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

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

Radio Astronomy in LSST Era

A community meeting on the topic of "Radio Astronomy in the LSST Era" was hosted by the National Radio Astronomy Observatory in Charlottesville, VA (2013 May 6--8). The focus of the workshop was on time domain radio astronomy and sky surveys. For the time domain, the extent to which radio and visible wavelength observations are required to understand several classes of transients was stressed, but there are also classes of radio transients for which no visible wavelength counterpart is yet known, providing an opportunity for discovery. From the LSST perspective, the LSST is expected to generate as many as 1 million alerts nightly, which will require even more selective specification and identification of the classes and characteristics of transients that can warrant follow up, at radio or any wavelength. The LSST will also conduct a deep survey of the sky, producing a catalog expected to contain over 38 billion objects in it. Deep radio wavelength sky surveys will also be conducted on a comparable time scale, and radio and visible wavelength observations are part of the multi-wavelength approach needed to classify and understand these objects. Radio wavelengths are valuable because they are unaffected by dust obscuration and, for galaxies, contain contributions both from star formation and from active galactic nuclei. The workshop touched on several other topics, on which there was consensus including the placement of other LSST "Deep Drilling Fields," inter-operability of software tools, and the challenge of filtering and exploiting the LSST data stream. There were also topics for which there was insufficient time for full discussion or for which no consensus was reached, which included the procedures for following up on LSST observations and the nature for future support of researchers desiring to use LSST data products.Comment: Conference summary, 29 pages, 1 figure; to be published in the Publ. Astron. Soc. Pacific; full science program and presentations available at http://science.nrao.edu/science/event/RALSST201

Radio Monitoring of the Tidal Disruption Event Swift J164449.3+573451. I. Jet Energetics and the Pristine Parsec-Scale Environment of a Supermassive Black Hole

We present continued radio observations of the tidal disruption event SwiftJ164449.3+573451 extending to \sim216 days after discovery. The data are part of a long-term program to monitor the expansion and energy scale of the relativistic outflow, and to trace the parsec-scale environment around a previously-dormant supermassive black hole (SMBH). The new observations reveal a significant change in the radio evolution starting at \sim1 month, with a brightening at all frequencies that requires an increase in the energy by about an order of magnitude, and an overall density profile around the SMBH of rho \propto r^{-3/2} (0.1-1.2 pc) with a significant flattening at r\sim0.4-0.6 pc. The increase in energy cannot be explained with continuous injection from an L \propto t^{-5/3} tail, which is observed in the X-rays. Instead, we conclude that the relativistic jet was launched with a wide range of Lorentz factors, obeying E(>Gamma) \propto Gamma^{-2.5}. The similar ratio of duration to dynamical timescale for Sw1644+57 and GRBs suggests that this result may be applicable to GRBs as well. The radial density profile may be indicative of Bondi accretion, with the inferred flattening at r\sim0.5 pc in good agreement with the Bondi radius for a \sim10^6 M_sun black hole. The density at \sim0.5 pc is about a factor of 30 times lower than inferred for the Milky Way galactic center, potentially due to a smaller number of mass-shedding massive stars. From our latest observations (\sim216 d) we find that the jet energy is E_{iso}\sim5x10^{53} erg (E_j\sim2.4x10^{51} erg for theta_j=0.1), the radius is r\sim1.2 pc, the Lorentz factor is Gamma\sim2.2, the ambient density is n\sim0.2 cm^{-3}, and the projected size is r_{proj}\sim25 microarcsec. Assuming no future changes in the observed evolution we predict that the radio emission from Sw1644+57 should be detectable with the EVLA for several decades, and will be resolvable with VLBI in a few years.Comment: Submitted to ApJ; 22 pages, 2 tables, 9 figure