Mathematical Modeling in Cultural Heritage MACH 2023

This book collects contributions presented at the INdAM Workshop "Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage–MACH2023” held in Rome, Italy in September 2023. The book is focused on mathematical modeling and simulation techniques with the aim of improving the current strategies of conservation and restoration in cultural heritage, sharing different experiences and approaches. The main topics are corrosion and sulphation of materials, damage and fractures, stress in thermomechanical systems, contact and adhesion problems, phase transitions and reaction-diffusion models, restoration techniques, additive manufacturing, with a particular focus on the effective improvements of the fruition of cultural heritage. The final goal is to strengthen the bridge between the experts in different fields of cultural heritage and the mathematical community.

A reaction diffusion model with a stochastic boundary condition.- A stochastic interacting particle model for the marble sulphation process.- Mathematical Modelling of Calcium Carbonate Sulphation - A Computational Study.- Space feature curves recognition and approximation for artifacts characterization.- Homogenization of a Kresling-tube origami.- Modelling paintings on canvas and simulation of local crack patterns.- Griffith criterion for steady and unsteady-state crack propagation.- Artificial Intelligence algorithms for the characterisation of visitors trajectories in a cultural context.- Museum for social inclusion: the challenge of mathematical exhibitions and educational experiences.- Applications and Open Issues in the Structural Health Monitoring of Historic Buildings.- An archaeological view on the sidelines of the structural analysis of Porta Maggiore, Rome.- Assessing structural resilience: some thoughts on Porta Maggiore, Rome.- A multidisciplinary Mission for Aga Khan Necropolis, the Egyptian Italian Mission at West Aswan (EIMAWA).

Gabriella Bretti is a senior researcher at IAC-CNR. Her actual research interests are focused on modeling and numerics for nonlinear PDEs, flows in heterogeneous media, differential models in mathematical biology and medicine, inverse problems and mathematical models of chemical damage and consolidation of lapideus materials. The mentioned topics imply the application of interdisciplinary methodologies and techniques requiring the integration between mathematics, physics, engineering and chemistry.

Cecilia Cavaterra is an associate professor of Mathematical Analysis at Università degli Studi di Milano. She got a Ph.D. in Mathematics at Alma Mater Studiorum—Università di Bologna. Her main research interests concern nonlinear partial differential equations, dynamical systems, inverse and control problems. Recently, she studied some models describing the degradation of monumental stones in Cultural Heritage and some models in tumor growth dynamics. She was one of the editors of the two volumes Mathematical Modeling in Cultural Heritage, Springer INdAM Series 41, 2021 and Springer INdAM Series 55, 2023.

Margherita Solci is an associate professor of Mathematical Analysis at Università degli Studi di Sassari. She got a Ph.D. in Mathematics at Università di Pavia. Her research activity focuses on Calculus of Variations, Gamma-convergence, homogenization, analysis of discrete-to-continuum models via variational convergence. Recently, she worked on evolution problems for structural damage in archaeological buildings. She was one of the editors of the two volumes Mathematical Modeling in Cultural Heritage, Springer INdAM Series 41, 2021 and Springer INdAM Series 55, 2023.