Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

Pressure drop of gas–liquid Taylor flow in round micro-capillaries for low to intermediate Reynolds numbers

In this paper, a model is presented that describes the pressure drop of gas-liquid Taylor flow in round capillaries with a channel diameter typically less than 1 mm. The analysis of Bretherton (J Fluid Mech 10:166-188, 1961) for the pressure drop over a single gas bubble for vanishing liquid film thickness is extended to include a non-negligible liquid film thickness using the analysis of Aussillous and Qu,r, (Phys Fluids 12(10):2367-2371, 2000). This result is combined with the Hagen-Poiseuille equation for liquid flow using a mass balance-based Taylor flow model previously developed by the authors (Warnier et al. in Chem Eng J 135S:S153-S158, 2007). The model presented in this paper includes the effect of the liquid slug length on the pressure drop similar to the model of Kreutzer et al. (AIChE J 51(9):2428-2440, 2005). Additionally, the gas bubble velocity is taken into account, thereby increasing the accuracy of the pressure drop predictions compared to those of the model of Kreutzer et al. Experimental data were obtained for nitrogen-water Taylor flow in a round glass channel with an inner diameter of 250 mu m. The capillary number Ca (gl) varied between 2.3 x 10(-3) and 8.8 x 10(-3) and the Reynolds number Re (gl) varied between 41 and 159. The presented model describes the experimental results with an accuracy of +/- 4% of the measured values.

Mixed radix Reed-Muller expansions

The choice of radix is crucial for multi-valued logic synthesis. Practical examples, however, reveal that it is not always possible to find the optimal radix when taking into consideration actual physical parameters of multi-valued operations. In other words, each radix has its advantages and disadvantages. Our proposal is to synthesise logic in different radices, so it may benefit from their combination. The theory presented in this paper is based on Reed-Muller expansions over Galois field arithmetic. The work aims to firstly estimate the potential of the new approach and to secondly analyse its impact on circuit parameters down to the level of physical gates. The presented theory has been applied to real-life examples focusing on cryptographic circuits where Galois Fields find frequent application. The benchmark results show the approach creates a new dimension for the trade-off between circuit parameters and provides information on how the implemented functions are related to different radices.

Rayleigh-Taylor Instability of an Ultrathin Foil Accelerated by the Radiation Pressure of an Intense Laser

We report experimental evidence for a Rayleigh-Taylor-like instability driven by radiation pressure of an ultraintense (1021W/cm2) laser pulse. The instability is witnessed by the highly modulated profile of the accelerated proton beam produced when the laser irradiates a 5 nm diamondlike carbon (90% C, 10% H) target. Clear anticorrelation between bubblelike modulations of the proton beam and transmitted laser profile further demonstrate the role of the radiation pressure in modulating the foil. Measurements of the modulation wavelength, and of the acceleration from Doppler-broadening of back-reflected light, agree quantitatively with particle-in-cell simulations performed for our experimental parameters and which confirm the existence of this instability. © 2012 American Physical Society.

Asymmetric Total Synthesis of (+)-Inthomycin C Via O-Directed Free Radical Alkyne Hydrostannation with Ph3SnH and Catalytic Et3B: Reinstatement of the Zeeck-Taylor (3R)-Structure for (+)-Inthomycin C

A new pathway to (+)-inthomycin C is reported that exploits an O-directed free radical hydrostannation reaction on (−)-12 and a Stille cross-coupling as key steps. Significantly, the latter process was effected on 19 where a gauche-pentane repulsive interaction could interfere. Our stereochemical studies on the alkynol (−)-12 and the enyne (+)-7 confirm that Ryu and Hatakeyama’s (3S)-stereochemical revision of (+)-inthomycin C is invalid and that Zeeck and Taylor’s original (3R)-stereostructure for (+)-inthomycin C is correct.