A multiscale Darcy–Brinkman model for fluid flow in fractured porous media

The aim of this work is to present a reduced mathematical model for describing fluid flow in porous media featuring open channels or fractures. The Darcy’s law is assumed in the porous domain while the Stokes–Brinkman equations are considered in the fractures. We address the case of fractures whose thickness is very small compared to the characteristic diameter of the computational domain, and describe the fracture as if it were an interface between porous regions. We derive the corresponding interface model governing the fluid flow in the fracture and in the porous media, and establish the well-posedness of the coupled problem. Further, we introduce a finite element scheme for the approximation of the coupled problem, and discuss solution strategies. We conclude by showing the numerical results related to several test cases and compare the accuracy of the reduced model compared with the non-reduced one.     

Usage of the Polyphenylene Oxide Dosimeter to Measure Annual Solar Erythemal Exposures

Poly (2, 6-dimethyl-1, 4-phenylene oxide) (PPO) film is a useful dosimetric tool for measuring solar UV in underwater and terrestrial environments. However, little is known about how the response of PPO changes with fluctuations in atmospheric ozone and also to seasonal variations. To resolve this issue this article presents a series of long-term in-air solar erythemal response measurements made over a year from 2007 to 2008 with PPO. This data showed that the PPO dose response varies with modulations of the solar spectrum resulting from changes in season and atmospheric ozone. From this, it was recommended that PPO only be calibrated in the season in which it is to be used at the same time as measurements were being made in the field. Extended solar UV measurements made by PPO with a neutral density filter (NDF) based on polyethylene are also detailed. These measurements showed that the lifetime of PPO could be extended by 5 days before saturation. As the dynamic range for PPO is known to be 5 days during summer at a sub-tropical location, the advantage of using the NDF is that half the number of dosimeters is needed to be fabricated and measured before and after exposure.     

Optimal robust estimates using the Hellinger distance

Optimal robust M-estimates of a multidimensional parameter are described using Hampel’s infinitesimal approach. The optimal estimates are derived by minimizing a measure of efficiency under the model, subject to a bounded measure of infinitesimal robustness. To this purpose we define measures of efficiency and infinitesimal sensitivity based on the Hellinger distance. We show that these two measures coincide with similar ones defined by Yohai using the Kullback–Leibler divergence, and therefore the corresponding optimal estimates coincide too. We also give an example where we fit a negative binomial distribution to a real dataset of “days of stay in hospital” using the optimal robust estimates.     

Coupling Biot and Navier–Stokes equations for modelling fluid–poroelastic media interaction

The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier–Stokes equations with the Biot system. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier–Stokes/Biot system with the appropriate transmission conditions at the interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it happens in hemodynamics applications.     

On the reducibility of the postulation Hilbert scheme

We give a condition in terms of the possible graded Betti numbers compatible with a given Hilbert functionH of 0-dimensional subschemes of ℙ ⁿ which implies the reducibility of the postulation Hilbert scheme and of its subscheme which parametrizes reduced subschemes with Hilbert functionH.     

Sulle algebre per cui vale il teorema degli zeri di Hilbert generalizzato

Riassunto In questo lavoro studiamo quelleA-algebreB, chiamate algebre di Hilbert, in cui è vera una generalizzazione del teorema degli zeri di Hilbert. In particolare studiamo alcune proprietà che implicano cheB sia un'algebra di Hilbert e proviamo il passaggio di queste proprietà rispetto a certi cambiamenti di base. Infine studiamo alcuni anelli di frazioni dell'anello dei polinomi sopra un corpo algebricamente chiusoK ed in un insieme di indeterminate di cardinalità non inferiore a quella diK.

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Summary In this paper we study thoseA-algebrasB, named Hilbert algebras, in which a generalization of Hilbert's Nullstellensatz is verified. Particularly we look at some properties implying thatB is an Hilbert algebra and we prove the passage of this property with respect to certain base change. At last we study some rings of fractions of the polynomial ring generated over an algebrically closed fieldK by a set of indeterminates with cardinality greater or equal then the cardinality ofK.

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Lavoro eseguito nell'ambito dei gruppi di ricerca del C.N.R.