Zero Viscosity Limit for Analytic Solutions of the Primitive Equations

The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be O(\u3bd). The main assumption is spatial analyticity of the initial datum

Provenance and sediment dispersal in the Po-Adriatic source-to-sink system unraveled by bulk-sediment geochemistry and its linkage to catchment geology

The Po-Adriatic region offers an excellent case for reconstructing sediment provenance and transport pathways of a multi-sourced sediment-routing system. Through a comprehensive set of ~1,400 geochemical data, a model for provenance and sediment flux was built based on distinct compositional fingerprints of 53 fluvial systems and their comparison to coastal, shelf and deep-marine sediments. Geochemically unique catchment lithologies (mafic/ultramafic rocks, limestones and dolostones) were used as end-members to assess exclusive source-rock signatures. Following calibration with sedimentary facies, selected key elements and element ratios poorly sensitive to particle size (Ni/Cr, MgO, Ni/Al2O3, Cr/V, Ca/Al2O3 and Ce/V) were adopted as provenance indicators. The high-Ni and high-Cr source-rock signature of mafic/ultramafic rocks widely exposed in the Po River watershed and along the Albanian Dinarides contrasts markedly with the high-Ca (and locally high-Mg) geochemical composition of Eastern Alpine, Apennine, and Eastern Adriatic (Montenegro, Croatia, Slovenia) river catchments, which are, instead, carbonate-rich and virtually ophiolite-free. Relatively high Ce values from Apulian river samples serve as a key marker for a minor, but very distinct sediment provenance from southern Apennine alkaline volcanic rocks. Despite along-shore mixing and dilution with sediment sourced from other river catchments, the geochemical signature of Adriatic shelf muds primarily reflects composition of sediment eroded from the contiguous continental areas. Chromium-rich and nickel-rich detritus generated in mafic and ultramafic complexes of the Western Alps and conveyed through the Po River into the Adriatic Sea records a geochemical signal that can be traced downstream as long as 1000 km, from the Alpine zone of sediment production to the area of final deposition, offshore Apulia. While longitudinal dispersion linked to the general cyclonic, counter-clockwise Adriatic circulation is prevailing along the Western Adriatic Sea, conspicuous detrital input from transversal pathways to the deep sea is revealed across the Eastern Adriatic shelf using heavy metals as provenance tracers. Estimates of fluvial sediment loads and compositional fingerprinting of fluvial, coastal and shelf sediments indicate that previously neglected ophiolite-rich successions of Albania represent a major sediment-conveyor to the offshore sinks (Southern Adriatic Deep and Mid-Adriatic Deep) through significant cross-shore and NNW-directed sediment transport in the Eastern Adriatic Sea. A cut-off value of the Ni/Cr ratio targeted around 0.8 represents an effective tool for the differentiation in marine sediments of Ni-rich (serpentine-rich) ophiolite detritus of Albanian origin from mafic/ultramafic sources of Alpine affinity. High trace-metal contents found within the Adriatic deep basin are mostly of natural origin and only minimally reflect metal contamination

Middle to late Holocene environmental evolution of the Pisa coastal plain (Tuscany, Italy) and early human settlements

A cross-disciplinary (sedimentological, geochemical, micropalaeontological and archaeological) examination of 12 continuous cores, up to 20m long, integrated with stratigraphical, geomorphological and historical investigations, allows for reliable delineation of the middle-late Holocene environmental evolution in the Pisa old town area, with special emphasis on the Etruscan age transition. Depositional facies were identified through integration of sedimentological and micropalaeontological (benthic foraminifers, ostracods, phytoclasts and palynomorphs) data, while sediment dispersal patterns were reconstructed on the basis of geochemical analyses. Facies architecture was chronologically constrained by combined archaeological and radiocarbon dating. The turnaround from early Holocene, transgressive conditions to the ensuing (middle-late Holocene) phase of sea-level highstand is witnessed by a prominent shallowing-upward succession of lagoonal, paludal and then poorly drained floodplain deposits supplied by two river systems (Arno and Serchio). This 'regressive' trend, reflecting coastal progradation under nearly stable sea-level conditions, was interrupted by widespread swamp development close to the Iron-Etruscan age transition. The expansion of vast, low-lying paludal areas across the alluvial plain was mostly induced by the intricate, short-term evolution of the meandering Arno and Serchio river systems. These changes in the fluvial network, which occurred during a period of variable climate conditions, strongly influenced the early Etruscan culture (7th-5th century BC) in terms of human settlement and society behaviour. Conversely, a strong impact of human frequentation on depositional environments is observed at the transition to the Roman age (from the 1st century BC onwards), when the wetlands were drained and the modern alluvial plain started to form. The palaeoenvironmental reconstruction fits in with the original geographical descriptions mentioned in Strabo's Chronicles, and provides chronologically constrained data of fluvial evolution from the Pisa old town area. © 2013 Elsevier Ltd and INQUA

