Gabriella Bretti

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

In this paper we propose a mathematical model of the capillary and permeability properties of lime-based mortars from the historic built heritage of Catania (Sicily, Italy) produced by using two different types of volcanic aggregate, i.e. ghiara and azolo. In order to find a formulation for the capillary pressure and the permeability as functions o...

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...

The present work extends a previous paper where an agent-based and two-dimensional partial differential diffusion model was introduced for describing immune cell dynamics (leukocytes) in cancer-on-chip experiments. In the present work, new features are introduced for the dynamics of leukocytes and for their interactions with tumor cells, improving...

Functionally graded materials (FGMs), possessing properties that vary smoothly from one region to another, have been receiving increasing attention in recent years, particularly in the aerospace, automotive and biomedical sectors. However, they have yet to reach their full potential. In this paper, we explore the potential of FGMs in the context of...

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...

The INdAM Workshop Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage (MACH2021) took place in Rome on September 13–15, 2021.

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...

Using a mathematical model of concrete carbonation that describes the variation in porosity as a consequence of the involved chemical reactions, we both validated and calibrated the related numerical algorithm of degradation. Once calibrated, a simulation algorithm was used as a forecasting tool for predicting the effects on the porosity of concret...

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...

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...

The present paper was inspired by recent developments in laboratory experiments within the framework of cancer-on-chip technology, an immune-oncology microfluidic chip aiming at study�ing the fundamental mechanisms of immunocompetent behavior. We focus on the laboratory setting where cancer is treated with chemotherapy drugs, and in this case, 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...

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...

Two-dimensional dissipative and isotropic kinetic models, like the ones used in neutron transport theory, are considered. Especially, steady-states are expressed for constant opacity and damping, allowing to derive a scattering $S$-matrix and corresponding ``truly 2D well-balanced'' numerical schemes. A first scheme is obtained by directly implemen...

Differential models, numerical methods and computer simulations play a fundamental role in applied sciences. Since most of the differential models inspired by real world applications have no analytical solutions, the development of numerical methods and efficient simulation algorithms play a key role in the computation of the solutions to many rele...

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...

A correction to this paper has been published: https://doi.org/10.1007/s42985-021-00091-x

A (2 + 2)-dimensional kinetic equation, directly inspired by the run-and-tumble modeling of chemotaxis dynamics is studied so as to derive a both "2D well-balanced" and "asymptotic-preserving" numerical approximation. To this end, exact stationary regimes are expressed by means of Laplace transforms of Fourier-Bessel solutions of associated ellipti...

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...

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers have been studied, and several integer sequences related to them have been introduced. In this article other types of Sheffer polynomials are considered, by introducing the adjoint Poisson-Charlier and the adjoint Related polynomials.

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...

Two-dimensional dissipative and isotropic kinetic models, like the ones used in neutron transport theory, are considered. Especially, steady-states are expressed for constant opacity and damping , allowing to derive a scattering S-matrix and corresponding "truly 2D well-balanced" numerical schemes. A first scheme is obtained by directly implementin...

Dissipative kinetic models inspired by neutron transport are studied in a (1+1)-dimensional context: first, in the two-stream approximation, then in the general case of continuous velocities. Both are known to relax, in the diffusive scaling, toward a damped heat equation. Accordingly, it is shown that "uniformly accurate" L-splines discretizations...

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...

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 a recent paper, we have introduced new sets of Sheffer and Brenke polynomial sequences based on higher order Bell numbers. In this paper, by using a more compact notation, we show another family of exponential polynomials belonging to the Sheffer class, called, for shortness, Sheffer–Bell polynomials. Furthermore, we introduce a set of logarithm...

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers have been studied, and several integer sequences related to them have been introduced. In this article new sets of Sheffer polynomials are derived by introducing a sort of adjointness property. In particular, the adjoint Hahn and the hyperbolic Hahn-type...

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers have been studied , and several integer sequences related to them have been introduced. In this article other types of Sheffer polynomials are considered, by introducing the adjoint Peters and adjoint Pidduk polynomials.

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 paper we propose two numerical algorithms to solve a coupled PDE-ODE systemwhich models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow vehicle depends on the density of cars and, at the same time, it causes a capacity drop in the road, thus limiti...

In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow vehicle depends on the density of cars and, at the same time, it causes a capacity drop in the road, thus limit...

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers have been studied, and several integer sequences related to them have been introduced. In this article other types of Sheffer polynomials are considered, by introducing a sort of adjointness property. As first examples, the adjoint Hermite and Bernoulli...

