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The Cosmic-Ray Extremely Distributed Observatory (CREDO) is a project dedicated to global studies of extremely extended cosmic-ray phenomena, the cosmic-ray ensembles (CRE), beyond the capabilities of existing detectors and observatories. Up to date cosmic-ray research has been focused on detecting single air showers, while the search for ensembles of cosmic-rays, which may overspread a significant fraction of the Earth, is a scientific terra incognita. Instead of developing and commissioning a completely new global detector infrastructure, CREDO proposes approaching the global cosmic-ray analysis objectives with all types of available detectors, from professional to pocket size, merged into a worldwide network. With such a network it is possible to search for evidences of correlated cosmic-ray ensembles. One of the observables that can be investigated in CREDO is a number of spatially isolated events collected in a small time window which could shed light on fundamental physics issues. The CREDO mission and strategy requires active engagement of a large number of participants, also non-experts, who will contribute to the project by using common electronic devices (e.g. smartphones). In this note the status and perspectives of the project is presented., Comment: This article belongs to the Special Issue Selected Papers from the 7th International Conference on New Frontiers in Physics (ICNFP 2018)

In the past few years, cosmic-rays beyond the GZK cut-off ($E > 5 \times 10^{19}$ eV) have been detected by leading collaborations such as Pierre Auger Observatory. Such observations raise many questions as to how such energies can be reached and what source can possibly produce them. Although at lower energies, mechanisms such as Fermi acceleration in supernovae front shocks seem to be favored, top-down scenarios have been proposed to explain the existence of ultra-high energy cosmic-rays: the decay of super-massive long-lived particles produced in the early Universe may yield to a flux of ultra-high energy photons. Such photons might be presently generating so called super-preshowers, an extended cosmic-ray shower with a spatial distribution that can be as wide as the Earth diameter. The Cosmic Ray Extremely Distributed Observatory (CREDO) mission is to find such events by means of a network of detectors spread around the globe. CREDO's strategy is to connect existing detectors and create a worldwide network of cosmic-ray observatories. Moreover, citizen-science constitutes an important pillar of our approach. By helping our algorithms to recognize detection patterns and by using smartphones as individual cosmic-ray detectors, non-scientists can participate in scientific discoveries and help unravel some of the deepest mysteries in physics., Comment: excited QCD Conference, CREDO Collaboration, 7 pages, 3 figures

Although the photon structure is most efficiently studied with the accelerator instruments, there is also a scientifically complementary potential in investigations on photons produced in the outer space. This potential is already being explored with gamma ray telescopes, ultra-high energy cosmic ray observatories and, since very recently, by the Cosmic-Ray Extremely Distributed Observatory (CREDO). Unlike the former instruments focused on detection of single photons, CREDO aims at the detection of cascades (ensembles) of photons originating even at astrophysical distances. If at least a part of such a cascade reaches Earth, it might produce a unique pattern composed of a number of air showers observable by an appropriately dense array of standard detectors. If the energies of air showers constituting the pattern are relatively low and if the typical distances between the neighbors are large, the ensemble character of the whole phenomenon might remain uncovered, unless the CREDO strategy is implemented., Comment: 9 pages, 5 figures, talk given at the PHOTON 2017 Conference, CERN

The Cosmic-Ray Extremely Distributed Observatory (CREDO) is an infrastructure for global analysis of extremely extended cosmic-ray phenomena, so-called super-preshowers, beyond the capabilities of existing, discrete, detectors and observatories. To date cosmic-ray research has been focused on detecting single air showers, while the search for ensembles of cosmic-ray events induced by super-preshowers is a scientific terra incognita - CREDO explores this uncharted realm. Positive detection of super-preshowers would have an impact on ultra-high energy astrophysics, cosmology and the physics of fundamental particle interactions as they can theoretically be formed within both classical (photon-photon interactions) and exotic (Super Heavy Dark Matter particle decay and interaction) scenarios. Some super-preshowers are predicted to have a significant spatial extent - a unique signature only detectable with the existing cosmic-ray infrastructure taken as a global network. An obvious, although yet unprobed, super-preshower 'detection limit' would be located somewhere between an air shower, induced by a super-preshower composed of tightly collimated particles, and a super-preshower composed of particles spread so widely that only few of them can reach the Earth. CREDO will probe this detection limit, leading to either an observation of an as yet unseen physical phenomenon, or the setting upper limits to the existence of large extraterrestrial cascades which would constrain fundamental physics models. While CREDO's focus is on testing physics at energies close to the Grand Unified Theories range, the broader phenomena are expected to be composed of particles with energies ranging from GeV to ZeV. This motivates our advertising of this concept across the astroparticle physics community.

