Secondary electron emission yield behaviour of polymers

The secondary electron emission yields of highly-insulating, thin polymer foils have been measured for incident primary beam energies, 50 ? E_p ? 2500 eV. The results follow closely a ‘universal’ reduced yield curve determined by the energy loss law, dE_p/dx = -A/E_p^n-1, where n = 2 and A is a constant proportional to the density of the solid, as predicted by the elementary theory of Lye and Dekker (1957). This behaviour remains true up to high primary beam energies and, as such, is unique to these low density solids.     

Construction of universal rotations from point-to-point transformations

For a desired range of offsets, universal rotations of arbitrary flip angle can be constructed based on point-to-point rotations of I(y) with half the flip angle. This approach allows, for example, creation of broadband or bandselective refocusing pulses from broadband or bandselective excitation pulses. Furthermore, universal rotations about any axis can be obtained from point-to-point transformations that can easily be optimized using optimal control algorithms. The construction procedure is demonstrated on the examples of a broadband refocusing pulse, a broadband 120(x) degrees rotation and a z-rotation with offset pattern.     

Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H2O and D2O

We present a new approach that combines electronic structure methods and molecular dynamics simulations to investigate the infrared spectroscopy of condensed phase systems. This approach is applied to the OH stretch band of dilute HOD in liquid D2O and the OD stretch band of dilute HOD in liquid H2O for two commonly employed models of water, TIP4P and SPC/E. Ab initio OH and OD anharmonic transition frequencies are calculated for 100 HOD x (D2O)n and HOD x(H2O)n (n = 4-9) clusters randomly selected from liquid water simulations. A linear empirical relationship between the ab initio frequencies and the component of the electric field from the solvent along the bond of interest is developed. This relationship is used in a molecular dynamics simulation to compute frequency fluctuation time-correlation functions and infrared absorption line shapes. The normalized frequency fluctuation time-correlation functions are in good agreement with the results of previous theoretical approaches. Their long-time decay times are 0.5 ps for the TIP4P model and 0.9 ps for the SPC/E model, both of which appear to be somewhat too fast compared to recent experiments. The calculated line shapes are in good agreement with experiment, and improve upon the results of previous theoretical approaches. The methods presented are simple, and transferable to more complicated systems.     

Negatively pinched -manifolds admit hyperbolic metrics

We show that any compact 3-manifold carrying a metric with sufficiently pinched negative Ricci curvature admits a hyperbolic metric. This proof is a corrected version of the proof first suggested by Maung Min-Oo. The key insight in this new proof is that the error in Min-Oo's paper does not occur if the type curvature is considered instead of the type curvature.

     

The isotope exchange depth profiling (IEDP) technique using SIMS and LEIS

The determination of the mass transport kinetics of oxide materials for use in electrochemical systems such as fuel cells, sensors and oxygen separators is a significant challenge. Several techniques have been proposed to derive these data experimentally with only the oxygen isotope exchange depth profile technique coupled with secondary ion mass spectrometry (SIMS) providing a direct measure of these kinetic parameters. Whilst this allows kinetic information to be obtained, there is a lack of knowledge of the surface chemistry of these complex processes. The advent of low-energy ion scattering (LEIS) now offers the opportunity of correlating exchange kinetics with chemical processes at materials atomic surfaces, giving unprecedented levels of information on electrochemical systems with isotopic discrimination. Here, the challenges of these techniques, including sample preparation, are discussed and the advantages of the combined approach of SIMS and LEIS illustrated with reference to key literature data.     

Derivation of Smoluchowski equations with corrections for Fokker-Planck and BGK collision models

The time evolution of the phase space distribution function for a classical particle in contact with a heat bath and in an external force field can be described by a kinetic equation. From this starting point, for either Fokker-Planck or BGK (Bhatnagar-Gross-Krook) collision models, we derive, with a projection operator technique, Smoluchowski equations for the configuration space density with corrections in reciprocal powers of the friction constant. For the Fokker-Planck model our results in Laplace space agree with Brinkman, and in the time domain, with Wilemski and Titulaer. For the BGK model, we find that the leading term is the familiar Smoluchowski equation, but the first correction term differs from the Fokker-Planck case primarily by the inclusion of a fourth order space derivative or super Burnett term. Finally, from the corrected Smoluchowski equations for both collision models, in the spirit of Kramers, we calculate the escape rate over a barrier to fifth order in the reciprocal friction constant, for a particle initially in a potential well.     

Formation of H and D atoms in pyrolysis of 1,3-butadiene and 1,3 butadiene-1,1,4,4,-d4 behind shock waves

Highly dilute mixtures of 1,3-butadiene and 1,3-butadiene-1,1,4,4-d₄ were pyrolyzed behind reflected and incident shock waves, respectively. Concentrations of H and D atoms were measured by resonance absorption spectroscopy. In the early stages of the reaction, nearly equal amounts of H and D were formed from CD₂CHCHCD₂, indicating that loss of H from C₂ followed by loss of D from C₁ is a more important reaction than breaking of the central C? C bond. Overall, rate constants for atom-forming reactions are much slower than rate constants for disappearance of butadiene in earlier experiments, suggesting that most of the butadiene disappears by processes that do not involve H or D atoms or by radicals that produce them rapidly.