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.

The role of comics in science communications has been subject of a number of recent papers. While some debate on an accepted definition of what constitutes a science comics is still ongoing, the role of comics in science outreach is now universally recognized. [1] Here we present the Comics&Science comic books published by CNR Edizioni and edited by Roberto Natalini and Andrea Plazzi. The Comics&Science concept was implemented in the first place as a section of the Lucca Comics&Games festival, followed by the printed series in 2013. Comics&Science's philosophy is to have science elements, ideas and "bits" integrated into cartoons by the best professional writers and artists. The story must be fun, entertaining and overall artistically and aesthetically significant. Each issue is completed by articles and pieces about and around the topics touched by the story. A Comics&Science issue almost always starts with the cartoonist visiting a research lab/facility. Tipically, the artist has little or no formal scientific background and up to now this has proved to be an effective starting point for exchanging opinions and a cross-debate of sorts. Following the Comics&Science "protocol", Italian hugely popular cartoonist Zerocalcare (millions of books sold in the last few years) visited the Elettra and Fermi light sources prior to working to his "Light Issue", co-edited by the Istituto di Struttura della Materia-CNR (ISM- CNR) and Elettra Sincrotrone Trieste. The upcoming Comics&Science issue (Fall 2019) will be featuring a Periodic Table-inspired story by writer Giovanni Eccher and artist Sergio Ponchione, as a joint venture between the Department of Chemical Science and Technology of Materials (CNR-DSCTM) and the Young Chemists Group and the Group for the Diffusion of the Chemistry Culture of the Italian Chemical Society.

Here we present some studies on the behavior of individuals in a biological networks. The first study is about Physarum polycephalum slime mold and its ability to find the shortest path in a maze. Here we present a PDE chemotaxis model that reproduce its behavior in a network, schematized as a planar graph, (1). In particular, suitable transmission and boundary conditions at each node of the graph are considered to mimic the choice of such an organism to move from an arc to another arc of the network, motivated by the search for food. Several numerical tests are presented for special network geometries to show the qualitative agreement between our model and the laboratory observed behavior of the mold. The second study is about tumor associated macrophages and the mathematical modeling of the behavior of cell populations in a microfluidic chip, an environment constructed in laboratory to mimic complex biological systems. In particular, the developed model consists of reaction-diffusion-transport equations with chemotaxis: birth/death processes, interaction with chemoattractant, interaction and competition between species. Suitable transmission conditions are included in the algorithm and numerical tests are presented.

In this interdisciplinary paper, we study the formation of iron precipitates - the so-called Liesegang rings - in Lecce stones in contact with iron source. These phenomena are responsible of exterior damages of lapideous artifacts, but also in the weakening of their structure. They originate in presence of water, determining the flow of carbonate compounds mixing with the iron ions and then, after a sequence of reactions and precipitation, leading to the formation of Liesegang rings. In order to model these phenomena observed in situ and in laboratory experiments, we propose a modification of the classical Keller-Rubinow model and show the results obtained with some numerical simulations, in comparison with the experimental tests. Our model is of interest for a better understanding of damage processes in monumental stones.

Rapporto tecnico-scientifico del convegno "Mathematics for BioMedicine" dell'Istituto per le Applicazioni del Calcolo M. Picone del CNR, svolto a Roma in data 8-11 ottobre 2018, co-organizzato da Istituto per le Applicazioni del Calcolo M. Picone e Accademia Nazionale dei Lincei e finanziato da INdAM (Istituto Nazionale di Alta Matematica). Topics: immunology, cardiovascular disease, Neurology and aging desease, oncology, epidemiology, endocrinology, stem cells and tissue regeneration. Il report raccoglie obiettivi, abstract, agenda, dati sui partecipanti.

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

Many studies have shown that Physarum polycephalum slime mold is able to find the shortest path in a maze. In this paper we study this behavior in a network, using a hyperbolic model of chemotaxis. Suitable transmission and boundary conditions at each node are considered to mimic the behavior of such an organism in the feeding process. Several numerical tests are presented for special network geometries to show the qualitative agreement between our model and the observed behavior of the mold.

Kinetic BGK numerical schemes for the approximation of incompressible Navier-Stokes equations are derived via classical discrete velocity vector BGK approximations, but applied to an inviscid compressible gas dynamics system with small Mach number parameter, according to the approach of Carfora and Natalini (2008). As the Mach number, the grid size and the timestep tend to zero, the low Mach number limit and the time-space convergence of the scheme are achieved simultaneously, and the numerical viscosity tends to the physical viscosity of the Navier-Stokes system. The method is analyzed and formulated as an explicit finite volume/difference flux vector splitting (FVS) scheme over a Cartesian mesh. It is close in spirit to lattice Boltzmann schemes, but it has several advantages. The first is that the scheme is expressed only in terms of momentum and mass compressible variables. It is therefore very easy to implement, and several types of boundary conditions are straightforward to apply. The second advantage is that the scheme satisfies a discrete entropy inequality, under a CFL condition of parabolic type and a subcharacteristic stability condition involving a cell Reynolds number that ensures that diffusion dominates advection at the level of the grid size. This ensures the robustness of the method, with explicit uniform bounds on the approximate solution. Moreover the scheme is proved to be second-order accurate in space if the parameters are well chosen, this is the case in particular for the Lax-Friedrichs scheme with Mach number proportional to the grid size. The scheme falls then into the class of artificial compressibility methods, the novelty being its exceptionally good theoretical properties. We show the efficiency of the method in terms of accuracy and robustness on a variety of classical two-dimensional benchmark tests. The method is finally applied in three dimensions to compute the permeability of a porous medium defined by a complex idealized Kelvin-like cell. Relations between our scheme and compressible low Mach number schemes are discussed.

