Elastic Curves with Variable Bending Stiffness

We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and total torsion while simultaneously allowing for a variable bending stiffness along the arc-length of the curve. Physically, this can be understood as a model for an elastic wire with isotropic cross-section of varying thickness. We derive the corresponding Euler-Lagrange equations for variations that are compactly supported away from the end points thus obtaining characterizations for elastic curves with variable bending stiffness. Moreover, we provide a collection of alternative characterizations, e.g., in terms of the curvature function. Adding to numerous known results relating elastic curves to dynamics, we establish connections between elastic curves with variable bending stiffness and damped pendulums and the flow of vortex filaments with finite thickness

Human MFAP1 is a cryptic ortholog of the Saccharomyces cerevisiae Spp381 splicing factor

Detailed results of MFAP1 and Spp381 ortholog searches with InParanoid 8. The protein sequence of Homo sapiens MFAP1 (UniProt ID: P55081) (hs), the putative Wickerhamomyces ciferrii MFAP1 ortholog (UniProt ID: K0KNQ2) (wc), or Saccharomyces cerevisiae Spp381 (UniProt ID: P38282) (sc) were used to search the InParanoid 8 [37] ortholog database and used as templates in BLAST searches against the 273 species (246 eukaryotes plus 27 prokaryotes) covered by the InParanoid 8 program. Orthologs found in the InParanoid 8 database and identified in BLAST searches against the 273 InParanoid species are marked by a black box; orthologs either found in the InParanoid 8 database or identified by the InParanoid BLAST search are marked with a grey box; species with no identified ortholog are not marked. Species names are colored according to the taxonomic group they belong to. The phylogenetic tree on the right is based on pairwise species distances derived from shared ortholog content as reported by InParanoid 8 [37]. See Additional file 2 for UniProt IDs of identified orthologs. (TIF 695 kb

Lattice location and stability of implanted Cu in ZnO

The lattice location of copper in single-crystalline zinc oxide was studied by means of the emission channeling technique. Following 60 keV room-temperature implantation at a fluence of $\,2.3\!\times\!10^{13}$ cm\!^{-2}, the angular distribution of \beta\!^{-}-particles emitted by the radioactive isotope $^{67}$Cu was measured by a position-sensitive detector. The $\beta$ - emission patterns give direct evidence that in the as-implanted state a large fraction of Cu atoms (60--70%) occupy almost ideal substitutional Zn sites with root mean square (rms) displacements of 0.16--0.17 Å. However, following annealing at 600°C and above Cu was found to be located on sites that are characterized by large rms displacements (0.3--0.5 Å) from Zn sites

Lattice location and perturbed angular correlation studies of implanted Ag in SrTiO3_{3}

Lattice site location and local environment characterization of implanted $^{111}\!$Ag in SrTiO$_{3}$ by means of the emission channeling (EC) and $\gamma$-$\gamma$-perturbed angular correlation (PAC) techniques are reported. The angular distribution of \beta\!^{-}-particles emitted from the $^{111}\!$Ag decay was monitored with a position-sensitive detector as a function of annealing temperature up to 900 ºC. In the as-implanted state Ag occupies several lattice sites in SrTiO$_{3}$. Upon annealing, near-Sr and near-Ti occupancies increased to 58% and 28%, while an octahedral interstitial fraction vanished. Ag on near-Sr and near-Ti sites are still displaced by $\sim$0.2--0.5 Å from ideal cubic positions. Subsequent PAC measurements confirmed that ~20% of $^{111}\!$Ag atoms are in specific sites of non-cubic environment, characterized by a unique electrical-field-gradient (EFG), while ~80% were subject to a wide EFG distribution

Lattice sites of implanted Fe in Si

The angular distribution of $\beta^{-}$-particles emitted by the radioactive isotope $^{59}$Fe was monitored following implantation into Si single crystals at fluences from $1.4 \times 10^{12}$ cm$^{-2}$ to $1 \times 10^{14}$ cm$^{-2}$. We identified Fe on three distinct sites: ideal substitutional, displaced substitutional and displaced tetrahedral interstitial. Whereas displaced substitutional Fe was dominating for annealing temperatures below 500 °C, annealing between 500-700 °C caused the majority of Fe to occupy displaced tetrahedral interstitial sites. Ideal substitutional positions were increasingly populated following annealing at 800 °C and above. A comparison of the emission channeling results to Mössbauer and electron paramagnetic resonance experiments is given

Lattice sites of implanted Cu and Ag in ZnO

The group $\textrm{I}$b impurities Cu and Ag on substitutional Zn sites are among possible candidates for p-type doping of ZnO. In order to explore possible lattice sites of Cu and Ag in ZnO the radioactive impurities $^{67}\!$Cu and $^{111}\!$Ag were implanted at doses of $4\!\times\!10^{12}$cm$^{-2}\to1\!\times\!10^{14}$cm$^{-2}$ at 60 keV into ZnO single crystals. The emission channeling effects of \beta\!^{-} -particles from the decay were studied by means of position-sensitive electron detectors, giving direct evidence that in the as-implanted state large fractions of Cu and Ag atoms (60--70% for Cu and 30% for Ag) occupy almost ideal substitutional Zn sites with root mean square (rms) displacements of 0.014--0.017 nm. However, following vacuum annealing at 600 °C and above both Cu and Ag were found to be located increasingly on sites that are characterized by large rms displacements (0.03--0.05 nm) from Zn sites. We conclude that in high-temperature treated ZnO Cu and Ag are most likely not simply replacing Zn atoms but are incorporated in complexes with other crystal defects or as clusters

Crystal field analysis of Pm3+^{3+} (4f4)andSm^{f4}) and Sm^{3+}(4 (4^{f5}) and lattice location studies of 147^{147}Nd and 147^{147}Pm in w-AlN

We report a detailed crystal field analysis of Pm3+ and Sm3+ as well as lattice location studies of 147Pm and 147Nd in 2H-aluminum nitride (w-AlN). The isotopes of mass 147 were produced by nuclear fission and implanted at an energy of 60 keV. The decay chain of interest in this work is 147Nd→147Pm→147Sm (stable). Lattice location studies applying the emission channeling technique were carried out using the β− particles and conversion electrons emitted in the radioactive decay of 147Nd→147Pm. The samples were investigated as implanted, and also they were investigated after annealing to temperatures of 873 K as well as 1373 K. The main fraction of about 60% of both 147Pm as well as 147Nd atoms was located on substitutional Al sites in the AlN lattice; the remainder of the ions were located randomly within the AlN lattice. Following radioactive decay of 147Nd, the cathodoluminescence spectra of Pm3+ and Sm3+ were obtained between 500 nm and 1050 nm at sample temperatures between 12 K and 300 K. High-resolution emission spectra, representing intra-4f electron transitions, were analyzed to establish the crystal-field splitting of the energy levels of Sm3+ (4f5) and Pm3+ (4f4) in cationic sites having C3v symmetry in the AlN lattice. Using crystal-field splitting models, we obtained a rms deviation of 6 cm−1 between 31 calculated-to-experimental energy (Stark) levels for Sm3+ in AlN. The results are similar to those reported for Sm3+ implanted into GaN. Using a set of crystal-field splitting parameters Bnm, for Pm3+ derived from the present Sm3+ analysis, we calculated the splitting for the 5F1, 5I4, and 5I5 multiplet manifolds in Pm3+ and obtained good agreement between the calculated and the experimental Stark levels. Temperature-dependent lifetime measurements are also reported for the emitting levels 4F5∕2 (Sm3+) and 5F1 (Pm3+)