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

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.

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Urban areas are a high-stake target of climate change mitigation and adaptation measures. To understand, predict, and improve the energy performance of cities, the scientific community develops numerical models that describe how they interact with the atmosphere through heat and moisture exchanges at all scales. In this review, we present recent advances that are at the origin of last decade’s revolution in computer graphics, and recent breakthroughs in statistical physics that extend well-established path-integral formulations to nonlinear coupled models. We argue that this rare conjunction of scientific advances in mathematics, physics, computer, and engineering sciences opens promising avenues for urban climate modeling and illustrate this with coupled heat transfer simulations in complex urban geometries under complex atmospheric conditions. We highlight the potential of these approaches beyond urban climate modeling for the necessary appropriation of the issues at the heart of the energy transition by societies.