Constructing a polynomial whose nodal set is the three-twist knot 525_2

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_2$. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain complex polynomial which depends on an additional parameter. For sufficiently small values of this parameter, the nodal lines form the three-twist knot. Further mathematical properties of this map are explored, including the relationship of the phase critical points with the Morse-Novikov number, which is nonzero as this knot is not fibred. We also find analogous functions for other knots with six crossings. The particular function we find, and the general procedure, should be useful for designing knotted fields of particular knot types in various physical systems.Comment: 19 pages, 6 figure

Conceptual design study of a Harrier V/STOL research aircraft

MCAIR recently completed a conceptual design study to define modification approaches to, and derive planning prices for the conversion of a two place Harrier to a V/STOL control, display and guidance research aircraft. Control concepts such as rate damping, attitude stabilization, velocity command, and cockpit controllers are to be demonstrated. Display formats will also be investigated, and landing, navigation and guidance systems flight tested. The rear cockpit is modified such that it can be quickly adapted to faithfully simulate the controls, displays and handling qualities of a Type A or Type B V/STOL. The safety pilot always has take command capability. The modifications studied fall into two categories: basic modifications and optional modifications. Technical descriptions of the basic modifications and of the optional modifications are presented. The modification plan and schedule as well as the test plan and schedule are presented. The failure mode and effects analysis, aircraft performance, aircraft weight, and aircraft support are discussed

ZZE-Configuration of chromophore ß-153 in C-phycocyanin from Mastigocladus laminosus

The photochemistry of C-phycocyanin has been studied after denaturation in the dark. It shows an irreversible reaction which has characteristics of a Ζ,Ζ,Ε- to Z,Z,Z-isomerization of dihydrobilins. Its amplitude depends on the reaction conditions, with a maximum corresponding to 15% conversion of one of the three PC chromophores. This chromophore is suggested to be ß-153, for which recent X-ray data T. Schirmer, W. Bode, and R. Huber, J. Mol. Biol., submitted, show ring D being highly twisted out of the plane of the other rings. During unfolding, there is thus a probability of falling into the photochemically labile Z,Z,^-configuration

The multifrequency behaviour of the recurrent nova RS Ophiuchi

This review concentrates on the multifrequency behaviour of RS Ophiuchi and in particular during its latest outburst. Confirmation of the 1945 outburst, bipolar outflows and its possible fate as a Type Ia Supernova are discussed.Comment: 5 pages, 5 figures, in The Golden Age of Cataclysmic Variables and Related Objects, F. Giovannelli & L. Sabau-Graziati (eds.), Mem. SAIt. 83 N.2 (in press

Improving Performance of Iterative Methods by Lossy Checkponting

Iterative methods are commonly used approaches to solve large, sparse linear systems, which are fundamental operations for many modern scientific simulations. When the large-scale iterative methods are running with a large number of ranks in parallel, they have to checkpoint the dynamic variables periodically in case of unavoidable fail-stop errors, requiring fast I/O systems and large storage space. To this end, significantly reducing the checkpointing overhead is critical to improving the overall performance of iterative methods. Our contribution is fourfold. (1) We propose a novel lossy checkpointing scheme that can significantly improve the checkpointing performance of iterative methods by leveraging lossy compressors. (2) We formulate a lossy checkpointing performance model and derive theoretically an upper bound for the extra number of iterations caused by the distortion of data in lossy checkpoints, in order to guarantee the performance improvement under the lossy checkpointing scheme. (3) We analyze the impact of lossy checkpointing (i.e., extra number of iterations caused by lossy checkpointing files) for multiple types of iterative methods. (4)We evaluate the lossy checkpointing scheme with optimal checkpointing intervals on a high-performance computing environment with 2,048 cores, using a well-known scientific computation package PETSc and a state-of-the-art checkpoint/restart toolkit. Experiments show that our optimized lossy checkpointing scheme can significantly reduce the fault tolerance overhead for iterative methods by 23%~70% compared with traditional checkpointing and 20%~58% compared with lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1

The symbiotic star CH Cygni. III. A precessing radio jet

VLA, MERLIN and Hubble Space Telescope imaging observations of the extended regions of the symbiotic system CH Cygni are analysed. These extensions are evidence of a strong collimation mechanism, probably an accretion disk surrounding the hot component of the system. Over 16 years (between 1985 and 2001) the general trend is that these jets are seen to precess. Fitting a simple ballistic model of matter ejection to the geometry of the extended regions suggests a period of 6520 +/- 150 days, with a precession cone opening angle of 35 +/- 1 degrees. This period is of the same order as that proposed for the orbital period of the outer giant in the system, suggesting a possible link between the two. Anomalous knots in the emission, not explained by the simple model, are believed to be the result of older, slower moving ejecta, or possibly jet material that has become disrupted through sideways interaction with the surrounding medium.Comment: 9 pages, 4 figure