Note on the Similarity Solutions of Unsteady Jets in Rotating Fluids

The structure of time dependent jets in rotating fluids using similarity transformations is studied theoretically for which exact solutions are discussed. Approximate solution using a modified yon Mises transformation is also explored.

Propagation of Wollemi pine from tip cuttings and lower segment cuttings does not require rooting hormones

Domestication of the recently discovered and highly endangered Wollemi pine has relied almost entirely upon serial propagation of cuttings from a very small conservation collection. This study assessed the requirement for applied auxin to induce rooting in tip cuttings and lower segment cuttings of Wollemi pine. Both types of cuttings proved easy-to-root, with mean rooting of 71% for tip cuttings and 82% for lower segments. Auxin application (at 1.5, 3.0 or 8.0 g indole-3-butyric acid/L) did not accelerate root protrusion from propagation tubes or affect final rooting percentages.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Phase relations between Al2O3---Cr2O3 and FeAl2O4---FeCr2O4 solid solutions at 1823 K

Tie-lines between the corundum and spinel solid solutions have been determined experimentally at 1823 K. Next, activities of FeCr2O4 and FeAl2O4 in the spinel solid solution were determined by combining the tie-line data with literature values for the activities of Cr2O3 and Al2O3 in the corundum phase. Activities and the Gibbs energy of mixing for the spinel solid solution were also obtained from a model based on cation distribution between nonequivalent crystallographic sites in the oxide lattice. The difference between the Gibbs energy of mixing obtained experimentally and from the model has been attributed to a strain enthalpy term which is relatively unchanged in magnitude from the reported at 1373 K. The integral enthalpy of mixing obtained from experimental data at 1373 and 1823 K using the second law is compared with the model result.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

Dipole ordering in dilute solutions of ferroelectrics in antiferroelectric materials

The coefficients of thermal expansion reported by Worlton et al. [6] in the case of zircon are given in Table II along with the present data. Although Oql > or• in both cases, the anisotropy is more marked in the case of DyV04. From Table II, it is clear that the coefficient of volume expansion (,6) is almost the same for both compounds.

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).

Establishment and management of salt-tolerant amenity grasses to reduce urban salinity effect

This project built upon the successful outcomes of a previous project (TU02005) by adding to the database of salt tolerance among warm season turfgrass cultivars, through further hydroponic screening trials. Hydroponic screening trials focussed on new cultivars or cultivars that were not possible to cover in the time available under TU02005, including: 11 new cultivars of Paspalum vaginatum; 13 cultivars of Cynodon dactylon; six cultivars of Stenotaphrum secundatum; one accession of Cynodon transvaalensis; 12 Cynodon dactylon x transvaalensis hybrids; two cultivars of Sporobolus virginicus; five cultivars of Zoysia japonica; one cultivar of Z. macrantha, one common form of Z. tenuifolia and one Z. japonica x tenuifolia hybrid. The relative salinity tolerance of different turfgrasses is quantified in terms of their growth response to increasing levels of salinity, often defined by the salt level that equates to a 50% reduction in shoot yield, or alternatively the threshold salinity. The most salt tolerant species in these trials were Sporobolus virginicus and Paspalum vaginatum, consistent with the findings from TU02005 (Loch, Poulter et al. 2006). Cynodon dactylon showed the largest range in threshold values with some cultivars highly sensitive to salt, while others were tolerant to levels approaching that of the more halophytic grasses. Coupled with the observational and anecdotal evidence of high drought tolerance, this species and other intermediately tolerant species provide options for site specific situations in which soil salinity is coupled with additional challenges such as shade and high traffic conditions. By recognising the fact that a salt tolerant grass is not the complete solution to salinity problems, this project has been able to further investigate sustainable long-term establishment and management practices that maximise the ability of the selected grass to survive and grow under a particular set of salinity and usage parameters. Salt-tolerant turf grasses with potential for special use situations were trialled under field conditions at three sites within the Gold Coast City Council, while three sites, established under TU02005 within the Redland City Council boundaries were monitored for continued grass survival. Several randomised block experiments within Gold Coast City were established to compare the health and longevity of seashore paspalum (Paspalum vaginatum), Manila grass (Zoysia matrella), as well as the more tolerant cultivars of other species like buffalo grass (Stenotaphrum secundatum) and green couch (Cynodon dactylon). Whilst scientific results were difficult to achieve in the field situation, where conditions cannot be controlled, these trials provided valuable observational evidence of the likely survival of these species. Alternatives to laying full sod such as sprigging were investigated, and were found to be more appropriate for areas of low traffic as the establishment time is greater. Trials under controlled and protected conditions successfully achieved a full cover of Paspalum vaginatum from sprigs in a 10 week time frame. Salt affected sites are often associated with poor soil structure. Part of the research investigated techniques for the alleviation of soil compaction frequently found on saline sites. Various methods of soil de-compaction were investigated on highly compacted heavy clay soil in Redlands City. It was found that the heavy duplex soil of marine clay sediments required the most aggressive of treatments in order to achieve limited short-term effects. Interestingly, a well constructed sports field showed a far greater and longer term response to de-compaction operations, highlighting the importance of appropriate construction in the successful establishment and management of turfgrasses on salt affected sites. Fertiliser trials in this project determined plant demand for nitrogen (N) to species level. This work produced data that can be used as a guide when fertilising, in order to produce optimal growth and quality in the major turf grass species used in public parkland. An experiment commenced during TU02005 and monitored further in this project, investigated six representative warm-season turfgrasses to determine the optimum maintenance requirements for fertiliser N in south-east Queensland. In doing so, we recognised that optimum level is also related to use and intensity of use, with high profile well-used parks requiring higher maintenance N than low profile parks where maintaining botanical composition at a lower level of turf quality might be acceptable. Kikuyu (Pennisetum clandestinum) seemed to require the greatest N input (300-400 kg N/ha/year), followed by the green couch (Cynodon dactylon) cultivars ‘Wintergreen’ and ‘FLoraTeX’ requiring approximately 300 kg N/ha/year for optimal condition and growth. ‘Sir Walter’ (Stenotaphrum secundatum) and ‘Sea Isle 1’ (Paspalum vaginatum) had a moderate requirement of approximately 200 kg/ha/year. ‘Aussiblue’ (Digitaria didactyla)maintained optimal growth and quality at 100-200 kg N/ha/year. A set of guidelines has been prepared to provide various options from the construction and establishment of new grounds, through to the remediation of existing parklands by supporting the growth of endemic grasses. They describe a best management process through which salt affected sites should be assessed, remediated and managed. These guidelines, or Best Management Practices, will be readily available to councils. Previously, some high salinity sites have been turfed several times over a number of years (and Council budgets) for a 100% failure record. By eliminating this budgetary waste through targeted workable solutions, local authorities will be more amenable to investing appropriate amounts into these areas. In some cases, this will lead to cost savings as well as resulting in better quality turf. In all cases, however, improved turf quality will be of benefit to ratepayers, directly through increased local use of open space in parks and sportsfields and indirectly by attracting tourists and other visitors to the region bringing associated economic benefits. At the same time, environmental degradation and erosion of soil in bare areas will be greatly reduced.

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.