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This work focuses on the mathematical analysis of the controlled release of a standardized extract of A. chica from chitosan/alginate (C/A) membranes, which can be used for the treatment of skin lesions. Four different types of C/A membranes were tested: a dense membrane (CA), a dense and flexible membrane (CAS), a porous membrane (CAP) and a porous and flexible membrane (CAPS). The Arrabidae chica extract release profiles were obtained experimentally in vitro using PBS at 37 °C and pH 7. Experimental data of release kinetics were analyzed using five classical models from the literature: Zero Order, First Order, Higuchi, Korsmeyer–Peppas and Weibull functions. Results for the Korsmeyer–Peppas model showed that the release of A. chica extract from four membrane formulations was by a diffusion through a partially swollen matrix and through a water filled network mesh; however, the Weibull model suggested that non-porous membranes (CA and CAS) had fractal geometry and that porous membranes (CAP and CAPS) have highly disorganized structures. Nevertheless, by applying an explicit optimization method that employs a cost function to determine the model parameters that best fit to experimental data, the results indicated that the Weibull model showed the best simulation for the release profiles from the four membranes: CA, CAS and CAP presented Fickian diffusion through a polymeric matrix of fractal geometry, and only the CAPS membrane showed a highly disordered matrix. The use of this cost function optimization had the significant advantage of higher fitting sensitivity. [ABSTRACT FROM AUTHOR]

In this contribution we consider the problem of flux identification in a scalar conservation law modelling the phenomenon of sedimentation. The experimental observation data used for the calibration consist of a solid concentration profile at a fixed time. The identification problem is formulated as an optimization one, where the distance between the profiles of the model simulation and observation data is minimized by a least squares cost function. The direct problem is approximated by a monotone finite volume scheme. The numerical solution of the calibration problem is obtained by a continuous genetic algorithm. Numerical results are presented in order to validate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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