Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes

This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance $\mu \propto L^{-1}$ from the substrate, where $L$ is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance $\xi \propto L^{-1/3}$. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.

Next-to-leading order QCD corrections to the polarized hadroproduction of heavy flavors

We present the complete next-to-leading order QCD corrections to the polarized hadroproduction of heavy flavors which soon will be studied experimentally in polarized pp collisions at the BNL Relativistic Heavy Ion Collider (RHIC) in order to constrain the polarized gluon density Δg. It is demonstrated that the dependence on unphysical renormalization and factorization scales is strongly reduced beyond the leading order. The sensitivity of the charm quark spin asymmetry to Δg is analyzed in some detail, including the limited detector acceptance for leptons from charm quark decays at the BNL RHIC.

Next-to-leading order QCD corrections to the polarized photoproduction of heavy flavors

We present a calculation of the next-to-leading order ... QCD corrections to heavy flavor photoproduction with longitudinally polarized beams. We apply our results to study the longitudinal spin asymmetry for the total charm quark production cross section which will be utilized by the forthcoming COMPASS experiment at CERN to obtain first direct information on the polarized gluon density Δg. We also briefly discuss the main theoretical uncertainties inherent in this calculation. In particular we demonstrate that the factorization scale dependence is considerably reduced in next-to-leading order.

NLO QCD Corrections to the Polarized Photo- and Hadroproduction of Heavy Quarks

The complete details of our calculation of the NLO QCD corrections to heavy flavor photo- and hadroproduction with longitudinally polarized initial states are presented. The main motivation for investigating these processes is the determination of the polarized gluon density at the COMPASS and RHIC experiments, respectively, in the near future. All methods used in the computation are extensively documented, providing a self-contained introduction to this type of calculations. Some employed tools also may be of general interest, e.g., the series expansion of hypergeometric functions. The relevant parton level results are collected and plotted in the form of scaling functions. However, the simplification of the obtained gluon-gluon virtual contributions has not been completed yet. Thus NLO phenomenological predictions are only given in the case of photoproduction. The theoretical uncertainties of these predictions, in particular with respect to the heavy quark mass, are carefully considered. Also it is shown that transverse momentum cuts can considerably enhance the measured production asymmetries. Finally unpolarized heavy quark production is reviewed in order to derive conditions for a successful interpretation of future spin-dependent experimental data.

On the importance of Vaisala RS92 radiosonde humidity corrections for a better agreement between measured and modeled satellite radiances

A study has been carried out to assess the importance of radiosonde corrections in improving the agreement between satellite and radiosonde measurements of upper-tropospheric humidity. Infrared [High Resolution Infrared Radiation Sounder (HIRS)-12] and microwave [Advanced Microwave Sounding Unit (AMSU)-18] measurements from the NOAA-17 satellite were used for this purpose. The agreement was assessed by comparing the satellite measurements against simulated measurements using collocated radiosonde profiles of the Atmospheric Radiation Measurement (ARM) Program undertaken at tropical and midlatitude sites. The Atmospheric Radiative Transfer Simulator (ARTS) was used to simulate the satellite radiances. The comparisons have been done under clear-sky conditions, separately for daytime and nighttime soundings. Only Vaisala RS92 radiosonde sensors were used and an empirical correction (EC) was applied to the radiosonde measurements. The EC includes correction for mean calibration bias and for solar radiation error, and it removes radiosonde bias relative to three instruments of known accuracy. For the nighttime dataset, the EC significantly reduces the bias from 0.63 to 20.10 K in AMSU-18 and from 1.26 to 0.35 K in HIRS-12. The EC has an even greater impact on the daytime dataset with a bias reduction from 2.38 to 0.28 K in AMSU-18 and from 2.51 to 0.59 K in HIRS-12. The present study promises a more accurate approach in future radiosonde-based studies in the upper troposphere.

Evaluation of the use of radiosonde humidity data to predict the occurrence of persistent contrails

Regular visual observations of persistent contrails over Reading, UK, have been used to evaluate radiosonde measurements of temperature and humidity defining cold ice-supersaturated atmospheric regions which are assumed to be a necessary condition for persistent condensation trails (contrails) to form. Results show a good correlation between observations and predictions using data from Larkhill, 63 km from Reading. A statistical analysis of this result and the forecasts using data from four additional UK radiosonde stations are presented. The horizontal extent of supersaturated layers could be inferred from this to be several hundred kilometres. The necessity of bias corrections to radiosonde humidity measurements is discussed and an analysis of measured ice-supersaturated atmospheric layers in the troposphere is presented. It is found that ice supersaturation is more likely to occur in winter than in summer, with frequencies of 17.3% and 9.4%, respectively, which is mostly due to the layers being thicker in winter than in summer. The most probable height for them to occur is about 10 km.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Resistivity imaging survey of the Roman barrows at Bartlow, Cambridgeshire, UK

