Scaling Limits for Width Two Partially Ordered Sets: The Incomparability Window

We study the structure of a uniformly randomly chosen partial order of width 2 on n elements. We show that under the appropriate scaling, the number of incomparable elements converges to the height of a one dimensional Brownian excursion at a uniformly chosen random time in the interval [0, 1], which follows the Rayleigh distribution.     

A study of enthalpic relaxation of a liquid crystal

A liquid crystal, BL038, which was observed not to crystallize, has a glass transition at 215 K and a nematic to isotropic transition at 380 K. Samples aged below the glass transition at various temperatures T _a, exhibited an endotherm at the transition which developed with extent of ageing time, t _a. We attribute this endotherm to the relaxation of the glass towards the equilibrium liquid. The progress of the relaxation process was measured using differential scanning calorimetry. On subsequent reheating, the aged glass showed an apparent shift in the glass transition to higher temperatures. The endotherm was used to define the extent of enthalpic relaxation and the maximum value observed was found to increase initially then decrease, with the extent of undercooling from the glass transition temperature, Δ T, passing through a maximum for a Δ T = 15 K. From the temperature dependence of the relaxation times, an apparent activation enthalpy for the relaxation process of 85 ± 10 kJ mol^-1 was determined. The small value of the activation enthalpy compared with that found in the ageing of polymers reflects differences in the molecular species involved in relaxation processes.     

Total synthesis of lansiumamides A and B and alatamide

The total syntheses of lansiumamide A, lansiumamide B and alatamide have been completed taking advantage of the dihalo-olefination of N-formylimides. The syntheses are convergent, flexible and allow for the generation of analogues not accessible through other routes.     

Polarization-selective switching in holographically formed polymer dispersed liquid crystals

We have developed an optical stack of holographically formed polymer dispersed liquid-crystal (H-PDLC) devices that is fully operational with nonpolarized light sources. The device consists of two H-PDLC transmission gratings separated by a passive polarization rotator that can output a diffracted s-polarized, p-polarized, or s- and p-polarized beam simultaneously.     

Cold compaction of polymeric powders in tapered dies

Tests involving the cold compaction of four polymeric powders in circular section tapered dies were carried out to study the force transmitted through the powders. It was found that the decreasing cross-sectional area could be used to compensate for the force loss in order to keep the transmitted pressure high but the effect was not as large as had been anticipated. The optimum angle of taper was found to be in the region of 75 to 80°. A mathematical model was developed for the compaction of plastic powders in tapered dies. It was found that an equation of the type

could be used to prodict the transmitted pressured in a tapered die from a knowledge of the compaction characteristics for a cylindrical die.     

Q value of the superallowed decay of 46V and its influence on Vud and the unitarity of the Cabibbo-Kobayashi-Maskawa matrix

The masses of the radioactive nuclei (46)V and its decay daughter (46)Ti have been measured with the Canadian Penning Trap on-line Penning trap mass spectrometer to a precision of 1 x 10(-8). A Q(EC) value of 7052.90(40) keV for the superallowed beta decay of (46)V is obtained from the difference of these two masses. With this precise Q value, the Ft value for this decay is determined with improved precision. An investigation of an earlier Q-value measurement for (46)V uncovers a set of 7 measurements that cannot be reconciled with modern data and affects previous evaluations of V(ud) from superallowed Fermi decays. A new evaluation, adding our new data and removing the discredited subset, yields new values for G(V) and V(ud). When combined with recent results for V(us), this yields modified constraints for the unitarity of the Cabibbo-Kobayashi-Maskawa matrix and other extensions of the standard model.     

Cross sections and transverse single-spin asymmetries in forward neutral-pion production from proton collisions at sqrt[s]=200 GeV

Measurements of the production of forward high-energy pi(0) mesons from transversely polarized proton collisions at sqrt[s]=200 GeV are reported. The cross section is generally consistent with next-to-leading order perturbative QCD calculations. The analyzing power is small at x(F) below about 0.3, and becomes positive and large at higher x(F), similar to the trend in data at sqrt[s]< or =20 GeV. The analyzing power is in qualitative agreement with perturbative QCD model expectations. This is the first significant spin result seen for particles produced with p(T)>1 GeV/c at a polarized proton collider.     

Azimuthal anisotropy and correlations at large transverse momenta in p + p and Au + Au collisions at square root sNN=200 GeV

Results on high transverse momentum charged particle emission with respect to the reaction plane are presented for Au + Au collisions at square root s(NN)=200 GeV. Two- and four-particle correlations results are presented as well as a comparison of azimuthal correlations in Au + Au collisions to those in p + p at the same energy. The elliptic anisotropy v(2) is found to reach its maximum at p(t) approximately 3 GeV/c, then decrease slowly and remain significant up to p(t) approximately 7-10 GeV/c. Stronger suppression is found in the back-to-back high-p(t) particle correlations for particles emitted out of plane compared to those emitted in plane. The centrality dependence of v(2) at intermediate p(t) is compared to simple models based on jet quenching.     

High-speed horizontal-path atmospheric turbulence correction with a large-actuator-number microelectromechanical system spatial light modulator in an interferometric phase-conjugation engine

Results of atmospheric propagation for a high-speed, large-actuator-number adaptive optics system are presented. The system uses a microelectromechanical system- (MEMS-) based spatial light modulator correction device with 1024 actuators. Tests over a 1.35-km path achieved correction speeds in excess of 800 Hz and Strehl ratios close to 0.5. The wave-front sensor was based on a quadrature interferometer that directly measures phase. This technique does not require global wave-front reconstruction, making it relatively insensitive to scintillation and phase residues. The results demonstrate the potential of large-actuator-number MEMS-based spatial light modulators to replace conventional deformable mirrors.