A new analytical potential energy surface is presented for the reaction of hydrogen abstraction from methane by a hydrogen atom. It is based on an analytical expression proposed by Jordan and Gilbert [J. Chem. Phys. 102, 5669 (1995)], and its fittable parameters were obtained by a multibeginning optimization procedure to reproduce high-level ab initio electronic structure calculations obtained at the CCSD(T)/cc-pVTZ level. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath. No experimental information is used. By comparison with the reference results we show that the resulting surface reproduces well not only the ab initio data used in the fitting but also other thermochemical and kinetic results computed at the same ab initio level, such as equilibrium constants, rate constants, and kinetic isotope effects, which were not used in the fit. In this way we show that the new potential energy surface is correctly fitted and almost as accurate as the CCSD(T)/cc-pVTZ method in describing the kinetics of the reaction. We analyze the limitations of the functional form and the fitting method employed, and suggest some solutions to their drawbacks. In a forthcoming communication, we test the quality of the new surface by comparing its results with experimental values.

Motivated by some relevant physical applications, we study the existence and uniqueness of T-periodic solutions for a second order differential equation with a piecewise constant singularity which changes sign. Other questions like the stability and robustness of the periodic solution are considered.

Maintenance of the rail track plays an important role in the policies that promote railway transport in the European Union. Each member state has its own railway infrastructure manager that is regulated by the standards set by the European Committee for Standardization (CEN). The standards define three levels for the track geometric quality: the alert limit (AL), the intervention limit (IL), and the immediate action limit (IAL). In the United States, the Federal Railroad Administration (FRA) manages the railroad safety and national rail transportation policy. They classify nine classes of tracks depending on the maximum allowable speed for freight and passenger trains; each classification has its own track geometric limits from nominal values. Usually, track-survey cars are used to measure the parameters of the geometric quality of the tracks in long sectors, whereas traditional surveying methods (TSMs) or an automated measuring system based on a track-surveying trolley assisted by a robotic total station is chosen for short sectors. In this paper, the authors analyze the precision and performance obtained with the TSM and with an automatic measuring system in its different working modes (stop and go and kinematic), comparing the measured geometric values with the nominal values for a section of a track. The results indicate that TSM and stop-and-go modes yield similar precisions, so both methods can be used to detect the geometric quality levels defined in the CEN and FRA standards. In contrast, kinematic is less accurate, so there are situations where it cannot be used to determine the geometric quality levels. Finally, the authors discuss some recommendations to improve the performance and working methods with the track-surveying trolley.