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.

Effect of Crowding Agents, Signal Peptide, and Chaperone SecB on the Folding and Aggregation of E. coli Maltose Binding Protein

SecB, a soluble cytosolic chaperone component of the Secexport pathway, binds to newly synthesized precursor proteins and prevents their premature aggregation and folding and subsequently targets them to the translocation machinery on the membrane. PreMBP, the precursor form of maltose binding protein, has a 26-residue signal sequence attached to the N-terminus of MBP and is a physiological substrate of SecB. We examine the effect of macromolecular crowding and SecB on the stability and refolding of denatured preMBP and MBP. PreMBP was less stable than MBP (ΔTm =7( 0.5 K) in both crowded and uncrowded solutions. Crowding did not cause any substantial changes in the thermal stability ofMBP(ΔTm=1(0.4 K) or preMBP (ΔTm=0(0.6 K), as observed in spectroscopically monitored thermal unfolding experiments. However, both MBP and preMBP were prone to aggregation while refolding under crowded conditions. In contrast to MBP aggregates, which were amorphous, preMBP aggregates form amyloid fibrils.Under uncrowded conditions, a molar excess of SecB was able to completely prevent aggregation and promote disaggregation of preformed aggregates of MBP. When a complex of the denatured protein and SecB was preformed, SecB could completely prevent aggregation and promote folding of MBP and preMBP even in crowded solution. Thus, in addition to maintaining substrates in an unfolded, export-competent conformation, SecB also suppresses the aggregation of its substrates in the crowded intracellular environment. SecB is also able to promote passive disaggregation of macroscopic aggregates of MBP in the absence of an energy source such as ATP or additional cofactors. These experiments also demonstrate that signal peptide can reatly influence protein stability and aggregation propensity.

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.

A combined XPS-UPS-EELS study of nitrogen adsorbed on clean and barium-promoted iron surfaces: The nature of the precursor to dissociation

For N2 on a clean Fe surface, the adsorbed precursor in a parallel orientation becomes predominant around 110 K, while at lower temperatures it coexists with a weakly adsorbed species. On a Ba-promoted Fe surface, however, N2 is present exclusively in the precursor state in the temperature range 80–150 K following moderate exposure. Besides exhibiting a low N-N stretching frequency of 1530 cm−1, the precursor shows a clear separation between the 5σ and 1π levels in the UPS; the precursor dissociates to give a nitridic species around 160 K.

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).

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.