Some natural zero one laws for ordinals below ε0

We are going to prove that every ordinal α with ε_0 > α ≥ ω^ω satisfies a natural zero one law in the following sense. For α < ε_0 let Nα be the number of occurences of ω in the Cantor normal form of α. (Nα is then the number of edges in the unordered tree which can canonically be associated with α.) We prove that for any α with ω ω  ≤ α < ε_0 and any sentence ϕ in the language of linear orders the asymptotic density of ϕ along α is an element of  {0,1}. We further show that for any such sentence ϕ the asymptotic density along ε_0 exists although this limit is in general in between 0 and 1. We also investigate corresponding asymptotic densities for ordinals below ω^ω

Identification of Shocks in the Spectra from Black Holes

We study the spectral properties of a low angular momentum flow as a function of the shock strength, compression ratio, accretion rate and flow geometry. In the absence of a satisfactory description of magnetic fields inside the advective disk, we consider the presence of only stochastic fields and use the ratio of the field energy to the gravitational energy density as a parameter. We not only include `conventional' synchrotron emission and Comptonization by Maxwell-Bolzmann electrons in the gas, but we also compute these effects due to power-law electrons. For strong shocks, a bump is produced due to the post-shock flow. A power-law spectral components due to the thermal and non-thermal electrons appear after this bump.Comment: 8 pages, 5 figures, Astronomy and Space Science (in press), Proceedings of the Hong Kong Conference (2004) Edited by Cheng and Romer

Particle Acceleration at Relativistic Shocks

I review the current status of Fermi acceleration theory at relativistic shocks. I first discuss the relativistic shock jump conditions, then describe the non-relativistic Fermi mechanism and the differences introduced by relativistic flows. I present numerical calculations of the accelerated particle spectrum, and examine the maximum energy attainable by this process. I briefly consider the minimum energy for Fermi acceleration, and a possible electron pre-acceleration mechanism.Comment: 17 pages, 4 figures. To appear in "Relativistic Flows in Astrophysics", A.W. Guthmann, M. Georganopoulos, A. Marcowith and K. Manolokou, eds., Lecture Notes in Pysics, Springer Verla

Three-dimensional fast electron transport for ignition-scale inertial fusion capsules

Three-dimensional hybrid PIC simulations are presented to study electron energy transport and deposition in a full-scale fast ignition configuration. Multi-prong core heating close to ignition is found when a few GA, few PW beam is injected. Resistive beam filamentation in the corona seeds the 3D current pattern that penetrates the core. Ohmic heating is important in the low-density corona, while classical Coulomb deposition heats the core. Here highest energy densities (few Tbar at 10 keV) are observed at densities above 200 g/cc. Energy coupling to the core ranges from 20 to 30%; it is enhanced by beam collimation and decreases when raising the beam particle energy from 1.5 to 5.5 MeV.Comment: 5 pages, 5 figure

Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. II: anisotropy

We investigate the effects of stochasticity in the spatial and temporal distribution of supernova remnants on the anisotropy of cosmic rays observed at Earth. The calculations are carried out for different choices of the diffusion coefficient D(E) for propagation in the Galaxy. The propagation and spallation of nuclei are taken into account. At high energies we assume that $D(E)\sim(E/Z)^{\delta}$, with $\delta=1/3$ and $\delta=0.6$ being the reference scenarios. The large scale distribution of supernova remnants in the Galaxy is modeled following the distribution of pulsars with and without accounting for the spiral structure of the Galaxy. Our calculations allow us to determine the contribution to anisotropy resulting from both the large scale distribution of SNRs in the Galaxy and the random distribution of the nearest remnants. The naive expectation that the anisotropy amplitude scales as D(E) is shown to be an oversimplification which does not reflect in the predicted anisotropy for any realistic distribution of the sources. The fluctuations in the anisotropy pattern are dominated by nearby sources, so that predicting or explaining the observed anisotropy amplitude and phase becomes close to impossible. We find however that the very weak energy dependence of the anisotropy amplitude below $10^{5}$ GeV and the rise at higher energies, can best be explained if the diffusion coefficient is $D(E)\sim E^{1/3}$. Faster diffusion, for instance with $\delta=0.6$, leads in general to an exceedingly large anisotropy amplitude. The spiral structure introduces interesting trends in the energy dependence of the anisotropy pattern, which qualitatively reflect the trend seen in the data. For large values of the halo size we find that the anisotropy becomes dominated by the large scale regular structure of the source distribution, leading indeed to a monotonic increase of $\delta_A$ with energy.Comment: 21 Pages, to appear in JCA

