Numerical investigation of the elastic scattering of hydrogen (isotopes) and helium at graphite (0001) surfaces at beam energies of 1 to 4 eV using a split-step Fourier method

We report simulations of the elastic scattering of atomic hydrogen isotopes and helium beams from graphite (0001) surfaces in an energy range of 1–4 eV. To this aim, we numerically solve a time-dependent Schrödinger equation using a split-step Fourier method. The hydrogen- and helium-graphite potentials are derived from density functional theory calculations using a cluster model for the graphite surface. We observe that the elastic interaction of tritium and helium with graphite differs fundamentally. Whereas the wave packets in the helium beam are directed to the centers of the aromatic cycles constituting the hexagonal graphite lattice, they are directed toward the rings in case of the hydrogen beams. These observations emphasize the importance of swift chemical sputtering for the chemical erosion of graphite and provide a fundamental justification of the graphite peeling mechanism observed in molecular dynamics studies. Our investigations imply that wave packet studies, complementary to classical atomistic molecular dynamics simulations open another angle to the microscopic view on the physics underlying the sputtering of graphite exposed to hot plasma.     

A note on the star chromatic number

A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make some simple observations that lead to a purely combinatorial treatment. Our methods yield shorter proofs and offer further insight.     

Some results on the Oberwolfach problem

Aequationes mathematicae -     

Fluorescent Rhodamines and Fluorogenic Carbopyronines for Super‐Resolution STED Microscopy in Living Cells

A range of bright and photostable rhodamines and carbopyronines with absorption maxima in the range of λ=500–630 nm were prepared, and enabled the specific labeling of cytoskeletal filaments using HaloTag technology followed by staining with 1 μm solutions of the dye–ligand conjugates. The synthesis, photophysical parameters, fluorogenic behavior, and structure–property relationships of the new dyes are discussed. Light microscopy with stimulated emission depletion (STED) provided one‐ and two‐color images of living cells with an optical resolution of 40–60 nm.     

Far‐Red Emitting Fluorescent Dyes for Optical Nanoscopy: Fluorinated Silicon–Rhodamines (SiRF Dyes) and Phosphorylated Oxazines

Far‐red emitting fluorescent dyes for optical microscopy, stimulated emission depletion (STED), and ground‐state depletion (GSDIM) super‐resolution microscopy are presented. Fluorinated silicon–rhodamines (SiRF dyes) and phosphorylated oxazines have absorption and emission maxima at about λ≈660 and 680 nm, respectively, possess high photostability, and large fluorescence quantum yields in water. A high‐yielding synthetic path to introduce three aromatic fluorine atoms and unconventional conjugation/solubilization spacers into the scaffold of a silicon–rhodamine is described. The bathochromic shift in SiRF dyes is achieved without additional fused rings or double bonds. As a result, the molecular size and molecular mass stay quite small (<600 Da). The use of the λ=800 nm STED beam instead of the commonly used one at λ=750–775 nm provides excellent imaging performance and suppresses re‐excitation of SiRF and the oxazine dyes. The photophysical properties and immunofluorescence imaging performance of these new far‐red emitting dyes (photobleaching, optical resolution, and switch‐off behavior) are discussed in detail and compared with those of some well‐established fluorophores with similar spectral properties.