Ultrafast dynamics of polybutadiene probed by optically heterodyne-detected optical-Kerr-effect spectroscopy

The ultrafast dynamics of polybutadiene have been studied using ultrafast optical-Kerr-effect spectroscopy. The data are compared with measurements on 1,3- and 1,4-pentadiene. The two diene derivatives have quite distinct subpicosecond dynamics, with an important contribution from an intramolecular torsional mode in the 1,4-derivative. The main part of the polymer spectral density can be assigned, by analogy with the data for 1,4-pentadiene, to intramolecular torsional motion about carbon–carbon single bonds. The picosecond diffusive orientational relaxation times of the dienes are not well described by simple hydrodynamics.     

Solid phase synthesis of 5-aminopyrazoles and derivatives

The development of a novel solid phase synthesis of some 5-aminopyrazoles and derivatives is described. Reaction of hydrazines with solid supported β-keto-nitrile (1) affords 5-aminopyrazoles (2) the amino group of which is readily acylated or sulphonylated. Generation of the solid supported β-keto-nitrile (1) is non trivial and represents a key step in the overall synthesis.     

A Flexible, Fast, and Optimal Modeling Approach Applied to Crew Rostering at London Underground

We present a general modeling approach to crew rostering and its application to computer-assisted generation of rotation-based rosters (or rotas) at the London Underground. Our goals were flexibility, speed, and optimality, and our approach is unique in that it achieves all three. Flexibility was important because requirements at the Underground are evolving and because specialized approaches in the literature did not meet our flexibility-implied need to use standard solvers. We decompose crew rostering into stages that can each be solved with a standard commercial MILP solver. Using a 167 MHz Sun UltraSparc 1 and CPLEX 4.0 MILP solver, we obtained high-quality rosters in runtimes ranging from a few seconds to a few minutes within 2% of optimality. Input data were takes from different depots with crew sizes ranging from 30–150 drivers, i.e., with number of duties ranging from about 200–1000. Using an argument based on decomposition and aggregation, we prove the optimality of our approach for the overall crew rostering problem.     

View factor for inclined plane with Gaussian source

The view factor (angle factor) for a differential inclined plane in the case of a radiating source of radially Gaussian intensity is considered. This information is useful for modelling of solar radiation in certain applications. The view factor is expressed in terms of two integrals, one of which is obtained in closed form in terms of special functions, and the other is approximated. A compact estimate for the view factor is presented which is suitable for machine computation. While the relative error associated with the final estimate is typically less than 0.01%, and in all cases, less than 0.2%, the method is easily extended to yield even greater accuracy.