Infrapoliteal percutaneous transluminal angioplasty: A safe and successful procedure

Aim:To review outcome of 40 consecutive infrapopliteal percutaneous transluminal angioplasty (PTA) procedures performed over a 65 month period.Chief outcome measures:The indication for PTA was intermittent claudication in 20 (50%) cases and rest pain, ulceration or gangrene in the remainder.Results:There was one technical failure; the remaining 39 limbs were all clinically improved by 24 h and this improvement was maintained at 3 months in 36 (90%). There were no deaths nor limb loss related to PTA and 2 embolic complications were successfully treated percutaneously. The primary and secondary symptomatic patencies at 24 months were 59 and 79% respectively. The actuarial limb salvage rate at 1 year for the 20 limbs presenting with critical ischaemia was 77%, and 10 of the 14 procedures performed for ulceration or gangrene resulted in healing with only minor surgical intervention.Conclusions:With modern endovascular techniques, infrapopliteal PTA is a safe, worthwhile and durable procedure

At what peak velocity ratio value should duplex-detected infrainguinal vein graft stenoses be revised?

Objectives:To determine the peak velocity ratio (PVR) threshold at which to intervene and correct duplex detected vein graft stenoses.Design:Prospective study.Materials:Infrainguinal vein grafts in patients attending the vascular studies for routine postoperative surveillance.Methods:Colour duplex detected stenotic vein graft lesions with a peak velocity ratio (PVR) between 2.0 and 2.9 were identified and monitored by serial duplex scans performed monthly for 3 months and then at 3-monthly intervals thereafter. At the end of the study period, the outcome of these lesions were analysed.Results:Thirty-eight lesions were identified from 32 grafts. Of these lesions, sixteen (42%) resolved, 11 (29%) remained stable and 11 (29%) progressed to a PVR of ≥3.0 and underwent angioplasty. There were no occlusions in any of the grafts during the period of study.Conclusion:Colour duplex detected vein graft stenoses with a PVR of less than 3.0 can be treated expectantly if grafts with stenoses with a PVR 2.0–2.9 are scanned every month for at least 3 months after detection

Gamma-ray emission expected from Kepler's SNR

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants (SNRs) is used to investigate the properties of Kepler's SNR and, in particular, to predict the gamma-ray spectrum expected from this SNR. Observations of the nonthermal radio and X-ray emission spectra as well as theoretical constraints for the total supernova (SN) explosion energy E_sn are used to constrain the astronomical and particle acceleration parameters of the system. Under the assumption that Kepler's SN is a type Ia SN we determine for any given explosion energy E_sn and source distance d the mass density of the ambient interstellar medium (ISM) from a fit to the observed SNR size and expansion speed. This makes it possible to make predictions for the expected gamma-ray flux. Exploring the expected distance range we find that for a typical explosion energy E_sn=10^51 erg the expected energy flux of TeV gamma-rays varies from 2x10^{-11} to 10^{-13} erg/(cm^2 s) when the distance changes from d=3.4 kpc to 7 kpc. In all cases the gamma-ray emission is dominated by \pi^0-decay gamma-rays due to nuclear CRs. Therefore Kepler's SNR represents a very promising target for instruments like H.E.S.S., CANGAROO and GLAST. A non-detection of gamma-rays would mean that the actual source distance is larger than 7 kpc.Comment: 6 pages, 4 figures. Accepted for publication in Astronomy and Astrophysics, minor typos correcte

On the multiplicity of the O-star Cyg OB2 #8A and its contribution to the gamma-ray source 3EG J2033+4118

We present the results of an intensive spectroscopic campaign in the optical waveband revealing that Cyg OB2 #8A is an O6 + O5.5 binary system with a period of about 21.9 d. Cyg OB2 #8A is a bright X-ray source, as well as a non-thermal radio emitter. We discuss the binarity of this star in the framework of a campaign devoted to the study of non-thermal emitters, from the radio waveband to gamma-rays. In this context, we attribute the non-thermal radio emission from this star to a population of relativistic electrons, accelerated by the shock of the wind-wind collision. These relativistic electrons could also be responsible for a putative gamma-ray emission through inverse Compton scattering of photospheric UV photons, thus contributing to the yet unidentified EGRET source 3EG J2033+4118.Comment: 8 pages, 4 figures, conference on "The Multiwavelength Approach to Gamma-Ray Sources", to appear in Ap&S