Resistivity imaging was carried out on four large Roman barrows at Bartlow in Cambridgeshire. The geophysical survey formed part of a wider research project designed to record and assess the landscape context of the largest surviving Roman burial mounds in Britain. The barrows today range in height from 6.6 m to 13.2 m and their steep profile loosed particular practical and modelling challenges. Data were obtained using a Campus Geopulse resistance meter with up to 50 electrodes spaced at 1 m intervals and lines up to 76 m long. A total of 24 lines was obtained. Topographic corrections were applied to the pseudosections, whichwere inverted using Res 2 Dinv and Res3 Dinv. Resistivity imaging was particularly successful in identifying evidence for the antiquarian explorations of the site. Central collapse features or in-filled tunnels image as high resistance features in all barrows and in one (Barrow IV) there is also a low resistance feature in the approximate position of a known antiquarian tunnel. Barrow VI had a thick covering of high-resistivity that may relate to nineteenth century landscaping and reconstruction of this monument. Resistivity imaging also revealed possible evidence for ancient revetments in all four large barrows. Copyright (c) 2006 John Wiley & Sons, Ltd.

Mersenne numbers

These notes have been issued on a small scale in 1983 and 1987 and on request at other times. This issue follows two items of news. First, WaIter Colquitt and Luther Welsh found the 'missed' Mersenne prime M110503 and advanced the frontier of complete Mp-testing to 139,267. In so doing, they terminated Slowinski's significant string of four consecutive Mersenne primes. Secondly, a team of five established a non-Mersenne number as the largest known prime. This result terminated the 1952-89 reign of Mersenne primes. All the original Mersenne numbers with p < 258 were factorised some time ago. The Sandia Laboratories team of Davis, Holdridge & Simmons with some little assistance from a CRAY machine cracked M211 in 1983 and M251 in 1984. They contributed their results to the 'Cunningham Project', care of Sam Wagstaff. That project is now moving apace thanks to developments in technology, factorisation and primality testing. New levels of computer power and new computer architectures motivated by the open-ended promise of parallelism are now available. Once again, the suppliers may be offering free buildings with the computer. However, the Sandia '84 CRAY-l implementation of the quadratic-sieve method is now outpowered by the number-field sieve technique. This is deployed on either purpose-built hardware or large syndicates, even distributed world-wide, of collaborating standard processors. New factorisation techniques of both special and general applicability have been defined and deployed. The elliptic-curve method finds large factors with helpful properties while the number-field sieve approach is breaking down composites with over one hundred digits. The material is updated on an occasional basis to follow the latest developments in primality-testing large Mp and factorising smaller Mp; all dates derive from the published literature or referenced private communications. Minor corrections, additions and changes merely advance the issue number after the decimal point. The reader is invited to report any errors and omissions that have escaped the proof-reading, to answer the unresolved questions noted and to suggest additional material associated with this subject.

Evaluation of the S(T) assimilation method with the Argo dataset

Recent observations from the Argo dataset of temperature and salinity profiles are used to evaluate a series of 3-year data assimilation experiments in a global ice–ocean general circulation model. The experiments are designed to evaluate a new data assimilation system whereby salinity is assimilated along isotherms, S(T ). In addition, the role of a balancing salinity increment to maintain water mass properties is investigated. This balancing increment is found to effectively prevent spurious mixing in tropical regions induced by univariate temperature assimilation, allowing the correction of isotherm geometries without adversely influencing temperature–salinity relationships. In addition, the balancing increment is able to correct a fresh bias associated with a weak subtropical gyre in the North Atlantic using only temperature observations. The S(T ) assimilation method is found to provide an important improvement over conventional depth level assimilation, with lower root-mean-squared forecast errors over the upper 500 m in the tropical Atlantic and Pacific Oceans. An additional set of experiments is performed whereby Argo data are withheld and used for independent evaluation. The most significant improvements from Argo assimilation are found in less well-observed regions (Indian, South Atlantic and South Pacific Oceans). When Argo salinity data are assimilated in addition to temperature, improvements to modelled temperature fields are obtained due to corrections to model density gradients and the resulting circulation. It is found that observations from the Argo array provide an invaluable tool for both correcting modelled water mass properties through data assimilation and for evaluating the assimilation methods themselves.