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...

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...

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...

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...

In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common path along the network. We show that the algorithm selects automatically an admissible solution at junctions, hen...

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...

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...

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.

The purpose of neuroimaging is to investigate the brain functionality through the localization of the regions where biolectric current flows, starting from the measurements of the magnetic field produced in the outer space. Assuming that each component of the current density vector possesses the same sparse representation with respect to a preassigne...

Many problems in applied sciences require to spatially resolve an unknown electrical current distribution from its external magnetic field. Electric currents emit magnetic fields which can be measured by sophisticated superconducting devices in a noninvasive way. Applications of this technique arise in several fields, such as medical imaging and no...

In this paper we introduce a simulation algorithm based on fluid dynamic models to reproduce the behavior of traffic in a portion of the urban network in Rome. Numerical results, obtained comparing experimental data with numerical solutions, show the effectiveness of our approximation.

Neuronal current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current o ws. The reconstruction of an electric current dis- tribution from its magnetic eld measured in the outer space, gives rise to a highly ill-posed and ill-conditioned inverse problem. We use a joint spar...

Magnetic tomography is an ill-posed and ill-conditioned inverse problem since, in general, the solution is non-unique and the measured magnetic field is affected by high noise. We use a joint sparsity constraint to regularize the magnetic inverse problem. This leads to a minimization problem whose solution can be approximated by an iterative thresh...

We introduce some numerical approximations to a quasilinear problem, proposed by G. I. Barenblatt to describe non-equilibrium two-phase uid o w in permeable porous media, with the application to the secondary oil recovery from natural reservoirs. Taking into account the theoreti- cal results of global existence and uniqueness, approximated solution...

In this paper we introduce a computation algorithm to trace car paths on road networks, whose load evolution is modeled by conservation laws. This algorithm is composed by two parts: computation of solutions to conservation equations on each road and localization of car position resulting by interactions with waves produced on roads. Some applicati...

Neuronal current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured by sophisticated superconducting devices in a noninvasive way, gives rise to a highly ill-posed and ill-cond...

This paper is focused on continuum-discrete models for supply chains. In particular, we consider the model introduced in [ ], where a system of conservation laws describe the evolution of the supply chain status on sub-chains, while at some nodes solutions are determined by Riemann solvers. Fixing the rule of flux maximization, two new Riemann Solv...

We introduce a simulation algorithm based on a fluid-dynamic model for traffic flows on road networks, which are considered as graphs composed by arcs that meet at some junctions. The approximation of scalar conservation laws along arcs is made by three velocities Kinetic schemes with suitable boundary conditions at junctions. Here we describe the...

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are studied as graphs composed by arcs that meet at some nodes, corresponding to junctions, which play a key-role. Indeed interactions occur at junctions and there the problem is underdetermined. The approximation of scalar conser...

We introduce new Laguerre-type population dynamics models. These models arise quite naturally by substituting in classical models the ordinary derivatives with the Laguerre derivatives and therefore by using the so called Laguerre-type exponentials instead of the ordinary exponential. The L-exponentials en(t) are increasing convex functions for t⩾0...

New computation algorithms for a fluid-dynamic 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 efficient method, the Fast Godunov scheme (FG) which reduces the number of evaluations for the numerical flux. Then a new meth...

We consider a mathematical model for fluid-dynamic flows on net-works which is based on conservation laws. Road networks are considered as graphs composed by arcs that meet at some junctions. The crucial point is represented by junctions, where interactions occur and the problem is under-determined. The approximation of scalar conservation laws alo...

Multidimensional extensions of the Bernoulli and Appell polynomi-als are defined generalizing the corresponding generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper) polynomials. Furthermore the differential equations satisfied by the corresponding 2D polynomials are derived exploiting the factorization method, introduced in...

We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and usin...

Particular solutions of a class of higher order ordinary dieren- tial equations, with non-constant coecients, are determined by using the equa- tions.

A quadrature rule using Appell polynomials and generalizing both the Euler-MacLaurin quadrature formula and a similar quadrature rule, obtained in Bretti et al [15], which makes use of Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the extrema of the considered interval, is derived. An expression...

The use of Euler polynomials and Euler numbers allows us to con- struct a quadrature rule similar to the well-known Euler-MacLaurin quadra- ture formula, using Euler (instead of Bernoulli) numbers, and even (instead of odd) order derivatives of a given function evaluated at the extrema of the considered interval. An expression of the remainder term...