arXiv subjects

Gabriella Bretti

Publications and source records attributed to Gabriella Bretti.

14 recordsLinked to original sources

arXiv2026

A complete simulation framework for stone degradation on 3D real geometries

We present a complete workflow for predicting stone degradation phenomena, such as marble sulfation, in works of art. The main challenge is to accurately acquire the geometry of the artwork and then use it to perform simulations based on a mathematical model of the degradation process, typically formulated as a system of partial differential equations (PDEs). To address this, we generate a point cloud of the object surface using photogrammetric techniques and subsequently post-process it to obtain a level-set description of the three-dimensional geometry. This representation is then incorporated into the numerical discretization of the PDE system. Combined with suitable time-stepping and preconditioning strategies, the resulting framework enables the prediction of degradation evolution, such as the growth of gypsum crust thickness on marble, under different scenarios.

cs.CE↗

arXiv2026

Dissolution of carbonate stones caused by CO2 pollutant: an erosion model

In this paper we introduce a new mathematical model describing the erosion process caused in carbonate stones by the dissolution of the porous matrix due to the penetration of carbonic acid present in the environment. Such model is formulated as nonlinear reaction-transport system in porous media governed by Darcy flow. We propose a numerical algorithm based on finite difference approximation that relies on level-set method at the boundaries and we show numerical tests that are in accordance with the literature in terms of the advancement of the erosion front.

math.NA↗

arXiv2026

Bayesian methods for the identification of model parameters for water transport in porous media

The structure of the nonlinear inverse problem arising from capillarity-driven imbibition in porous media is investigated, considering a degenerate parabolic PDE with compactly supported diffusivity and boundary-driven fluxes as the governing forward model. The inverse problem -- inferring hydraulic model parameters from sparse integral absorption measurements -- is inherently ill-posed: the nonlinear forward operator induces anisotropic parameter sensitivity and structured correlations that render the calibration landscape non-convex and partially unidentifiable. To characterise this structure rigorously, Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) is adopted as a likelihood-free inferential framework, bypassing the analytical intractability of the likelihood while providing full posterior distributions over the parameter space. Two physically motivated parameterisations of the diffusivity function are analysed -- the Natalini-Nitsch (NN) and the BkP formulations. It is shown that the posterior geometry obtained via ABC-SMC encodes, in directly readable form, the sensitivity structure of the nonlinear forward operator: the principal component decomposition of the posterior covariance provides a natural hierarchy of parameter sensitivity, with low-variance eigendirections identifying the parameter combinations to which the forward map is most responsive. This geometric decomposition constitutes a principled and computationally efficient alternative to classical sensitivity analysis, arising as a byproduct of the calibration procedure. These findings are established through both synthetic experiments, confirming accurate parameter recovery, and real laboratory imbibition data from materials of cultural heritage relevance.

math.DS↗

arXiv2026

Structural Identifiability and Comparative Calibration of Water Retention Curves for Imbibition in Porous Media

This paper investigates the structural identifiability and a comparative calibration of four water retention curves (WRCs) within the framework of the Richards equation coupled with Darcy's law for capillary imbibition in porous media. The considered models -- two classical physically-based laws and two abstract parametrisations developed for building stones -- are consistently reformulated by expressing the hydraulic conductivity $K(\Theta)$ and capillary pressure $\psi(\Theta)$ independently, allowing the nonlinear diffusion coefficient $D(\Theta)$ to be reconstructed in a unified structural form. This common representation enables a rigorous mathematical comparison across models with different theoretical foundations. All models are calibrated against the same experimental imbibition dataset using a grid-based optimisation strategy with adaptive refinement. The analysis reveals a structural property of the associated inverse problem: the hydraulic conductivity and the capillary pressure scale enter the governing equation multiplicatively and therefore cannot be independently identified from imbibition data. Only their product acts as an observable diffusion parameter, where model discrimination is primarily governed by the shape of the resulting effective diffusion function. To the best of our knowledge, this is the first study providing a coherent cross-calibration of these WRCs against an identical dataset within a unified computational framework. Our open-source implementation, released within the Stoneverse platform, provides a reproducible baseline for further developments, including probabilistic inversion and learning-based approaches.

math.DS↗

arXiv2026

Finite elements for the space approximation of a differential model for salts crystallization

This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A numerical method based on finite-element space discretization and implicit-explicit time marching is proposed as an extension of a one-dimensional finite-difference framework introduced in the literature. Within the same one-dimensional setting, a sensitivity analysis is performed, based on the techniques developed therein. They are also used as a comparison tool for the finite-element formulation, here introduced for more realistic simulations in higher space dimensions. Considerations about stability will be provided, together with an experimental convergence analysis highlighting the performance of the proposed approach. Numerical results in two and three space dimensions, obtained by an efficient code implementation, will be presented and discussed.

