Roberto Natalini

Italian National Research Council | CNR · Institute for Applied Mathematics "Mauro Picone" IAC

IIn this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the chemoattractant is considered as a continuous signal which solves a diffusive equation. For this model we prove the...

The present work is devoted to modeling and simulation of the carbonation process in concrete. To this aim we introduce some free boundary problems which describe the evolution of calcium carbonate stones under the attack of CO 2 dispersed in the atmosphere, taking into account both the shrinkage of concrete and the influence of humidity on the car...

Many paintings from the 19th century have exhibited signs of fading and discoloration, often linked to cadmium yellow, a pigment widely used by artists during that time. In this work, we develop a mathematical model of the cadmium sulfide photocatalytic reaction responsible for these damages. By employing non-local integral operators, we capture th...

One of the most crucial and lethal characteristics of solid tumors is represented by the increased ability of cancer cells to migrate and invade other organs during the so-called metastatic spread. This is allowed thanks to the production of matrix metalloproteinases (MMPs), enzymes capable of degrading a type of collagen abundant in the basal memb...

Recently, a growing interest in reproducing biological phenomena by in silico models has been registered. In this framework, the present work is inspired by new advancements in Organs-on-chip technology and, in particular, in Cancer-on-chip experiment, where tumor cells are treated with chemotherapy drugs and secrete chemical signals in the environ...

A general class of hybrid models has been introduced recently, gathering the advantages multiscale descriptions. Concerning biological applications, the particular coupled structure fits to collective cell migrations and pattern formation scenarios. In this context, cells are modelled as discrete entities and their dynamics is given by ODEs, while...

In this paper we present a survey about a series of works developed in the last 20 years, with our group, on chemical aggression of stone artifacts. Here we describe the modelling of different phenomena responsible for exterior and internal degradation of porous materials, such as the evolution of gypsum crust in marble stones, the sodium sulphate...

In recent years an increasing interest is registered in the direction of developing techniques to combine experimental data and mathematical models, in order to produce systems, i.e., in silico models, whose solutions could reproduce and predict experimental outcomes. Indeed, the success of informed models is mainly due to the consistent improvemen...

Usually, clinicians assess the correct hemodynamic behavior and fetal well-being during the gestational age thanks to their professional expertise, with the support of some indices defined for Doppler fetal waveforms. Although this approach has demonstrated to be satisfactory in the most of the cases, it can be largely improved with the aid of more...

How can Science be told in, and with comics, if ever? In recent years, the CNR Edizioni Comics&Science label tried to answer this question with a variety of projects, all spawned by the all-time classic comic book format. Let us recapitulate, with an open eye on future developments.

Endothelial cell (EC) migration is crucial for a wide range of processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. We have previously demonstrated that ECs cultured on 15-μm wide adhesive line patterns exhibit three distinct migration phenotypes: (a) “running” cells that are polarized...

In this paper we introduce a mathematical model of concrete carbonation Portland cement specimens. The main novelty of this work is to describe the intermediate chemical reactions, occurring in the carbonation process of concrete, involving the interplay of carbon dioxide with the water present into the pores. Indeed, the model here proposed, besid...

In the context of hyperbolic systems of balance laws, the Shizuta–Kawashima coupling condition guarantees that all the variables of the system are dissipative even though the system is not totally dissipative. Hence it plays a crucial role in terms of sufficient conditions for the global in time existence of classical solutions. However, it is easy...

Digital transformation is a process that companies start with different purposes. Once an enterprise embarks on a digital transformation process it translates all its business processes (or, at least, part of them) into a digital replica. Such a digital replica, the so-called digital twin, can be described by Mathematical Science tools allowing cos...

The present work is inspired by laboratory experiments, investigating the cross-talk between immune and cancer cells in a confined environment given by a microfluidic chip, the so called Organ-on-Chip (OOC). Based on a mathematical model in form of coupled reaction–diffusion-transport equations with chemotactic functions, our effort is devoted to t...

The present work is motivated by the development of a mathematical model mimicking the mechanisms observed in lab-on-chip experiments, made to reproduce on microfluidic chips the in vivo reality. Here we consider the Cancer-on-Chip experiment where tumor cells are treated with chemotherapy drug and secrete chemical signals in the environment attrac...

In this paper, we study linear parabolic equations on a finite oriented star-shaped network; the equations are coupled by transmission conditions set at the inner node, which do not impose continuity on the unknown. We consider this problem as a parabolic approximation of a set of the first-order linear transport equations on the network, and we pr...

This article deals with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined with b...

