# Roberto NataliniItalian National Research Council | CNR · Institute for Applied Mathematics "Mauro Picone" IAC

Roberto Natalini

35.35

·

PhD

## About

201

Publications

15,713

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

3,345

Citations

Introduction

Roberto Natalini is the Director of the Istituto per le Applicazioni del Calcolo "Mauro Picone"of the Italian CNR.
His research themes include: fluid dynamics, road traffic, chemical damage of monuments, biomathematics. He coordinates the public awareness site MaddMaths! http://maddmaths.simai.eu/, and is Chair of the Raising Public Awareness of the European Mathematical Society. He is also the Scientific head of the Mathematical Desk for Italian Industries http://www.sportellomatematico.it/.

Education

October 1983 - June 1986

October 1979 - July 1983

## Publications

Publications (201)

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...

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...

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 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...

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...

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...

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...

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...

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...

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 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 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 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...

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...

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...

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...

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...

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...

In this paper we study a semilinear hyperbolic-parabolic system modeling biological phenomena evolving on a network composed by oriented arcs. We prove the existence of global (in time) smooth solutions to this problem. The result is obtained by using energy estimates with suitable trans-mission conditions at nodes.

The intracellular signalling network of the p53 protein plays important roles in genome protection and the control of cell cycle phase transitions. Recently observed oscillatory behaviour in single cells under stress conditions has inspired several research groups to simulate and study the dynamics of the protein with the aim of gaining a proper un...

A new partial differential model for monitoring and detecting copper corrosion products (mainly brochantite and cuprite) is proposed to provide predictive tools suitable for describing the evolution of damage induced on bronze specimens by sulfur dioxide (SO2SO2) pollution. This model is characterized by the movement of a double free boundary. Nume...

Gene therapy is a promising approach for treating a wide range of human pathologies such as genetic disorders as well as diseases acquired over the lifetime of an individual. Viral and non-viral vectors are used to vehiculate sequences of genes that can be expressed for therapeutic purposes. Plasmid DNA is receiving considerable attention for intra...

We consider two models which were both designed to describe the movement of
eukaryotic cells responding to chemical signals. Besides a common standard
parabolic equation for the diffusion of a chemoattractant, like chemokines or
growth factors, the two models differ for the equations describing the movement
of cells. The first model is based on a q...

In this paper we introduce the Mathematical Desk for Italian Industry, a project based on applied and industrial mathematics developed by a team of researchers from the Italian National Research Council in collaboration with two major Italian associations for applied mathematics, SIMAI and AIRO. The scope of this paper is to clarify the motivations...

In this paper we deal with a semilinear hyperbolic chemotaxis model in one
space dimension evolving on a network, with suitable transmission conditions at
nodes. This framework is motivated by tissue-engineering scaffolds used for
improving wound healing. We introduce a numerical scheme, which guarantees
global mass densities conservation. Moreover...

In this paper we propose a "discrete in continuous" mathematical model for
the morphogenesis of the posterior lateral line system in zebrafishes. Our
model follows closely the results obtained in recent biological experiments. We
rely on a hybrid description: discrete for the cellular level and continuous
for the molecular level. We prove the exist...

Various molecular pharmacokinetic-pharmacodynamic (PK-PD) models have been proposed in the last decades to represent and predict drug effects in anticancer chemotherapies. Most of these models are cell population based since clearly measurable effects of drugs can be seen much more easily on populations of cells, healthy and tumour, than in individ...

New computation algorithms for a fluiddynamic mathematical model of flows on networks are proposed, described and tested. First we improve the classical Godunov scheme (G) for a special flux function, thus obtaining a more efficien t method, the Fast Godunov scheme (FG) which reduces the number of evaluations for the numerical flux. Then a new meth...

A conversation with Emma Castelnuovo about some recollections of her life. Among the various themes discussed are: Mauro Picone and the Istituto per le Applicazioni del Calcolo; Fascism and the racial laws; Italian mathematics after World War II; Renato Caccioppoli; mathematics teaching; and the role of mathematics in the society.

In this paper the Lab-on-Chip section for a protein assay is designed and optimized. To avoid severe reliability problems related to activated surface stability, a dynamic assay approach is adopted: protein-to-protein neutralization is performed while proteins diffuse freely in the reaction chamber. The related refraction index change is detected v...

A new partial differential model for monitoring and detecting copper
corrosion products (mainly brochantite and cuprite) is proposed to provide
predictive tools suitable for describing the evolution of damage induced on
bronze specimens by sulfur dioxide (SO_2) pollution. This model is
characterized by the movement of a double free boundary. Numeri...

We introduce a numerical scheme to approximate a quasi-linear hyperbolic
system which models the movement of cells under the influence of chemotaxis.
Since we expect to find solutions which contain vacuum parts, we propose an
upwinding scheme which handles properly the presence of vacuum and, besides,
which gives a good approximation of the time as...

In this paper we design and analyse a physiologically based model representing the accumulation of protein p53 in the nucleus after triggering of ATM by DNA damage. The p53 protein is known to have a central role in the response of the cell to cytotoxic or radiotoxic insults resulting in DNA damage. A reasonable requirement for a model describing i...

We introduce a new class of finite difference schemes for approximating the solutions
to an initial-boundary value problem on a bounded interval for a one-dimensional dissipative hyperbolic
system with an external source term, which arises as a simple model of chemotaxis. Since the
solutions to this problem may converge to nonconstant asymptotic st...

We introduce a new class of finite differences schemes to approximate one
dimensional dissipative semilinear hyperbolic systems with a BGK structure.
Using precise analytical time-decay estimates of the local truncation error, it
is possible to design schemes, based on the standard upwind approximation,
which are increasingly accurate for large tim...

A system of nonlinear hyperbolic partial differential equations is derived using mixture theory to model the formation of biofilms. In contrast with most of the existing models, our equations have a finite speed of propagation, without using artificial free boundary conditions. Adapted numerical scheme will be described in detail and several simula...

We present a one space dimensional model with finite speed of propagation for population dynamics, based both on the hyperbolic Cattaneo dynamics and the evolutionary game theory. We prove analytical properties of the model and global estimates for solutions, by using a hyperbolic nonlinear Trotter product formula.

We introduce a new class of finite difference schemes for approximating the solutions to an initial-boundary value problem on a bounded interval for a one-dimensional dissipative hyperbolic system with an external source term, which arises as a simple model of chemotaxis. Since the solutions to this problem may converge to nonconstant asymptotic st...

n this article, we consider a simple hyperbolic relaxation system on networks which models the movement of fibroblasts on an artificial scaffold. After proving the uniqueness of stationary solutions with a given total mass, we present an adapted numerical scheme which takes care of boundary conditions and display some numerical tests.

Copper corrosion product growth is simulated during the early stage of exposure to sulfur dioxide atmosphere. The mathematical model, based on mass balance equations, describes the formation of free boundaries by copper hydroxy sulphate and cuprous oxide, bounding regions with different dynamics. The chemical data, collected during the experiments,...

We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical properties of the model and global estimates. The asymptotic behavior and the stability of solutions in the case of...

We consider a simple model for signal transport in the cytoplasm. Following some recent experimental evidences, the standard diffusion model is supplemented by advection operated through an attachement/detachement mechanism along microtubules. This model is given by a system of partial differential equations which are cast in different dimensions a...

We consider models of Ran-driven nuclear transport of molecules such as proteins in living cells The mathematical model presented is the first to take into account for the active transport of molecules along the cytoplasmic microtubules All parameters entering the models are thoroughly discussed The model is tested by numerical simulations based on...

Mycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the infection in the formation of a granuloma. The mo...