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

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

Imaging Pulsed Laser Deposition oxide growth by in-situ Atomic Force Microscopy

To visualize the topography of thin oxide films during growth, thereby enabling to study its growth behavior quasi real-time, we have designed and integrated an atomic force microscope (AFM) in a pulsed laser deposition (PLD) vacuum setup. The AFM scanner and PLD target are integrated in a single support frame, combined with a fast sample transfer method, such that in-situ microscopy can be utilized after subsequent deposition pulses. The in-situ microscope can be operated from room temperature (RT) up to 700$^\circ$C and at (process) pressures ranging from the vacuum base pressure of 10$^{-6}$ mbar up to 1 mbar, typical PLD conditions for the growth of oxide films. The performance of this instrument is demonstrated by resolving unit cell height surface steps and surface topography under typical oxide PLD growth conditions.Comment: 8 pages, 8 figure

Determining the energetics of vicinal perovskite oxide surfaces

The energetics of vicinal SrTiO$_3$(001) and DyScO$_3$(110), prototypical perovskite vicinal surfaces, has been studied using topographic atomic force microscopy imaging. The kink formation and strain relaxation energies are extracted from a statistical analysis of the step meandering. Both perovskite surfaces have very similar kink formation energies and exhibit a similar triangular step undulation. Our experiments suggest that the energetics of perovskite oxide surfaces is mainly governed by the local oxygen coordination.Comment: 16 pages, 4 figure

Naturschutzforschung am Auerhuhn in der Schweiz: eine Übersicht

The Western Capercaille Tetrao urogallus is a large forest grouse with narrow habitat preferences and large home ranges. As Capercaille populations are declining in most of their central European range and the species has been shown to be an umbrella for high species richness, a profound knowledge of the species' ecology is essential for the conservation of the charismatic bird

A new simplified clarification approach for lentiviral vectors using diatomaceous earth improves throughput and safe handling

Lentiviral vectors have proven their great potential to serve as a DNA delivery tool for gene modified cell therapy and gene therapy applications. The downstream processing of these vectors is however still a great challenge, particularly because of the low stability of the virus. Harvesting and clarification are critical and until now insufficiently characterized steps for lentivirus processing. To address this bottleneck, we analyzed whether lentiviral vectors produced by transient transfection of HEK293 T/17 SF suspension cells can be efficiently clarified with a lab-scale method with the filter aid diatomaceous earth (DE) and bioburden reducing membrane filters achieving high lentivirus recoveries. Using a design of experiment approach we found that higher DE concentrations are advantageous for a higher turbidity reduction and shorter filtration times, but at the same time LV titer decreases with increasing DE concentration. A DE concentration of 9 g/L was identified with a DoE as a robust set-point. Clarification with DE was compared with for lab-scale traditionally employed centrifugation and subsequent bioburden reduction filtration of viral vectors. The use of DE allows to perform a harvest and clarification process, which does not only facilitate faster and safer virus handling, but enables a lower material consumption due to the extremely increased filter capacity, thus representing an efficient and robust lab-scale clarification process

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

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

A genetically encoded reporter of synaptic activity in vivo

To image synaptic activity within neural circuits, we tethered the genetically encoded calcium indicator (GECI) GCaMP2 to synaptic vesicles by fusion to synaptophysin. The resulting reporter, SyGCaMP2, detected the electrical activity of neurons with two advantages over existing cytoplasmic GECIs: it identified the locations of synapses and had a linear response over a wider range of spike frequencies. Simulations and experimental measurements indicated that linearity arises because SyGCaMP2 samples the brief calcium transient passing through the presynaptic compartment close to voltage-sensitive calcium channels rather than changes in bulk calcium concentration. In vivo imaging in zebrafish demonstrated that SyGCaMP2 can assess electrical activity in conventional synapses of spiking neurons in the optic tectum and graded voltage signals transmitted by ribbon synapses of retinal bipolar cells. Localizing a GECI to synaptic terminals provides a strategy for monitoring activity across large groups of neurons at the level of individual synapses