Labyrinthine pathways towards supercycle attractors in unimodal maps

We uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps characterized each by a Lyapunov exponent that diverges to minus infinity. Amongst the main novel properties are the following: i) The basins of attraction for the phases of the cycles develop fractal boundaries of increasing complexity as the period-doubling structure advances towards the transition to chaos. ii) The fractal boundaries, formed by the preimages of the repellor, display hierarchical structures organized according to exponential clusterings that manifest in the dynamics as sensitivity to the final state and transient chaos. iii) There is a functional composition renormalization group (RG) fixed-point map associated to the family of supercycles. iv) This map is given in closed form by the same kind of $q$-exponential function found for both the pitchfork and tangent bifurcation attractors. v) There is a final stage ultra-fast dynamics towards the attractor with a sensitivity to initial conditions that decreases as an exponential of an exponential of time.Comment: 8 pages, 13 figure

An evolutionary model for GHz Peaked Spectrum Sources. Predictions for high frequency surveys

We have explored, in the general framework of the ``young source'' scenario, evolutionary models for GHz Peaked Spectrum (GPS) galaxies and quasars which reproduce the observed counts, redshift and peak frequency distributions of currently available samples. Substantially different cosmological evolution properties are found for the two populations: the quasar luminosity function must evolve strongly up to $z\sim 1$, while the data on galaxies may be consistent with no evolution. The models show that GPS sources (mostly quasars) may comprise quite a significant fraction of bright ($S> 1$Jy) radio sources at $\nu \geq 30$GHz if the intrinsic distribution of peak frequencies extends up to $\sim 1000$GHz. In any case, however, their fraction decreases rapidly with decreasing flux and their contribution to small scale fluctuations in the frequency range covered by the forthcoming space missions MAP and Planck Surveyor is expected to be minor.Comment: 7 pages, 4 figures, A&A accepte

Gluon and Ghost Dynamics from Lattice QCD

The two point gluon and ghost correlation functions and the three gluon vertex are investigated, in the Landau gauge, using lattice simulations. For the two point functions, we discuss the approach to the continuum limit looking at the dependence on the lattice spacing and volume. The analytical structure of the propagators is also investigated by computing the corresponding spectral functions using an implementation of the Tikhonov regularisation to solve the integral equation. For the three point function we report results when the momentum of one of the gluon lines is set to zero and discuss its implications.Comment: Proceedings of Light Cone 2016, held in Lisbon, September 2016. Minor changes in text. To appear in Few B Sy

Application of the method of multiple scales to unravel energy exchange in nonlinear locally resonant metamaterials

In this paper, the effect of weak nonlinearities in 1D locally resonant metamaterials is investigated via the method of multiple scales. Commonly employed to the investigate the effect of weakly nonlinear interactions on the free wave propagation through a phononic structure or on the dynamic response of a Duffing oscillator, the method of multiple scales is here used to investigate the forced wave propagation through locally resonant metamaterials. The perturbation approach reveals that energy exchange may occur between propagative and evanescent waves induced by quadratic nonlinear local interaction