term studies and proposed solutions to manage these issues. We reaffirm our commitment to data sharing and collaboration, both of which have been common and fruitful practices supported for many decades by researchers involved in long-term studies. We acknowledge the potential benefits of PDA (e.g., [2]), but believe that several potential negative consequences for science have been underestimated [1] (see also 3 and 4). The objective of our recent paper [1] was to define practices to simultaneously maximize the benefits and minimize the potential unwanted consequences of PDA.

Developing agronomic solutions to improve barley yield and grain quality

The main aim of this project is to develop variety management packages to help tailor commercial malt and feed barley production in the Northern GRDC Region to commercial malt and feed barley specifications. Field trials are designed to give information.

Cropping solutions for the sugarcane farming systems of the Burdekin

The successful inclusion of break crops into the Burdekin sugar farming system will allow growers to diversify and capitalise on alternate crop income sources, particularly during cyclical downturns in sugar price. Secondly if cane productivity is improved through the inclusion of break crops, millers and growers stand to gain additional economic benefit compared to the current sugarcane monoculture.

DAN00106 Developing agronomic solutions to improve barley yield and grain quality

Producing management packages for new northern barley varieties. Evaluating silage barley varieties.

GM solutions to root diseases of cereals - A situation analysis and business case

Root disease causes about $503 million in losses annually to Australia's wheat and barley industries. Because of these large losses and in many cases the difficulty in reducing these losses through breeding or management, root diseases are candidates for solutions through genetic modification (GM). Through an extensive review of the scientific literature and patents, a range of approaches to GM solutions to root diseases are critically discussed. Given the high cost of regulatory approval for GM crops and a complex intellectual property (IP) landscape, it is likely that research in this area will be done in collaboration with international partners.

Continued delivery of applied solutions to weed issues in central Queensland

Developing best practices in Central Queensland to (a) manage difficult to control weeds; (b) improve herbicide efficacy under adverse conditions, and (c) manage weeds in wide-row crop systems.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Kinetic Ising model: Some exact solutions

Exact expressions for the response functions of kinetic Ising models are reported. These results valid for magnetisation in one dimension are based on a general formalism that yield the earlier results of Glauber and Kimball as special cases.

Improving Flow-Insensitive Solutions for Non-Separable Dataflow Problems

Flow-insensitive solutions to dataflow problems have been known to be highly scalable; however also hugely imprecise. For non-separable dataflow problems this solution is further degraded due to spurious facts generated as a result of dependence among the dataflow facts. We propose an improvement to the standard flow-insensitive analysis by creating a generalized version of the dominator relation that reduces the number of spurious facts generated. In addition, the solution obtained contains extra information to facilitate the extraction of a better solution at any program point, very close to the flow-sensitive solution. To improve the solution further, we propose the use of an intra-block variable renaming scheme. We illustrate these concepts using two classic non-separable dataflow problems --- points-to analysis and constant propagation.