Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

A note on the effect of the HCl concentration on the heat of solution of thorium tetrachloride /

Work performed at the Argonne National Laboratory.

The art of hatching and bringing up domestick fowls of all kinds at any time of the year. Either by means of the heat of hot-beds, or that of common fire.

Goldsmiths'-Kress no. 08498.8-1, suppl.

Thermometrical observations as connected with navigation : the utility ... in ascertaining the relative heat of the sea-water ... to discover the passage of a vessel through the Gulf Stream and from deep water into soundings ... to avoid danger ... /

Mode of access: Internet.

Identities: Of light and heat, of caloric and electricity ...

Mode of access: Internet.

Allergy, asthma, hay fever, urticaria and allied manifestations of reaction,

Mode of access: Internet.

Incidence of Stagonospora meliloti and Acrocalymma medicaginis in Lucerne crowns and roots in eastern Australia, and their comparative aggressiveness to Lucerne and inheritance of reaction to S. meliloti in lucerne

The research presented indicates that lucerne crown and root rot caused by Stagonospora meliloti is prevalent in southern New South Wales, whereas Acrocalymma medicaginis is the more commonly observed pathogen in Queensland. Although both pathogens cause reddening of internal root and crown tissue of lucerne, they can be distinguished by symptomatology. S. meliloti causes a diffuse red blotching of the internal tissue accompanied by the presence of an external lesion, whereas A. medicaginis causes red streaking at the extremity of wedge-shaped, dry-rotted tissue. Inoculation of propagules of a susceptible lucerne clone indicated that S. meliloti was the more aggressive pathogen. Although A. medicaginis does not cause leaf disease, there was a strong relationship between the leaf and root reaction of clones to S. meliloti. Inheritance of resistance to S. meliloti in lucerne appeared to be conditioned by a single dominant gene, based on segregations observed in S-1 and F-1 populations, but not in a backcross population from the same family where an excess of susceptible individuals (74% v. expected of 50%) was obtained in a cross of a resistant F-1 individual to the susceptible parent. Resistance appears to be highly heritable, however, and amenable to population improvement by breeding. A conclusion of the research is that breeding for resistance to S. meliloti for lucernes to be grown in southern Australia would appear to be a worthwhile objective. Presently, no highly resistant cultivars exist anywhere in the world.

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

The diamond grinding of reaction bonded silicon carbide

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