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.

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.

Photoproduction of heavy quarks in next-to-leading order QCD with longitudinally polarized initial states

We present all relevant details of our calculation of the complete next-to-leading order O(αS2α) QCD corrections to heavy flavor photoproduction with longitudinally polarized point-like photons and hadrons. In particular we provide analytical results for the virtual plus soft gluon cross section. We carefully address the relevance of remaining theoretical uncertainties by varying, for instance, the factorization and renormalization scales independently. Such studies are of importance for a meaningful first direct determination of the polarized gluon density Δg from the total charm production spin asymmetry by the upcoming COMPASS experiment. It is shown that the scale uncertainty is considerably reduced in next-to-leading order, but the dependence on the charm quark mass is sizable at fixed target energies. Finally, we study several differential single-inclusive heavy quark distributions and, for the polarized HERA option, the total bottom spin asymmetry.

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.

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.

Impact of hydrographic data assimilation on the modelled Atlantic meridional overturning circulation

Here we make an initial step toward the development of an ocean assimilation system that can constrain the modelled Atlantic Meridional Overturning Circulation (AMOC) to support climate predictions. A detailed comparison is presented of 1° and 1/4° resolution global model simulations with and without sequential data assimilation, to the observations and transport estimates from the RAPID mooring array across 26.5° N in the Atlantic. Comparisons of modelled water properties with the observations from the merged RAPID boundary arrays demonstrate the ability of in situ data assimilation to accurately constrain the east-west density gradient between these mooring arrays. However, the presence of an unconstrained "western boundary wedge" between Abaco Island and the RAPID mooring site WB2 (16 km offshore) leads to the intensification of an erroneous southwards flow in this region when in situ data are assimilated. The result is an overly intense southward upper mid-ocean transport (0–1100 m) as compared to the estimates derived from the RAPID array. Correction of upper layer zonal density gradients is found to compensate mostly for a weak subtropical gyre circulation in the free model run (i.e. with no assimilation). Despite the important changes to the density structure and transports in the upper layer imposed by the assimilation, very little change is found in the amplitude and sub-seasonal variability of the AMOC. This shows that assimilation of upper layer density information projects mainly on the gyre circulation with little effect on the AMOC at 26° N due to the absence of corrections to density gradients below 2000 m (the maximum depth of Argo). The sensitivity to initial conditions was explored through two additional experiments using a climatological initial condition. These experiments showed that the weak bias in gyre intensity in the control simulation (without data assimilation) develops over a period of about 6 months, but does so independently from the overturning, with no change to the AMOC. However, differences in the properties and volume transport of North Atlantic Deep Water (NADW) persisted throughout the 3 year simulations resulting in a difference of 3 Sv in AMOC intensity. The persistence of these dense water anomalies and their influence on the AMOC is promising for the development of decadal forecasting capabilities. The results suggest that the deeper waters must be accurately reproduced in order to constrain the AMOC.

The calculation of force constants and normal co-ordinates II: methyl fluoride

The mathematical difficulties which can arise in the force constant refinement procedure for calculating force constants and normal co-ordinates are described and discussed. The method has been applied to the methyl fluoride molecule, using an electronic computer. The best values of the twelve force constants in the most general harmonic potential field were obtained to fit twenty-two independently observed experimental data, these being the six vibration frequencies, three Coriolis zeta constants and two centrifugal stretching constants DJ and DJK, for both CH3F and CD3F. The calculations have been repeated both with and without anharmonicity corrections to the vibration frequencies. All the experimental data were weighted according to the reliability of the observations, and the corresponding standard errors and correlation coefficients of the force constants have been deduced. The final force constants are discussed briefly, and compared with previous treatments, particularly with a recent Urey-Bradley treatment for this molecule.

The microwave spectrum of thietan-2,2,4,4-d4

The microwave spectrum for thietan-2,2,4,4-d4 is analysed in six of its lowest puckering states and up to J = 25. The close lying pairs of states of vp = 0/1, 2/3 and 4/5 are treated with a vibration-rotation hamiltonian which includes an off-diagonal coupling term in vp. Additional corrections to this coupling term in higher powers of the angular momentum operator are derived and their importance for improving the fit of calculated to observed data is tested. The variation of the centrifugal distortion constants with vp follows the model of Creswell and Mills (1974, J. molec. Spectrosc., 52, 392). A value is determined for the derivative with respect to the puckering coordinate of the ac-component of the inverse moment of inertia tensor.

Improved fluorescent proteins for single-molecule research in molecular tracking and co-localization

Three promising variants of autofluorescent proteins have been analyzed photophysically for their proposed use in single-molecule microscopy studies in living cells to compare their superiority to other fluorescent proteins previously reported regarding the number of photons emitted. The first variant under investigation the F46L mutant of eYFP has a 10% greater photon emission rate and > 50% slower photobleaching rate on average than the standard eYFP fluorophore. The monomeric red fluorescent protein (mRFP) has a fivefold lower photon emission rate, likely due to the monomeric content, and also a tenfold faster photobleaching rate than the DsRed fluorescent protein. In contrast, the previously reported eqfp611 has a 50% lower emission rate yet photobleaches more than a factor 2 slowly. We conclude that the F46L YFP and the eqfp611 are superior new options for single molecule imaging and tracking studies in living cells. Studies were also performed on the effects of forced quenching of multiple fluorescent proteins in sub-micrometer regions that would show the effects of dimerization at low concentration levels of fluorescent proteins and also indicate corrections to stoichiometry patterns with fluorescent proteins previously in print. We also introduce properties at the single molecule level of new FRET pairs with combinations of fluorescent proteins and artificial fluorophores.

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, $\chi N \rightarrow \infty$. However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to $\chi N = 512,000$, by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.