Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

The interstellar gas-phase formation of CO2 – Assisted or not by water molecules?

Using state of the art methods of quantum chemistry, potential energy surfaces for the formation of and CO₂ (³B₂) from CO + O (¹D) and CO + O (³P), respectively, have been studied. At the MRSDCI level, we show that the formation of from O (³P) is strongly connected with the height of the barrier localized on the CO + O (³P) entrance channel. At the CCSD(T) level with a large basis set we calculate this barrier to be 5.9 kcal/mol. Consequently, we confirm that the gas-phase formation of CO₂ in interstellar molecular clouds is inefficient. To mimic the formation of CO₂, through the Eley–Rideal mechanism, on the water ice surfaces of interstellar grains, we have extended our study to consider the formation of CO₂ in the presence of water molecules. We show, using density functional and CCSD(T) methods, that the barrier located on the CO + O (³P) reaction entrance channel is hardly affected by the presence of water molecules. We therefore suggest that CO₂ formation, through the Eley–Rideal mechanism, on the water ice surfaces of interstellar grains, should be inefficient too.     

Comparison of Scintillation Detection Efficiencies of Depleted Uranium (DU) in Wounds

Three tissue-equivalent cylindrical wound phantoms with varying activities of DU metal imbedded at varying depths were used to compare the efficiencies of a bismuth germinate (BGO) detector, a sodium iodide (NaI), and two identical wound probes with smaller sodium iodide crystals. Our results show that the BGO detector had the highest efficiency (1.0·10^-3) and the lowest minimum detectable activity (MDA = 5.8 kBq) for the shallow depth DU phantom, relative to the other detectors. The BGO detector also had the highest peak efficiencies (1.7·10^-3 and 5.8·10^-4) and the lowest MDAs (3.5 and 10.0 kBq) for the medium and deep phantoms, respectively. Other detectors' performance data are presented.     

Order selection for heteroscedastic autoregression: A study on concentration

We consider an autoregressive model where the variance is allowed to be a function of time, unconditional on the past. Pötscher (1989) has proven that, regardless of the shape of the variance function, order selection can be made consistently. However, this procedure does not account for the non-stationary behavior. We consider the concentration of the variance function and its effect on order selection. We show that an order free estimate of the variance function can be constructed and propose an order selection criterion based on this estimate. Consistency is established and simulation results verify a large increase in the probability of selecting the correct order for finite samples.     

Modification of the velocity distribution of H(2) molecules in a supersonic beam by intense pulsed optical gradients

We report the acceleration and deceleration of H(2) molecules in a supersonic molecular beam by means of its interaction with an intense optical gradient from a nanosecond far-off-resonant optical pulse. The strong optical gradients are formed in the interference pattern of two intense optical pulses at 532 nm. The velocity distribution of the molecular beam, before and after the applied optical pulse, is measured by a velocity-mapped ion imaging technique. Changes in velocity up to 202 m s(-1)+/- 61 m s(-1) are observed in a molecular beam initially travelling at a mean speed of 563 m s(-1). We report the dependence of this change in velocity with the strength of the optical gradient applied.     

Cyclic Relative Difference Sets and their p-Ranks

By modifying the constructions in Helleseth et al. [10] and No [15], we construct a family of cyclic ((q ^3k –1)/(q–1), q–1, q ^3k–1, q ^3k–2) relative difference sets, where q=3 ^e . These relative difference sets are liftings of the difference sets constructed in Helleseth et al. [10] and No [15]. In order to demonstrate that these relative difference sets are in general new, we compute p-ranks of the classical relative difference sets and 3-ranks of the newly constructed relative difference sets when q=3. By rank comparison, we show that the newly constructed relative difference sets are never equivalent to the classical relative difference sets, and are in general inequivalent to the affine GMW difference sets.