The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for...

The aim of this preliminary study is to understand and simulate the hydric behaviour of a porous material in the presence of protective treatments. In particular, here the limestone Lumaquela deAjarte is considered before and after the application of the silane-based product ANC. A recently developed mathematical model was applied in order to descr...

The degradation of monumental stones resulting from the mutual interaction between mechanical actions and environment/pollution conditions is investigated here. In particular, the stone degradation is estimated as a function of the environmental conditions and the prediction of damaging phenomena, which can compromise permanently the fruition of mo...

In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [13]. Unlike previous results on the Cucker-Smale model, our approach is not based on the empirical measures, but, using an...

In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike previous results on the Cucker-Smale model, our approach is not based on the empirical measures, but, using an...

This article is concerned with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined...

In this paper, 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...

In this paper we study linear parabolic equations on a finite oriented starshaped network; the equations are coupled by transmission conditions set at the inner node, which do not impose continuity on the unknown. We consider this problem as a parabolic approximation of a set of first order linear transport equations on the network and we prove tha...

The present work was inspired by the recent developments in laboratory experiments made on chip, where culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis, and takes into account the interactions among cell populations and the possibility of drug administration for dr...

In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to describe the cell migration and self-organization...

In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to describe the cell migration and self-organization...

The aim of this preliminary study is to understand and simulate the hydric behaviour of a porous material in the presence of protective treatments. In particular, here the limestone Lumaquela deAjarte is considered before and after the application of the silane-based product ANC. A recently developed mathematical model was applied in order to descr...

Background and objective: The paper focuses on the numerical strategies to optimize a plasmid DNA delivery protocol, which combines hyaluronidase and electroporation. Methods: A well-defined continuum mechanics model of muscle porosity and advanced numerical optimization strategies have been used, to propose a substantial improvement of a pre-ex...

The definition of an innovative therapeutic protocol requires the fine tuning of all the involved operations in order to maximize the efficiency. In some cases, the price of the experiments, or their duration, represents a great obstacle and the full potential of the protocol risks to be reduced or even hidden by a non-optimal application. The impl...

We consider a simple example of a partially dissipative hyperbolic system violating the Shizuta-Kawashima condition, i.e. such that some eigendirections do not exhibit dissipation at all. In the space-time resonances framework introduced by Germain, Masmoudi and Shatah, we prove that, when the source term has a Nonresonant Bilinear Form, as propose...

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 c...

We present a rigorous convergence result for the smooth solutions to a singular semilinear hyperbolic approximation, a vector BGK model, to the solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our proof is based on the use of a constant right symmetrizer, weighted with respect to the parameter of the singular pertubation s...

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 c...

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.

Gigliola Staffilani is an Italian mathematician working in the USA as the Abby Rockefeller Mauze Professor of Mathematics at the Massachusetts Institute of Technology. Her research concerns harmonic analysis and partial differential equations. In 2014, she was elected to the American Academy of Arts and Sciences. Here the interview by Roberto Natal...

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...

La ricerca a livello internazionale in didattica della matematica ha prodotto nel tempo importanti risultati relativi all'apprendimento-insegnamento, alcuni dei quali svilup-pati nel nostro Paese, dove la disciplina ha una radicata tradizione di ricerca. Il pre-sente manuale intende condividere, spiegare e commentare alcuni di questi risultati, a p...

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 nume...

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 illustrat...

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 illustrat...

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 pres...

We present a rigorous convergence result for the smooth solutions to a singular semilinear hyperbolic approximation, a vector BGK model, to the solutions to the incompressible Navier-Stokes equations in Sobolev spaces. Our proof is based on the use of a constant right symmetrizer, weighted with respect to the parameter of the singular pertubation s...

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 both the tissue’s composition and its mechanical response is included in the...

This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many prominent researchers in both Mathematical Analysis and Numerical Computing, the goal being to promote interdisciplinary collaborations. Accordingly, the following thematic areas were developed: 1. Lagrang...

In this paper we propose a new mathematical model describing the effect of phosphocitrate (PC) on sodium sulphate crystallization inside bricks. This model describes salt and water transport, and crystal formation in a one dimensional symmetry. This is a preliminary study that takes into account mathematically the effects of inhibitors inside a por...

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-Plank integro-di...

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-Plank integro-di...

We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with...

In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility constraint, and the gradient of a compressible pressure depending on the volume fractions of some of the diff...

In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility constraint, and the gradient of a compressible pressure depending on the volume fractions of some of the diff...

