Motivated by the recent interest in models of guarded (co-)recursion we study its equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and Esik. Models of these axioms includ
e both standard (e.g., cpo-based) models of iteration theories and models of guarded recursion such as complete metric spaces or the topos of trees studied by Birkedal et al. We show that the standard result on the satisfaction of all Conway axioms by a unique dagger operation generalizes to the guarded setting. We also introduce the notion of guarded trace operator on a category, and we prove that guarded trace and guarded fixpoint operators are in one-to-one correspondence. Our results are intended as first steps leading to the description of classifying theories for guarded recursion and hence completeness results involving our axioms of guarded fixpoint operators in future work.
CoREAS is a Monte Carlo simulation code for the calculation of radio emission from extensive air showers. It is based on the endpoint formalism for radiation from moving charges implemented directly in CORSIKA. Consequently, the full complexity of th
e air-shower physics is taken into account without the need for approximations or assumptions on the emission mechanism. We present results of simulations for an unthinned shower performed with CoREAS for both MHz and GHz frequencies. At MHz frequencies, the simulations predict the well-known mixture of geomagnetic and charge excess radiation. At GHz frequencies, the emission is strongly influenced by Cherenkov effects arising from the varying refractive index in the atmosphere. In addition, a qualitative difference in the symmetry of the GHz radiation pattern is observed when compared to the ones at lower frequencies. We also discuss the strong increase in the ground area subtended by the radio emission when going from near-vertical to very inclined geometries, making very inclined air showers the most promising ones for cosmic ray radio detection.
We present a new methodology for calculating the electromagnetic radiation from accelerated charged particles. Our formulation --- the `endpoint formulation --- combines numerous results developed in the literature in relation to radiation arising fr
om particle acceleration using a complete, and completely general, treatment. We do this by describing particle motion via a series of discrete, instantaneous acceleration events, or `endpoints, with each such event being treated as a source of emission. This method implicitly allows for particle creation/destruction, and is suited to direct numerical implementation in either the time- or frequency-domains. In this paper, we demonstrate the complete generality of our method for calculating the radiated field from charged particle acceleration, and show how it reduces to the classical named radiation processes such as synchrotron, Tamms description of Vavilov-Cherenkov, and transition radiation under appropriate limits. Using this formulation, we are immediately able to answer outstanding questions regarding the phenomenology of radio emission from ultra-high-energy particle interactions in both the Earths atmosphere and the Moon. In particular, our formulation makes it apparent that the dominant emission component of the Askaryan Effect (coherent radio-wave radiation from high-energy particle cascades in dense media) comes from coherent `bremsstrahlung from particle acceleration, rather than coherent Vavilov-Cherenkov radiation.
We discuss acceleration measurements for a large sample of extragalactic radio jets from the MOJAVE program which studies the parsec-scale jet structure and kinematics of a complete, flux-density-limited sample of Active Galactic Nuclei (AGN). Accele
rations are measured from the apparent motion of individual jet features or components which may represent patterns in the jet flow. We find that significant accelerations are common both parallel and perpendicular to the observed component velocities. Parallel accelerations, representing changes in apparent speed, are generally larger than perpendicular acceleration that represent changes in apparent direction. The trend for larger parallel accelerations indicates that a significant fraction of these changes in apparent speed are due to changes in intrinsic speed of the component rather than changes in direction to the line of sight. We find an overall tendency for components with increasing apparent speed to be closer to the base of their jets than components with decreasing apparent speed. This suggests a link between the observed pattern motions and the underlying flow which, in some cases, may increase in speed close to the base and decrease in speed further out; however, common hydro-dynamical processes for propagating shocks may also play a role. About half of the components show non-radial motion, or a misalignment between the components structural position angle and its velocity direction, and these misalignments generally better align the component motion with the downstream emission. Perpendicular accelerations are closely linked with non-radial motion. When observed together, perpendicular accelerations are usually in the correct direction to have caused the observed misalignment.
