A Finite Difference method for the Wide-Angle `Parabolic' equation in a waveguide with downsloping bottom

We consider the third-order wide-angle `parabolic' equation of underwater acoustics in a cylindrically symmetric fluid medium over a bottom of range-dependent bathymetry. It is known that the initial-boundary-value problem for this equation may not be well posed in the case of (smooth) bottom profiles of arbitrary shape if it is just posed e.g. with a homogeneous Dirichlet bottom boundary condition. In this paper we concentrate on downsloping bottom profiles and propose an additional boundary condition that yields a well posed problem, in fact making it $L^2$-conservative in the case of appropriate real parameters. We solve the problem numerically by a Crank-Nicolson-type finite difference scheme, which is proved to be unconditionally stable and second-order accurate, and simulates accurately realistic underwater acoustic problems.Comment: 2 figure

The enigmatic spin evolution of PSR J0537-6910: r-modes, gravitational waves and the case for continued timing

We discuss the unique spin evolution of the young X-ray pulsar PSR J0537-6910, a system in which the regular spin down is interrupted by glitches every few months. Drawing on the complete timing data from the Rossi X-ray Timing Explorer (RXTE, from 1999-2011), we argue that a trend in the inter-glitch behaviour points to an effective braking index close to $n=7$, much larger than expected. This value is interesting because it would accord with the neutron star spinning down due to gravitational waves from an unstable r-mode. We discuss to what extent this, admittedly speculative, scenario may be consistent and if the associated gravitational-wave signal would be within reach of ground based detectors. Our estimates suggest that one may, indeed, be able to use future observations to test the idea. Further precision timing would help enhance the achievable sensitivity and we advocate a joint observing campaign between the Neutron Star Interior Composition ExploreR (NICER) and the LIGO-Virgo network.Comment: 10 pages, 4 figures, emulate ApJ forma

Neutron star glitches have a substantial minimum size

Glitches are sudden spin-up events that punctuate the steady spin down of pulsars and are thought to be due to the presence of a superfluid component within neutron stars. The precise glitch mechanism and its trigger, however, remain unknown. The size of glitches is a key diagnostic for models of the underlying physics. While the largest glitches have long been taken into account by theoretical models, it has always been assumed that the minimum size lay below the detectability limit of the measurements. In this paper we define general glitch detectability limits and use them on 29 years of daily observations of the Crab pulsar, carried out at Jodrell Bank Observatory. We find that all glitches lie well above the detectability limits and by using an automated method to search for small events we are able to uncover the full glitch size distribution, with no biases. Contrary to the prediction of most models, the distribution presents a rapid decrease of the number of glitches below ~0.05 $\mu$Hz. This substantial minimum size indicates that a glitch must involve the motion of at least several billion superfluid vortices and provides an extra observable which can greatly help the identification of the trigger mechanism. Our study also shows that glitches are clearly separated from all the other rotation irregularities. This supports the idea that the origin of glitches is different to that of timing noise, which comprises the unmodelled random fluctuations in the rotation rates of pulsars.Comment: 8 pages; 4 figures. Accepted for publication in MNRA

Requirements upon Agreements in Favour of the NCC and the German Chambers – Clashing with the Brussels Ibis Regulation?

In recent years, the Netherlands and Germany have added themselves to the ever-growing number of countries opting for the creation of an international commercial court. The Netherlands Commercial Court (NCC) and the German Chambers for International Commercial Disputes (Kammern für internationale Handelssachen, KfiH) will conduct proceedings entirely in English and follow their own, diverging rules of civil procedure. Aspiring to become the future venues of choice in international commercial disputes, the NCC law and the legislative proposal for the establishment of the KfiH allow parties to agree on their jurisdiction and entail detailed provisions regulating such agreements. In particular, the NCC requires the parties’ express and in writing agreement to litigate before it. In a similar vein, the KfiH legislative proposal requires in some instances an express and in writing agreement. Although such strict formal requirements are justified by the need to safeguard the procedural rights of weaker parties such as small enterprises and protect them from the peculiarities of the NCC and the KfiH, this article questions their compliance with the requirements upon choice of court agreements under Article 25 (1) Brussels Ibis Regulation. By qualifying agreements in favour of the NCC and the KfiH first as functional jurisdiction agreements and then as procedural or court language agreements this article concludes that the formal requirements set by the NCC law and the KfiH proposal undermine the effectiveness of the Brussels Ibis Regulation, complicate the establishment of these courts’ jurisdiction and may thus threaten their attractiveness as future litigation destinations

Tailoring the specificity of the type C feruloyl esterase FoFaeC from Fusarium oxysporum towards methyl sinapate by rational redesign based on small molecule docking simulations

The type C feruloyl esterase FoFaeC from Fusarium oxysporum is a newly discovered enzyme with high potential for use in the hydrolysis of lignocellulosic biomass but it shows low activity towards sinapates. In this work, small molecule docking simulations were employed in order to identify important residues for the binding of the four model methyl esters of hydroxycinnamic acids, methyl ferulate/caffeate/sinapate/p-coumarate, to the predicted structure of FoFaeC. Subsequently rational redesign was applied to the enzyme’ active site in order to improve its specificity towards methyl sinapate. A double mutation (F230H/T202V) was considered to provide hydrophobic environment for stabilization of the methoxy substitution on sinapate and a larger binding pocket. Five mutant clones and the wild type were produced in Pichia pastoris and biochemically characterized. All clones showed improved activity, substrate affinity, catalytic efficiency and turnover rate compared to the wild type against methyl sinapate, with clone P13 showing a 5-fold improvement in catalytic efficiency. Although the affinity of all mutant clones was improved against the four model substrates, the catalytic efficiency and turnover rate decreased for the substrates containing a hydroxyl substitution