Hervé Le Meur

Julien Berger, Hervé Le Meur, Denys Dutykh et al.

The reliability of a model is its accuracy in predicting the physical phenomena using the known input parameters. It also depends on the model's ability to estimate relevant parameters using observations of the physical phenomena. In this paper, the reliability of the VTT model is investigated under these two criteria for various given temperature and relative humidity constant in time. First of all, experiments are conducted on bamboo fiberboard. Using these data, five parameters of the VTT model, defining the mold vulnerability class of a material, are identified. The results highlight that the determined parameters are not within the range of the classes defined in the VTT model. In addition, the quality of the parameter estimation is not satisfactory. Then the sensitivity of the numerical results of the VTT model is analyzed by varying an input parameter. These investigations show that the VTT mathematical formulation of the physical model of mold growth is not reliable. An improved model is proposed with a new mathematical formulation. It is inspired by the logistic equation whose parameters are estimated using the experimental data obtained. The parameter estimation is very satisfactory. In the last parts of the paper, the numerical predictions of the improved model are compared to experimental data from the literature to prove its reliability.

Ainagul Jumabekova, Julien Berger, Denys Dutykh et al.

The goal of this study is to propose an efficient numerical model for the predictions of capillary adsorption phenomena in a porous material. The Scharfetter-Gummel numerical scheme is proposed to solve an advection-diffusion equation with gravity flux. Its advantages such as accuracy, relaxed stability condition, and reduced computational cost are discussed along with the study of linear and nonlinear cases. The reliability of the numerical model is evaluated by comparing the numerical predictions with experimental observations of liquid uptake in bricks. A parameter estimation problem is solved to adjust the uncertain coefficients of moisture diffusivity and hydraulic conductivity.

François Dubois, Hervé Le Meur, Claude Reiss

This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define "antigenicity", whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which they have been designed. We consider also the mutation and multiplication of the virus. An original infection term is derived. So as to compare our system of differential equations with well-known models, we study some of them and compare their predictions to ours in the reduced case of only one antigenicity. In this particular case, our model does not yield any major qualitative difference. We prove mathematically that, in this case, our model is biologically consistent (positive fields) and has a unique continuous solution for long time evolution. In conclusion, this model improves the ability to simulate more advanced phases of the disease.