Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

The critical behavior of long straight rigid rods of length $k$ ($k$-mers) on square and triangular lattices at intermediate density has been studied. A nematic phase, characterized by a big domain of parallel $k$-mers, was found. This ordered phase is separated from the isotropic state by a continuous transition occurring at a intermediate density $\theta_c$. Two analytical techniques were combined with Monte Carlo simulations to predict the dependence of $\theta_c$ on $k$, being $\theta_c(k) \propto k^{-1}$. The first involves simple geometrical arguments, while the second is based on entropy considerations. Our analysis allowed us also to determine the minimum value of $k$ ($k_{min}=7$), which allows the formation of a nematic phase on a triangular lattice.Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physic

Diversity Of Short Gamma-Ray Burst Afterglows From Compact Binary Mergers Hosting Pulsars

Short gamma-ray bursts (sGRBs) are widely believed to result from the mergers of compact binaries. This model predicts an afterglow that bears the characteristic signatures of a constant, low density medium, including a smooth prompt-afterglow transition, and a simple temporal evolution. However, these expectations are in conflict with observations for a non-negligible fraction of sGRB afterglows. In particular, the onset of the afterglow phase for some of these events appears to be delayed and, in addition, a few of them exhibit late- time rapid fading in their lightcurves. We show that these peculiar observations can be explained independently of ongoing central engine activity if some sGRB progenitors are compact binaries hosting at least one pulsar. The Poynting flux emanating from the pulsar companion can excavate a bow-shock cavity surround- ing the binary. If this cavity is larger than the shock deceleration length scale in the undisturbed interstellar medium, then the onset of the afterglow will be delayed. Should the deceleration occur entirely within the swept-up thin shell, a rapid fade in the lightcurve will ensue. We identify two types of pulsar that can achieve the conditions necessary for altering the afterglow: low field, long lived pulsars, and high field pulsars. We find that a sizable fraction (~20-50%) of low field pulsars are likely to reside in neutron star binaries based on observations, while their high field counterparts are not. Hydrodynamical calculations motivated by this model are shown to be in good agreement with observations of sGRB afterglow lightcurves.Comment: Accepted to ApjL. Direct comparison to observed X-Ray afterglows now included. 5 Figure

Gas and dust from solar metallicity AGB stars

We study the asymptotic giant branch (AGB) evolution of stars with masses between $1~M_{\odot} - 8.5~M_{\odot}$. We focus on stars with a solar chemical composition, which allows us to interpret evolved stars in the Galaxy. We present a detailed comparison with models of the same chemistry, calculated with a different evolution code and based on a different set of physical assumptions. We find that stars of mass $\ge 3.5~M_{\odot}$ experience hot bottom burning at the base of the envelope. They have AGB lifetimes shorter than $\sim 3\times 10^5$ yr and eject into their surroundings gas contaminated by proton-capture nucleosynthesis, at an extent sensitive to the treatment of convection. Low mass stars with $1.5~M_{\odot} \le M \le 3~M_{\odot}$ become carbon stars. During the final phases the C/O ratio grows to $\sim 3$. We find a remarkable agreement between the two codes for the low-mass models and conclude that predictions for the physical and chemical properties of these stars, and the AGB lifetime, are not that sensitive to the modelling of the AGB phase. The dust produced is also dependent on the mass: low-mass stars produce mainly solid carbon and silicon carbide dust, whereas higher mass stars produce silicates and alumina dust. Possible future observations potentially able to add more robustness to the present results are also discussed.Comment: 27 pages, 24 figures; accepted for publication in MNRA