Phase Space Reduction and the Instanton Crossover in (1+1)-Dimensional Turbulence

We study (1+1)-dimensional turbulence in the framework of the Martin-Siggia-Rose field theory formalism. The analysis is focused on the asymptotic behaviour at the right tail of the probability distribution function (pdf) of velocity differences, where shock waves do not contribute. A BRS-preserving scheme of phase space reduction, based on the smoothness of the relevant velocity fields, leads to an effective theory for a few degrees of freedom. The sum over fluctuations around the instanton solution is written as the expectation value of a functional of the time-dependent physical fields, which evolve according to a set of Langevin equations. A natural regularization of the fluctuation determinant is provided from the fact that the instanton dominates the action for a finite time interval. The transition from the turbulent to the instanton dominated regime is related to logarithmic corrections to the saddle-point action, manifested on their turn as multiplicative power law corrections to the velocity differences pdf.Comment: The revised version contains more detailed discussions on some technical point

Reconstruction of the paleoenvironmental changes around the Miocene–Pliocene boundary along a West–East transect across the Mediterranean

In order to reconstruct the environmental changes at the end of the Messinian salinity crisis, a multidisciplinary study has been carried out with a high sampling resolution of the late Messinian-early Zanclean (Zone MPl 1) sediments along a West-East Mediterranean transect. The studied examples comprise sections from southern Spain (Vera/Almanzora), Balearic Basin (ODP Site 975), Tyrrhenian Basin (ODP Site 974), Sicily (Eraclea Minoa), Zakynthos (Kalamaki), Corfu (Aghios Stefanos), Crete (Aghios Vlasis). Previously analyzed sections from the Levantine Basin (Cyprus and ODP Sites 968 and 969) are used for comparison. The sections have been correlated using planktonic foraminiferal assemblages, sedimentological and stable isotope variations, and compared to the astronomical cyclicity defined in the Miocene-Pliocene boundary stratotype of Eraclea Minoa, Sicily. Variations of CaCO3 content, stable isotopes of carbonates (\u3b418O, \u3b413C), and foraminiferal assemblages indicate similar environmental transition at the Miocene-Pliocene boundary in all of the investigated sections. The latest Messinian deposits are barren of fossils or characterized by only reworked planktonic foraminifers, except for the sporadic presence of Ammonia tepida, brackish or lacustrine ostracods and brackish mollusks typical of the "Lago-Mare" facies. The oxygen and carbon isotopic compositions of carbonates usually exhibit large variations with dominantly low \u3b4 values indicating freshwater dilution. The earliest Pliocene (MPl 1, cycle 1) shows a rapid and progressive increase of the \u3b418O values, which indicates the restoration of marine conditions after the Lago-Mare event. Normal marine environments were definitely established and stabilized at the top of cycle 1. These data confirm that the inflow of marine waters occurred contemporaneously within the whole Mediterranean at the base of Pliocene, although stable marine conditions occurred only about 20 kyrs later