We consider an evolution system describing the phenomenon of marble sulphation of a monument, accounting of the surface rugosity. We first prove a local in time well posedness result. Then, stronger assumptions on the data allow us to establish the existence of a global in time solution. Finally, we perform some numerical simulations that illustrate the main feature of the proposed model.

Integral estimates for weak solutions to a class of Dirichlet problems for nonlinear, fully anisotropic, elliptic equations with a zero order term are obtained by symmetrization techniques. The anisotropy of the principal part of the operator is governed by a general n-dimensional Young function of the gradient which is not necessarily of polynomial type and need not satisfy the $\Delta_2$-condition.

This paper is concerned with diffusive approximations of some numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport, run-and-tumble models of chemotaxis dynamics, and Vlasov-Fokker-Planck plasma modeling. The well-balanced method applied to such kinetic equations leads to time-marching schemes involving a ``{\it scattering $S$-matrix}'', itself derived from a normal modes decomposition of the stationary solution. One common feature these models share is the type of diffusive approximation: their macroscopic densities solve drift-diffusion systems, for which a distinguished numerical scheme is Il'in/Scharfetter-Gummel's ``{\it exponential fitting}'' discretization. We prove that these well-balanced schemes relax, within a parabolic rescaling, towards such type of discretization by means of an appropriate decomposition of the $S$-matrix, hence are {\it asymptotic preserving

Localization phenomena (sometimes called ``{\it flea on the elephant}'') for the operator $L^\varepsilon=-\varepsilon^2 \Delta u + p(\xx) u$, $p(\xx)$ being an asymmetric double-well potential, are studied both analytically and numerically, mostly in two space dimensions within a perturbative framework. Starting from a classical harmonic potential, the effects of various perturbations are retrieved, especially in the case of two asymmetric potential wells. These findings are illustrated numerically by means of an original algorithm, which relies on a discrete approximation of the Steklov-Poincar\'e operator for $L^\varepsilon$, and for which error estimates are established. Such a two-dimensional discretization produces less mesh-imprinting than more standard finite-differences and captures correctly sharp layers.

A binary mixture saturating a horizontal porous layer, with large pores and uniformly heated from below, is considered. The instability of a vertical uid motion (throughflow) when the layer is salted by one salt (either from above or from below) is analyzed. Ultimately boundedness of solutions is proved, via the existence of positively invariant and attractive sets (i.e. absorbing sets). The critical Rayleigh numbers at which steady or oscillatory instability occurs, are recovered. Sufficient conditions guaranteeing that a secondary steady motion or a secondary oscillatory motion can be observed after the loss of stability, are found. When the layer is salted from above, a condition guaranteeing the occurrence of "cold" instability is determined. Finally, the influence of the velocity module on the increasing/decreasing of the instability thresholds is investigated.

The feasibility of liver transplantation from old healthy donors suggests that this organ is able to preserve its functionality during aging. To explore the biological basis of this phenomenon, we characterized the epigenetic profile of liver biopsies collected from 45 healthy liver donors ranging from 13 to 90 years old using the Infinium HumanMethylation450 BeadChip. The analysis indicates that a large remodeling in DNA methylation patterns occurs, with 8823 age-associated differentially methylated CpG probes. Notably, these age-associated changes tended to level off after the age of 60, as confirmed by Horvath's clock. Using stringent selection criteria we further identified a DNA methylation signature of aging liver including 75 genomic regions. We demonstrated that this signature is specific for liver compared to other tissues and that it is able to detect biological age-acceleration effects associated with obesity. Finally we combined DNA methylation measurements with available expression data. Although the intersection between the two omic characterizations was low, both approaches suggested a previously unappreciated role of epithelial-mesenchymal transition and Wnt signaling pathways in the aging of human liver.

In this paper we deal with the analysis of the solutions of traffic flow models at multiple scales, both in the case of a single road and of road networks. We are especially interested in measuring the distance between traffic states (as they result from the mathematical modeling) and investigating whether these distances are somehow preserved passing from the microscopic to the macroscopic scale. By means of both theoretical and numerical investigations, we show that, on a single road, the notion of Wasserstein distance fully catches the human perception of distance independently of the scale, while in the case of networks it partially loses its nice properties.