We propose a stochastic model in evolutionary game theory where individuals (or subpopulations) can mutate changing their strategies randomly (but rarely) and explore the external environment. This environment affects the selective pressure by modifying the payoff arising from the interactions between strategies. We derive a Fokker-Planck integro-differential equation and provide Monte Carlo simulations for the Hawks vs Doves game. In particular we show that, in some cases, taking into account the external environment favors the persistence of the low-fitness strategy.

We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures with the transport of enzymes or drugs in the extracellular space. The effect of the matrix-degrading enzymes on the tissue composition and its mechanical response are accounted for. Numerical simulations in 1D, 2D and axisymmetric (3D) configurations show how an injection of matrix-degrading enzymes alters the porosity of a biological tissue. We eventually exhibit numerically the main consequences of a matrix-degrading enzyme pretreatment in the framework of chemotherapy: the removal of the diffusive hindrance to the penetration of therapeutic molecules in tumors and the reduction of interstitial fluid pressure which improves transcapillary transport. Both effects are consistent with previous biological observations.

We tackle the issue of measuring and understanding the visitors' dynamics in a crowded museum in order to create and calibrate a predictive mathematical model. The model is then used as a tool to manage, control and optimize the fruition of the museum. Our contribution comes with one successful use case, the Galleria Borghese in Rome, Italy.

Interview to the MIT professor of Mathematics Gigliola Staffilani

Storia sulla rivista Topolino sul primo calcolatore del CNR nel 1955

Volume di Comics&Science dedicato alle donne in matematica

Albo di Comics&Science dedicato alla fisica delle particelle in collaborazione con ISM e una storia di Zerocalcare

Many studies have shown that Physarum polycephalum slime mold is able to find the shortest path in a maze. Here we study this behavior in a network, using a hyperbolic model of chemotaxis [1]. Suitable transmission and boundary conditions at each node are considered to mimic the behavior of such an organism in the feeding process. Several numerical tests are presented for special network geometries to show the qualitative agreement between our model and the observed behavior of the mold.

According to the European Charter for Researchers «all researchers should ensure [...] that the results of their research are disseminated and exploited, e.g. communicated, transferred into other research settings or, if appropriate, commercialised ...». Therefore, it's part of the researchers' mission to raise the general public awareness with respect to science. This need is further emphasized by a survey of Eurobarometer 2010: society is strongly interested in science but, at the same time, is often scared by the risks connected with new technologies. Moreover, irrational attitudes towards science are prompted by a broad scientific illiteracy. The result is a remarkable distance between the community of scientists and the society at large. Mathematics, in this context, has a peculiarity: on one hand, it is seen as less ``dangerous'' than other sciences, as it is not directly related to current issues perceived as controversial and potentially risky (for example, Ogm or nuclear power). On the other hand, however, too often it is seen as a dry, cold discipline, very far from everyday life, with results determined by who knows millennia ago, and not susceptible of review. One more reason to communicate it. In a time when innovation, technological progress and, ultimately, the well-being of a society depend decisively on the mathematical culture that this society can express, the widespread ignorance of the basics of mathematics is politically, socially and culturally dangerous: raising the percentage of people who dominate at least its basics can be an important engine to accelerate the transition to an authentic ``knowledge society''.

We propose a model of a density-dependent compressible-incompressible fluid, which is intended as a simplified version of models based on mixture theory as, for instance, those arising in the study of biofilms, tumor growth and vasculogenesis. Though our model is, in some sense, close to the density-dependent incompressible Euler equations, it presents some differences that require a different approach from an analytical point of view. In this paper, we establish a result of local existence and uniqueness of solutions in Sobolev spaces to our model, using the Leray projector. Besides, we show the convergence of both a continuous version of the Chorin-Temam projection method, viewed as a singular perturbation approximation, and the artificial compressibility method.

[object Object]Metals, extensively used in technology applications as well as in art metal works, have a chemical affinity for oxygen, water, sulphur and are particularly susceptible to electrochemical processes due to the environment. For this reason the monitoring of the effect of environmental conditions (temperature, humidity, pollutant concentration) on their mechanical and physical properties are considered a primary necessity for metal conservation and preservation. The complexity of the degradation phenomena requires to develop predictive tools, able to simulate involved chemical processes. In the present work a mathematical model, based on partial differential equation, is proposed. The model describes the evolution of corrosion processes, which occur on copper-tin alloy specimens exposed to sulphur dioxide atmosphere (SO 2 ).