Andrés Fraguela

Reconstruction of capacitance tomography images of simulated two-phase flow regimes

Reconstruction of electrical capacitance tomography (ECT) images is performed using simulated gas-oil distributions. An inverse problem has to be solved to find the permittivity coefficient, using measurements of the capacitances. The least squares optimal solution is sought using a Gauss-Newton method, with a sufficient descent condition and a backtracking for the steplength. The Tikhonov regularisation method is used, to control the measurement error propagation due to the ill-posednes of the inverse problem. It is shown that the reconstruction is very sensitive to the Tikhonov regularisation parameter and the L-curve method to find its value is used. When the optimal regularisation parameter is used, convergence is attained to points where no further precision in the permittivity parameter is possible. Simulation examples using typical two-phase flow regimes are presented, and the approximated images as well as the range of values for the regularization parameter for different regimes are shown.

Mathematical modelling of thermoregulation processes for premature infants in closed convectively heated incubators

The low-weight newborns and especially the premature infants have difficulty in maintaining their temperature in the range considered to be normal. Several studies revealed the importance of thermal environment and moisture to increase the survival rate of newborns. This work models the process of heat exchange and energy balance in premature newborns during the first hours of life in a closed incubator. In addition, a control problem was proposed and solved in order to maintain thermal stability of premature newborns to increase their rate of survival and weight. For this purpose, we propose an algorithm to control the temperature inside the incubator. It takes into account the measurements of the body temperature of a premature newborn which are recorded continuously. We show that using this model the temperature of a premature newborn inside the incubator can be kept in a thermal stability range.