Local bifurcations in differential equations with state-dependent delay

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this record.A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDEJ.S. gratefully acknowledges the financial support of the EPSRC via grants EP/N023544/1 and EP/N014391/1. J.S. has also received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement number 643073

Energy Dissipation on Stepped Spillways

The author provided interesting data on stepped spillway flows. The writer would like to add some information on flow resistance of skimming flows and discuss the energy dissipation on stepped chutes. It will be shown that the author's results are not dissimilar with results previously obtained by other researchers

Probing the centre of the large circumstellar disc in M17

We investigated the nature of the hitherto unresolved elliptical infrared emission in the centre of the ~20000 AU disc silhouette in M 17. We combined high-resolution JHKsL'M' band imaging carried out with NAOS/CONICA at the VLT with [Fe II] narrow band imaging using SOFI at the NTT. The analysis is supported by Spitzer/GLIMPSE archival data and by already published SINFONI/VLT Integral Field Spectroscopy data. For the first time, we resolve the elongated central infrared emission into a point-source and a jet-like feature that extends to the northeast in the opposite direction of the recently discovered collimated H2 jet. They are both orientated almost perpendicular to the disc plane. In addition, our images reveal a curved southwestern emission nebula whose morphology resembles that of the previously detected northeastern one. Both nebulae are located at a distance of 1500 AU from the disc centre. We describe the infrared point-source in terms of a protostar that is embedded in circumstellar material producing a visual extinction of 60 <= Av <= 82. The observed Ks band magnitude is equivalent to a stellar mass range of 2.8 Msun <= Mstar <= 8 Msun adopting conversions for a main-sequence star. Altogether, we suggest that the large M 17 accretion disc is forming an intermediate to high-mass protostar. Part of the accreted material is expelled through a symmetric bipolar jet/outflow.Comment: 6 pages, 3 figures, accepted by MNRAS (16 May 2008

Interferon β-1a in relapsing multiple sclerosis: four-year extension of the European IFNβ-1a Dose-C omparison Study

Background: Multiple sclerosis (MS) is a chronic disease requiring long-term monitoring of treatment. Objective: To assess the four-year clinical efficacy of intramuscular (IM) IFNb-1a in patients with relapsing MS from the European IFNb-1a Dose-C omparison Study. Methods: Patients who completed 36 months of treatment (Part 1) of the European IFNb-1a Dose-C omparison Study were given the option to continue double-blind treatment with IFNb-1a 30 mcg or 60 mcg IM once weekly (Part 2). Analyses of 48-month data were performed on sustained disability progression, relapses, and neutralizing antibody (NA b) formation. Results: O f 608/802 subjects who completed 36 months of treatment, 493 subjects continued treatment and 446 completed 48 months of treatment and follow-up. IFNb-1a 30 mcg and 60 mcg IM once weekly were equally effective for up to 48 months. There were no significant differences between doses over 48 months on any of the clinical endpoints, including rate of disability progression, cumulative percentage of patients who progressed (48 and 43, respectively), and annual relapse rates; relapses tended to decrease over 48 months. The incidence of patients who were positive for NAbs at any time during the study was low in both treatment groups. Conclusion: C ompared with 60-mcg IM IFNb-1a once weekly, a dose of 30 mcg IM IFNb-1a once weekly maintains the same clinical efficacy over four years

Camera-based in-process quality measurement of hairpin welding

The technology of hairpin welding, which is frequently used in the automotive industry, entails high-quality requirements in the welding process. It can be difficult to trace the defect back to the affected weld if a non-functioning stator is detected during the final inspection. Often, a visual assessment of a cooled weld seam does not provide any information about its strength. However, based on the behavior during welding, especially about spattering, conclusions can be made about the quality of the weld. In addition, spatter on the component can have serious consequences. In this paper, we present in-process monitoring of laser-based hairpin welding. Using an in-process image analyzed by a neural network, we present a spatter detection method that allows conclusions to be drawn about the quality of the weld. In this way, faults caused by spattering can be detected at an early stage and the affected components sorted out. The implementation is based on a small data set and under consideration of a fast process time on hardware with limited computing power. With a network architecture that uses dilated convolutions, we obtain a large receptive field and can therefore consider feature interrelation in the image. As a result, we obtain a pixel-wise classifier, which allows us to infer the spatter areas directly on the production lines

Power dependence of supercontinuum noise in uniform and tapered PCFs

An error was made in the calculation of the relative intensity noise (RIN) because of an incorrectly specified value of the photodetector DC transimpedance gain