Jérémi Dauchet

A novel experimental bench dedicated to the accurate radiative analysis of photoreactors: The case study of CdS catalyzed hydrogen production from sacrificial donors

Abstract This article is dedicated to the presentation of a novel experimental bench designed to study the photoproduction of H 2 . It is composed of three main parts: a light source, a fully equipped flat torus reactor and the related analytical system. The reactor hydrodynamic behaviour has been carefully examined and it can be considered as perfectly mixed. The photon flux density is accurately known thanks to reconciled quantum sensor and actinometry experiments. The incident photon direction is perpendicular to the reactor windows; in such a configuration the radiative transfer description may be properly approximated as a one dimensional problem in Cartesian geometry. Based on accurate pressure measurement in the gas tight photoreactor, the production rates of H 2 (using CdS particles in association with sulfide and sulfite ions as hole scavengers) are easily and trustingly obtained. First estimations of apparent quantum yield have proven to be dependent on mean volumetric rate of radiant light energy absorbed hence demonstrating the need for the use of a radiative transfer approach to understand the observed phenomena and for the proper formulation of the thermo-kinetic coupling.

Addressing nonlinearities in Monte Carlo

Monte Carlo is famous for accepting model extensions and model refinements up to infinite dimension. However, this powerful incremental design is based on a premise which has severely limited its application so far: a state-variable can only be recursively defined as a function of underlying state-variables if this function is linear. Here we show that this premise can be alleviated by projecting nonlinearities onto a polynomial basis and increasing the configuration space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles, and concentrated solar power plant production, we prove the real-world usability of this advance in four test cases which were previously regarded as impracticable using Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to acute problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise on model refinement or system complexity, and convergence rates remain independent of dimension.

Monte Carlo efficiency improvement by multiple sampling of conditioned integration variables

We present a technique that permits to increase the efficiency of multidimensional Monte Carlo algorithms when the sampling of the first, unconditioned random variable consumes much more computational time than the sampling of the remaining, conditioned random variables while its variability contributes only little to the total variance. This is in particular relevant for transport problems in complex and randomly distributed geometries. The proposed technique is based on an new Monte Carlo estimator in which the conditioned random variables are sampled more often than the unconditioned one. A significant contribution of the present Short Note is an automatic procedure for calculating the optimal number of samples of the conditioned random variable per sample of the unconditioned one. The technique is illustrated by a current research example where it permits to increase the efficiency by a factor 100. Increase of multidimensional Monte Carlo algorithms efficiency.Significant improvements when considering complex and randomly distributed geometries.Automatic procedure to determine the optimal number of samples.General concept easily applicable to several fields.

Reformulation of the modal method based on Gegenbauer polynomial expansion for cylindrical structures with arbitrary cross sections

The work presented here focuses on the numerical modeling of cylindrical structure eigenmodes with an arbitrary cross section using Gegenbauer polynomials. The new eigenvalue equation leads to considerable reduction in computation time compared to the previous formulation. The main idea of this new formulation involves considering that the numerical scheme can be partially separated into two independent parts and the size of the eigenvalue matrix equation may be reduced by a factor of 2. We show that the ratio of the computation times between the first and current versions follows a linear relation with respect to the number of polynomials.