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 photo catalytic reaction responsible for these damages. By employing nonlo cal integral operators, we capture the interplay between chemical processes and environmental factors, offering a detailed representation of the degradation mechanisms. Furthermore, we present a second order positivity-preserving numerical method designed to accurately simulate the phenomenon and ensure reliable predictions across different scenarios, along with a comprehensive sensitivity analysis of the model.

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 concrete exposed to increasing levels of CO2 emissions, as well as to rising temperatures. Taking into account future projections of environmental modifications deriving from climate changes, some scenarios were produced numerically by the mathematical algorithm that showed the effects of different pollution levels and global warming on the porosity of Portland cement in a time window of years. Finally, a theoretical study on the effects of pollution levels on the carbonation constant determining the advancement in the carbonation front was carried out for the analyzed scenarios.

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. Such a digital replica, the so-called digital twin, can be described by Mathematical Science tools allowing cost reduction on industrial processes, faster time-to-market of new products and, in general, an increase of competitive advantage for the company. Digital twin is a descriptive or predictive model of a given industrial process or product that is a valuable tool for business management, both in planning--because it can give different scenario analysis--and in managing the daily operations; moreover, it permits optimization of product and process operations. We present widespread applied mathematics tools that can help this modeling process, along with some successful cases.

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 carbonation process. Indeed, two different regimes are described according to the relative humidity in the environment. Finally, some numerical simulations here presented are in substantial accordance with experimental results taken from literature.

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, besides describing transport and diffusion processes inside the porous medium, takes into account both fast and slow phenomena as intermediate reactions of the carbonation process. As a model validation, by using the mathematical based simulation algorithm we are able to describe the effects of the interaction between concrete and CO on the porosity of material as shown by the numerical results in substantial accordance with experimental results of accelerated carbonation taken from literature. We also considered a further reaction: the dissolution of calcium carbonate under an acid environment. As a result, a trend inversion in the evolution of porosity can be observed for long exposure times. Such an increase in porosity results in the accessibility of solutions and pollutants within the concrete leading to an higher permeability and diffusivity thus significantly affecting its durability.

In this work we developed a mathematical model describing the crystallization process of salt dissolved in water flowing within a porous medium (in this case the common brick). Starting from this model a numerical tool was developed that allows to describe the effects of salt penetrating inside porous media and to forecast the effects of the application of crystallization inibitors.

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 compounds 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.

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 porous stone. To this aim, we introduce two model parameters: the crystallization rate coefficient, which depends on the nucleation rate, and the specific volume of precipitated salt. These two parameters are determined by numerical fitting of our model for both the case of the brick treated with PC and non treated one.

Sap transport in trees has long fascinated scientists, and a vast literature exists on experimental and modelling studies of trees during the growing season when large negative stem pressures are generated by transpiration from leaves. Much less attention has been paid to winter months when trees are largely dormant but nonetheless continue to exhibit interesting flow behaviour. A prime example is sap exudation, which refers to the peculiar ability of sugar maple (Acer saccharum) and related species to generate positive stem pressure while in a leafless state. Experiments demonstrate that ambient temperatures must oscillate about the freezing point before significantly heightened stem pressures are observed, but the precise causes of exudation remain unresolved. The prevailing hypothesis attributes exudation to a physical process combining freeze-thaw and osmosis, which has some support from experimental studies but remains a subject of active debate. We address this knowledge gap by developing the first mathematical model for exudation, while also introducing several essential modifications to this hypothesis. We derive a multiscale model consisting of a nonlinear system of differential equations governing phase change and transport within wood cells, coupled to a suitably homogenized equation for temperature on the macroscale. Numerical simulations yield stem pressures that are consistent with experiments and provide convincing evidence that a purely physical mechanism is capable of capturing exudation.

We develop a mathematical model for a three-phase free boundary problem in one dimension that involves interactions between gas, water and ice. The dynamics are driven by melting of the ice layer, while the pressurized gas also dissolves within the meltwater. The model incorporates the Stefan condition at the water-ice interface along with Henry's law for dissolution of gas at the gas-water interface. We employ a quasi-steady approximation for the phase temperatures and then derive a series solution for the interface positions. A non-standard feature of the model is an integral free boundary condition that arises from mass conservation owing to changes in gas density at the gas-water interface, which makes the problem non-self-adjoint. We derive a two-scale asymptotic series solution for the dissolved gas concentration, which because of the non-self-adjointness gives rise to a Fourier series expansion in eigenfunctions that do not satisfy the usual orthogonality conditions. Numerical simulations of the original governing equations are used to validate series approximations.

In this paper we introduce the Mathematical Desk for Italian Industry, a project based on applied and industrial mathematics developed by a team of researchers from the Italian National Research Council in collaboration with two major Italian associations for applied mathematics, SIMAI and AIRO. The scope of this paper is to clarify the motivations for this project and to present an overview on the activities, context and organization of the Mathematical Desk, whose mission is to build a concrete bridge of common interests between the Italian scientific community of applied mathematics and the world of the Italian enterprises. Some final considerations on the strategy for the future development of the Mathematical Desk project complete the paper.