Substituent effects on the geometry of some trigonal radicals

A simple level of ab initio molecular orbital theory with a split-valence shell basis with d-type polarization functions (6–31G*) is used to predict equilibrium geometries for the ground and some low-lying excited states of AH_n molecules and cations where A is carbon, nitrogen, oxygen or fluorine. The results are shown to be close to the limit for single determinant wave functions in cases where corresponding computations with more extensive bases are available. Comparison with experimental results also shows good agreement although a systematic underestimation of bond lengths up to 3 per cent is evident. For systems where no experimental data are available, the results provide predictions of equilibrium geometry.     

TRINAT: measuring β-decay correlations with laser-trapped atoms

TRIUMF’s neutral atom trap for β decay (TRINAT) has been used to measure the most accurate β-ν correlation. Plans include improving that measurement, and also carrying out a full program of spin-polarized β decay correlation measurements complementary to the decay of the neutron     

Override and update

Override and update are natural constructions for combining partial functions, which arise in various program specification contexts. We use an unexpected connection with combinatorial geometry to provide a complete finite system of equational axioms for the first order theory of the override and update constructions on partial functions, resolving the main unsolved problem in the area.     

Certain hyperbolic regular polygonal tiles are isoperimetric

Geometriae Dedicata - The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular...     

Interstitials in platinum

The defect production rate in platinum irradiated with energetic charged particles is measured as a function of irradiation temperature from below stage I to above the ‘so-called’ stage III. On the basis of these measurements, supplemented by recovery studies, and by other types of irradiations a consistent model of defect production and recovery is platinum on the basis that two distinct interstitial species are present is put forward.     

Distribution of Eigenvalues of Highly Palindromic Toeplitz Matrices

Consider the ensemble of real symmetric Toeplitz matrices whose entries are i.i.d. random variables chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous work (Bryc et al., Ann. Probab. 34(1):1–38, 2006; Hammond and Miller, J. Theor. Probab. 18(3):537–566, 2005) showed that the spectral measures (the density of normalized eigenvalues) converge almost surely to a universal distribution almost that of the Gaussian, independent of p. The deficit from the Gaussian distribution is due to obstructions to solutions of Diophantine equations and can be removed (see Massey et al., J. Theor. Probab. 20(3):637–662, 2007) by making the first row palindromic. In this paper we study the case where there is more than one palindrome in the first row of real symmetric Toeplitz matrices. Using the method of moments and an analysis of the resulting Diophantine equations, we show that the spectral measures converge almost surely to a universal distribution. Assuming a conjecture on the resulting Diophantine sums (which is supported by numerics and some theoretical arguments), we prove that the limiting distribution has a fatter tail than any previously seen limiting spectral measure.     

The stability of solitons in biomembranes and nerves

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small-amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation. Solitary waves pass through each other with only minor dissipation when their amplitude is small. Large-amplitude solitons fall apart into several pulses and small-amplitude noise upon collision when the maximum density of the membrane is limited by the density of the solid phase membrane.     

An atomistic surface simulation study predicting morphologies and segregation in yttrium lithium fluoride

The aim of this research on the laser material yttrium lithium fluoride (YLiF₄) is to provide the first study of its surface structure, morphology and the properties of rare-earth doped surfaces. The study utilises the METADISE computer code to model the surfaces using interatomic potentials. Equilibrium and growth morphologies are predicted and a detailed profile of segregation of rare-earth dopants to the three dominating surfaces is given. The (001), (011) and (112) surfaces dominate the morphology. Rare-earth dopants La to Sm show segregation to these surfaces, with the (112) surface being of particular interest. As this work demonstrates, it is likely to have dopants clustered towards it.