Roberto Natalini
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View article: An Integro-Differential Model of Cadmium Yellow Photodegradation
An Integro-Differential Model of Cadmium Yellow Photodegradation Open
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 …
View article: Numerical study on a multi-dimensional pressureless Euler-type model with non-local interactions and chemotaxis for collective cell migration
Numerical study on a multi-dimensional pressureless Euler-type model with non-local interactions and chemotaxis for collective cell migration Open
In this paper we propose a numerical study of macroscopic models for collective cell migration, focusing on a multi-dimensional pressureless Euler-type model with non-local interactions coupled with chemotaxis, rigorously derived from micr…
View article: A relaxation scheme for the equations of isentropic gas dynamics on a network with jump transmission conditions
A relaxation scheme for the equations of isentropic gas dynamics on a network with jump transmission conditions Open
In this paper we propose a new numerical scheme of relaxation type to approximate the Euler equations of isentropic gas dynamics on the arcs of a network. At the junction mass conservation and a jump transmission condition on the density a…
View article: A model for membrane degradation using a gelatin invadopodia assay
A model for membrane degradation using a gelatin invadopodia assay Open
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 …
View article: Microscopic, kinetic and hydrodynamic hybrid models of collective motions withchemotaxis: a numerical study
Microscopic, kinetic and hydrodynamic hybrid models of collective motions withchemotaxis: a numerical study Open
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 …
View article: The Mean-Field Limit for Hybrid Models of Collective Motions with Chemotaxis
The Mean-Field Limit for Hybrid Models of Collective Motions with Chemotaxis Open
In 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 chemoa…
View article: Parameter estimation tools for cardiovascular flow modeling of fetal circulation
Parameter estimation tools for cardiovascular flow modeling of fetal circulation Open
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 approac…
View article: A forecasting model for the porosity variation during the carbonation process
A forecasting model for the porosity variation during the carbonation process Open
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, involvin…
View article: Applied Mathematics Tools in Digital Transformation
Applied Mathematics Tools in Digital Transformation Open
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. …
View article: A moving boundary problem for reaction and diffusion processes in concrete: Carbonation advancement and carbonation shrinkage
A moving boundary problem for reaction and diffusion processes in concrete: Carbonation advancement and carbonation shrinkage Open
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 dispersed in …
View article: How to improve the decay of the numerical error for large times: the case of dissipative BGK systems
How to improve the decay of the numerical error for large times: the case of dissipative BGK systems Open
We introduce new finite differences schemes to approximate one dimensional dissipative semilinear hyperbolic systems with a BGK structure. Using accurate analytical time-decay properties of the local truncation error, it is possible to des…
View article: Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment
Estimation Algorithm for a Hybrid PDE–ODE Model Inspired by Immunocompetent Cancer-on-Chip Experiment Open
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 experim…
View article: On the mean field limit for Cucker-Smale models
On the mean field limit for Cucker-Smale models Open
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…
View article: Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips
Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips Open
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 chemotaxi…
View article: Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation
Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation Open
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 i…
View article: Asymptotic behavior of 2D stably stratified fluids with a damping term\n in the velocity equation
Asymptotic behavior of 2D stably stratified fluids with a damping term\n in the velocity equation Open
This article is concerned with the asymptotic behavior of the two-dimensional\ninviscid Boussinesq equations with a damping term in the velocity equation.\nPrecisely, we provide the time-decay rates of the smooth solutions to that\nsystem.…
View article: Forecasting Visitors’ behaviour in Crowded Museums
Forecasting Visitors’ behaviour in Crowded Museums Open
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…
View article: Vanishing viscosity approximation for linear transport equations on\n finite starshaped networks
Vanishing viscosity approximation for linear transport equations on\n finite starshaped networks Open
In this paper we study linear parabolic equations on a finite oriented\nstarshaped network; the equations are coupled by transmission conditions set at\nthe inner node, which do not impose continuity on the unknown. We consider this\nprobl…
View article: Mass-preserving approximation of a chemotaxis multi-domain transmission model for microfluidic chips
Mass-preserving approximation of a chemotaxis multi-domain transmission model for microfluidic chips Open
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, a…
View article: A hybrid model of collective motion of discrete particles under alignment and continuum chemotaxis
A hybrid model of collective motion of discrete particles under alignment and continuum chemotaxis Open
In this paper we propose and study a hybrid discrete in continuous\nmathematical model of collective motion under alignment and chemotaxis effect.\nStarting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale\nmodel (Cuc…