math.NA↗

arXiv2026

Towards uncertainty quantification of a model for cancer-on-chip experiments

This study is a first step towards using data-informed differential models to predict and control the dynamics of cancer-on-chip experiments. We consider a conceptualized one-dimensional device, containing a cancer and a population of white blood cells. The interaction between the cancer and the population of cells is modeled by a chemotaxis model inspired by Keller-Segel-type equations, which is solved by a Hybridized Discontinuous Galerkin method. Our goal is using (synthetic) data to tune the parameters of the governing equations and to assess the uncertainty on the predictions of the dynamics due to the residual uncertainty on the parameters remaining after the tuning procedure. To this end, we apply techniques from uncertainty quantification for parametric differential models. We first perform a global sensitivity analysis using both Sobol and Morris indices to assess how parameter uncertainty impacts model predictions, and fix the value of parameters with negligible impact. Subsequently, we conduct an inverse uncertainty quantification analysis by Bayesian techniques to compute a data-informed probability distribution of the remaining model parameters. Finally, we carry out a forward uncertainty quantification analysis to compute the impact of the updated (residual) parametric uncertainties on the quantities of interest of the model. The whole procedure is sped up by using surrogate models, based on sparse-grids, to approximate the mapping of the uncertain parameters to the quantities of interest.

cs.CE↗

arXiv2025

Data-Informed Mathematical Characterization of Absorption Properties in Artificial and Natural Porous Materials

In this work, we characterize the water absorption properties of selected porous materials through a combined approach that integrates laboratory experiments and mathematical modeling. Specifically, experimental data from imbibition tests on marble, travertine, wackestone and mortar mock-ups are used to inform and validate the mathematical and simulation frameworks. First, a monotonicity-preserving fitting procedure is developed to preprocess the measurements, aiming to reduce noise and mitigate instrumental errors. The imbibition process is then simulated through a partial differential equation model, with parameters calibrated against rough and smoothed data. The proposed procedure appears particularly effective to characterize absorption properties of different materials and it represents a reliable tool for the study and preservation of cultural heritage.

math.NA↗

arXiv2024

Mathematical modelling of the water absorption properties for historical lime-based mortars from Catania (Sicily, Italy)

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 of the saturation level inside the porous medium we calibrate the numerical algorithm against imbibition data. The validation of the mathematical model was done by comparing the experimental retention curve with the one obtained by the simulation algorithm. Indeed, with the proposed approach it was possible to reproduce the main features of the experimentally observed phenomenon for both materials.

math.NA↗

arXiv2022

Parameter estimation tools for cardiovascular flow modeling of fetal circulation

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 advanced techniques, i.e. numerical analysis and simulation. Another key aspect limiting the analysis is that clinicians rely on a limited number of Doppler waveforms observed during the clinical examination. Moreover, the use of simple velocimetric indicators for deriving possible malfunctions of the fetal cardiovascular system can be misleading, being the fetal assessment based on a mere statistical analysis (comparison with physiological ranges), without any deep physio-pathological interpretations of the observed hemodynamic changes. The use of a lumped mathematical model, properly describing the entire fetal cardiovascular system, would be absolutely helpful in this context: by targeting physiological model parameters on the clinical reliefs, we could gain deep insights of the full system. The calibration of model parameters may also help in formulating patient-specific early diagnosis of fetal pathologies. In the present work, we develop a robust parameter estimation algorithm based on two different optimization methods using synthetic data. In particular, we deal with the inverse problem of recognizing the most significant parameters of a lumped fetal circulation model by using time tracings of fetal blood flows and pressures obtained by the model. This represents a first methodological work for the assessment of the accuracy in the identification of model parameters of an algorithm based on closed-loop mathematical model of fetal circulation and opens the way to the application of the algorithm to clinical data.

physics.med-ph↗

arXiv2021

Two algorithms for a fully coupled and consistently macroscopic PDE-ODE system modeling a moving bottleneck on a road

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 limiting the car flux. The first algorithm, based on the Wave Front Tracking method, is suitable for theoretical investigations and convergence results. The second one, based on the Godunov scheme, is used for numerical simulations. The case of multiple bottlenecks is also investigated.

math.DS↗

arXiv2018

A mathematical and experimental study on iron rings formation in porous stones

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 compunds 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.

cond-mat.soft↗

arXiv2016

On modeling Maze solving ability of slime mold via a hyperbolic model of chemotaxis

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.

math.NA↗

arXiv2013

An easy-to-use algorithm for simulating traffic flow on networks: numerical experiments

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, hence ad hoc external procedures (e.g., maximization of the flux via a linear programming method) usually employed in classical approaches are no needed. Since users have not to deal explicitly with vehicle dynamics at junction, the numerical code can be implemented in minutes. We perform a detailed numerical comparison with a Godunov-based scheme coming from the classical theory of traffic flow on networks which maximizes the flux at junctions.

math.NA↗

arXiv2012

A hyperbolic model of chemotaxis on a network: a numerical study

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 our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation.

math.NA↗