First-principles prediction of a decagonal quasicrystal containing boron

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants. These approximant structures imply a deterministic decoration of tiles by atoms that can be extended quasiperiodically. Experimentally observed structural disorder corresponds to phason (tile flip) fluctuations. First-principles total energy calculations reveal that many distinct tilings lie close to stability at low temperatures. Transfer matrix calculations based on these energies suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B$_{38}$Mg$_{17}$Ru$_{45}$ forms a decagonal quasicrystal that is metastable at low temperatures and may be thermodynamically stable at high temperatures.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Depleted pyrochlore antiferromagnets

I consider the class of "depleted pyrochlore" lattices of corner-sharing triangles, made by removing spins from a pyrochlore lattice such that every tetrahedron loses exactly one. Previously known examples are the "hyperkagome" and "kagome staircase". I give criteria in terms of loops for whether a given depleted lattice can order analogous to the kagome \sqrt{3} \times \sqrt{three} state, and also show how the pseudo-dipolar correlations (due to local constraints) generalize to even the random depleted case.Comment: 6pp IOP latex, 1 figure; Proc. "Highly Frustrated Magnetism 2008", Sept 2008, Braunschwei

Method of fabricating an object with a thin wall having a precisely shaped slit

A method is described for making a structure with a cavity and a thin wall with a precisely shaped slit. An object with a cavity having two openings, one of which is to be closed by a thin wall with a slit, is placed on the surface of a fixture. The fixture surface has a slot conforming to the size and shape of the slit to be formed in the thin wall

Bethe Ansatz solution of a decagonal rectangle triangle random tiling

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.Comment: 17 pages, 4 figures, some remarks added and typos correcte

Methods for obtaining and handling marine eggs and embryos

2nd EditionFrom the Preface: The Introduction to the first edition of this book (1957) (see page viii) stated that the volume was admittedly incomplete, and that new methods for obtaining, handling and studying marine eggs and embryos would undoubtedly be forthcoming. This prediction has been abundantly borne out in the intervening 14 years, and a complete revision of the book is clearly called for. A major re-writing is now (June, 1971) in progress. However, steadily continuing sales have resulted in the first edition going out of print, and it seemed advisable to re-issue it, with certain minor changes, as a stopgap measure, pending the major re-writing in progress. In the interim, it is appropriate here to point out some of the newer sources of information now available, and to note a few of the advances which have been made since 1957.Preparation of the first edition was completed under a National Science Foundation grant (NSF-G2477); the present revision was made possible, in part, by a grant from the National Institutes of Health, GM 15311

Non-relativistic Lee Model on two Dimensional Riemannian Manifolds

This work is a continuation of our previous work (JMP, Vol. 48, 12, pp. 122103-1-122103-20, 2007), where we constructed the non-relativistic Lee model in three dimensional Riemannian manifolds. Here we renormalize the two dimensional version by using the same methods and the results are shortly given since the calculations are basically the same as in the three dimensional model. We also show that the ground state energy is bounded from below due to the upper bound of the heat kernel for compact and Cartan-Hadamard manifolds. In contrast to the construction of the model and the proof of the lower bound of the ground state energy, the mean field approximation to the two dimensional model is not similar to the one in three dimensions and it requires a deeper analysis, which is the main result of this paper.Comment: 18 pages, no figure