Mathematical Modeling in Cultural Heritage: MACH2021 (Springer INdAM Series, 55)

Preface
Contents
Round Table of MACH2021
	1 Introduction to the Issues Faced in the Round Table
	2 The Importance of Science and Cultural Aspects and the Impact on Political Strategies on Cultural Heritage
	3 Critical Issues Emerged in the Management of CH During Covid-19 Pandemic, Arising Opportunities and Problems that Need to Be Faced with New Investments
	References
Numerical Simulation of the Athens 1999 Earthquake Including Simplified Models of the Acropolis and the Parthenon: Initial Results and Outlook
	1 Introduction
	2 Mathematical Model and Its Numerical Discretization
	3 Computational Setting for the September 7, 1999 Athens Earthquake
		3.1 Numerical Model of the Seismic Source, Regional Crustal Properties and Geological Setting
		3.2 Computational Models Setup
	4 Numerical Results and Comparison with Observed Records
		4.1 Simulation of the 1999 Athens Earthquake
		4.2 Seismic Response of the Parthenon
	5 Conclusions and Future Developments
	References
Randomness in a Nonlinear Model of Sulphation Phenomena
	1 Introduction
	2 The Deterministic Model
	3 Stochastic Boundary Condition for the S02 Concentration
	4 A Nonlinear Model with Stochastic Dynamical Boundary Conditions
	5 Conclusions
	References
Automatic Description of Rubble Masonry Geometries by Machine Learning Based Approach
	1 Introduction
	2 The Data Set Used
		2.1 Preparation of Geometrical Data
	3 Basic Concepts About CNN
	4 Variational Autoencoder (VAE)
	5 Implementation
	6 Experimentations
	7 Closing Remarks
	References
A Model for Craquelure: Brittle Layers on Elastic Substrates
	1 A Model for a Brittle Layer on an Elastic Substrate
	2 Analytical Treatment of the Model
	3 Analysis of the Results in Terms of Craquelure
	4 Conclusions
	References
Themes and Reflections upon Structural Analysis in the Fieldof Archaeology
	1 Knowing to Model
	2 The Restoration of Architectural Knowledge
	References
Mathematical Methods for the Shape Analysis and Indexingof Tangible CH Artefacts
	1 Introduction
	2 Quantitative Analysis and Shape Characterisation of Cultural Assets
		2.1 Main Dimensions, Area, Volume
		2.2 Thickness, Roundness, Straightness
		2.3 Curvature-Based Shape Characterisation
		2.4 Colourimetric Properties
		2.5 Feature Curve Recognition
		2.6 Pattern Analysis
	3 Similarity Reasoning and Query-Based Search Engine
		3.1 Similarity Measures and Compatibility of Feature Curves
		3.2 Conceptual Model of a Search Engine
	4 3D Semantic Annotation of Cultural Artefacts
		4.1 Cultural Heritage Artefact Partonomy
		4.2 The CH Platform
		4.3 Managing Annotation Attributes, Relations and Constraints
	5 Concluding Remarks
	References
A Semi-analytical Approach to Approximate Chattering Timeof Rocking Structures
	1 Introduction
	2 Analytical Dynamics
	3 Chattering Time Approximation
	4 Conclusions
	References
Numerical Modelling of Historical Masonry Structures with the Finite Element Code NOSA-ITACA
	1 Introduction
	2 The NOSA-ITACA Code for the Structural Analysis of Masonry Buildings
	3 The Constitutive Equation of Masonry-Like Materials
	4 Static and Modal Analysis
		4.1 The Case Study of the San Francesco Church
		4.2 The Case Study of the Maddalena Bridge
	5 Ambient Vibration Test and Finite Element Model Updating
	6 Structural Health Monitoring and Linear Perturbation
	7 Conclusions
	References
From Point Clouds to 3D Simulations of Marble Sulfation
	1 Introduction
	2 Computing the Levelset from a Point Cloud
	3 3D Numerical Simulations of Marble Sulfation
	4 Numerical Experiments
		4.1 Numerical Computation of a Levelset Function
		4.2 Sulfation of the Cube&spheres Object
		4.3 Sulfation of a Stone Frog
	5 Conclusions
	References
Multiscale Carbonation Reactions: Status of Things and Two Modeling Exercises Related to Cultural Heritage
	1 Introduction
		1.1 Motivation
		1.2 Organization of the Work
	2 Mass Balance Equations for a Generic Two-Scale Setting
	3 A Brief Literature Review on Multiscale Carbonation Models
	4 Two Multiscale Modeling Tasks
		4.1 Scenario A: Carbonation of Concrete
		4.2 Scenario B: Carbonation of Nanolimes
	5 Discussion
	References
Forecasting Damage and Consolidation: Mathematical Modelsof Reacting Flows in Porous Media
	1 Introduction
	2 Mathematical Models for Cultural Heritage
		2.1 Surface Deposition/Reaction Models
			Free Boundary Models: Swelling/Shrinkage Phenomena
			A Mathematical Model for Marble Sulfation Including Surface Rugosity
			Models for Chemo-Mechanical Damage
		2.2 Capillary Penetration/Internal Reaction Models: Chemo-Physical Damage
			Models for Transport and Diffusion of Fluids in Porous Media
			Mathematical Models for Consolidation of Building Stones
	3 Conclusions
	References
Models and Mathematical Issues in Color Film Restorations
	1 Introduction
	2 Models of Color Perception
		2.1 Retinex
		2.2 Random Image Exploration: Milano Retinex
		2.3 Scale-Based Algorithms
		2.4 Variational-Based Algorithms: PDE Models
	3 Film Restoration Through SCAs
	4 Conclusions
	References