Time delay of light signals in an energy-dependent spacetime metric

In this note we review the problem of time delay of photons propagating in a spacetime with a metric that explicitly depends on the energy of the particles (Gravity-Rainbow approach). We show that corrections due to this approach -- which is closely related to DSR proposal -- produce for small redshifts ($z<<1$) smaller time delays than in the generic Lorentz Invariance Violating case.Comment: 5 pages. This version contains two new references with respect to the published versio

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

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

The linear elasticity tensor of incompressibile materials

With a universally accepted abuse of terminology, materials having much larger stiffness for volumetric than for shear deformations are called incompressible. This work proposes two approaches for the evaluation of the correct form of the linear elasticity tensor of so-called incompressible materials, both stemming from non-linear theory. In the approach of strict incompressibility, one imposes the kinematical constraint of isochoric deformation. In the approach of quasi-incompressibility, which is often employed to enforce incompressibility in numerical applications such as the Finite Element Method, one instead assumes a decoupled form of the elastic potential (or strain energy), which is written as the sum of a function of the volumetric deformation only and a function of the distortional deformation only, and then imposes that the bulk modulus be much larger than all other moduli. The conditions which the elasticity tensor has to obey for both strict incompressibility and quasi-incompressibility have been derived, regardless of the material symmetry. The representation of the linear elasticity tensor for the quasi-incompressible case differs from that of the strictly incompressible case by one parameter, which can be conveniently chosen to be the bulk modulus. Some important symmetries have been studied in detail, showing that the linear elasticity tensors for the cases of isotropy, transverse isotropy and orthotropy are characterised by one, three and six independent parameters, respectively, for the case of strict incompressibility, and two, four and seven independent parameters, respectively, for the case of quasi-incompressibility, as opposed to the two, five and nine parameters, respectively, of the general compressible cas