Simultaneous diagonal flips in plane triangulations

Simultaneous diagonal flips in plane triangulations are investigated. It is proved that every triangulation with n ≥ 6 vertices has a simultaneous flip into a 4‐connected triangulation, and that the set of edges to be flipped can be computed in (n) time. It follows that every triangulation has a simultaneous flip into a Hamiltonian triangulation. This result is used to prove that for any two n‐vertex triangulations, there exists a sequence of (logn) simultaneous flips to transform one into the other. Moreover, Ω(log n) simultaneous flips are needed for some pairs of triangulations. The total number of edges flipped in this sequence is (n). The maximum size of a simultaneous flip is then studied. It is proved that every triangulation has a simultaneous flip of at least edges. On the other hand, every simultaneous flip has at most n ? 2 edges, and there exist triangulations with a maximum simultaneous flip of edges. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 307–330, 2007     

Behavior of silver substitution in single-grain TSMG YBCO bulk superconductor

Ag concentration in the single-grain TSMG Y₁Ba₂(Cu_1?xAg_x)₃O₇ bulk superconductor with nominal Ag concentration for x = 0.05 was measured by WDX microprobe. The partition coefficient of Ag between Y123 crystal and the melt, k_Ag, was estimated to be k_Ag = 0.1. It is also shown that the solubility of Ag in the Y₂BaCuO₅ phase is below the WDX detection limit. As the measured Ag concentration is about four times higher than the concentration of Ag for optimum chemical pinning, the clustering of Ag atoms is supposed and a mechanism of Ag clustering is proposed.     

Investigating the interaction of x-ray free electron laser radiation with grating structure

The interaction of free electron laser pulses with grating structure is investigated using 4.6±0.1 nm radiation at the FLASH facility in Hamburg. For fluences above 63.7±8.7 mJ/cm², the interaction triggers a damage process starting at the edge of the grating structure as evidenced by optical and atomic force microscopy. Simulations based on solution of the Helmholtz equation demonstrate an enhancement of the electric field intensity distribution at the edge of the grating structure. A procedure is finally deduced to evaluate damage threshold.     

Isotope dependence of the lifetime of the vibration of oxygen in silicon

By simply changing the isotopes of the Si atoms that neighbor an oxygen Oi atom in crystalline silicon, the measured decay rate tau of the asymmetric-stretch vibration (nu3=1136 cm-1) of oxygen (Oi) in silicon changes by a factor of approximately 2.5. These data establish that nu3 decays by creating one nu1 symmetric-stretch, local-vibrational mode of the Si-Oi-Si structure. If the residual energy (nu3-nu1) is less than the maximum frequency num of the host lattice, as for 28Si-16O-28Si in natural silicon, then it is emitted as one lattice mode, and tau depends on the density of one-phonon states at nu3-nu1. If (nu3-nu1)>num, as for 16O in single-isotope 30Si silicon, two lattice modes are created in addition to nu1, increasing tau. Prediction of tau for a particular defect clearly requires a detailed knowledge of that defect.     

Potentiometric and relaxometric properties of a gadolinium-based MRI contrast agent for sensing tissue pH

The pH-sensitive contrast agent, GdDOTA-4AmP (Gd1) has been successfully used to map tissue pH by MRI. Further studies now demonstrate that two distinct chemical forms of the complex can be prepared depending upon the pH at which Gd(3+) is mixed with ligand 1. The desired pH-sensitive form of this complex, referred to here as a Type II complex, is obtained as the exclusive product only when the complexation reaction is performed above pH 8. At lower pH values, a second complex is formed that, by analogy with an intermediate formed during the preparation of GdDOTA, we tentatively assign to a Type I complex where the Gd(3+) is coordinated only by the appended side-chain arms of 1. The proportion of Type I complex formed is largely determined by the pH of the complexation reaction. The magnitude of the pH-dependent change in the relaxivity of Gd1 was found to be less than earlier reported (Zhang, S.; Wu, K.; Sherry, A. D. Angew. Chem., Int. Ed. 1999, 38, 3192), likely due to contamination of the earlier sample by an unknown amount of Type I complex. Examination of the nuclear magnetic relaxation dispersion and relaxivity temperature profiles, coupled with information from potentiometric titrations, shows that the amphoteric character of the phosphonate side chains enables rapid prototropic exchange between the single bound water of the complex with the bulk water thereby giving Gd1 a unique pH-dependent relaxivity that is quite useful for the pH mapping of tissues by MRI.     

Microanalysis of Glass Containing Alkali Ions

 The common problems connected with alkali ion migration during EPMA were studied on glasses containing nearly all possible alkali ions (Na, K, Rb, Cs). Binary silica glasses were prepared by melting from a very pure batch in Pt crucible. The glasses were carefully polished using alcohol to prevent surface corrosion by water and they were stored in vacuum. The specimens were coated with carbon layers approximately 30-nm thick and exposed to a 50- keV electron beam of 100 μm diameter. It was found that all alkali ions migrate under the electron beam, but the rate of the migration depends on the current density. The decay curves (characteristic X-ray intensity versus time) are similar in shape in all cases. The decay curve shows two transport regimes, the first being linear-like, the second being the exponential-like. The first transport regime busts into the rapid alkali migration after a time known as the incubation period. The period is in general longer for the larger-alkali ions size. It was found that even large rubidium and caesium ions migrate inside the glass with the same mechanism as sodium and potassium ions. While for K, Rb, and Cs ions the incubation periods were observed under the suitable experimental conditions, binary glass containing Na exhibits no observable incubation period. Except for the binary Na₂O + SiO₂ glass, the suitable experimental conditions for reliable quantitative EPMA can be found.