Mechanics of couple-stress fluid coatings

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors

Ultra-high-energy cosmic ray acceleration by relativistic blast waves

We consider the acceleration of charged particles at the ultra-relativistic shocks, with Lorentz factors \Gamma_s >> 1 relative to the upstream medium, arising in relativistic fireball models of gamma-ray bursts (GRBs). We show that for Fermi-type shock acceleration, particles initially isotropic in the upstream medium can gain a factor of order \Gamma_s^2 in energy in the first shock crossing cycle, but that the energy gain factor for subsequent shock crossing cycles is only of order 2, because for realistic deflection processes particles do not have time to re-isotropise upstream before recrossing the shock. We evaluate the maximum energy attainable and the efficiency of this process, and show that for a GRB fireball expanding into a typical interstellar medium, these exclude the production of ultra-high-energy cosmic rays (UHECRs), with energies in the range 10^{18.5} - 10^{20.5} eV, by the blast wave. We propose, however, that in the context of neutron star binaries as the progenitors of GRBs, relativistic ions from the pulsar wind bubbles produced by these systems could be accelerated by the blast wave. We show that if the known binary pulsars are typical, the maximum energy, efficiency, and spectrum in this case can account for the observed population of UHECRs.Comment: Accepted for MNRAS (Letters), with minor revisions. LaTeX, 5 pages, uses mn.st

Does the detection of X-ray emission from SN1998bw support its association with GRB980425?

We show that the recent identification of X-ray emission from SN1998bw is naturally explained as synchrotron emission from a shock driven into the wind surrounding the progenitor by a mildly relativistic shell ejected by the supernova, the existence of which was inferred earlier from radio observations. X-ray observations imply a shell energy E~10^{49.7}erg, and constrain the initial shell velocity \beta*c and normalized wind mass loss rate, \dot{m}=(\dot{M}/10^{-5}M_sun/yr)/(v_w/10^3 km/s), to satisfy \beta^3*\dot{m}~10^{-1.5}. The inferred energy is consistent with energy estimates based on radio observations provided \dot{m}~0.04, in which case radio observations imply \beta~0.8, consistent with the X-ray constraint \beta^3*\dot{m}~10^{-1.5}. While X-ray observations allow to determine the parameters characterizing the pre-explosion wind and the mildly relativistic shell ejected by SN1998bw, they do not provide evidence for existence of an off-axis "standard" GRB jet associated with SN1998bw, that may have produced GRB980425. However, as recently pointed out in (astro-ph/0310320), the lack of observational signatures typically expected to be produced by such an off-axis jet on a 1yr time scale, may be due to a low \dot{m}<0.1, which implies that an off-axis jet will become observable only on >10yr time scale.Comment: Minor changes. Accepted to ApJ

TeV neutrinos from core collapse supernovae and hypernovae

A fraction of core collapse supernovae of type Ib/c are associated with Gamma-ray bursts, which are thought to produce highly relativistic jets. Recently, it has been hypothesized that a larger fraction of core collapse supernovae produce slower jets, which may contribute to the disruption and ejection of the supernova envelope, and explain the unusually energetic hypernovae. We explore the TeV neutrino signatures expected from such slower jets, and calculate the expected detection rates with upcoming Gigaton Cherenkov experiments. We conclude that individual jetted SNe may be detectable from nearby galaxies.Comment: 4 pages 2 figures. Modified from the published version. Errors in Eqs. 2, 3, 5 are corrected and predicted neutrino event rates are modified accordingly. The conclusions for the diffuse flux remain unchanged, and those for individual nearby sources are strengthene

Mutation and selection in a large population

In this paper we study a large, but finite population, in which mutation and selection occur at a single genetic locus in a diploid organism. We provide theoretical results for the equilibrium allele frequencies, their variances and covariances and their equilibrium distribution, when the population size is larger than the reciprocal of the mean mutation rate. [[We are also able to infer that the equilibrium distribution of allele frequencies takes the form of a constrained multivariate Gaussian distribution.]] Our results provide a rapid way of obtaining useful information in the case of complex mutation and selection schemes when the population size is large. We present numerical simulations to test the applicability of our theoretical formulations. The results of these simulations are in very reasonable agreement with the theoretical predictions

Angular size and emission time scales of relativistic fireballs

The detection of delayed X-ray, optical and radio emission, ``afterglow,'' associated with gamma-ray bursts (GRBs) is consistent with models, where the bursts are produced by relativistic expanding blast waves, driven by expanding fireballs at cosmological distances. In particular, the time scales over which radiation is observed at different wave bands agree with model predictions. It had recently been claimed that the commonly used relation between observation time t and blast wave radius r, t=r/2\gamma^{2}c where \gamma(r) is the fluid Lorentz factor, should be replaced with t=r/16\gamma^{2}c due to blast wave deceleration. Applying the suggested deceleration modification would make it difficult to reconcile observed time scales with model predictions. It would also imply an apparent source size which is too large to allow attributing observed radio variability to diffractive scintillation. We present a detailed analysis of the implications of the relativistic hydrodynamics of expanding blast waves to the observed afterglow. We find that modifications due to shock deceleration are small, therefore allowing for both the observed afterglow time scales and for diffractive scintillation. We show that at time t the fireball appears on the sky as a narrow ring of radius h=r/\gamma and width 0.1h, where r and t are related by t=r/2\gamma^{2}c.Comment: Submitted to ApJL (11 pages, LaTeX

Improving the Convergence of an Iterative Algorithm Proposed By Waxman

In the iterative algorithm recently proposed by Waxman for solving eigenvalue problems, we point out that the convergence rate may be improved. For many non-singular symmetric potentials which vanish asymptotically, a simple analytical relationship between the coupling constant of the potential and the ground state eigenvalue is obtained which can be used to make the algorithm more efficient

Neutral beam model for the anomalous gamma-ray emission component in GRB 941017

Gonz\'alez et al. (2003) have reported the discovery of an anomalous radiation component from ~ 1 -- 200 MeV in GRB 941017. This component varies independently of and contains > 3 times the energy found in the prompt ~ 50 keV -- 1 MeV radiation component that is well described by the relativistic synchrotron-shock model. Acceleration of hadrons to very high energies can give rise to two additional emission components, one produced inside the GRB blast wave and one associated with an escaping beam of ultra-high energy (UHE; > 10^{14} eV) neutrons, gamma rays, and neutrinos. The first component extending to ~ 100 MeV is from a pair-photon cascade induced by photomeson processes with the internal synchrotron photons coincident with the prompt radiation. The outflowing UHE neutral beam can undergo further interactions with external photons from the backscattered photon field to produce a beam of hyper-relativistic electrons that lose most of their energy during a fraction of a gyroperiod in the assumed Gauss-strength magnetic fields of the circumburst medium. The synchrotron radiation of these electrons has a spectrum with vF_v index equal to +1 that can explain the anomalous component in GRB 941017. This interpretation of the spectrum of GRB 941017 requires a high baryon load of the accelerated particles in GRB blast waves. It implies that most of the radiation associated with the anomalous component is released at > 500 MeV, suitable for observations with GLAST, and with a comparable energy fluence in ~100 TeV neutrinos that could be detected with a km-scale neutrino telescope like IceCube.Comment: 4 pages, 1 figure, minor corrections, Astronomy and Astrophysics Letters, in pres