Nanowire gas sensors have many applications in health-care, safety, environmental montoring etc., yet the major problem that current research faces is a lack of understanding of the reactions that take place between the sensing film and the gas species and hence a substantial lack of selectivity of SnO2 nanowire sensing devices. We will present a mathematical model for SnO2 nanowire sensors. The surface reactions are described by parameter-dependent ordinary differential equations (ODEs) that give the net exchange of electrons between the gas and the SnO2 nanowire. The net exchange of electrons is then included in the nonlinear Poisson-Boltzmann equation for the computation of the electric potential. From the electric potential we obtain the concentrations of holes and electrons via Boltzmann distributions and finally the graded channel approximation returns the current I. The parameters of 4 different ODE models for the surface reactions have been determined by comparison of the ODE models with measurement data using inverse-modeling techniques. For each of the models, between 5 and 9 parameters were estimated, while the nonlinear nature of the model complicates inverse modeling. The results from the best parameter sets for each of the 4 models were compared, which also resulted in the affirmation of the hypothesis that chemisorption at SnO2 nanowires is a slow process compared to the ionization reaction. The equation corresponding to the affirmed hypothesis performs best compared to other model equations in representing accurately the measurement curve. The components of the parameter set are almost equilibrated and these factors are supported by the results of an F-Test used for the statistical comparison of model equations. The simulation results are always within the range of 5% with respect to the current measurements. Therefore this modeling procedure can yield predictive simulations of field-effect gas sensors.

• Thematic program: Modeling and Simulation of Nanostructures in biology and physics (2010)

The main feature of the two-dimensional Keller-Segel model is the blow-up behaviour of solutions for supercritical masses. We introduce a regularisation of the fully parabolic system by adding a cross-diffusion term to the equation for the chemical substance. This regularisation provides another helpful entropy dissipation term allowing to prove global existence of solutions for any initial mass. In the parabolic-elliptic case this model can be reformulated to the Keller-Segel model with nonlinear diffusion of power function type with an exponent above 1. Therefore solutions are known to be globally bounded. In the second part of the talk we return to the fully parabolic model and replace the cell diffusion and the additional cross-diffusion by nonlinear versions. We investigate the necessary conditions on the cross-diffusion perturbation such that we can allow a cell diffusion with an exponent below 1 and still obtain the global existence of solutions. Numerical simulations will be presented.

• Thematic program: Modeling and Simulation of Nanostructures in biology and physics (2010)

• Thematic program: Modeling and Simulation of Nanostructures in biology and physics (2010)

We consider a bidimensionnal Navier-Stokes type equation. Here typical wavelength of the oscillations considered is 1/epsilon. We force one variable to oscillate like 1/epsilon^2 thanks to a polarized source term. We study the interactions between those oscillations. To be more accurate, we consider a family of exact solutions that we perturb at initial time t=0. We prove that the oscillating cauchy problem associated with this new initial data is well-posed. To do so we exhibit a complete expansion of the solution as epsilon goes to 0. This expansion reveals a boundary layer in time for the velocity. A noticeable aspect is the creation of some dissipation on the mean term of the velocity due to some drift-diffusion mechanism.

• Thematic program: Modeling and Simulation of Nanostructures in biology and physics (2010)