Arnold maps with noise: Differentiability and non-monotonicity of the rotation number

Arnold's standard circle maps are widely used to study the quasi-periodic route to chaos and other phenomena associated with nonlinear dynamics in the presence of two rationally unrelated periodicities. In particular, the El Nino-Southern Oscillation (ENSO) phenomenon is a crucial component of climate variability on interannual time scales and it is dominated by the seasonal cycle, on the one hand, and an intrinsic oscillatory instability with a period of a few years, on the other. The role of meteorological phenomena on much shorter time scales, such as westerly wind bursts, has also been recognized and modeled as additive noise. We consider herein Arnold maps with additive, uniformly distributed noise. When the map's nonlinear term, scaled by the parameter $\epsilon$, is sufficiently small, i.e. $\epsilon < 1$, the map is known to be a diffeomorphism and the rotation number $\rho_{\omega}$ is a differentiable function of the driving frequency $\omega$. We concentrate on the rotation number's behavior as the nonlinearity becomes large, and show rigorously that $\rho _{\omega }$ is a differentiable function of $\omega$, even for $\epsilon \geq 1$, at every point at which the noise-perturbed map is mixing. We also provide a formula for the derivative of the rotation number. The reasoning relies on linear-response theory and a computer-aided proof. In the diffeomorphism case of $\epsilon <1$, the rotation number $\rho_{\omega }$ behaves monotonically with respect to $\omega$. We show, using again a computer-aided proof, that this is not the case when $\epsilon \geq 1$ and the map is not a diffeomorphism.Comment: Electronic copy of final peer-reviewed manuscript accepted for publication in the Journal of Statistical Physic

Chemical and NORM management in the Contaminated Sites of the Italian National Priority List

Contaminated Sites of the Italian National Priority List, being the legacy of industrial development, have different types of contamination to be managed with different approaches, different legislative procedures, and different control authorities; in particular between chemical and radiological contamination. This may lead to a bottleneck and to a delay in the operations needed for remediation. A synergistic approach involving all affected stakeholders certainly could reduce the time and cost of interventions measures

The ALICE Silicon Pixel Detector: readiness for the first proton beam

The Silicon Pixel Detector (SPD) is the innermost element of the ALICE Inner Tracking System (ITS). The SPD consists of two barrel layers of hybrid silicon pixels surrounding the beam pipe with a total of 48 10^7 pixel cells. The SPD features a very low material budget, a 99.9% efficient bidimensional digital response, a 12 micron spatial precision in the bending plane (rf ) and a prompt signal as input to the L0 trigger. The SPD commissioning in the ALICE experimental area is well advanced and it includes calibration runs with internal pulse and cosmic ray runs. In this contribution the commissioning of the SPD is reviewed and the first results from runs with cosmic rays and circulating proton beams are presented

Introduction to the special issue on the statistical mechanics of climate

We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions

Filosofia e storiografia. Studi in onore di Giovanni Papuli, I. Dall'Antichità al Rinascimento

Il volume raccoglie i contributi della storia del pensiero filosofico dall'Antichità fino al Rinascimento, con particolare riguardo alle tematiche della Metafisica di Aristotele, del Neoplatonismo, dell’Aristotelismo padovano e del Tardo Rinascimento

Phase-locking patterns in a resonate and fire neural model with periodic drive

In this paper we studied a resonate and fire relaxation oscillator subject to time dependent modulation to investigate phase-locking phenomena occurring in neurophysiological systems. The neural model (denoted LFHN) was obtained by linearization of the FitzHugh-Nagumo neural model near an hyperbolic fixed point and then by introducing an integrate-and-fire mechanism for spike generation. By employing specific tools to study circle maps, we showed that this system exhibits several phase-locking patterns in the presence of periodic perturbations. Moreover, both the amplitude and frequency of the modulation strongly impact its phase-locking properties. In addition, general conditions for the generation of firing activity were also obtained. In addition, it was shown that for moderate noise levels the phase-locking patterns of the LFHN persist. Moreover, in the presence of noise, the rotation number changes smoothly as the stimulation current increases. Then, the statistical properties of the firing map were investigated too. Lastly, the results obtained with the forced LFHN suggest that such neural model could be used to fit specific experimental data on the firing times of neurons