Stability of an Ultra-Relativistic Blast Wave in an External Medium with a Steep Power-Law Density Profile

We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These accelerating solutions apply, for example, to the breakout of a gamma-ray burst outflow from the boundary of a massive star, as assumed in the popular collapsar model. We show that short wavelength perturbations may grow but only by a modest factor <~ 10.Comment: 12 pages, 3 figures, submitted to Physical Review

The Gradient Expansion for the Free-Energy of a Clean Superconductor

We describe a novel method for obtaining the gradient expansion for the free energy of a clean BCS superconductor. We present explicit results up to fourth order in the gradients of the order parameter.Comment: 33 pages, Late

Efficiency and spectrum of internal gamma-ray burst shocks

We present an analysis of the Internal Shock Model of GRBs, where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction, of order 20 %, of the wind kinetic energy can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and provided the minimum Lorentz factor is higher than 10^(2.5)L_(52)^(2/9), where L=10^(52)L_(52)erg/s is the wind luminosity. For a high, >10 %, efficiency wind, spectral energy breaks in the 0.1 to 1 MeV range are obtained for sources with dynamical time R/c < 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit to wind Lorenz factor and the upper limit, around (R/10^7 cm)^(-5/6) MeV to observed break energies are set by Thomson optical depth due to electron positron pairs produced by synchrotron photons. Natural consequences of the model are absence of bursts with peak emission energy significantly exceeding 1 MeV, and existence of low luminosity bursts with low, 1 keV to 10 keV, break energies.Comment: 10 pages, 5 ps-figures. Expanded discussion of magnetic field and electron energy fraction. Accepted for publication in Astrophysical Journa

Statistics of clustering of ultra-high energy cosmic rays and the number of their sources

Observation of clustering of ultra-high energy cosmic rays (UHECR) suggests that they are emitted by compact sources. Assuming small deflection of UHECR during the propagation, the statistical analysis of clustering allows to estimate the spatial density of the sources, h, including those which have not yet been observed directly. When applied to astrophysical models involving extra-galactic sources, the estimate based on 14 events with energy E>10^{20} eV gives h ~ 6 X 10^{-3} Mps^{-3}. With increasing statistics, this estimate may lead to exclusion of the models which associate the production of UHECR with exceptional galaxies such as AGN, powerful radio-galaxies, dead quasars, and models based on gamma ray bursts.Comment: The version accepted for publication in Phys. Rev. Lett. Notations changed to conventional ones. The estimate of the effective GZK radius replaced by the result of numerical simulatio

Frizzled-8 integrates Wnt-11 and transforming growth factor-β signaling in prostate cancer

Wnt-11 promotes cancer cell migration and invasion independently of β-catenin but the receptors involved remain unknown. Here, we provide evidence that FZD8 is a major Wnt-11 receptor in prostate cancer that integrates Wnt-11 and TGF-β signals to promote EMT. FZD8 mRNA is upregulated in multiple prostate cancer datasets and in metastatic cancer cell lines in vitro and in vivo. Analysis of patient samples reveals increased levels of FZD8 in cancer, correlating with Wnt-11. FZD8 co-localizes and co-immunoprecipitates with Wnt-11 and potentiates Wnt-11 activation of ATF2-dependent transcription. FZD8 silencing reduces prostate cancer cell migration, invasion, three-dimensional (3D) organotypic cell growth, expression of EMT-related genes, and TGF-β/Smad-dependent signaling. Mechanistically, FZD8 forms a TGF-β-regulated complex with TGF-β receptors that is mediated by the extracellular domains of FZD8 and TGFBR1. Targeting FZD8 may therefore inhibit aberrant activation of both Wnt and TGF-β signals in prostate cancer

Constraining Sources of Ultra High Energy Cosmic Rays Using High Energy Observations with the Fermi Satellite

We analyze the conditions that enable acceleration of particles to ultra-high energies, ~10^{20} eV (UHECRs). We show that broad band photon data recently provided by WMAP, ISOCAM, Swift and Fermi satellites, yield constraints on the ability of active galactic nuclei (AGN) to produce UHECRs. The high energy (MeV - GeV) photons are produced by Compton scattering of the emitted low energy photons and the cosmic microwave background or extra-galactic background light. The ratio of the luminosities at high and low photon energies can therefore be used as a probe of the physical conditions in the acceleration site. We find that existing data excludes core regions of nearby radio-loud AGN as possible acceleration sites of UHECR protons. However, we show that giant radio lobes are not excluded. We apply our method to Cen A, and show that acceleration of protons to ~10^{20} eV can only occur at distances >~ 100 kpc from the core.Comment: Extended discussion on former results; Accepted for publication in JCA

High energy cosmic-rays: puzzles, models, and giga-ton neutrino telescopes

The existence of cosmic rays of energies exceeding 10^20 eV is one of the mysteries of high energy astrophysics. The spectrum and the high energy to which it extends rule out almost all suggested source models. The challenges posed by observations to models for the origin of high energy cosmic rays are reviewed, and the implications of recent new experimental results are discussed. Large area high energy cosmic ray detectors and large volume high energy neutrino detectors currently under construction may resolve the high energy cosmic ray puzzle, and shed light on the identity and physics of the most powerful accelerators in the universe.Comment: 12 pages, 7 figures; Summary of review talk, PASCOS 03 (Mumbai, India

A modified Wright-Fisher model that incorporates Ne: A variant of the standard model with increased biological realism and reduced computational complexity.

The Wright-Fisher model is an important model in evolutionary biology and population genetics. It has been applied in numerous analyses of finite populations with discrete generations. It is recognised that real populations can behave, in some key aspects, as though their size that is not the census size, N, but rather a smaller size, namely the effective population size, Ne. However, in the Wright-Fisher model, there is no distinction between the effective and census population sizes. Equivalently, we can say that in this model, Ne coincides with N. The Wright-Fisher model therefore lacks an important aspect of biological realism. Here, we present a method that allows Ne to be directly incorporated into the Wright-Fisher model. The modified model involves matrices whose size is determined by Ne. Thus apart from increased biological realism, the modified model also has reduced computational complexity, particularly so when Ne⪡N. For complex problems, it may be hard or impossible to numerically analyse the most commonly-used approximation of the Wright-Fisher model that incorporates Ne, namely the diffusion approximation. An alternative approach is simulation. However, the simulations need to be sufficiently detailed that they yield an effective size that is different to the census size. Simulations may also be time consuming and have attendant statistical errors. The method presented in this work may then be the only alternative to simulations, when Ne differs from N. We illustrate the straightforward application of the method to some problems involving allele fixation and the determination of the equilibrium site frequency spectrum. We then apply the method to the problem of fixation when three alleles are segregating in a population. This latter problem is significantly more complex than a two allele problem and since the diffusion equation cannot be numerically solved, the only other way Ne can be incorporated into the analysis is by simulation. We have achieved good accuracy in all cases considered. In summary, the present work extends the realism and tractability of an important model of evolutionary biology and population genetics