Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

Improving the photoactivity of bismuth vanadate thin film photoanodes through doping and surface modification strategies

Currently, one of the most attractive and desirable ways to solve the energy challenge is harvesting energy directly from the sunlight through the so-called artificial photosynthesis. Among the ternary oxides based on earth–abundant metals, bismuth vanadate has recently emerged as a promising photoanode. Herein, BiVO4 thin film photoanodes have been successfully synthesized by a modified metal-organic precursor decomposition method, followed by an annealing treatment. In an attempt to improve the photocatalytic properties of this semiconductor material for photoelectrochemical water oxidation, the electrodes have been modified (i) by doping with La and Ce (by modifying the composition of the BiVO4 precursor solution with the desired concentration of the doping element), and (ii) by surface modification with Au nanoparticles potentiostatically electrodeposited. La and Ce doping at concentrations of 1 and 2 at% in the BiVO4 precursor solution, respectively, enhances significantly the photoelectrocatalytic performance of BiVO4 without introducing important changes in either the material structure or the electrode morphology, according to XRD and SEM characterization. In addition, surface modification of the electrodes with Au nanoparticles further enhances the photocurrent as such metallic nanoparticles act as co-catalysts, promoting charge transfer at the semiconductor/solution interface. The combination of these two complementary ways of modifying the electrodes has resulted in a significant increase in the photoresponse, facilitating their potential application in artificial photosynthesis devices.