Multiple CSLs for the body centered cubic lattice

Ordinary Coincidence Site Lattices (CSLs) are defined as the intersection of a lattice $\Gamma$ with a rotated copy $R\Gamma$ of itself. They are useful for classifying grain boundaries and have been studied extensively since the mid sixties. Recently the interests turned to so-called multiple CSLs, i.e. intersections of $n$ rotated copies of a given lattice $\Gamma$, in particular in connection with lattice quantizers. Here we consider multiple CSLs for the 3-dimensional body centered cubic lattice. We discuss the spectrum of coincidence indices and their multiplicity, in particular we show that the latter is a multiplicative function and give an explicit expression of it for some special cases.Comment: 4 pages, SSPCM (31 August - 7 September 2005, Myczkowce, Poland

Coincidences in 4 dimensions

The coincidence site lattices (CSLs) of prominent 4-dimensional lattices are considered. CSLs in 3 dimensions have been used for decades to describe grain boundaries in crystals. Quasicrystals suggest to also look at CSLs in dimensions $d>3$. Here, we discuss the CSLs of the root lattice $A_4$ and the hypercubic lattices, which are of particular interest both from the mathematical and the crystallographic viewpoint. Quaternion algebras are used to derive their coincidence rotations and the CSLs. We make use of the fact that the CSLs can be linked to certain ideals and compute their indices, their multiplicities and encapsulate all this in generating functions in terms of Dirichlet series. In addition, we sketch how these results can be generalised for 4--dimensional $\Z$--modules by discussing the icosian ring.Comment: 6 pages, conference "Quasicrystals - The Silver Jubilee

Grain boundary energies and cohesive strength as a function of geometry

Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters needed to describe the grain boundary geometry; two parameters in 2D and 5 parameters in 3D. However, we find that the cohesive law is not a smooth function of these parameters. In fact, it is discontinuous at geometries for which the two grains have repeat distances that are rational with respect to one another. Using atomistic simulations, we extract grain boundary energies and cohesive laws of grain boundary fracture in 2D with a Lennard-Jones potential for all possible geometries which can be simulated within periodic boundary conditions with a maximum box size. We introduce a model where grain boundaries are represented as high symmetry boundaries decorated by extra dislocations. Using it, we develop a functional form for the symmetric grain boundary energies, which have cusps at all high symmetry angles. We also find the asymptotic form of the fracture toughness near the discontinuities at high symmetry grain boundaries using our dislocation decoration model.Comment: 12 pages, 19 figures, changed titl

Coincidence isometries of a shifted square lattice

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate them, we calculate the set of coincidence isometries, as well as generating functions for the number of coincidence site lattices and coincidence isometries, for specific examples.Comment: 10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool

The quest for companions to post-common envelope binaries. II. NSVS14256825 and HS0705+6700

We report new mid-eclipse times of the two close binaries NSVS14256825 and HS0705+6700, harboring an sdB primary and a low-mass main-sequence secondary. Both objects display clear variations in the measured orbital period, which can be explained by the action of a third object orbiting the binary. If this interpretation is correct, the third object in NSVS14256825 is a giant planet with a mass of roughly 12 M_Jup. For HS0705+6700, we provide evidence that strengthens the case for the suggested periodic nature of the eclipse time variation and reduces the uncertainties in the parameters of the brown dwarf implied by that model. The derived period is 8.4 yr and the mass is 31 M_Jup, if the orbit is coplanar with the binary. This research is part of the PlanetFinders project, an ongoing collaboration between professional astronomers and student groups at high schools.Comment: Accepted by Astron. and Astrophy

The genotype of barley cultivars influences multiple aspects of their associated microbiota via differential root exudate secretion

Plant-associated microbe play vital roles in promoting plant growth and health, with plants secreting root exudates into the rhizosphere to attract beneficial microbes. Exudate composition defines the nature of microbial recruitment, with different plant species attracting distinct microbiota to enable optimal adaptation to the soil environment. To more closely examine the relationship between plant genotype and microbial recruitment, we analysed the rhizosphere microbiomes of landrace (Chevallier) and modern (NFC Tipple) barley (Hordeum vulgare) cultivars. Distinct differences were observed between the plant associated microbiomes of the 2 cultivars, with the plant-growth promoting rhizobacterial genus Pseudomonas substantially more abundant in the Tipple rhizosphere. Striking differences were also observed between the phenotypes of recruited Pseudomonas populations, alongside distinct genotypic clustering by cultivar. Cultivar-driven Pseudomonas selection was driven by root exudate composition, with the greater abundance of hexose sugars secreted from Tipple roots attracting microbes better adapted to growth on these metabolites and vice versa. Cultivar-driven selection also operates at the molecular level, with both gene expression and the abundance of ecologically relevant loci differing between Tipple and Chevallier Pseudomonas isolates. Finally, cultivar-driven selection is important for plant health, with both cultivars showing a distinct preference for microbes selected by their genetic siblings in rhizosphere transplantation assay

Exponential distribution of long heart beat intervals during atrial fibrillation and their relevance for white noise behaviour in power spectrum

The statistical properties of heart beat intervals of 130 long-term surface electrocardiogram recordings during atrial fibrillation (AF) are investigated. We find that the distribution of interbeat intervals exhibits a characteristic exponential tail, which is absent during sinus rhythm, as tested in a corresponding control study with 72 healthy persons. The rate of the exponential decay lies in the range 3-12 Hz and shows diurnal variations. It equals, up to statistical uncertainties, the level of the previously uncovered white noise part in the power spectrum, which is also characteristic for AF. The overall statistical features can be described by decomposing the intervals into two statistically independent times, where the first one is associated with a correlated process with 1/f noise characteristics, while the second one belongs to an uncorrelated process and is responsible for the exponential tail. It is suggested to use the rate of the exponential decay as a further parameter for a better classification of AF and for the medical diagnosis. The relevance of the findings with respect to a general understanding of AF is pointed out

A Precision Measurement of pp Elastic Scattering Cross Sections at Intermediate Energies

We have measured differential cross sections for \pp elastic scattering with internal fiber targets in the recirculating beam of the proton synchrotron COSY. Measurements were made continuously during acceleration for projectile kinetic energies between 0.23 and 2.59 GeV in the angular range $30 \leq \theta_{c.m.} \leq 90$ deg. Details of the apparatus and the data analysis are given and the resulting excitation functions and angular distributions presented. The precision of each data point is typically better than 4%, and a relative normalization uncertainty of only 2.5% within an excitation function has been reached. The impact on phase shift analysis as well as upper bounds on possible resonant contributions in lower partial waves are discussed.Comment: 23 pages 29 figure