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

ILLUMINATING THE DARKEST GAMMA-RAY BURSTS WITH RADIO OBSERVATIONS

We present X-ray, optical, near-infrared (IR), and radio observations of gamma-ray bursts (GRBs) 110709B and 111215A, as well as optical and near-IR observations of their host galaxies. The combination of X-ray detections and deep optical/near-IR limits establish both bursts as "dark." Sub-arcsecond positions enabled by radio detections lead to robust host galaxy associations, with optical detections that indicate z ≾ 4 (110709B) and z ≈ 1.8-2.9 (111215A). We therefore conclude that both bursts are dark due to substantial rest-frame extinction. Using the radio and X-ray data for each burst we find that GRB 110709B requires A_V^(host) ≳ 5.3 mag and GRB 111215A requires A_V^(host) ≳ 8.5 mag (assuming z = 2). These are among the largest extinction values inferred for dark bursts to date. The two bursts also exhibit large neutral hydrogen column densities of N H, int ≳ 10^(22) cm^(–2) (z = 2) as inferred from their X-ray spectra, in agreement with the trend for dark GRBs. Moreover, the inferred values are in agreement with the Galactic A_V -N_H relation, unlike the bulk of the GRB population. Finally, we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming-corrected energy of E_γ + E_K ≈ (7-9) × 10^(51) erg (z = 2) expanding into a wind medium with a high density, Ṁ ≈ (6-20) x 10^(-5) M_☉ yr^(–1) (n ≈ 100-350 cm^(–3) at ≈ 10^(17) cm). While the energy release is typical of long GRBs, the inferred density may be indicative of larger mass-loss rates for GRB progenitors in dusty (and hence metal rich) environments. This study establishes the critical role of radio observations in demonstrating the origin and properties of dark GRBs. Observations with the JVLA and ALMA will provide a sample with sub-arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in GRB progenitors

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