Reply to Comment on "Synchronization dynamics in non-normal networks: the trade-off for optimality"

We reply to the recent note "Comment on Synchronization dynamics in non-normal networks: the trade-off for optimality", showing that the authors base their claims mainly on general theoretical arguments that do not necessarily invalidate the adequacy of our previous study. In particular, they do not specifically tackle the correctness of our analysis but instead limit their discussion on the interpretation of our results and conclusions, particularly related to the concept of optimality of network structure related to synchronization dynamics. Nevertheless, their idea of optimal networks is strongly biased towards their previous work and does not necessarily correspond to our framework, making their interpretation subjective and not consistent. We bring here further evidence from the existing and more recent literature, omitted in the Comment note, that the synchronized state of oscillators coupled through optimal networks, as intended by the authors, can indeed be highly fragile to small but finite perturbations, confirming our original results

Forested Infiltration Area (FIA) Design in the Arborea Nitrate Vulnerable Zone (Sardinia, Italy)

This research aims to test a Managed Aquifer Recharge (MAR) technique based on Forested Infiltration Areas (FIAs) to reduce the groundwater nitrate contamination of a sandy phreatic aquifer in the Arborea NVZ (Sardinia, Italy). The FIA system in Arborea will be supplied with drainage water having an average NO3 concentration of 70 mg L−1, pumped from a dewatering pumping station. The water will be treated before infiltration through an innovative passive treatment system, consisting of a mixture of inert and organic materials, to attenuate organic and inorganic contamination and to prevent clogging processes at the infiltrating surface. The experiment will be conducted for a duration of two years. Monthly monitoring will define, ante operam, the quality baseline of drainage water and groundwater and will assess, post operam, the efficiency of the FIA system. An estimation of the infiltration rate in the sandy soils based on preliminary surveys showed a potential recharge rate of around 0.7 hm3 year−1 per 0.4 ha of the FIA system

Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions

A stochastic model of autocatalytic chemical reactions is studied both numerically and analytically. The van Kampen perturbative scheme is implemented, beyond the second order approximation, so to capture the non Gaussianity traits as displayed by the simulations. The method is targeted to the characterization of the third moments of the distribution of fluctuations, originating from a system of four populations in mutual interaction. The theory predictions agree well with the simulations, pointing to the validity of the van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of observables. We give a bound for the perturbation in order to solve this inversion. And apply this result to a particular case of the control theory, as a first example, and to the ``quantum adiabatic transformation'', as another example.Comment: Version 8.0. 26 pages, Latex2e, final version published in J. Phys.

Scaling of the Critical Function for the Standard Map: Some Numerical Results

The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table