Cell Index data recorded by xCELLigence of the different experiments in our study. Panels (a),(c),(e),(g),(i) describe the basal migration, (b),(d),(f),(h),(j) the migration in presence of FBS. In each panel the curves represent an independent experiment carried out in quadruplicated and averaged. The observed curves in Figs 3 and 4 are obtained as...

Basal migration xCELLigence raw data. The file contains 19 different spreadsheets organized with respect to cell lines, initial cell numbers, and independent experimental replicates. Within the same spreadsheet the first column contains the time (in hours), second and third column contain the mean basal migration Cell Index of a quadruplicate exper...

Migration xCELLigence raw data. The file contains 17 different spreadsheets organized with respect to cell lines, initial cell numbers, and independent experimental replicates. Within the same spreadsheet the first column contains the time (in hours), second and third column contain the mean migration Cell Index of a quadruplicate experiment and it...

Doubling times of Sarc, HT1080, and A375 cell lines. Cells (2 × 103 cells/well) were seeded on E-plates and allowed to grow for 70 h in serum containing medium. The impedance value of each well was automatically monitored by the xCELLigence system and expressed as a Cell Index. Doubling times were calculated, using the xCELLigence RTCA software, fr...

Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This technology measures impedance changes caused by the gradual increase of electrode surface occupation by cells...

Experiments of cell migration and chemotaxis assays have been classically performed in the so-called Boyden Chambers. A recent technology, xCELLigence Real Time Cell Analysis, is now allowing to monitor the cell migration in real time. This technology measures impedance changes caused by the gradual increase of electrode surface occupation by cells...

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 compressible-incompressible model seems to be very close to the density-dependent incompressibl...

Deterioration of copper and bronze artifacts is one of the main concerns for people working in cultural heritage. In particular a significant effort has been devoted to study the corrosion due to environmental conditions, such as temperature, moisture and the concentration of pollutants. We introduce a mathematical model able to describe the corros...

Sportello Matematico per l’Industria Italiana is a project developed by the National Research Council of Italy to build an effective and high-quality network of research groups in Industrial Mathematics in Italy. Here we will recall the objectives and the main actions taken by the project team during its first year of activities.

The workshop, organized under the sponsorship of the Istituto Nazionale di Alta Matematica, in collaboration with the Istituto delle Applicazioni del Calcolo of the Italian National Research Council, aims at bringing altogether skilled European researchers in both Mathematical Analysis and Numerical Computing fields, both belonging to various moder...

In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open neighborhood of the physical parameters, the system is totally dissipative near its unique non vanishing equilibrium...

This article introduces the papers in the special section of the Lettera Matematica International Edition dedicated to author David Foster Wallace.

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 nume...

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-organ...

While Wallace’s nonfiction is voraciously eclectic—exploring film, pornography, luxury cruises—the only time that he devoted an entire book of his nonfiction to a single subject was when he completed his 2004 study of Cantorian mathematics. Everything and More’s very uniqueness may make it seem an anomalous subset of Wallace’s output, yet—this essa...

Starting from the results of recent biological experiments, we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our hybrid description is discrete on the cellular level and continuous on the molecular level. We prove the existence of steady solutions corresponding to the fo...

Mathematicians of the future will be expected to have a variety of skills to enable them to increase the impact of the mathematical sciences in meeting scientific, economic and technological demands. The project ‘Sportello Matematico per l’Industria Italiana’ begun in 2012 in the Istituto per le Applicazioni del Calcolo “Mauro Picone” of the Italia...

An integro-differential model for evolutionary dynamics with mutations is investigated by improving the understanding of its behavior using numerical simulations. The proposed numerical approach can handle also density dependent fitness, and gives new insights about the role of mutation in the preservation of cooperation.

In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387–1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two im...

In this paper we study the effect of rare mutations, driven by a marked point process, on the evolutionary behavior of a population. We derive a Kolmogorov equation describing the expected values of the different frequencies and prove some rigorous analytical results about their behavior. Finally, in a simple case of two different quasispecies, we...

We prove the global existence and uniqueness of smooth solutions to a nonlinear system of parabolic–elliptic equations, which describes the chemical aggression of a permeable material, like calcium carbonate rocks, in the presence of acid atmosphere. This model applies when convective flows are not negligible, due to the high permeability of the ma...

In this paper we propose a new mathematical model describing the effect of phosphocitrate (PC) on sodium sulphate crystallization inside bricks. This model describes salt and water transport, and crystal formation in a one dimensional symmetry. This is the first study that takes into account mathematically the effects of inhibitors inside a porous...