Fabrizio Clarelli

Heat exchange between a conducting plate and the environment is described here by means of an unknown nonlinear function F of the temperature u. In this paper we construct a method for recovering F by means of polynomial expansion, perturbation theory and the toolbox of thermal inverse problems. We test our method on two examples: In the rst one, we heat the plate (initially at 20 C) from one side, read the temperature on the same side and identify the heat exchange law on the opposite side (active thermography); in the second example we measure the temperature of one side of the plate (initially at 1500 C) and study the heat exchange while cooling (passive thermography).

Identifying optimal dosing of antibiotics has proven challenging—some antibiotics are most effective when they are administered periodically at high doses, while others work best when minimizing concentration fluctuations. Mechanistic explanations for why antibiotics differ in their optimal dosing are lacking, limiting our ability to predict optimal therapy and leading to long and costly experiments. We use mathematical models that describe both bacterial growth and intracellular antibiotic-target binding to investigate the effects of fluctuating antibiotic concentrations on individual bacterial cells and bacterial populations. We show that physicochemical parameters, e.g. the rate of drug transmembrane diffusion and the antibiotic-target complex half-life are sufficient to explain which treatment strategy is most effective. If the drug-target complex dissociates rapidly, the antibiotic must be kept constantly at a concentration that prevents bacterial replication. If antibiotics cross bacterial cell envelopes slowly to reach their target, there is a delay in the onset of action that may be reduced by increasing initial antibiotic concentration. Finally, slow drug-target dissociation and slow diffusion out of cells act to prolong antibiotic effects, thereby allowing for less frequent dosing. Our model can be used as a tool in the rational design of treatment for bacterial infections. It is easily adaptable to other biological systems, e.g. HIV, malaria and cancer, where the effects of physiological fluctuations of drug concentration are also poorly understood.

Abstract: We introduce a mathematical model to improve our understanding of consolidation processes and to take into account the fine scale evolution of reaction pathways. We focus on a silicone called TEOS (Tetraethyl Orthosilicate). The model is based on differential equations, inspired by the theory of porous media, which describes the process of consolidation in terms of filtration and solidification. Our main goal is the prediction of the ultimate depth of filtration of TEOS, according to the environmental and material data. The ...

Abstract In physiology, the appearance of some inflammatory lung diseases is accompanied by an over production of nitric oxide which is detectable and measurable in the human breath. We propose a mathematical model describing the evolution of the concentration of such chemical compound based on a hyperbolic first order partial differential equation which takes into account the dominating effect of the advection due to the high velocity of the air with respect to diffusive effect.

In this article, a system of nonlinear hyperbolic-elliptic partial differential equations is introduced to model the formation of biofilms. First, a short introduction to some basic concepts about biofilms is given. Then a detailed derivation of the model is presented, which is mainly based on the theory of mixtures, also in comparison with previous models. Adapted numerical schemes will be presented and numerical simulations will be discussed. Keywords: Biofilms; Cyanobacteria; Theory of mixtures; Hyperbolic equations.

Abstract Mycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the infection in the formation of a granuloma.

Abstract. We introduce some free boundary problems which describe the evolution of calcium carbonate stones under the attack of atmospheric SO2 , taking into account both swelling of the external gypsum layer and the influence of humidity. Different behaviors are described according to the relative humidity of the environment, and in all cases reliable explicit quasi-steady approximations are introduced under reasonable assumptions on the data. Some numerical simulations are also
performed to describe gypsum formation using experimental data, which show a good agreement with the quasi-steady solutions. The influence of the cleaning the crust and of the change in concentration of pollution is evaluated and discussed.

Key words. free boundary problems, chemical damage, porous media, swelling, influence of humidity, damage of cultural heritage.

AMS subject classifications. Primary, 76S05; Secondary, 35R35

Deterioration of stones is a complex problem and one of the main concern for people working in the field of conservation and restoration of cultural heritage. One important point in cultural heritage is to obtain information about the damage in a non-invasive way. By this paper, we propose a new non-invasive tool that permits evaluation of the thickness of CaSO4*2H2O (gypsum) grown (sulfation) on marble stones, using a mathematical model on data detected by pulsed infrared thermography.

A system of nonlinear hyperbolic partial differential
equations is derived using mixture theory to model the formation of biofilms. In contrast with most of the existing models, our equations have a finite speed of propagation, without using artificial free boundary conditions. Adapted numerical scheme will be described in detail and several simulations will be presented in one and more space dimensions in the particular case of cyanobacteria biofilms. Besides, the numerical scheme we present is able to deal in a natural and effective way with regions where one of the phases is vanishing.

In physiology, the appearance of some inflammatory lung diseases is accompanied by an over production of nitric oxide which is detectable and measurable in the human breath. We propose a mathematical model describing the evolution of the concentration of such chemical compound based on a hyperbolic first order partial differential equation which takes into account the dominating effect of the advection due to the high velocity of the air with respect to diffusive effect. We take into account the geometry of the bronchial tree and ...

"A new partial differential model for monitoring and detecting copper
corrosion products (mainly brochantite and cuprite) is proposed to provide
predictive tools suitable for describing the evolution of damage induced on
bronze specimens by sulfur dioxide (SO_2) pollution. This model is
characterized by the movement of a double free boundary. Numerical simulations
show a nice agreement with experimental result."