Improvements to air mass calculations for ground-based infrared measurements

High-resolution ground-based infrared solar spectra are routinely recorded at the Network for the Detection of Stratospheric Change (NDSC) stations. These data sets play a key role in providing a long-term record of atmospheric composition and their links to climate change. The analysis of observed infrared spectra involves comparison to a computer-modeled atmosphere where knowledge of the air mass distribution is an essential component. This note summarises improvements made to an existing and widely used computer code (FSCATM) to perform refractive ray-tracing and calculation of the air mass distribution. Changes were made towards higher vertical resolution in the troposphere and increased numerical precision. The revised FSCATM improves the analysis of infrared spectra mostly through the more accurate representation of the temperature profile. Air mass differences with respect to earlier versions are documented and are typically <0.7%, exceptions being extreme cases of inversion layers. The current version provides ray tracing and air mass calculations for any terrestrial observation site. The output files are reported in a format compatible with the SFIT and SFIT2 retrieval algorithms, which are widely used for NDSC infrared atmospheric studies. The improved computer code, documentation, reference profiles, and test cases are available electronically.     

Sensitivity of trust-region algorithms to their parameters

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of extensive numerical tests. MSC classification: 65K05, 90C26, 90C30     

Structure–electrical property study of anisotropic polyaniline films

The relationships of the structure and electrical properties of anisotropic HCl‐doped polyaniline (PANI) films cast from N,N′‐dimethylpropylene urea (DMPU) solutions and stretched to different draw ratios were studied. The anisotropic structure of the stretched PANI films was examined by X‐ray diffraction, near‐infrared wave‐guide coupling, and polarized infrared measurements. The PANI emeraldine base (EB) films cast from DMPU solutions had a single‐phase noncrystalline structure, and stretching of the films did not cause crystallization to occur. The transition moment angles of two weakly absorbing infrared bands were determined, and the Hermans' orientation functions for the PANI EB films were calculated. The PANI films were then doped with HCl, and the electrical properties were determined by impedance spectroscopy. With a specially designed test fixture, the in‐plane and through‐plane impedance was obtained. The conductivity along the stretch direction increased with orientation. The in‐plane conductivity was significantly higher than the through‐plane conductivity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 823–841, 2003     

Thiol–norbornene materials: Approaches to develop high Tg thiol–ene polymers

The ability to prepare high T_g low shrinkage thiol–ene materials is attractive for applications such as coatings and dental restoratives. However, thiol and nonacrylated vinyl materials typically consist of a flexible backbone, limiting the utility of these polymers. Hence, it is of importance to synthesize and investigate thiol and vinyl materials of varying backbone chemistry and stiffness. Here, we investigate the effect of backbone chemistry and functionality of norbornene resins on polymerization kinetics and glass transition temperature (T_g) for several thiol–norbornene materials. Results indicate that T_gs as high as 94 °C are achievable in thiol–norbornene resins of appropriately controlled chemistry. Furthermore, both the backbone chemistry and the norbornene moiety are important factors in the development of high T_g materials. In particular, as much as a 70 °C increase in T_g was observed in a norbornene–thiol specimen when compared with a sample prepared using allyl ether monomer of analogous backbone chemistry. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5686–5696, 2007     

Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems

Multi-valued solutions are constructed for 2 × 2 first-order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non-zero 3-jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non-tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizable n-th order system for which there are exactly two speeds. © 1993 John Wiley & Sons, Inc.     

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.     

Staffing Rosters with Breaks — A Case Study

A complex manual rostering system for directory assistance, telephone operators has been rationalized and the technique of integer programming used to automatically generate staff rosters. These rosters can be generated by relatively unskilled clerical staff. They result in operator costs comparable to manually generated rosters and can be produced in a fraction of the time taken to produce their manual counterparts. Implementation is reported.     

Ab initio potential energy surface and pressure broadening coefficients for the He-CH3F complex

Symmetry-adapted perturbation theory has been applied to compute the He-CH₃F potential with the CH₃F molecule assumed rigid. The potential has a global minimum of −48.9 cm⁻¹ at the center of mass separation of 7.2 bohr with the helium atom lying along the C-F bond on the hydrogen’s side. The computed points were fitted to an analytic energy surface with a correct asymptotic behaviour. This potential has been used to compute the pressure broadening (PB) coefficients for the (j, k) = (0, 0) → (1, 0) and (1, 0) → (2, 0) rotational transitions of CH₃F perturbed by helium for a wide range of temperatures. Close-coupling results are compared with the experimental data of Willey et al. [J. Chem. Phys. 97 (1992) 4723], Beaky et al. [J. Mol. Struct. 352/353 (1995) 245] and infinite order sudden results are compared with those of Grigoriev et al. [J. Mol. Struct. 186 (1997) 48] for the ν₆ band of CH₃F perturbed by helium at room temperature. To our knowledge, present work is the first attempt of making fully ab initio calculations of collisional cross-sections and pressure broadening coefficients for this simple symmetric top system at low and room temperature.