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

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

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

Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richness-dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with \Omega_m = 0.3 and, for comparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high redshift clusters are clustered more strongly (in comoving scale) than low redshift clusters of the same mass. The increased correlations with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation-scale versus cluster mean separation relation, R_0 - d, is found to be, remarkably, independent of redshift to z <~ 2 for LCDM and z <~ 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving R_0 - d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters so that the R_0 - d relation remains essentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ~ 0 and provide precise determination of cosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200

Thermal radio emission from novae & symbiotics with the Square Kilometre Array

The thermal radio emission of novae during outburst enables us to derive fundamental quantities such as the ejected mass, kinetic energy, and density profile of the ejecta. Recent observations with newly-upgraded facilities such as the VLA and e-MERLIN are just beginning to reveal the incredibly complex processes of mass ejection in novae (ejections appear to often proceed in multiple phases and over prolonged timescales). Symbiotic stars can also exhibit outbursts, which are sometimes accompanied by the expulsion of material in jets. However, unlike novae, the long-term thermal radio emission of symbiotics originates in the wind of the giant secondary star, which is irradiated by the hot white dwarf. The effect of the white dwarf on the giant's wind is strongly time variable, and the physical mechanism driving these variations remains a mystery (possibilities include accretion instabilities and time-variable nuclear burning on the white dwarf's surface). The exquisite sensitivity of SKA1 will enable us to survey novae throughout the Galaxy, unveiling statistically complete populations. With SKA2 it will be possible to carry out similar studies in the Magellanic Clouds. This will enable high-quality tests of the theory behind accretion and mass loss from accreting white dwarfs, with significant implications for determining their possible role as Type Ia supernova progenitors. Observations with SKA1-MID in particular, over a broad range of frequencies, but with emphasis on the higher frequencies, will provide an unparalleled view of the physical processes driving mass ejection and resulting in the diversity of novae, whilst also determining the accretion processes and rates in symbiotic stars.Comment: 13 pages, 3 figures, in proceedings of "Advancing Astrophysics with the Square Kilometre Array", PoS(AASKA14)116, in pres