Applications of biopolymers to processes of environmental control

Two new methods of insolubilizing in cellulose triacetate membranes, natural or synthetic polyelectrolytes, able to bind heavy metal ions, were experimented and discussed. The efficiency of the obtained membranes was tested by monitoring the cupric ion adsorption with a copper ion selective electrode (ISE

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids

We consider the flow of an upper convected Maxwell fluid in the limit of high Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be imposed on the solutions. We derive equations for the resulting boundary layer and prove the well-posedness of these equations. A transformation to Lagrangian coordinates is crucial in the argument

MAPPA cores: an interdisciplinary approach

In the urban and periurban area of Pisa, 18 cores ranging in depth between 7 and 15 m were performed and analysed through an interdisciplinary approach, which led to an improved stratigraphic log representation. The acquired data also improved our knowledge about the palaeoenvironmental and human settlement evolution of Pisa area over the past 6000 years, evidencing the mutual interaction existing between landscape and human activities

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur

Complications and Mortality Rate of Cytoreductive Surgery with Hyperthermic Intraperitoneal Chemotherapy: Italian Peritoneal Surface Malignancies Oncoteam Results Analysis

Background: Cytoreductive surgery with hyperthermic intraperitoneal chemotherapy may significantly improve survival for selected patients with peritoneal surface malignancies, but it has always been criticized due to the high incidence of postoperative morbidity and mortality. Methods: Data were collected from nine Italian centers with peritoneal surface malignancies expertise within a collaborative group of the Italian Society of Surgical Oncology. Complications and mortality rates were recorded, and multivariate Cox analysis was used to identify risk factors. Results: The study included 2576 patients. The procedure was mostly performed for ovarian (27.4%) and colon cancer (22.4%). The median peritoneal cancer index was 13. Overall postoperative morbidity and mortality rates were 34% and 1.6%. A total of 232 (9%) patients required surgical reoperation. Multivariate regression logistic analysis identified the type of perfusion (p ≤ 0.0001), body mass index (p ≤ 0.0001), number of resections (p ≤ 0.0001) and colorectal resections (p ≤ 0.0001) as the strongest predictors of complications, whereas the number of resections (p ≤ 0.0001) and age (p = 0.01) were the strongest predictors of mortality. Conclusions: Cytoreductive surgery with hyperthermic intraperitoneal chemotherapy is a valuable option of treatment for selected patients with peritoneal carcinomatosis providing low postoperative morbidity and mortality rates, if performed in high-volume specialized centers

Immunogenicity and safety after the third dose of BNT162b2 anti-SARS-CoV-2 vaccine in patients with solid tumors on active treatment: a prospective cohort study

Background: Although a full course of coronavirus disease 2019 (COVID-19) vaccine is effective in cancer patients, the duration of the protection and the efficacy of a booster dose against the new variants remain unknown. We prospectively evaluated the immunogenicity of the third dose of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) BNT162b2 messenger RNA vaccine in cancer patients undergoing active treatment. Patients and methods: Patients with solid cancer, vaccinated with a booster dose during active treatment, were enrolled in this study. Patients were classified into SARS-CoV-2 naïve (without previous COVID-19 infection) and SARS-CoV-2 experienced (with previous COVID-19 infection). Neutralizing antibody (NT Ab) titer and total anti-Spike immunoglobulin G (IgG) concentration were quantified in serum. Heparinized whole blood samples were used for SARS-CoV-2 Interferon Gamma Release Assay (IGRA). The primary endpoint was to assess the increase of IgG antibody level between baseline and 3 weeks after the booster. Results: One hundred and forty-two consecutive patients were recruited. In SARS-CoV-2-naïve subjects, the median level of IgG was 157 BAU/ml [interquartile range (IQR) 62-423 BAU/ml] at T0 and reached a median of 2080 BAU/ml (IQR 2080-2080 BAU/ml) at 3 weeks after booster administration (T1; P < 0.0001). A median 16-fold increase of SARS-CoV-2 NT Ab titer (IQR 4-32) was observed in naïve subjects (from median 20, IQR 10-40, to median 640, IQR 160-640; P < 0.0001). Median interferon-γ level at T1 was significantly higher than that measured at T0 in SARS-CoV-2-naïve subjects (P = 0.0049) but not in SARS-CoV-2-experienced patients. The median level of SARS-CoV-2 NT Abs was 32-fold lower against Omicron compared to the wild-type strain (P = 0.0004) and 12-fold lower compared to the Delta strain (P = 0.0110). Conclusions: The third dose is able to trigger both the humoral and the cell-mediated immune response in cancer patients on active treatment. Our preliminary data about the neutralization of the SARS-CoV-2 vaccine against variants of concern seem to confirm the lower vaccine activity