Medial surfaces of hyperbolic structures

We describe an algorithm for numerical computation of a medial surface and an associated medial graph for three-dimensional shapes bounded by oriented triangulated surface manifolds in three-dimensional Euclidean space (domains). We apply the construction to bicontinuous domain shapes found in molecular self-assemblies, the cubic infinite periodic minimal surfaces of genus three: Gyroid (G), Diamond (D) and Primitive (P) surfaces. The medial surface is the locus of centers of maximal spheres, i.e. spheres wholly contained within the domains which graze the surface tangentially and are not contained in any other such sphere. The construction of a medial surface is a natural generalization of Voronoi diagrams to continuous surfaces. The medial surface provides an explicit construction of the volume element associated with a patch of the bounding surface, leading to a robust measure of the surface to volume ratio for complex forms. It also allows for sensible definition of a line graph (the medial graph), particularly useful for domains consisting of connected channels, and not reliant on symmetries of the domains. In addition, the medial surface construction produces a length associated with any point on the surface. Variations of this length give a useful measure of global homogeneity of topologically complex morphologies. Comparison of medial surfaces for the P, D and G surfaces reveal the Gyroid to be the most globally homogeneous of these cubic bicontinuous forms (of genus three). This result is compared with the ubiquity of the G surface morphology in soft mesophases, including lyotropic liquid crystals and block copolymers.     

Observation of highly ionised species in plasma produced by picosecond laser pulses

Results are presented which show that in the case of the light elements highly ionised species can be detected in laser produced plasmas using a normal incidence spectrograph, the plasmas being formed by picosecond pulses from a high power Nd: glass laser. In particular hydrogenic ions of carbon, oxygen and fluorine have been observed when the incident laser flux density onto a solid target was about 3×10¹⁴W/cm².     

The preparation and electrochemistry of manganese(II) complexes of an unsaturated pentadentate macrocyclic ligand

The preparation of a series of six and seven coordinate manganese(II) complexes [Mn^(II)(L)X]⁺, and [Mn^(II)(L)X₂]^2? (X = halide, water, triphenylphosphine oxide, imidazole, 1-methyl imidazole and pyridine) incorporating the pentadentate planar macrocylic ligand L is described. Cyclic voltammetry of these complexes in acetonitrile each shows a reversible one-electron reduction wave near - 1.4 V vs a Ag/AgNO₃ reference electrode. Quantitative reduction of these complexes by controlled potential electrolysis at a platinum gauze at - 1.4 V yields the corresponding one-electron reduction products which have been shown by ESR spectroscopy to be manganese(II)-ligand radical species, the electron being thought to reside on the di-imino pyridine moiety of the macrocyclic ligand. No metal reduced species could be isolated even in the presence of π-acceptor ligands such as CO or phosphines.     

Low-energy gamma-ray sources observed by the MISO telescope

Summary The MISO telescope is a gamma-ray detector operating in the (0.1÷20) MeV energy range. This instrument was flown success-fully from Palestine, Texas (U.S.A.) in May 1977, October 1978, September 1979 and May 1980. During the four flights, the telescope observed a number of galactic and extragalactic sources. The Crab Nebula was detected in 1980 and its spectrum was measured up to 2 MeV. Cygnus X-1 was observed in 1979 and 1980 and was found to be in different hard X-ray states on each occasion: in a superlow state in 1979 and in a low state in 1980. The COS-B high-energy (E>50 MeV) gamma-ray sources CG 135+1 (1978) and CG 195+4 (1978) were also observed by the same instrument. From the region containing CG 135+1 a 5σ excess was measured in the counting rate of the telescope above 120 keV. No statistically significant low-energy gamma-ray flux was detected from CG 195+4. The Seyfert galaxies NCG 4151 (1977, 1979, 1980), and MCG 8-11-11 (1979), the BL LAC object MK 501 (1979) and the ?peculiar? galaxy NGC 1275 (1979) were also searched for gamma-ray emission. The data on NGC 4151 and MCG 8-11-11 are consistent with power law spectra having photon indices α∼1 in the (0.1÷3) MeV energy range. Above this energy, the MISO and SAS-2/COS-B measurements require spectral breaks to α≥3. Upper limits were obtained on the emission from both MK 501 and NGC 1275. Paper presented at the 2° Convegno Nazionale di Fisica Cosmica, held at L'Aquila, 29 May–2 June 1984.     

ipso-Fluorination of aryltrimethylsilanes using xenon difluoride

Reaction of aryltrimethylsilanes with xenon difluoride in C₆F₆/Pyrex^® at room temperature gives aryl fluorides in good yield. The reaction is inhibited when acetonitrile is used as solvent but proceeds well in CFCl₃/Pyrex^® or CH₂Cl₂/Pyrex^®. Pyrex^® appears to be a very effective heterogeneous catalyst for this ipso-fluorination. The reaction does not proceed in PTFE, quartz, soda glass or glassy-carbon flasks or Pyrex^® flasks pre-rinsed with 2 M NaOH. Aryltrimethylstannanes and arylboronic acids and their esters do not undergo ipso-fluorination under similar conditions. Plausible mechanisms involving electrophilic addition of polarised xenon difluoride [FXe^δ+?F→Pyrex^δ−] followed by ligand coupling are discussed.