A stochastic infinite dimensional version of the GOY model is rigorously investigated. Well posedness of strong solutions, existence and p-integrability of invariant measures is proved. Existence of solutions to the zero viscosity equation is also proved. With these preliminary results, the asymptotic exponents ζ p of the structure function are investigated. Necessary and sufficient conditions for ζ 2 ≥ 2/3 and ζ 2 = 2/3 are given and discussed on the basis of numerical simulations.

The spatial distribution of shallow landslides is strongly influenced by different climatic conditions and environmental settings. This makes difficult the implementation of an exhaustive monitoring technique for\ud correctly assessing the landslide susceptibility in different environmental contexts. In this work, a unique methodological strategy, based on the statistical implementation of the generalized additive model (GAM), was performed. This method was used to investigate the shallow landslide predisposition of four sites with different geological, geomorphological and land-use characteristics: the Rio Frate and the Versa catchments (Southern\ud Lombardy) and the Vernazza and the Pogliaschina catchments (Eastern Liguria). A good predictive overall accuracy was evaluated computing by the area under the ROC curve (AUROC), with values ranging from 0.76 to 0.82 and estimating the mean accuracy of the model (0.70–0.75). The method showed a high flexibility, which led to a good identification of the most significant predisposing factors for shallow landslide occurrence\ud in the different investigated areas. In particular, detailed susceptibility maps were obtained, allowing to identify the shallow landslide prone areas. This methodology combined with the use of the rainfall thresholds \ud for triggering shallow landslides may provide an innovative tool useful for the improvement of spatial planning and early warning systems

We explore the quantum phases emerging from the interplay between spin and motional degrees of freedom of a one-dimensional quantum fluid of spinful fermionic atoms, effectively interacting via a photon-mediating mechanism with tunable sign and strength g, as it can be realized in present-day experiments with optical cavities. We find the emergence, in the very same system, of spin-and atomic-density wave ordering, accompanied by the occurrence of superfluidity for g > 0, while cavity photons are seen to drive strong correlations at all g values, with fermionic character for g > 0, and bosonic character for g < 0. Due to the long-range nature of interactions, to infer these results we combine mean-field and exact diagonalization methods supported by bosonization analysis.

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