a b s t r a c tAt the kinetic level, the meaning of null-collisions is straightforward: they correspond to pure-forward scattering events. We here discuss their technical significance in integral terms. We first consider a most standard null-collision Monte Carlo algorithm and show how it can be rigorously justified starting from a Fredholm equivalent to the radiative transfer equation. Doing so, we also prove that null-collision algorithms can be slightly modified so that they deal with unexpected occurrences of negative values of the nullcollision coefficient (when the upper bound of the heterogeneous extinction coefficient is nonstrict). We then describe technically, in full details, the resulting algorithm, when applied to the evaluation of the local net-power density within a bounded, heterogeneous, multiple scattering and emitting/absorbing medium. The corresponding integral formulation is then explored theoretically in order to distinguish the statistical significance of introducing null-collisions from that of the integral-structure underlying modification.

International audienceThe Monte Carlo method is partially reviewed with the objective of illustrating how some of the most recent methodological advances can benefit to concentrated solar research. This review puts forward the practical consequences of writing down and handling the integral formulation associated to each Monte Carlo algorithm. Starting with simple examples and up to the most complex multiple reflection, multiple scattering configurations, we try to argue that these formulations are very much accessible to the non specialist and that they allow a straightforward entry to sensitivity computations (for assistance in design optimization processes) and to convergence enhancement techniques involving subtle concepts such as control variate and zero variance. All illustration examples makePROMES - UPR CNRS 8521 - 7, rue du Four Solaire, 66120 Font Romeu Odeillo, France use of the public domain development environment EDStar (including advanced parallelized computer graphics libraries) and are meant to serve as start basis either for the upgrading of existing Monte Carlo codes, or for fast implementation of ad hoc codes when specific needs cannot be answered with standard concentrated solar codes (in particular as far as the new generation of solar receivers is concerned). (C) 2013 Elsevier Ltd. All rights reserved

International audienceThe present text illustrates the practice of integral formulation, zero-variance approaches and sensitivity evaluations in the field of radiative transfer Monte Carlo simulation, as well as the practical implementation of the corresponding algorithms, for such realistic systems as photobioreactors involving spectral integration, multiple scattering and complex geometries. We try to argue that even in such non-academic contexts, strong benefits can be expected from the effort of translating the considered Monte Carlo algorithm into a rigorously equivalent integral formulation. Modifying the initial algorithm to simultaneously compute sensitivities is then straightforward (except for domain deformation sensitivities) and the question of enhancing convergence is turned into that of modeling a set of well identified physical quantities