Spherical geometry and integrable systems

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.Comment: 15 pages, 5 figure

Propagation of UHECRs in cosmological backgrounds: some results from SimProp

Ultra-High-Energy Cosmic Ray (UHECR) nuclei propagating in cosmological radiation backgrounds produce secondary particles detectable at Earth. SimProp is a one dimensional code for extragalactic propagation of UHECR nuclei, inspired by the kinetic approach of Aloisio et al. As in this approach, only a subset of nuclei and nuclear channels are used as representative. We discuss the validation of the code and present applications to UHECR experimental results. In particular we present the expected fluxes of neutrinos produced in some astrophysical scenario.Comment: Poster presented by A. Di Matteo at the 33rd International Cosmic Ray Conference, Rio De Janeiro (Brasil) July 2-9 201

Discrete Reductive Perturbation Technique

We expand a partial difference equation (P$\Delta$E) on multiple lattices and obtain the P$\Delta$E which governs its far field behaviour. The perturbative--reductive approach is here performed on well known nonlinear P$\Delta$Es, both integrable and non integrable. We study the cases of the lattice modified Korteweg--de Vries (mKdV) equation, the Hietarinta equation, the lattice Volterra--Kac--Van Moerbeke (VKVM) equation and a non integrable lattice KdV equation. Such reductions allow us to obtain many new P$\Delta$Es of the nonlinear Schr\"odinger (NLS) type.Comment: 18 pages, 1 figure. submitted to Journal of Mathematical Physic

Cosmogenic neutrinos and ultra-high energy cosmic ray models

We use an updated version of {\it SimProp}, a Monte Carlo simulation scheme for the propagation of ultra-high energy cosmic rays, to compute cosmogenic neutrino fluxes expected on Earth in various scenarios. These fluxes are compared with the newly detected IceCube events at PeV energies and with recent experimental limits at EeV energies of the Pierre Auger Observatory. This comparison allows us to draw some interesting conclusions about the source models for ultra-high energy cosmic rays. We will show how the available experimental observations are almost at the level of constraining such models, mainly in terms of the injected chemical composition and cosmological evolution of sources. The results presented here will also be important in the evaluation of the discovery capabilities of the future planned ultra-high energy cosmic ray and neutrino observatories.Comment: 15 pages, 8 figures, some reference added, version accepted for publication in JCA

On the Integrability of the Discrete Nonlinear Schroedinger Equation

In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a reductive perturbation technique to show an obstruction to its integrability.Comment: 4 pages, accepted in EP

Detection of GRB signals with Fluorescence Detectors

Gamma Ray Bursts are being searched in many ground based experiments detecting the high energy component (GeV $\div$ TeV energy range) of the photon bursts. In this paper, Fluorescence Detectors are considered as possible candidate devices for these searches. It is shown that the GRB photons induce fluorescence emission of UV photons on a wide range of their spectrum. The induced fluorescence flux is dominated by GRB photons from 0.1 to about 100 MeV and, once the extinction through the atmosphere is taken into account, it is distributed over a wide angular region. This flux can be detected through a monitor of the diffuse photon flux, provided that its maximum value exceeds a threshold value, that is primarily determined by the sky brightness above the detector. The feasibility of this search and the expected rates are discussed on the basis of the current GRB observations and the existing fluorescence detectors.Comment: 16 pages 9 eps figure