A Variational Approach to the Structure and Thermodynamics of Linear Polyelectrolytes with Coulomb and Screened Coulomb Interactions

A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between {\em all}monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as $N^3$ rather than $N^4$ as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed. An analysis of the high and low temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities.The accuracy of the approximations introduced are tested against Monte Carlo simulations for problem sizes ranging from $N=20$ to 1024. Very good accuracy is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the harmonic variational Ansatz becomes less efficient with shorter range interactions. As a by-product a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes -- 2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on low-$T$ approximations to end-end and monomer-monomer separations. It is argued that the former increases faster than linearly with the number of bonds.Comment: 40 pages LaTeX, 13 postscript figure

Design procedure for low-drag subsonic airfoils

Airfoil has least amount of drag under given restrictions of boundary layer transition position, lift coefficient, thickness ratio, and Reynolds number based on airfoil chord. It is suitable for use as wing and propeller aircraft sections operating at subsonic speeds and for hydrofoil sections and blades for fans, compressors, turbines, and windmills

Elucidating the Correlation of the Quasar \ion{Fe}{2}/\ion{Mg}{2} Ratio with Redshift

Interpretation of the \ion{Fe}{2}(UV)/\ion{Mg}{2} emission ratios from quasars has a major cosmological motivation. Both Fe and Mg are produced by short-lived massive stars. In addition, Fe is produced by accreting white dwarf supernovae somewhat after star formation begins. Therefore, we expect that the Fe/Mg ratio will gradually decrease with redshift. We have used data from the Sloan Digital Sky Survey to explore the dependence of the \ion{Fe}{2}(UV)/\ion{Mg}{2} ratio on redshift and on luminosity in the redshift range of $0.75< z< 2.20$, and we have used predictions from our 830-level model for the \ion{Fe}{2} atom in photoionization calculations to interpret our findings. We have split the quasars into several groups based upon the value of their \ion{Fe}{2}(UV)/\ion{Mg}{2} emission ratios, and then checked to see how the fraction of quasars in each group varies with the increase of redshift. We next examined the luminosity dependence of the \ion{Fe}{2}(UV)/\ion{Mg}{2} ratio, and we found that beyond a threshold of \ion{Fe}{2}(UV)/\ion{Mg}{2} =~ 5, and $M_{2500} < -25\rm mag$, the \ion{Fe}{2}(UV)/\ion{Mg}{2} ratio increases with luminosity, as predicted by our model. We interpret our observed variation of the \ion{Fe}{2}(UV)/\ion{Mg}{2} ratio with redshift as a result of the correlation of redshift with luminosity in a magnitude limited quasar sample.Comment: ApJL accepte

Submillimeter Atmospheric Transparency at Maunakea, at the South Pole, and at Chajnantor

For a systematic assessment of submillimeter observing conditions at different sites, we constructed tipping radiometers to measure the broad band atmospheric transparency in the window around 350 $\mu$m wavelength. The tippers were deployed on Maunakea, Hawaii, at the South Pole, and in the vicinity of Cerro Chajnantor in northern Chile. Identical instruments permit direct comparison of these sites. Observing conditions at the South Pole and in the Chajnantor area are better than on Maunakea. Simultaneous measurements with two tippers demonstrate conditions at the summit of Cerro Chajnantor are significantly better than on the Chajnantor plateau.Comment: Accepted by PAS

Flight investigation of insect contamination and its alleviation

An investigation of leading edge contamination by insects was conducted with a JetStar airplane instrumented to detect transition on the outboard leading edge flap and equipped with a system to spray the leading edge in flight. The results of airline type flights with the JetStar indicated that insects can contaminate the leading edge during takeoff and climbout. The results also showed that the insects collected on the leading edges at 180 knots did not erode at cruise conditions for a laminar flow control airplane and caused premature transition of the laminar boundary layer. None of the superslick and hydrophobic surfaces tested showed any significant advantages in alleviating the insect contamination problem. While there may be other solutions to the insect contamination problem, the results of these tests with a spray system showed that a continouous water spray while encountering the insects is effective in preventing insect contamination of the leading edges

EFFECTS OF TARIFFS AND TECHNICAL BARRIERS ON HIGH- AND LOW-VALUE POULTRY TRADE

A perfectly competitive spatial partial equilibrium model is constructed to evaluate some of the policy effects on world poultry trade. The model simulates the trade flows among six key exporting and importing countries and two aggregate rest-of-world regions. Effects of removal of restrictions based on tariffs, tariff-rate quotas (TRQs) and sanitary regulations are evaluated maintaining a distinction between "high-value" (mostly white meat) and "low-value" (mostly dark meat) poultry products. Results suggest that removal of sanitary barriers alone has relatively little effect compared to removal of tariffs and TRQs, but has more effect if sanitary and other barriers are removed simultaneously. Imposition of new sanitary barriers against US products by Russia would also shift trade flows, with production rising in Brazil.International Relations/Trade,