Analytical study of an exclusive genetic switch

The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be repressed. The model may be thought of as a minimal model of the power struggle between two competing parties. Exact solutions are given for the limits of vanishing binding/unbinding rates and infinite binding/unbinding rates. A mean field theory is introduced which is exact in the limit of vanishing binding/unbinding rates. The mean field theory and numerical simulations reveal that generically bistability occurs and the system is in a symmetry broken state. An exact perturbative solution which in principle allows the nonequilibrium stationary state to be computed is also developed and computed to first and second order.Comment: 28 pages, 6 figure

On the local existence of maximal slicings in spherically symmetric spacetimes

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.Comment: 4 pages. Accepted for publication in Journal of Physics: Conference Series, Proceedings of the Spanish Relativity Meeting ERE200

Submillimeter polarisation and magnetic field properties in the envelopes of proto-planetary nebulae CRL 618 and OH 231.8+4.2

We have carried out continuum and line polarisation observations of two Proto-planetary nebulae (PPNe), CRL 618 and OH 231.8+4.2, using the Submillimeter Array (SMA) in its compact configuration. The frequency range of observations, 330-345 GHz, includes the CO(J=3-2) line emission. CRL 618 and OH 231.8+4.2 show quadrupolar and bipolar optical lobes, respectively, surrounded by a dusty envelope reminiscent of their AGB phase. We report a detection of dust continuum polarised emission in both PPNe above 4 sigma but no molecular line polarisation detection above a 3 sigma limit. OH 231.8+4.2 is slightly more polarised on average than CRL 618 with a mean fractional polarisation of 4.3 and 0.3 per cent, respectively. This agrees with the previous finding that silicate dust shows higher polarisation than carbonaceous dust. In both objects, an anti-correlation between the fractional polarisation and the intensity is observed. Neither PPNe show a well defined toroidal equatorial field, rather the field is generally well aligned and organised along the polar direction. This is clearly seen in CRL 618 while in the case of OH 231.8+4.2, the geometry indicates an X-shaped structure coinciding overall with a dipole/polar configuration. However in the later case, the presence of a fragmented and weak toroidal field should not be discarded. Finally, in both PPNe, we observed that the well organised magnetic field is parallel with the major axis of the 12CO outflow. This alignment could indicate the presence of a magnetic outflow launching mechanism. Based on our new high resolution data we propose two scenarios to explain the evolution of the magnetic field in evolved stars.Comment: 11 pages, 8 figures and 1 table. Accepted for publication in the Monthly Notices of the Royal Astronomical Societ

Relativistic supernovae have shorter-lived central engines or more extended progenitors: the case of SN\,2012ap

Deep late-time X-ray observations of the relativistic, engine-driven, type Ic SN2012ap allow us to probe the nearby environment of the explosion and reveal the unique properties of relativistic SNe. We find that on a local scale of ~0.01 pc the environment was shaped directly by the evolution of the progenitor star with a pre-explosion mass-loss rate <5x10^-6 Msun yr-1 in line with GRBs and the other relativistic SN2009bb. Like sub-energetic GRBs, SN2012ap is characterized by a bright radio emission and evidence for mildly relativistic ejecta. However, its late time (t~20 days) X-ray emission is ~100 times fainter than the faintest sub-energetic GRB at the same epoch, with no evidence for late-time central engine activity. These results support theoretical proposals that link relativistic SNe like 2009bb and 2012ap with the weakest observed engine-driven explosions, where the jet barely fails to breakout. Furthermore, our observations demonstrate that the difference between relativistic SNe and sub-energetic GRBs is intrinsic and not due to line-of-sight effects. This phenomenology can either be due to an intrinsically shorter-lived engine or to a more extended progenitor in relativistic SNe.Comment: Version accepted to ApJ. Significantly broadened discussio

The Environment of Local Ultraluminous Infrared Galaxies

The spatial cluster-galaxy correlation amplitude, Bgc, is computed for a set of 76 (z < 0.3) ultraluminous infrared galaxies (ULIRGs) from the 1-Jy sample. The Bgc parameter is used to quantify the richness of the environment within 0.5 Mpc of each ULIRG. We find that the environment of local ULIRGs is similar to that of the field with the possible exceptions of a few objects with environmental densities typical of clusters with Abell richness classes 0 and 1. No obvious trends are seen with redshift, optical spectral type, infrared luminosity, or infrared color. We compare these results with those of local AGNs and QSOs at various redshifts. The 1-Jy ULIRGs show a broader range of environments than local Seyferts, which are exclusively found in the field. The distribution of ULIRG Bgc-values overlaps considerably with that of local QSOs, consistent with the scenario where some QSOs go through a ultraluminous infrared phase. However, a rigorous statistical analysis of the data indicates that these two samples are not drawn from the same parent population. The Bgc distribution of QSOs shows a distinct tail at high Bgc-values which is not apparent among the ULIRGs. This difference is consistent with the fact that some of the QSOs used for this comparison have bigger and more luminous hosts than the 1-Jy ULIRGs.Comment: 31 pages, 9 figures, 2 tables, accepted for publication in ApJ, volume 660n1 (May 1, 2007

Spatial and Temporal Variations in Small-Scale Galactic HI Structure Toward 3C~138

We present three epochs of VLBA observations of Galactic HI absorption toward the quasar 3C~138 with resolutions of 20 mas (~ 10 AU). This analysis includes VLBA data from observations in 1999 and 2002 along with a reexamination of 1995 VLBA data. Improved data reduction and imaging techniques have led to an order of magnitude improvement in sensitivity compared to previous work. With these new data we confirm the previously detected milliarcsecond scale spatial variations in the HI opacity at the level of Delta(tau_{max}) =0.50 \pm 0.05. The typical size scale of the optical depth variations is ~ 50 mas or 25 AU. In addition, for the first time we see clear evidence for temporal variations in the HI opacity over the seven year time span of our three epochs of data. We also attempted to detect the magnetic field strength in the HI gas using the Zeeman effect. From this analysis we have been able to place a 3 sigma upper limit on the magnetic field strength per pixel of ~45 muG. We have also been able to calculate for the first time the plane of sky covering fraction of the small scale HI gas of ~10%. We also find that the line widths of the milliarcsecond sizescale HI features are comparable to those determined from previous single dish measurements toward 3C~138, suggesting that the opacity variations cannot be due to changes in the HI spin temperature. From these results we favor a density enhancement interpretation for the small scale HI structures, although these enhancements appear to be of short duration and are unlikely to be in equilibrium.Comment: 34 pages, 8 figures. Figures 3 & 4 are in color. Accepted to A

On the Solutions of the Lorentz-Dirac Equation

We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic example of the non-relativistic harmonic oscillator with radiation reaction. We also illustrate removal of the noncasual pre-acceleration with the introduction of a small correction in the Lorentz-Dirac equation.Comment: 4 eps figs. to be published in GR