Any considerations on propagation of particles through the Universe must involve particle interactions: processes leading to production of particle cascades. While one expects existence of such cascades, the state of the art cosmic-ray research is oriented purely on a detection of single particles, gamma rays or associated extensive air showers. The natural extension of the cosmic-ray research with the studies on ensembles of particles and air showers is being proposed by the CREDO Collaboration. Within the CREDO strategy the focus is put on generalized super-preshowers (SPS): spatially and/or temporally extended cascades of particles originated above the Earth atmosphere, possibly even at astrophysical distances. With CREDO we want to find out whether SPS can be at least partially observed by a network of terrestrial and/or satellite detectors receiving primary or secondary cosmic-ray signal. This paper addresses electromagnetic SPS, e.g. initiated by VHE photons interacting with the cosmic microwave background, and the SPS signatures that can be seen by gamma-ray telescopes, exploring the exampleof Cherenkov Telescope Array. The energy spectrum of secondary electrons and photons in an electromagnetic super-preshower might be extended over awide range of energy, down to TeV or even lower, as it is evident from the simulation results. This means that electromagnetic showers induced by such particles in the Earth atmosphere could be observed by imaging atmospheric Cherenkov telescopes. We present preliminary results from the study of response of the Cherenkov Telescope Array to SPS events, including the analysis of the simulated shower images on the camera focal plane and implementedgeneric reconstruction chains based on the Hillas parameters., Comment: Proceedings of the 35th International Cosmic Ray Conference (ICRC 2017), Bexco, Busan, Korea

The main objective of the Cosmic-Ray Extremely Distributed Observatory (CREDO) is the detection and analysis of extended cosmic ray phenomena, so-called super-preshowers (SPS), using existing as well as new infrastructure (cosmic-ray observatories, educational detectors, single detectors etc.). The search for ensembles of cosmic ray events initiated by SPS is yet an untouched ground, in contrast to the current state-of-the-art analysis, which is focused on the detection of single cosmic ray events. Theoretical explanation of SPS could be given either within classical (e.g., photon-photon interaction) or exotic (e.g., Super Heavy Dark Matter decay or annihilation) scenarios, thus detection of SPS would provide a better understanding of particle physics, high energy astrophysics and cosmology. The ensembles of cosmic rays can be classified based on the spatial and temporal extent of particles constituting the ensemble. Some classes of SPS are predicted to have huge spatial distribution, a unique signature detectable only with a facility of the global size. Since development and commissioning of a completely new facility with such requirements is economically unwarranted and time-consuming, the global analysis goals are achievable when all types of existing detectors are merged into a worldwide network. The idea to use the instruments in operation is based on a novel trigger algorithm: in parallel to looking for neighbour surface detectors receiving the signal simultaneously, one should also look for spatially isolated stations clustered in a small time window., Comment: arXiv admin note: text overlap with arXiv:1709.05196

We study functions related to the experimentally observed Havriliak-Negami dielectric relaxation pattern in the frequency domain $\sim[1+(i\omega\tau_{0})^{\alpha}]^{-\beta}$ with $\tau_{0}$ being some characteristic time. For $\alpha = l/k< 1$ ($l$ and $k$ positive integers) and $\beta > 0$ we furnish exact and explicit expressions for response and relaxation functions in the time domain and suitable probability densities in their "dual" domain. All these functions are expressed as finite sums of generalized hypergeometric functions, convenient to handle analytically and numerically. Introducing a reparameterization $\beta = (2-q)/(q-1)$ and $\tau_{0} = (q-1)^{1/\alpha}$ $(1 < q < 2)$ we show that for $0 < \alpha < 1$ the response functions $f_{\alpha, \beta}(t/\tau_{0})$ go to the one-sided L\'{e}vy stable distributions when $q$ tends to one. Moreover, applying the self-similarity property of the probability densities $g_{\alpha, \beta}(u)$, we introduce two-variable densities and show that they satisfy the integral form of the evolution equation.

We study numerically self-trapped (polaron) states of quasiparticles (electrons, holes or excitons) in a deformable nanotube formed by a hexagonal lattice, wrapped into a cylinder (carbon- and boron nitride-type nanotube structures). We present a Hamiltonian for such a system taking into account an electron-phonon interaction, and determine conditions under which the lowest energy states are polarons.We compute a large class of numerical solutions of this model for a wide range of the parameters. We show that at not too strong electron-phonon coupling, the system admits ring-like localized solutions wrapped around the nanotube (the charge carrier is localized along the nanotube axis and uniformly distributed with respect to the azimuthal coordinate). At stronger coupling, solutions are localized on very few lattice sites in both directions of the nanotube. The transition from one type solution to the other one depends on the diameter of the nanotube. We show that for the values of the carbon nanotube parameters, the polarons have a ring-like structure wrapped around the nanotube with a profile resembling that of the nonlinear Schrodinger soliton., Comment: 16 pages, 21 figures