The paper concerns the uniform polynomial approximation of a function f, continuous on the unit Euclidean sphere of $R^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere. First, we focus on least squares polynomial approximation and prove that the related Lebesgue constants w.r.t. the uniform norm grow at the optimal rate. Then, we consider delayed arithmetic means of least squares polynomials whose degrees vary from n - m up to n + m, being m = ?n for any fixed parameter 0 < ? < 1. As n tends to infinity, we prove that these polynomials uniformly converge to f at the near-best polynomial approximation rate. Moreover, for fixed n, by using the same data points, we can further improve the approximation by suitably modulating the action ray m determined by the parameter ?. Some numerical experiments are given to illustrate the theoretical results.

L'Action Plan è il principale risultato del progetto Coffee B.R.E.A.K.S. e rappresenta un possibile percorso di implementazione del sistema di valutazione del personale CNR, a partire dallo status quo per ogni profilo professionale.

Here some issues are studied, related to the numerical solution of Richards' equation in a one dimensional spatial domain by a technique based on the Transversal Method of Lines (TMoL). The core idea of TMoL approach is to semi-discretize the time derivative of Richards' equation: afterward a system of second order differential equations in the space variable is derived as an initial value problem. The computational framework of this method requires both Dirichlet and Neumann boundary conditions at the top of the column. The practical motivation for choosing such a condition is argued. We will show that, with the choice of the aforementioned initial conditions, our TMoL approach brings to solutions comparable with the ones obtained by the classical Methods of Lines (hereafter referred to as MoL) with corresponding standard boundary conditions: in particular, an appropriate norm is introduced for effectively comparing numerical tests obtained by MoL and TMoL approach and a sensitivity analysis between the two methods is performed by means of a mass balance point of view. A further algorithm is introduced for deducing in a self-sustaining way the gradient boundary condition on top in the TMoL context.

In this paper, we consider a class of models describing multiphase fluids in the framework of mixture theory. The considered systems, in their more general form, contain both the gradient of a hydrostatic pressure, generated by an incompressibility constraint, and a compressible pressure depending on the volume fractions of some of the different phases. To approach these systems, we propose an approximation based on the Leray projection, which involves the use of a symbolic symmetrizer for quasi-linear hyperbolic systems and related paradifferential techniques. In two space dimensions, we prove the well-posedness of this approximation and its convergence to the unique classical solution to the original system. In the last part, we shortly discuss the three dimensional case.

We present a rigorous convergence result for smooth solutions to a singular semilinear hyperbolic approximation, called vector-BGK model, to the solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our proof deeply relies on the dissipative properties of the system and on the use of an energy which is provided by a symmetrizer, whose entries are weighted in a suitable way with respect to the singular perturbation parameter. This strategy allows us to perform uniform energy estimates and to prove the convergence by compactness.

In this work we present a methodology for the mapping of Snow Water Equivalent (SWE) temporal variations based on the Synthetic Aperture Radar (SAR) Interferometry technique and Sentinel-1 data. The shift in the interferometric phase caused by the refraction of the microwave signal penetrating the snow layer is isolated and exploited to generate maps of temporal variation of SWE from coherent SAR interferograms. The main advantage of the proposed methodology with respect to those based on the inversion of microwave SAR backscattering models is its simplicity and the reduced number of required in-situ SWE measurements. The maps, updated up to every 6 days, can attain a spatial resolution up to 20 m with sub-centimetre ASWE measurement accuracy in any weather and sun illumination condition. We present results obtained using the proposed methodology over a study area in Finland. These results are compared with in-situ measurements of ASWE, showing a reasonable match with a mean accuracy of about 6 mm.

Mathematical modeling and optimization provide decision-support tools of increasing popularity to the management of invasive species. In this paper we investigate problems formulated in terms of optimal control theory. A free terminal time optimal control problem is considered for minimizing the costs and the duration of an abatement program. Here we introduce a discount term in the objective function that destroys the non-autonomous nature of the state-costate system. We show that the alternative state-control optimality system is autonomous and its analysis provides the complete qualitative description of the dynamics of the discounted optimal control problem. By using the expression of its invariant we deduce several insights for detecting the optimal control solution for an invasive species obeying a logistic growth.

A challenging task in the management of Protected Areas is to control the spread of invasive species, either floristic or faunistic, and the preservation of indigenous endangered species, tipically competing for the use of resources in a fragmented habitat. In this paper, we present some mathematical tools that have been recently applied to contain the worrying diffusion of wolf-wild boars in a Southern Italy Protected Area belonging to the Natura 2000 network. They aim to solve the problem according to three different and in some sense complementary approaches: (i) the qualitative one, based on the use of dynamical systems and bifurcation theory; (ii) the Z-control, an error-based neural dynamic approach ; (iii) the optimal control theory. In the case of the wild-boars, the obtained results are illustrated and discussed. To refine the optimal control strategies, a further development is to take into account the spatio-temporal features of the invasive species over large and irregular environments. This approach can be successfully applied, with an optimal allocation of resources, to control an invasive alien species infesting the Alta Murgia National Park: Ailanthus altissima. This species is one of the most invasive species in Europe and its eradication and control is the object of research projects and biodiversity conservation actions in both protected and urban areas [11]. We lastly present, as a further example, the effects of the introduction of the brook trout, an alien salmonid from North America, in naturally fishless lakes of the Gran Paradiso National Park, study site of an on-going H2020 project (ECOPOTENTIAL).

Standard reaction-diffusion systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle model in which individuals move following a persistent random walk with finite speed and grow with logistic dynamics. We show that, when the number of individuals is very large, the individual-based model is well described by the continuous reactive Cattaneo equation (RCE), but for smaller values of the carrying capacity important finite-population effects arise. The effects of fluctuations on the propagation speed are investigated both considering the RCE with a cutoff in the reaction term and by means of numerical simulations of the individual-based model. Finally, a more general Lévy walk process for the transport of individuals is examined and an expression for the front speed of the resulting traveling wave is proposed.

In this talk I shall present different mathematical models aimed to describe evolving thermo-mechanics of ice in different topo-morphological and climatic conditions. Up-to-date computational glaciology address to the intensive use of the large amount of data, gathered in (alpine or polar) on-field campaigns, and to the 'brute force' adaptation of the mathematical modelling of glacier evolution based on Glen's law via phenomenological multi-parametrical functional factors and/or addenda. Although, reasonable to fully satisfactory numerical results have been being obtained with this approach adopted by the most popular open-source computational glaciology codes, with the aim to improve the comprehension of the physical mechanisms and processes, I shall discuss extensions of such models by explicit inclusion of natural phase transition occurrence (inherent and/or at a boundary interface) and by expansion of Glen's constitutive equation in order to take into account the effects of the presence of sand and rock fragments in glacier interstices. Several problems will be discussed: the description of the thermo-mechanical evolution of the icy crust of Europa, Juppiter's satellite; the check of the compatibility of the existence of a subglacial lake at Svalbard archipelago; the reproduction of the borehole measurements at the Murtel-Corvatsch glacier, Grisons Alps, Switzerland. Thus extraterrestrial, polar and alpine environments, respectively, will be considered.

The rheological behaviour of an emulsion made of an active polar component and an isotropic passive fluid is studied by lattice Boltzmann methods. Different flow regimes are found by varying the values of the shear rate and extensile activity (occurring, e.g., in microtubule-motor suspensions). By increasing the activity, a first transition occurs from the linear flow regime to spontaneous persistent unidirectional macro-scale flow, followed by another transition either to a (low shear) intermittent flow regime with the coexistence of states with positive, negative, and vanishing apparent viscosity, or to a (high shear) symmetric shear thinning regime. The different behaviours can be explained in terms of the dynamics of the polarization field close to the walls. A maximum entropy production principle selects the most likely states in the intermittent regime.